Essentials of Hydraulic Fracturing: Vertical and Horizontal Wellbores 1593703570, 9781593703578

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EEssentials ssentials of

Hyd raulic Hydraulic FFracturing racturing Vertical Ver tical and Ho Horizon rizontttal al Wellb llbore oress ore

Ralph W. Veatch / George E. King / Stephen A. Holditch

Disclaimer The recommendations, advice, descriptions, and the methods in this book are presented solely for educational purposes. The author and publisher assume no liability whatsoever for any loss or damage that results from the use of any of the material in this book. Use of the material in this book is solely at the risk of the user. Copyright © 2017 by PennWell Corporation 1421 South Sheridan Road Tulsa, Oklahoma 74112-6600 USA 800.752.9764 +1.918.831.9421 [email protected] www.pennwellbooks.com www.pennwell.com Marketing Manager: Sarah De Vos National Account Executive: Barbara McGee Coons Director: Matthew Dresher Managing Editor: Stephen Hill Production Manager: Sheila Brock Production Editor: Tony Quinn Cover Designer: Elizabeth Wollmershauser Book Designer: Susan Ormston Library of Congress Cataloging-in-Publication Data Veatch, Ralph W. Fundamentals of hydraulic fracturing : vertical and horizontal wellbores / Ralph W. Veatch, Stephen A. Holditch, George E. King. pages cm Includes bibliographical references and index. ISBN 978-1-59370-357-8 1. Oil wells--Hydraulic fracturing. 2. Hydraulic fracturing. I. Holditch, Stephen A. II. King, George E. III. Title. TN871.V38 2016 622'.3381--dc23 2015028261 All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transcribed in any form or by any means, electronic or mechanical, including photocopying and recording, without the prior written permission of the publisher. Printed in the United States of America 1 2 3 4 5  21 20 19 18 17

Acknowledgments The authors wish to acknowledge and thank the individuals listed below who reviewed certain chapters, as designated, and offered text insertions, figures, and tables pertinent to their chapter reviews. These are incorporated into the body of the text. General commentaries that were also provided are directly inserted at the chapter end, as noted by *. Chapter 1: Norman R. Warpinski Chapter 2: Ram G. Agarwal Chapter 4: John W. Ely* Chapter 5: Michael W. Conway Chapter 7: Earl P. Freeman and Brian D. Oleman Chapter 8: Michael B. Smith, Robert D. Barree, and Jennifer L. Miskimins* Chapter 10: Robert D. Barree, Bruce R. Meyer, and Jennifer L. Miskimins Chapter 12: Norman R Warpinski and Robert A. Woodroof Jr. All the authors of SPE Monograph V. 12. Halliburton Company, for permission to publish information and data contained in their manuals The Fracbook I: Design/Data Manual for Hydraulic Fracturing and The Fracbook II Design/Data Manual for Hydraulic Fracturing. The authors also appreciate Barree & Associates for contributing fracture treatment model design calculations pertinent to example 10–2 in chapter 10.

Preface In 1989, the publication SPE Monograph V. 12, Recent Advances in Hydraulic Fracturing, addressed four decades of fracturing technology. Since then, hydraulic fracturing has moved from vertical wellbore, massive hydraulic fracturing in tight microdarcy gas reservoirs to new frontiers addressing horizontal wellbore fracturing in massive nanodarcy formations. Accordingly, the industry has kept pace with advances in extended horizontal drilling and fracturing applications. New fracturing materials, techniques, and applications have emerged. However, the fundamental basics of fracture propagation behavior and diagnostics remain the same. This book focuses on consolidating the old and the new in a format that assists both current and future fracturing design engineers in their practice. It is beyond the scope of this book to extensively cover the entire gamut of fracturing intricacies; rather, the purpose is to provide [1] a basic understanding of (a) fracture propagation behavior, (b) the effects of fracturing on post-treatment well production, and (c) the important aspects pertinent to fracture treatment design application and [2] insight and methods for applying that knowledge to achieve maximum economic returns from a fracturing treatment. Ralph W. Veatch Stephen A. Holditch George E. King

Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Hydraulic Fracturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Primary Hydraulic Fracturing Treatment Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 The Typical Concept versus the Actual Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Treatment Implementation Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Non-Stimulation Fracturing Applications and Considerations . . . . . . . . . . . . . . . . . . . . . 18 Controllable Factors Pertinent to Hydraulic Fracturing Treatment Design . . . . . . . . . . . 19 Treatment Design Factors Imposed by Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 A Successful Fracturing Treatment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Refracturing of Previously Hydraulically Fractured Wells . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Environmental Impacts of Hydraulic Fracturing Treatments . . . . . . . . . . . . . . . . . . . . . . . 24 Disciplines Pertinent to Hydraulic Fracturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 The Design Engineer’s Job . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Hydraulic Fracturing in the Future—Let’s Do It Right! . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Issues to Be Addressed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Implications for the Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2  Overview: Important Fracture Design Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Factors Pertinent to Fracturing Behavior and Economics . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Preliminary Post-Fracture Production Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Formation Permeability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Mechanical Rock Properties and In Situ Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Fracture Propagation Behavior and Patterns—Near-Wellbore and Far-Field Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Formation Composition and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Fracturing Fluid Loss to the Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Fracturing Fluid System Rheology, Viscosity, and Proppant Transport . . . . . . . . . . . . . . 86 Propping Agents and Fracture Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Overview Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

3  Rock Mechanics and Fracture Propagation: Rock Properties—In Situ Stresses,

Net Fracturing Pressures, and Fracture Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Mechanical Rock Properties and In Situ Stresses in Fracture Propagation Models . . . 116 Mechanical Rock Properties Basic to Hydraulic Fracturing Behavior . . . . . . . . . . . . . . 118 In Situ Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Net Fracturing Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 v

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In Situ Stress and Net Fracturing Pressure Effects on Fracture Height, Width, Penetration, and Volumetric Propagation Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Calculating Fracture Height with In Situ Stress Profile Data . . . . . . . . . . . . . . . . . . . . . . 154 Pore Pressure Effects on In Situ Stress and Fracture Propagation Behavior . . . . . . . . . 162 Interval Interface Slippage, Ductility and Fluid-Loss Confining Effects . . . . . . . . . . . . . 169 Fracture Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Fracture Volume Calculations from Width, Height, and Lateral Penetration . . . . . . . . 178 Fracturing in Horizontal Wellbores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Hydraulic Fracturing Studies with a Quasi Three-Dimensional Rock Mechanics (Q-3D-RM) Spreadsheet Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Summary of Data Acquisition Pertinent to Mechanical Rock Properties, In Situ Stresses, and Net Fracturing Pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

4  Fracturing Fluid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Design Engineer and Service Company Engineer Interaction . . . . . . . . . . . . . . . . . . . . . 201 Fracturing Fluid System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Selecting a Fracturing Fluid System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Types of Fluid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Fluid System Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Base Fluid System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Fracturing Fluid System Performance Control Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Decision Flowcharts to Facilitate and Accelerate Fluid System Selection . . . . . . . . . . . 215 Particle Fraction Effect on Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Comments from Outside Reviewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 The Expanding World of Fracturing Fluid Systems and Additives . . . . . . . . . . . . . . . . . . 218 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

5  Fracturing Fluid Loss to the Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Total Fluid Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Terminology: Laboratory-Determined Spurt-Loss and Fluid-Loss Coefficient, and Field-Determined Fracturing Efficiency, Total Fluid-Loss Coefficient . . . . . . . . . . . 223 Determining Fluid-Loss Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Formation Permeability, Gel Concentration, Temperature, and Additives . . . . . . . . . . 254 CVC versus Pressure Differential between the Fracture and the Reservoir . . . . . . . . . 256 Fluid System Viscosity Increase by Virtue of Fluid Loss . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Effect of Fluid Shear on Fluid Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Reducing Floss into Vugs, Joints, Fissures, Fractures, Faults . . . . . . . . . . . . . . . . . . . . . . 261 Pad Volumes Calculated from Fracturing Fluid Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 262 Summary of Fluid-loss Considerations for Fracture Treatment Design . . . . . . . . . . . . . 265 Data and Information Resources for Fluid-loss Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 267 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

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Contents

6  Fracturing Fluid System Rheology and Proppant Transport . . . . . . . . . . . . . . . . . . . . . . 273 In-Fracture Fluid System Temperature—Wellbore to Fracture Tip . . . . . . . . . . . . . . . . . 274 Approaches to Fluid System In-Fracture Temperature Distribution . . . . . . . . . . . . . . . . 276 Algorithms for In-Fracture Temperature Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Whitsitt and Dysart approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 Apparent Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Fluid System Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Resources for Fluid System Apparent Viscosity and Rheology Data . . . . . . . . . . . . . . . . 290 Developing Equations for Fracturing Fluid Systems Rheology Behavior . . . . . . . . . . . . 291 Temperature and Shear Rate Effects on Apparent Viscosity Behavior . . . . . . . . . . . . . . 320 Apparent Viscosity of Foam Fluid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Fluid System Apparent Viscosity Increase due to Proppant Concentration . . . . . . . . . 329 Hydraulic Horsepower Injection Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 Tubular Friction Loss during Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Friction Loss (Turbulent Tubular Flow)—Proppant-Laden Slurries . . . . . . . . . . . . . . . . 350 Proppant Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Proppant Transport In Fractures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Laboratory Proppant Transport Testing Developments After 1990 . . . . . . . . . . . . . . . . 366 Fluid System Pumping, Staging, and Scheduling Considerations . . . . . . . . . . . . . . . . . . 370 Flowback—Fluid System Recovery and Cleanup Enhancement . . . . . . . . . . . . . . . . . . . . 371 Mitigating Microcrack Gumming in the Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Summary of Considerations for Fluid System Flow Behavior and Proppant Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Data and Information Resources (Hard Copy, Website, etc.) . . . . . . . . . . . . . . . . . . . . . . 373 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

7  Proppants and Fracture Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Proppants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 Fracture Permeability and Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 Proppant Transport, Closed Fracture Width, and Proppant Specific Gravity . . . . . . . . 414 Economic Perspectives of Fracture Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Closed Fracture Width versus Proppant Concentration and Post-Fracture Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 Proppant Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 Data Sources: Specifications for Fracture Permeability and Conductivity . . . . . . . . . . . 444 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

8  Fracture Propagation Computer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Model Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Model Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 About Model Fracturing Treatment Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Model Supplements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 vii

Essentials of Hydraulic Fracturing

Model Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Model Development History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Model Augmentations and Supplemental Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 Model—Construction, Capability, Applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 Modelling Fracture Propagation Blunting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 Modeling—Simultaneous Multi-Interval Propagation—Vertical or Deviated Wellbore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 Fluid Loss and Rheology Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 Treatment Designs—Predictions versus In Situ Propagation . . . . . . . . . . . . . . . . . . . . . . 492 Selecting the Appropriate Model for Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Model Design Limitations and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Recommended Fracturing Model Treatment Design and Analysis Practices . . . . . . . . 497 Supplemental Comments by Outside Reviewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 Fracturing Model Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504

9  Fracture Treatment Design, Implementation, and Post-Fracture Operations . . . . . . 505

Twelve Points to Improve Fracturing Success and Economic Returns . . . . . . . . . . . . . . 505 General Treatment Design Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 Candidacy Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 Pre-Design Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Data Acquisition Programs for Pre-Fracture Treatment Design . . . . . . . . . . . . . . . . . . . 519 Treatment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 Scenario Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524 Final Economic Optimized Treatment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526 Treatment Implementation Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 Management Involvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541 Onsite Fracturing Treatment Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542 Programs for Improving Economic Returns on Future Wells . . . . . . . . . . . . . . . . . . . . . . 543 Fracture Design Data and Analysis Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

10  Pre-Fracture Treatment: Model Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 Model Design Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 Fracturing Economic Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 About Treatment Designs: Vertical versus Horizontal Wellbores . . . . . . . . . . . . . . . . . . 552 About the Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 Model Approaches—Treatment Design Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 Example 10–1. Description, Data, and Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 GOHFER Model Treatment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 Example 10–1 Description and Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 598 Potential for Enhanced Economics by Propping Outside the Pay . . . . . . . . . . . . . . . . . . 609 Summary of Results for Examples 10–1 and 10–2, and Ideas for Redesign . . . . . . . . . . 610 Considerations for Treatment Redesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 Commentary on Pre-Fracture Treatment Designs with Models . . . . . . . . . . . . . . . . . . . 612 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

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Contents

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

11  Fracturing Horizontal Wellbores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 Fracturing Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619 Fracture Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 Complex and Planar Fractures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627 Well Spacing and Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633 Placement of Fractures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 Stress Factors Affecting Fracturing from Horizontal Wells . . . . . . . . . . . . . . . . . . . . . . . 638 Completion Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641 Microseismic and Other Monitoring Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641 Perforating Horizontal Wells for Fracturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642 Fracturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 Fracture Initiation and Early Fracture Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648 Fracture Extension and Later Stage Fracturing Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 649 Simultaneous and Sequential Fracturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651 Refracturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652 Fracture Hits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 Fracture Flowback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657

12  Fracturing Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667 Fracturing Diagnostic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668 Near-Wellbore Vertical Fracture Extent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670 Post-Fracture Wellbore In-Flow Production Profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679 Fracture Propagation Azimuth and Propagation Geometry . . . . . . . . . . . . . . . . . . . . . . . 682 Commentary on Fracturing Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701

Appendix A: Fracture Vertical Height Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 Descriptions and Comparisons of Figures A–1, A–2–1, and A–2–2 . . . . . . . . . . . . . . . 705 Utility of the Height Growth Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707 Regression of the Height Growth Curve Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707 The hS/h Calculation Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708 Calculating Relative Fracture Heights, hS/h, as a Function of ƒ(σ,Pƒ) and ∆σR . . . . . . 708 Preferential Downward versus Upward Vertical Growth . . . . . . . . . . . . . . . . . . . . . . . . . 712 Bounding Intervals with Multiple Layers Where σ, E, and KIC Vary from Layer to Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714 Appendix B: A Quasi-Three-Dimensional Rock Mechanics Spreadhseet (Q-3D-RMS) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 Differences between the Q-3D-RMS and Planar Three-Dimensional (P-3D) Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716 Q-3D-RMS Model Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716 Relative Fluid Viscosity Behavior and Retained ∆Pƒ/ΔXƒ . . . . . . . . . . . . . . . . . . . . . . . . 717 ix

Essentials of Hydraulic Fracturing

Well Injection Pressure (PW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 Creating and Using a Q-3D-RMS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 Fracturing Intervals in a Q-3D-RMS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 Q-3D-RMS versus Other Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721 Q-3D-RMS Model Vertical and Horizontal Configuration . . . . . . . . . . . . . . . . . . . . . . . . 721 Q-3D-RMS Model Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724 Q-3D-RMS Spreadsheet Model Calculations Using Chapter 3, Example 3–15 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 728 Commentary about this Q-3D-RMS Spreadsheet Model . . . . . . . . . . . . . . . . . . . . . . . . . 735 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736 Appendix C: Example Spreadsheet Program for Fracturing Fluid Efficiency and SIPD Type-Curve Fluid-Loss Coefficient Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739 Spreadsheet Calculations of Fracturing Fluid Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 740 Spreadsheet Applicable Master Type-Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741 Spreadsheet Processing of SIPD Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743 Appendix D: Bibliography for Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755 Answers to Selected Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781 About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 811

x

1 Introduction This book focuses more on the “how to” than the theoretical aspects of fracture treatment design and execution. Much of what is contained here is also presented more esoterically and comprehensively in the SPE monograph cited here: Gidley, John L., Stephen A. Holditch, Dale E. Nierode, Ralph W. Veatch, eds. 1989. Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12). Richardson, TX: Society of Petroleum Engineers. Additionally, fracturing advances that have emerged since monograph publication are presented herein. The SPE monograph, though published in 1989, covers basic theoretical fundamentals and approaches, and basic fracturing materials available at that time. The basic fundamentals seldom change, nor do the properties and behaviors of materials found in nature. The monograph exhaustively and esoterically addresses them. While it’s not necessary for readers to have a copy of the monograph, it is a good resource for reference. Many other books with basic information are also available and worth having in one’s technical library, such as • Reservoir Stimulation, 2nd ed. (1989), by Michael J. Economides and Kenneth G. Nolte. Schlumberger Educational Services, Houston. • Modern Fracturing, Enhancing Natural Gas Production (2007), by Michael J. Economides and Tony Martin. BJ Services and Energy Tribune Publishing, Houston. • Hydraulic Fracture Mechanics (1996), by Peter Valcó and Michael J. Economides. John Wiley & Sons, Hoboken, NJ. In the SPE monograph, and to some degree in the other books referenced above, the discussion of similar fracturing aspects are located in more than one chapter and in the appendices. Hence, efforts have been made in this book to consolidate, as much as possible, discussions pertinent to each separate aspect of fracture design into a single chapter. Hopefully, the authors’ consolidation efforts, and those made to put the presentation into a practical application format, will facilitate design engineers in their efforts to apply state-of-theart practices for fracturing treatment designs.

1

Essentials of Hydraulic Fracturing

The contents of this book are intended to serve • Design engineers currently involved in fracturing applications • As a textbook for university engineering students • Engineers designated for future fracturing involvement • Line managers responsible for economic returns from fracturing What it presents includes • Aspects that are basic to treatment design • Their effects (singularly and interactively) on fracture propagation and performance behavior • Their relative impact on post-frac production and revenue • Algorithms and examples pertinent to treatment design and analysis • Fracturing treatment design methods and processes • Pre- and post-fracturing approaches and diagnostics for evaluating treatment performance, and for improving performance on future wells The intended purpose of the book is to serve the reader in several ways, including but not limited to providing • An understanding of how basic factors and phenomena pertinent to fracture propagation geometry and fracture conductivity impact the results of a treatment • Awareness of important considerations pertinent to treatment design and execution • A menu of data requirements and procedures necessary to design and analyze treatments • Methods and procedures for processing design data and creating designs • Encouragement to communicate with all entities associated with fracturing the target well, including: management, geologists, geophysicists, reservoir engineers, computer modelers, consultants, field operating personnel, service companies, equipment and material suppliers, etc. • A focus on the most important goals of hydraulic fracturing, i.e., ˡˡ Safety ˡˡ Environmental prudence ˡˡ Maximum economic returns

Hydraulic Fracturing The following discussion is obviously oversimplified for experienced design engineers. However, it is cast as such to provide insight to those less familiar with the topic of hydraulic fracturing. Many fracturing treatments are unique to specific wells and to the design addressing them. It benefits even the experienced to revisit those mentioned in the simplified discussion.

2

Also, after some engineers have been involved in hydraulic fracturing for several years, especially in a given locale, they may develop somewhat of a “fracturing expert” posture. This may,

Chapter 1

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Introduction

in fact, be true for their locale. However, different plays can present significantly different challenges. Experience has demonstrated that unplugging a design from one play and plugging it into another may not yield the optimum results. Even in an area that has applied hydraulic fracturing for years, there is always room to improve results by thoroughly evaluating prior treatments and the production from those wells.

What is hydraulic fracturing? Hydraulic fracturing is a process for creating a “super highway” for reservoir fluids to flow from the reservoir extremities to the wellbore by • Using fluids to “hydraulically” overcome subsurface in situ forces, so as to create and open one or more fractures, and then • Using proppant particles to keep the created fractures from closing. The process involves injecting slurries of fluid and proppant particles down the wellbore and through perforations (or openhole sections) at sufficient injection rates and pressures to hydraulically break down the formation, and then ‘wedge open’ and propagate a fracture. During the process, some of the fluid leaks off into the formation. The remainder carries proppants into the fracture(s) to hold the fracture(s) open after injection has stopped. Figure 1–1 depicts a typical concept of a vertically oriented, symmetrical, planar, hydraulically generated fracture. Figure 1–1 (left) depicts fracturing in a vertical wellbore. On the right is a horizontal wellbore. Here, formations above and below the target pay confine vertical growth, such that the fracture grows preferentially horizontally as opposed to vertically. Otherwise, with minimal vertical confinement, fracture propagation is preferentially upward, downward, or both.

Fig. 1–1. Vertical fractures in vertical and horizontal wellbores Source: “Figure 1.1,” Gidley et al. 1989, 2. (Ref: SPE Monograph V.12, Fig. 1.1, P. 2) Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. 3

Essentials of Hydraulic Fracturing

Fracture width will be a function of the pressure in the fracture. In virtually all cases, the fracture width increases as injection continues because the viscous fracture fluid creates frictional flow resistance that causes the pressure in the fracture during injection to increase. Since pressure is highest near the wellbore, the fracture width is greatest near the wellbore, and gradually decreases toward the fracture extremities to include the fracture growth up, down, and out from the wellbore. During injection, a portion of the fluid system leaks out of the fracture and thus (by fluid loss) is not available for the wedging process. Continued injection (at rates exceeding the rate of fluid loss) exerts fracture extension pressure throughout the fracture. Thus, as injection continues, the fracture grows wherever the least resistance prevails. In this example, fracture width and horizontal penetration increases. Pumping is continued until all materials (per the treatment design) at the well site have been injected. If proppant bridges in the fracture (or perforation) such that it sufficiently inhibits further injection, the job terminates prematurely (i.e., the treatment screens out).

From the beginning Hydraulic fracturing was conceived in the mid-1940s by Stanolind Oil and Gas Company, Tulsa, OK. The first field test was conducted in 1947. Commercial fracturing commenced in 1949. The hydraulic fracturing patent was issued to Stanolind in 1953.

The first hydraulic fracturing field test The first field test occurred in 1947, on the Kansas, Hugoton Gas Field, Klepper Well No. 1. The target formation was a 240-foot-thick limestone, 2,500 feet deep. Figure 1–2 shows the setup. The treatment was comprised of 1,000 gallons of napalm-thickened gasoline, followed by 2,000 gallons of gasoline with 1% amine breaker, and river sand as the proppant. The Klepper No. 1 results were somewhat disappointing. However, treatments were extended to 23 additional Hugoton wells, resulting in significant production increases on 11. The endeavor demonstrated that fracturing could compete with acidizing as a stimulation process.

The first commercial fracture Two commercial hydraulic fracture jobs took place simultaneously on a chilly day, March 17, 1949, in different fields, both orchestrated by Halliburton’s research staff. One, under the direction of Dwight K. Smith, occurred near Duncan, OK, in the Alma Field of Stephens County. The formation was Deese sand at 5,500 ft depth. The other, under the direction of A. B. Waters, was on a well in Archer County, TX, near Holiday. Both treatments used a 6% napalm-gelled, 25/75 gasoline, lease-crude mixture, and Ottawa, Illinois-mined sand for proppant. Figure 1–3 shows the field setup.

4

Fig. 1–2. First hydraulic fracturing field test, Hugoton, Kansas. (Courtesy of Amoco Production Company.)

Fig. 1–3. First commercial fracturing treatment. (Courtesy of Halliburton Company.)

Essentials of Hydraulic Fracturing

Thereafter Hydraulic fracturing has extended worldwide. Hydraulic fracturing has become recognized as a generator of more incremental profit for the petroleum industry than any other process, outside of exploratory and development drilling. Fracturing treatments typically yield a higher return on investment (revenue/cost) than any other production enhancement process applied to a well. Initial fracture treatments were performed on millidarcy rocks mainly to remove drilling damage. Later, microdarcy tight gas and oil sands were fracture-treated to create economic wells. Much of the literature until recently has dealt with the technology required to stimulate millidarcy and microdarcy formations. However, more recently, formations with permeability in the nanodarcy range, previously thought too low for commercial stimulation, are now major contributors to world production. An amazing perspective—the industry is now commercializing formations where permeability is orders of magnitude below that used for cementing casing in wellbores. Also, many of these formations were considered source rocks for the millidarcy and microdarcy rocks that have been developed since the 1960s. Since 2000, fracturing laterally extensive horizontal wellbores and deep offshore wells has become common. Injecting multimillion-gallon volumes of fracturing fluid and proppants at injection rates exceeding 100 barrels per minute (bpm) or more and surface pressures of 10,000 to 15,000 psi has become a common practice. Treatment processes (pumping, blending, balancing proppant concentrations, etc.) control have progressed from well site to remote offsite, and from manual- to computer-controlled. Treatment monitoring and data recording and analyses have followed accordingly. Fluid system components and additives now come in liquid concentrate form, as opposed to the ‘old’ way of using a powdered form of the additive. The shift from powder to liquid has allowed for better mixing and measurement in the field. The design engineer must decide on one of dozens of different fluid system types for a specific well. There are also dozens of types of fracturing proppants to choose from, which complicates the job of a fracture design engineer. A plethora of fluid system additives have been developed to increase fluid apparent viscosity, reduce viscosity, mitigate fluid loss, stabilize fluid behavior, control fracture conductivity and formation damage, divert fluid flow, etc. The technology is changing so fast that it is difficult to keep up with the new products that continue to emerge as the needs arise. The knowledge base about how in situ rock properties and subsurface conditions affect fracture propagation behavior and conductivity performance has vastly expanded, and continues to do so. Along with our increased understanding of fracture propagation, a multitude of prediction and analytical algorithms have emerged. Applications of these have progressed from pencil/paper to electronic recording. Currently, more than half a dozen different basic types of fracture design and analysis computer models are accessible. Most of them are augmented with fluid system and proppant databases, along with pertinent analytics that facilitate processing and display. Diagnostics applicable to fracture propagation behavior and extent are continually improving. What still remains to be discovered? A better, more definitive understanding of • Where fractures go • What they look like • Why they behave like they do 6

• How to predict and determine this

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Because of this, there is plenty of room for new engineers, new ideas, and new solutions to continue the improvement of hydraulic fracturing.

The Primary Hydraulic Fracturing Treatment Goal The primary goal of all hydraulic fracturing treatments is to maximize the profitability of the well with prudent practices that encompass safety, health and environmental, treatment design, and treatment execution. Most of the time, we are trying to maximize revenue and minimize costs. However, sometimes the engineer must increase costs, such as using a premium proppant, to optimize the profitability. Revenue streams are derived from (1) production rate acceleration, (2) reduced operating costs, and (3) increased ultimate recovery of oil and gas. In regard to flow rate and recovery, experience has shown that flow rate acceleration typically dominates revenue streams in higher permeability (darcy and millidarcy) reservoirs (e.g., sand and calcareous formations), whereas low-permeability (tight) formations exhibit both flow rate and ultimate recovery increases from fracturing treatments. For the current horizontal wells that are stimulated with multistage hydraulic fracture treatments in nanodarcy reservoirs (shales), the increase in flow rate that leads to a shorter payout is very important. Drilling such wells is expensive and most operators need cash flow to keep the rigs running, as these nanodarcy wells have a high initial decline rate. Costs to achieve revenue depend on fracturing behavior (i.e., where fractures go, how they propagate, etc.). Here, the following axioms universally apply to fracturing in all formations: • To satisfactorily enhance formation productivity, fracture permeability must exceed formation permeability by orders of magnitude. • When a fracture propagates, its width will be increased. • Fractures always propagate where it is easiest to create fracture width (i.e., to push the earth apart). These axioms affect fracturing costs by virtue of • Treatment volume requirements • Proppant and fluid system prices • Fracturing treatment pumping and blending price schedules The goal of a fracture treatment design is to optimize the net present value (NPV) of the well by • Accelerating income by increasing producing rates • Reducing well life operating expenses • Increasing total cumulative production 7

Essentials of Hydraulic Fracturing

Fracturing is widely applied because it can be the most profitable portion of the development of an oil and gas field, especially in low-permeability reservoirs. Numerous case histories published in the literature have shown that throughout the world, a hydraulic fracture treatment is the most successful post-drilling process for increasing oil and gas production and economics. Better designs offer even better economic returns. Figure 1–4 shows the relation between desired fracture penetration and formation permeability. It conforms to perceptions that low-permeability formations require deeply penetrating fractures to maximize revenue. As can be seen, in microdarcy formations, penetration requirements are essential. In the higher millidarcy range, penetration has less impact, and fracture conductivity is the more important factor.

Fig. 1–4. Desired fracture penetration versus formation permeability In millidarcy formations, fracturing costs may be around 10%–20% of total combined well costs (i.e., drilling, logging, casing, perforating, fracturing, etc.), whereas, in nanodarcy and microdarcy formations, they can be as much as 40%–80% of the total costs. Hence, any error in either design or execution of fracturing tight formations implies significantly more negative economic consequences than in higher millidarcy range formations. Regardless of formation permeability, economic optimization involves maximizing NPV. Hence, credible effective permeability values are essential to good treatment design. It should be noted in figure 1–4 that for nanodarcy reservoirs, propped fracture lengths of 4,000 feet or more are required to economically produce the oil and gas from the reservoir. Routinely creating and propping such long fractures from a vertical wellbore is virtually impossible. Instead, the industry has developed methods to drill long horizontal wellbores in these nanodarcy reservoirs. These long wellbores are then hydraulically fracture-treated to connect the vertical extent of the reservoir to the horizontal wellbore. Using these two technologies, horizontal drilling and hydraulic fracturing, the industry has recently (since 2000) been able to economically develop nanodarcy reservoirs in multiple basins in North America. However, the key is still in the design and execution of the optimum fracture treatment. 8

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Figure 1–5 depicts the optimization concept. Typically, the rate of present value revenue gradually decreases, and eventually becomes imperceptibly small as fracture penetration (length) increases. Fracturing costs, on the other hand, continue accelerating as penetration increases. The fracture penetration correlative to the maximum NPV (present value of revenue minus the cost of creating a certain length fracture) constitutes the optimum economic penetration. This concept of optimum fracture penetration applies to all formations. Hence, this concept provides a target for fracture treatment design and well development when horizontal wells are used as a proxy for a long hydraulic fracture.

Fig. 1–5. Fracturing economic optimization concept

The Typical Concept versus the Actual Fracture The preceding discussion is an oversimplified description of the “typical” hydraulically created fracture as described in many technical papers and textbooks. Some fractures do, in fact, propagate in a textbook fashion, which is a vertical, planar fracture propagating in two opposite directions in a homogeneous formation. However, in nature, most formations are not homogeneous. Vertical and lateral changes in rock properties such as lithology, permeability, and in situ stress that govern propagation behavior will usually be complex. This heterogeneity in rock properties can result in hydraulically created fractures that differ significantly from the typical vertical, single-wing, planar example. Created fractures can be nonplanar with inclined or even have horizontal orientations. Created fractures can project elevation profiles that have very irregular silhouettes. They can be multistranded and asymmetrical about a wellbore. Such behavior is often more the rule than the exception. Experience and new technology, such as microseismic measurements, have brought an awareness that some fractures are not planar, or symmetric, or single-modal like the one shown in figure 1–1. Figure 1–6 shows several examples. The upper row depicts side view, elevation, and profiles. The lower row shows near-wellbore cross sections. The elevation profiles show computer-generated results for actual cases. The cross sections came from photos of minebacked fractures and downhole wellbores. Obviously, these deviate from the “typical fracture.” 9

Essentials of Hydraulic Fracturing

Fig. 1–6. Possible fracture configurations—profiles and cross sections Figure 1–7 shows both planar and nonplanar propagation in the Barnett shale formation. It depicts an aerial perspective of composite results from remote real-time microseismic mapping measurements for a series of four individual fracturing treatments in the same horizontal wellbore.

Observation Well Treatment Well

1000 ft

Fig. 1–7. Aerial perspective—fracture propagation behavior from real-time microseismic measurements Source: Daniels et al. 2007. 10

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Propagation behavior sometimes defies expectations, analysis, and evaluations. It becomes even more complicated with diatomites, granites, and current massive shales, where fracture patterns are thought to be dendritic and influenced by existing natural fractures. Experience has shown that hydraulically created fractures commonly behave much differently than per the simplified image. However, many theoretical approaches are based on behavior consistent with the typical behavior viewpoint. Thus, the design engineer is challenged to determine how to apply the theoretical concepts and design approaches to address “actual” fracturing behavior. Fortunately, fracture treatment has historically been very profitable regardless of our misperceptions of propagation behavior.

Typical hydraulic fracturing treatment execution The following discussion, also purposely oversimplified, addresses the basic phases of performing a fracturing treatment. Regardless of whether (1) fracturing treatments are conducted in vertical or horizontal wellbores or (2) fracture propagation is planar or dendritic, pumping the treatments are similar in one sense: The treatments will follow the same general sequence. After a well is completed (production casing is in place and perforated in the target zone), and all predesigned fluid system and proppant quantities have been delivered to the well site, then the well is ready for fracturing. The typical fracturing pumping sequence is as follows: • Initiating and propagating the fracture with a pad fluid (no proppant) • Injecting the proppant and extending the fracture • Flushing the slurry • Post-shut-in fracture closure on the proppant • Backflowing the injected fluid (i.e., post-frac cleanup)

Initiating and propagating the fracture—the pad stage Figure 1–8 depicts the pad stage of a vertical fracture in a vertical well into a formation with adequate barriers to prevent substantial vertical growth. The treatment is initiated using a “neat” (containing no proppant) fracturing fluid system. Fracturing pumps are used to increase the fluid pressure in the wellbore at the formation to a value that overcomes the in situ stresses and tensile strength of the rock so that the formation breaks down (cracks) and a fracture is initiated. The fracture is extended by continuing to pump the neat fluid into the fracture at an injection rate larger than the leakoff rate. During this stage, part of the injected fluid leaks off into natural pores, joints, fissures, and faults along the fracture face. Fluid loss control additives are often employed to reduce leakoff in millidarcy formations (but typically not in nanodarcy formations). As the fracture extends into the formation, the fracture width will also increase.

11

Essentials of Hydraulic Fracturing

Fig. 1–8. The first step—initiating the fracture

Extending the fracture and injecting the proppant—slurry stages After a predetermined pad volume has been injected to widen the fracture sufficiently to accept proppant, the selected propping agent is blended with the fluid system, creating a slurry that carries proppant into the fracture. Figure 1–9 shows the slurry stages. These stages typically begin with low proppant concentration stages, followed by stages where concentration is progressively increased. Fracture width and penetration progressively increases. In this example, vertical growth is confined by the adjacent overlying and underlying intervals. During this, fluid continues leaking out of the fracture. The remainder transports and distributes proppant in the created fracture as it propagates.

Fig. 1–9. Extending the fracture and injecting proppant 12

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At some point during these stages, a breaker (a chemical used to reduce the fluid viscosity after shut-in) is added to the slurry. Viscosity reduction at the end of the treatment is important because it promotes • Accelerated fracture closure • Increased fluid system flowback rates during cleanup • Reduced proppant transport during flowback Failure to add a breaker can leave unbroken fracture fluid in the fracture. If the fluid has any gel strength, the residual gel in the fracture may be trapped and will never clean up, leading to fracture plugging that shortens producible flow path lengths in the fracture. Flushing the slurry. To complete the treatment, a flush fluid (neat) is used to displace the slurry down the pipe to a point near the top of the perforations. This minimizes residual proppant in the downhole pipe, and thus mitigates post-frac wellbore cleanout operations.

Post-shut-in fracture closure on proppant After injection ceases, the well is usually left shut-in long enough for the fracture to close on the injected proppant. This results in proppant packs forming within the fracture. Closure tends to lock proppants in place, thus preventing them from reentering the wellbore during flowback or subsequent oil/gas production. In other cases, some operators choose to flow the well back immediately to help close the fracture and use the supercharge of pressure to assist in the cleanup. The choice of when to begin flowback is both formation-specific and operator-specific. During the shut-in period, the following things occur concurrently, for several reasons: • Fracture length continues extending for a short period depending on the formation permeability and leak-off, • Fluid viscosity declines (breaks), and • Fracture width decreases from fluid loss and pressure decline. Shut-in periods typically range from 2 to 24 hours, depending on fluid system breaking and closure time estimates. If no critical issues prevail, and shut-in time would result in commencing flowback operations after dusk, overnight shut-in is common. However, some operators will choose to flowback wells just 1–2 hours after the treatment ends. Fracture length continues extending for a short period. During injection, due to flow friction, the pressure in the fracture near the wellbore is higher than the pressure at the extremities of the fracture. Immediately after injection is stopped (at pumping shut-down), friction in the fracture begins to decrease but it takes time to go to zero. As long as the pressure in the fracture is greater than the fracture extension pressure, the fracture will continue to propagate or grow. Eventually, the pressure in the fracture is reduced below the fracture drops propagation pressure and the fracture will not grow in length or height. The fluid viscosity declines. Fracture fluids will break as functions of time, temperature, and chemical composition. In many gelled treatments, a breaker is added to reduce the viscosity of the fluid once it is in the fracture. The breaking agent reacts with the fluid system in one of several 13

Essentials of Hydraulic Fracturing

ways, reducing its viscosity. With a lower viscosity, the fluid lost to the formation increases, which, in turn, accelerates pressure decline and the closure rate of the fracture. The fracture width decreases from fluid loss. Fluid in the fracture continues leaking off in the formation after shut-in. This leakoff further reduces the pressure in the fracture, allowing the fracture width to decrease until the fracture comes to rest on the proppant pack or closes entirely in portions of the fracture that do not contain any propping agent.

Fracturing fluid flowback and well cleanup Figure 1–10 depicts fluid system flowback. After the shut-in period, the well is opened to allow broken fracturing fluid (load fluid) to flow out of the fracture, leaving the proppant packs in place. Eventually reservoir fluids (oil, gas, and/or formation water) appear in the flow stream. When the load fluid concentration drops to an acceptable level, the well is considered to be “cleaned up.”

Fig. 1–10. Backflowing the fluid Progressively, governmental regulations are requiring that cleanup load fluids be collected and transported to disposal or recycle sites. In offshore wells, subsurface reinjection has emerged as a common practice. It is not unusual for a significant volume of the injected fracturing fluid to remain unrecovered. This is typically expressed as a percentage of the total production that is allocated to the volume of injected fracturing fluid, as opposed to the amount retained by the formation. Some wells are considered cleaned up after only 10%–30% of the injected fluid has been produced. For others it may be on the order of 60%–70%. In terms of amount retained by the formation, there are several reasons for the differences: (a) fracturing fluid that resides in the fracture below the pay is essentially not producible, (b) fluid-loss portions that are retained by relative permeability in the formation, and (c) fluid portions retained by capillary imbibition after injection is stopped and the well is shut-in. The volume of residual fracturing fluid in the fracture interval below the pay can be readily quantified using fracture geometry calculations. Fluid loss and imbibition exhibit a combined effect. As permeability increases, fluid loss increases and capillary imbibition decreases. As permeability decreases, fluid loss decreases and capillary imbibition increases. The separate fluid loss and imbibition amounts are difficult to quantify. Regardless, the combined amount 14

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is a function of formation permeability. In many cases, high fluid loss retention, and thus low fracturing fluid returns, are exhibited by high permeability formations. Conversely, low permeability formations exhibit high returns. In fact, if you take the argument to its end point, when the formation permeability is zero, all the fracture fluid would stay in the fracture (zero leakoff ) and the load recovery would be almost 100% because of the relation to permeability.

Treatment Implementation Aspects Two fracture treatment implementation aspects warrant discussion. They both have been the subject of discussion since the advent of hydraulic fracturing: • Perforating for a fracture treatment • Multi-interval fracturing

Perforating Common sense would imply that a universal approach to fracture treatment perforating is to employ a sufficient number of perforations of sufficient hole diameter size with proper orientation such that the fluid system is not adversely affected, and the near-wellbore formation does not exhibit injection resistance. However, perforation discussions have not abated. One approach has been (and may still be) to align perforations with the preferential fracture propagation azimuth, which minimizes the redirection of fracturing fluid flow and near-wellbore tortuosity. This may be appropriate if the preferential fracture propagation azimuth is precisely known and the perforating gun orientation is precisely controlled. However, the probability of both happening concurrently is quite low. Consequently, the probability of exacerbating the problem of misdirected flow and near-wellbore tortuosity is high. Also, an aspect that seldom surfaces in perforating discussions is the condition outside the casing once a fracture has been created and continues to widen. It is inconceivable to think that the cement remains intact with both the casing and the formation during fracturing. Either the cement pulls away from the casing, the formation pulls away from the cement, or both the cement and the borehole wall disaggregate. And yet, the discussions still prevail.

Multi-interval fracturing In some vertical wells, multiple pay intervals over hundreds or even thousands of feet are encountered and must be fracture-treated to optimize profit. The completion methods for such reservoirs consist of ways to direct the injected fracture fluids into different, somewhat widely spaced intervals penetrated in a common wellbore. Some of these diversion methods involve • Mechanical wellbore isolation with packers and bridge plugs • Sand plugs • Casing rings and seals • Ball sealers • Limited entry 15

Essentials of Hydraulic Fracturing

Except for ball sealers and limited entry, the implementation of methods such as packers and bridge plugs starts with first fracturing the deepest interval. Subsequent treatments are sequentially performed, bottom to top, on uphole intervals. These involve a separate treatment of each interval. Ball sealers may possibly be included with one or more of the separate treatments. With limited entry and ball sealers, all intervals are included in a single fracturing treatment. Mechanical wellbore isolation, sand plugs, and casing rings and seals typically provide successful interval isolation. However, success can vary significantly when using ball sealers or limited entry.

Mechanical wellbore isolation A variety of different mechanical wellbore isolation tools are available. Only a few are mentioned to provide a general perspective of the many isolation methods employed. These include • Retrievable packers • Drillable bridge plugs • Casing rings and pump-down seals • Annulus casing packers • Pump-down bridge plugs • Sleeved casing ports Using any of these methods typically involves initially perforating and performing a full treatment on the lowermost interval (or, in horizontal wells, near the end of the casing). It is the operator’s option whether to backflow, or backflow and produce the well before proceeding to the next interval up the hole. Proceeding from bottom to top involves setting an isolation tool between the lower, previously fractured interval and the target upper interval before perforating or opening sleeved ports, and fracturing. This is repeated until all uphole intervals have been treated. In uncemented horizontal wells, annulus casing packers (and possibly sleeved ports) are installed at predetermined casing points during casing string insertion. Casing rings and pump-down seals consist of a series of progressively smaller internal-diameter (top to bottom) casing rings that are also installed at predetermined casing points during casing string insertion. The pump down seals are sized to pass through uphole rings and seat at their predesignated point. Important issues include placing the isolation tools, and clearing the wellbore for production. Good practice includes checking that there are no obstructions to placing each isolation tool. Bridge plugs typically provide the most dependable isolation. Retrievable packers have a somewhat higher probability of experiencing seating problems. Also, as proppant settling on top of them often adds difficulty to clearing the borehole.

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Sand plugs The use of sand plugs was introduced on a large scale in the 1960s in the northwest Louisiana Pine Island field. It worked successfully on over a thousand shallow (1,800 ft deep) Annona Chalk wells, and has been employed in deeper formations. After fracturing the lowermost interval, the fracturing fluid system is displaced with a specified volume of pea gravel, followed by sand mixed in water. The pea gravel and sand are allowed to settle in the casing to sufficiently cover and seal the lower fractured interval perforations. After shutdown, borehole pressure is maintained to prevent backflow from the lower interval. The process is sequentially repeated on the next upper interval. After all intervals are fractured, the wellbore is cleared by circulation wash.

Ball sealers Ball sealers are employed to enhance the possibility that separated perforation intervals are uniformly stimulated when all intervals are open during a treatment. Multiple separated intervals usually exhibit different in situ stresses. Fractures initiate at the lowest stress regime. Ball sealers are injected at various stages to divert fluid from preferentially entering only one or a few of the lower stress intervals. The number of ball sealers in an injection stage is determined by monitoring the surface pressure during each stage. Here, as ball sealers are injected at the surface and progressively seal downhole perforations, surface pressure increases. When the surface pressure begins to increase, it is presumed that the low-stress interval is sealed and that fractures have initiated in the next higher stress interval. Use of ball sealers is both logistically and economically advantageous over mechanical isolation. However, success using them varies from none, to poor, to good. The method is subject to poor ball-sealing in perforations and perforation hole-size enlargement from erosion.

Limited entry Limited entry, like ball sealers, is used to enhance stimulation uniformly when all perforated intervals are open during a treatment. It also offers similar advantages over mechanical isolation. The process involves high injection rates and small perforation hole diameters. Here, perforation friction affects diversion to the majority of the target intervals by maintaining a high wellbore pressure. Precalculated perforation friction levels are designed to maintain perforation injection pressure above the highest expected in situ stress. If effective, all intervals are stimulated, and preferential entry into only a few is inhibited. A downside to limited entry is perforation enlargement from erosion. If it occurs at one or more intervals, perforation friction can decrease to a level such that no fluid enters some of the higher stress zones. Also, as with ball sealers, success varies from none, to poor, to good. Perforation hole-size enlargement from erosion negates limited entry effectiveness.

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Essentials of Hydraulic Fracturing

Non-Stimulation Fracturing Applications and Considerations Hydraulic fracturing also applies to purposes other than production stimulation treatment applications and considerations, such as • Blowout well control • Formation sand production control • Geothermal energy development • Waste disposal • Enhanced recovery—Reservoir fluid displacement

Blowout well control Hydraulic fracturing in a sidetrack well drilled to kill an offsetting blowout well has proven successful in many cases. Success is due to near-wellbore in situ stress reduction in the blowout formation because of reduced pore pressure that results from blowout production. This is created by pressure depletion from blowout production. The in situ stress sink essentially guides fracture propagation from the kill well to the blowout well. Thus, the kill well needs to penetrate only the stress sink area, as opposed to the blowout well borehole itself. After the kill well fracture connection has been established, kill fluids (typically cement or heavy weighted fluids) are continually injected until the blowout well is under control.

Formation sand production control This procedure, sometimes called frac-and-pack, aims at creating a wide near-wellbore fracture and packing it with proppant sized to prevent unconsolidated formation sand or particles, from entering the borehole during production. If successful, it mitigates the need for using downhole mechanical sand screen to control sand production. Experience has demonstrated varying degrees of success, from poor to excellent. The important issue is to permanently lock a proppant pack across the entire interval. This can be difficult. A sand leak at any point can compromise the results. A highly viscous carrying fluid is required to transport high proppant concentrations. Typically, mixtures of several proppants with different mesh sizes are used to enhance sand control. Curable resin-coated proppants are commonly used to improve retention of the proppant pack screen.

Geothermal energy development Hydraulic fracturing has been used in producing wells since the 1970s to create fractured system heat-transfer paths for heating injected water or converting it to steam. Typically, efforts are conducted in thick, hot, granite formations. However, the process is also applicable to other rock type formations. Regardless, they require extensively large fracture systems. The fracture treatment design aspect involves injecting specific volume requirements to create those systems. 18

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The process has evolved to the current practice of • Drilling an extensive horizontal injection well into the hot formation • Performing a massive water fracturing (no proppant) treatment to create an extensive fracture system • Determining the fracture system boundaries from real-time microseismic mapping during treatment injection • Drilling and completing one or more extensive horizontal producing wells that penetrate and communicate with the created fracture system Geothermal operations are now worldwide. Steam-driven electrical generation is their primary focus.

Waste disposal and enhanced recovery This applies to continuous subsurface injection operations, as opposed to intentional fracturing. The physics involves formation permeability reduction adjacent to the injection surface. This is primarily caused by injection fluid particulates. Plugging occurs if injection fluid filtration methods do not remove particles larger than the smallest pore throats of a matrix. With continued injection, the innate matrix permeability eventually decreases. If injection continues at the same rate, in-fracture pressure eventually exceeds formation parting pressure. Thus, the fracture extends until in-fracture pressure decreases to a relief point. Sequential repetitions result in gradual fracture propagation. This can be subtle and possibly unperceivable. The fracturing aspect of this involves addressing net fracturing pressures and fracture propagation invasion into undesirable intervals or formation areas.

Controllable Factors Pertinent to Hydraulic Fracturing Treatment Design Treatment design entails balancing factors within the realm of human control versus those imposed by nature. Controllable factors include • Fracturing wellbore design—orientation, pipe, size, downhole equipment • Perforation programs—span, density, type, hole diameter • Injection interval isolation • Fracturing materials—fluid system, additives, proppant types and sizes • Injection volume—fluid, proppant • Pad fluid stage—rate, volume, fluids • Injection stages—rate, volume, fluids, proppants, slurry stages ˡˡ Fluids—types, additives ˡˡ Proppants—types, sizes ˡˡ Slurry proppant concentrations ˡˡ Slurry stages—volumes, fluid type, proppant type and size, slurry concentrations 19

Essentials of Hydraulic Fracturing

• Flush procedures • Shutdown procedures • Shut-in times • Flowback procedures Some of the above may not be completely controlled by the fracture design engineer. Certain aspects of wellbore design may be predetermined or already in place. The same situation could be true for perforation programs. Fluid and proppant selection may be limited by agreements with a specified pumping service company or proppant supplier. Proppant availability may be an issue. Hence, the design engineer may be faced with doing the best under existing constraints.

Treatment Design Factors Imposed by Nature Design engineers must work with the heterogeneous formations that they encounter and try to determine the average reservoir properties needed for designing the optimum treatment. As such, they must deal with a large, remote system that they did not create but must try to understand and represent in their engineering programs. The problem of heterogeneity is compounded by the fact that they are also privy to only the minute fraction of that system in the near-wellbore vicinity. Knowledge of the formation aspects listed below is very crucial to the fracture treatment design: • Geomechanical properties • Structure and tectonic variations • Reservoir size and hydrocarbon content and properties • In situ conditions: formation pressures and temperatures • Flow properties of both the formation fluids and fracturing fluid systems Each formation has unique properties within the reservoir, plus interactions that will govern fracture propagation and production performance behavior. Evaluating each property’s unique values impacts treatment volume requirements; fluid system and proppant selection; wellbore design, perforating, and completion programs; and ultimately treatment economics.

Formation geomechanical properties The geomechanical properties discussed here include rock elastic modulus, Poisson’s ratio, rock tensile properties, and in situ stress magnitudes and depth profiles. Each of these properties will vary in accord with variations in confinement pressure, reservoir pressure, and reservoir temperature are varied. In concert, these rock properties play a primary role in fracture propagation behavior. Variations between vertical formation layers or horizontal regions govern fracture vertical and horizontal growth and width. Directional relative in situ stress components govern vertical/horizontal propagation preference. The formation inhomogeneity and anisotropy impacts fracture propagation directional preference and fracture patterns (planar versus dendritic), especially in naturally fractured reservoirs.

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Formation structure and tectonic variations Pore and matrix structure affects formation permeability and fluid loss. Fissures, natural fractures, and faults that result in fluid loss can partially or totally inhibit fracture propagation. Faults that impart local variations of in situ stress directional components and magnitudes govern azimuthal propagation preference.

Formation thickness, hydrocarbon content, in situ conditions, and flow properties Net pay areal extent, thickness, porosity, permeability, and hydrocarbon content (oil versus gas) affect treatment economic optimization. Pore pressure and temperature are also important parameters to characterize.

Formation size, hydrocarbon content, and flow properties Net pay thickness, porosity, permeability, and hydrocarbon content dictate available potential production and thus revenue. The volume of oil and gas in place is a function of net pay thickness, areal extent, hydrocarbon saturation, and porosity. It seems obvious to say it, but the formation has to have enough oil and gas in place and a high enough recovery efficiency to produce enough hydrocarbons to pay for the costs of drilling, completing, fracturing, and producing the well. Sufficient oil or gas prices are also very important to determining pay out and profitability. Permeability and net pay affect the producing rate. In this regard, conventional rate prediction methods that yield folds of increase (FOI) are normalized on unit net pay. This can mask the effect of net pay magnitude. For example, consider the following for two different net pay cases: • Confined vertical fracture height = 300 ft. • Net formation pay thicknesses = 50 ft versus 250 ft. • Pre-frac producing rate = 2 barrels of oil per day (BOPD)/ft net pay. • Fracture conductivity is the maximum achievable for both the 50 and 250 ft cases. The example suggests the following: Fracture penetration Fracturing costs Expected FOI Net pay 50 ft 250 ft

500 800 1,000 $1,000,000 $2,000,000 $3,000,000 5.0 5.2 5.3 Initial post-frac $/day revenue at $70/barrel of oil (BO) net value $35,000 $36,400 $37,000 $175,000 $182.000 $186,500

Obviously, 250 ft of net pay yields the highest return. Granted, the example constitutes a “back-of-the-envelope” exercise. Regardless, it readily emphasizes the importance of full-cycle economic treatment designs, which do account for net pay thickness.

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Essentials of Hydraulic Fracturing

Reservoir pressure and temperature Reservoir temperature and pressure impact both the controllable and uncontrollable aspects of fracturing. Both fracturing fluid system rheology performance and fluid loss behavior are especially affected by the formation temperature. Reservoir pressure, which in gas formations is temperature-dependent, is a component of in situ stress. Reservoir fluid flow is also affected by both the reservoir pressure and temperature, via the pressure differential and fluid viscosity effects. Hence, reservoir pressure and temperature play a large interactive role in treatment design.

Reservoir flow properties Formation permeability must be used to determine the optimum values of fracture penetration (length) and fracture conductivity. Higher permeability formations typically require higher fracture conductivities and shorter fracture lengths for economic optimization. Lower permeability formations require deeper penetrating fractures and can produce adequately with lower fracture conductivities, provided the fracture fluid cleans up. Formation pore pressure impacts in situ stress profiles. Formation temperature and mineralogy govern fluid selection. Formation permeability also governs fluid loss behavior, thus impacting treatment volume requirements. Higher fluid leakoff into a formation implies that higher injection fluid volumes are required to create a given required fracture volume and thus fracture length.

Commentary on treatment design factors imposed by nature For good design practice, it is essential to that a priori knowledge of formation properties and in situ conditions be well established. It is also essential that design engineers have a perspective of the relative degree of importance between them pertinent to a particular well in a particular formation. In regard to economic returns, the cost differences between “large” and “small” volume treatments impact the required degree of design accuracy. Large volumes mean higher costs, and thus, require closer attention to the design. Here, poorly designed treatments that constitute 40%–80% of a well’s total cost can be much more financially disappointing than those where treatment costs are only 10%–20% of the total well costs.

A Successful Fracturing Treatment? Once a fracturing treatment has been completed and the money spent, the most important issue is “What effect did it have on the well’s economic returns?” A successful fracturing treatment is one that, without endangering the safety of any individual or damaging the environment, results in the highest possible achievable NPV returns. Although economic returns are extremely important, safety is of the utmost importance, and environmental aspects are essential. In some cases, determining success is relatively straightforward, especially for moderate- to high-permeability formations where expectations are somewhat more predictable. In others (e.g., tight gas clastic formations, coal-bed methane wells, or ultra-low-permeability gas-bearing 22

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shales), where unfractured performance is relatively unperceivable, engineers may have only a limited idea of what to expect from a fracture treatment. Also, there are generally somewhat different perceptions among the parties involved about what constitutes a “successful” treatment, as can be seen below: • The pumping service company: “All the materials brought on location were pumped downhole as prescribed, with minimal operating difficulties, no equipment breakdowns, and no screen-outs; the on-site barbecue lunch impressed the operating company’s field supervisor, and they were promised the next five jobs.” • The field-operating personnel: “The pumping service company arrived at the location on schedule with all the materials in the amounts requested, to specifications, all the required equipment in good working order, and adequate staff. They pumped the treatment according to the job prognosis, did not damage the well, did not destroy any of the lease roads, location, or company equipment, and took away all they brought in (including trash). No one at the job site got hurt, and the service company bought supper after the job.” • The design engineer: “The fracture length, conductivity, and production responses that the boss was told to expect were achieved or exceeded, and the design engineer’s computer, fracturing design, and analysis budgets were increased.” • The producing company’s management: “No one was injured, the environment remains intact, the well looks like it will make two times the expected economic returns, and they can triple the published booked reserves and sales value of the well.” Each, alone, is valid (to a degree). However, if all are satisfied, obviously the treatment was successful. The important thing is that each party consciously strived to bring about their perception of a successful fracturing treatment, and that if it did not occur, efforts were then commenced to improve things on the next treatment. On occasions, it has been perceived that one or more of the parties were a bit indifferent and manifested an attitude of “That one’s over, let’s get on with the next one!” This can often be costly to all parties. The above scenarios address short-term evaluation. Another important aspect omitted from the above is long-term post-post-fracturing production performance. In tight formations it may take several years for pressure transients to develop sufficiently to definitively infer fracture conductivity and penetration. This becomes more important as industry focuses on massive nanodarcy formations with perceived complex fracturing patterns, shales for example. Observations have emerged in some massive shales that a production cliff syndrome may occur. Here, post-fracture production initially conforms to expectations for a period (for example, 2–4 years). Then the production rate drops precipitously. Definitive methods for a priori predictions of if and when it may occur are yet to come. Precipitous rate drops could also be a failure of the propping agent to sustain fracture conductivity over time. Upside prediction errors in long-term production prediction can be more financially distressful for those involved in property acquisitions than for those dealing with divestitures. Regardless, long-term tracking of post-frac production performance is essential to treatment design for future wells.

23

Essentials of Hydraulic Fracturing

Refracturing of Previously Hydraulically Fractured Wells Refracturing of previously fractured wells has been common practice throughout the history of hydraulic fracturing. Refracturing pertains to wells that were successfully stimulated, and then produced until the oil and gas flow rates declined to an uncomfortably low level, as opposed to redoing an unsuccessful treatment. Economic and/or logistic success has ranged by varying degrees from poor to excellent. This has been for a variety of reasons. Although refracturing per se is not covered in this book, several aspects pertinent to refracturing are addressed. The primary one being in situ stress reduction in the target fracturing interval by virtue of reservoir pressure depletion. With a refracturing treatment, the reduced in situ stress from reduced pore pressure results in wider fractures and more vertical growth confinement. There is another stress-related issue that comes into play: the in situ stress field imposed by the residual proppant pack width. This can affect refracture propagation behavior. Other issues are pertinent, such as the inhibiting effects of in-place proppant packs on slurry flow.

Environmental Impacts of Hydraulic Fracturing Treatments Environmental issues have entered the fracturing world to a significant degree. They will continue to be a large factor in the environmentally friendly development of wells that need to be fracture-treated. To do it right requires a familiarity with pertinent regulations at all governmental levels and that corporate communication lines pertinent to environmental aspects are open and active. Recently, public interest has grown and may possibly continue doing so about several issues, such as • Does hydraulic fracturing affect drinking water aquifers? • Does hydraulic fracturing cause issues with earthquakes? These two issues are being debated as the authors write this book, so there will be much information to come in the following years. Design engineers have some control over the drinking water issue. These are discussed. In regard to earthquakes, there is not sufficient definitive information on a global basis to serve as guidance for a design engineer. Consequently, the issue is pending credible investigations pertinent to specific locales. Disposal is emerging as the cause.

Prospective subsurface fresh water issues? The following addresses two more commonly discussed fresh water pollution questions that are repeatedly discussed as possible causes of fresh water aquifer issues. • Wellbore annulus invasion—prospective vertically upward fluid migration outside the casing? • Prospective fracture vertical growth? 24

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Wellbore annulus invasion—prospective vertically upward fluid migration? One aspect that deserves particular attention is casing cementing practices—also referred to as wellbore integrity. Good cementing practices to achieve effective wellbore isolation are particularly essential to a fracturing treatment. Wellbore integrity applies to all wells whether they are or are not stimulation candidates. Poor wellbore annular isolation, if it occurs, has the potential to invoke the possibility of undesirable communication between intervals above and/or below the producing reservoir. The possibility is significantly attenuated if the surface pipe cement is intact with cement tops well above the estimated maximum potential fracture top. It is essential that the annulus cement be competent, channel-free, and high enough above the fracture interval top to prevent fluid upward migration and invasion into the upper annulus.

Prospective fracture vertical growth invasion? Figure 1–11 is a composite of fracture vertical height extents, top to bottom, from approximately 7,000 fracturing treatments in six shale plays. Darker gray indicates upward growth, and lighter gray downward. The heavy black line is fracture initiation depth. Also shown, at the top, is the depth range for typical potable water aquifers. Maximum depths rarely exceed 1,000 feet. Many water wells are less than 500 feet deep.

Fig. 1–11. Microseismic measurements: fracture tops and bottoms—six shale plays Source: Fisher and Warpinski (2011).

25

Essentials of Hydraulic Fracturing

These measurements come from tens of thousands of fracturing treatments in thousands of wells. As can be seen, none of the fractures in any treatment attains a height sufficient to penetrate a 2,000-foot-deep potable water formation, if it exists at that depth in the area. Measurements to date have indicated that even the massive hydraulic treatments do not pose any threat to subsurface potable water sources. It is clear that hydraulic fractures will not continue propagating to the surface once pumping is stopped.

Corporations and environmental regulations Prudent oil and gas operators, fracturing service companies, and product suppliers have maintained, and will continue to adhere to environmental regulations and employ prudent environmental practices. In regard to fracture treatment stimulation, design engineers typically get the initial look relative to potential environmental issues. If one or more appears, management must be made fully aware of it and provided documented support and suggested remedial measures. Governmental regulatory agencies are responsible to the public to ensure that regulations have been followed. This requires adequate funding and competent staff. Hence, governmental legislative bodies carry the responsibility of ensuring budgetary necessities for this, and for establishing regulatory agency oversight committees.

Disciplines Pertinent to Hydraulic Fracturing Table 1–1 lists the engineering and scientific disciplines that are integral to hydraulic fracturing treatment design. They are many, and varied. The variety constitutes an interesting attraction to engineers. Fracture treatment design is definitely a broadly focused endeavor. It requires that design engineers be sufficiently versed in each (or closely communicate with those who are) to address their pertinence to fracturing applications. Table 1–1. Disciplines integral to fracture treatment design

26

Engineering

Scientific

Chemical Electrical/electronic Environmental Formation evaluation Instrumentation Materials Mechanical Pressure transient analysis Production logging Reservoir engineering Well completions

Chemistry Computer science Economics Geology Geophysics Mathematics Physics Rheology Rock mechanics

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The Design Engineer’s Job Fracture stimulation considerations start before a drilling rig is on location, and continue until a well has produced for a time sufficient to determine long-term treatment results. This requires that design engineers interact with others (engineers, scientist, managers and operating personnel, outside contractors and suppliers, etc.) who are associated with one or more of the following activities: • Drilling • Completions • Well-site fracturing operations • Pre-fracturing diagnostic/data acquisition services • Fracturing services • Fracturing materials • Fracturing treatment execution • Post-frac production monitoring • Post-fracturing diagnostic/data acquisition services • Reservoir performance behavior Hence, the design engineer’s job is more than just addressing a fracturing treatment pumping prognosis, per se. Proper design extends to interacting with, and communicating to, others (both within and outside of the company) about the fracturing treatment. This pertains to the important aspects of hydraulic fracturing that relate to their activities, and why they are important. It is the design engineer’s responsibility to adequately address all of these activities. There are certain aspects where it may be difficult for some design engineers to become as involved as they should be. This is because of the different organizational structure between companies. For example, in some companies, design engineer job descriptions may be removed from drilling and/or completion assignments. In others they may be jacks of all trades who are involved in all. The latter is more beneficial because all of the above activities are pertinent to good fracturing practices. The former may result in the “building a boat in the basement” syndrome, where design engineers must work around issues that could be detrimental to achieving the best frac treatment possible. Such things as the wrong penetration depth, hole size, pipe, cementing practices, perforations, service pumping company, etc., could adversely affect the treatment and/ or the economic potential. If engineers are precluded from decisions in some aspects, then they should at least communicate their requirements to those responsible for such decisions. It is also important that design engineers be familiar with local, state, and federal regulations, and American Petroleum Institute (API) practices pertinent to drilling and well completions, as well as fracturing. These have expanded over the years to include environmental issues. Failing to adhere to requisite regulations or recommended practices is unacceptable.

27

Essentials of Hydraulic Fracturing

Hydraulic Fracturing in the Future— Let’s Do It Right! Figure 1–12 shows the locations of nearly 50 active shale plays on the North American continent. Most have been developed within the last decade. Massive shale treatments commenced in the Barnett formation, where two decades ago, such formations were deemed uncommercial. However, advances in horizontal drilling and fracturing have brought the United States from foreign dependence to self-reliance for oil and gas production. The future lies in such formations. Horizontal drilling puts the wells in place, and needless to say, hydraulic fracturing gets the oil and gas to the consumer. In that regard, the challenges associated with logistically and economically fracturing nanodarcy and microdarcy formations intensifies the need to apply good treatment design practices. Muskwa-Otter Park, Evie-Klua

Lower Besa River

Montney Doig Phosphate

MuskwaOtter Park Colorado Group

Bakken Utica Frederick Niobrara Brook Cody Heath Gammon Antrim Hilliard-BaxterMowry Mancos-Niobrara Niobrara Mancos ExcelloDevonian (Ohio) MontereyNew Mulky Temblor Hermosa Marcellus Albany Woodford Monterey Lewis Fayetteville Utica N Chattanooga Bend Pierre-Niobrara FloydAvalon W Conasauga Barnett Neal BarnettWoodford Tuscaloosa

North American Shale Plays (as of May 2011)

Current shale plays

Stacked plays

Shallowest/youngest Intermediate depth/age Deepest/oldest Mixed shale and chalk play Mixed shale and limestone play Mixed shale and tight dolostonesiltstone-sandstone play Prospective shale plays Basins

Eagle Ford La Casita

Pimienta, Tamaolipas

E

S

Eagle HaynesvilleFord Bossier

Eagle Ford Tithonian Pimienta

Horton Bluff

Miles 0

200

400

600

800

Maltrata

Fig. 1–12. Current and proposed North American shale plays Source: U.S. Department of Energy 2011.

Source rocks

28

Many of the shale gas and shale oil reservoirs the industry is currently developing are actually source rocks for conventional reservoirs that have been producing for decades. For example, everyone knows that the source rock for the Austin Chalk formation was the Eagle Ford shale. Other unconventional reservoirs, such as coal-bed methane, are self-sourcing formations. It is well established in North America that these source rocks still contain enormous volumes of oil and gas. The industry did not begin seriously developing shale gas and tight oil reservoirs until it was clear that most of the large conventional oil and gas reservoirs had been found and were being produced.

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The rest of the world outside of North America is still finding and producing oil and gas from high- to medium-permeability, conventional reservoirs. However, it is logical to conclude that every oil and gas basin in the world will eventually deplete its conventional oil and gas reserves and the operators will need to develop the unconventional reserves. When this happens, the exploration focus should be on the source rocks that filled the conventional reservoirs in the older oil and gas basins.

Enabling technologies It is clear that the shale gas revolution has been facilitated by new technologies. The combination of horizontal drilling and multistage hydraulic fracturing are given most of the credit. However, there are many other enabling technologies, such as improvements in drill bits, rotary steerable drilling and better downhole electronics that have been part of the drilling technology that has improved horizontal drilling. Likewise, better isolation tools for staging fracture treatments, better propping agents and fluids have improved the success of fracture treatments. Other technologies, such as improved microseismic imaging, have allowed operators to ‘see’ where the rock is cracking and in some cases, has led to improved fracture treatment designs. Also, improved three-dimensional seismic measurements and processing has allowed many operators to find the formation sweet spots and has minimized the drilling of wells in poor geologic areas.

Hydraulic fracturing—doing it right The oil and gas industry has the opportunity to completely change the energy outlook for the world as it has done in the United States by developing unconventional oil and gas reservoirs. However, the industry must be sure it protects the fresh water aquifers, minimizes air emissions, and takes care of quality of life issues for the communities in which the industry operates. The U.S. Department of Energy authorized the establishment of the Secretary of Energy Advisory Board Subcommittee on Shale Gas Production. The committee first met in May 2011 and issued two reports, one in August 2011 and the second in November 2011. The recommendations in that report are important to the development of shale gas both in the United States and around the world. Even though the report only addressed shale gas development, the findings of the report equally apply to shale oil and tight shale reservoirs. In fact, most shale reservoirs being developed have oil windows, condensate windows, and dry gas windows as a function of depth. The Shale Gas Production Subcommittee Report was balanced and discussed both the positive aspects of developing our shale gas production and what can go wrong if the development is not done correctly.

Benefits of shale gas development The report discusses the benefits of shale gas production, which are summarized as follows: • Shale gas is extremely important to the energy security of the United States. • In 2011, shale gas accounted for 30% of the total U.S. natural gas production. 29

Essentials of Hydraulic Fracturing

• Shale gas development has a large positive economic impact on local communities and states. • Shale gas development creates thousands of high-paying jobs. • Shale gas can be developed in an environmentally responsible manner. Again, all of these benefits can be attributed to the development of shale oil reservoirs, like those found in the Eagle Ford, the Permian, the Bakken, and others that have become prominent recently.

Issues to Be Addressed It is clear that there are many issues the oil and gas industry must address to be able to develop the shale gas resource and gain public support for the development.

Transparency of operations It was clear from the information gathered to prepare the report that the issue of transparency needs to be addressed. Many individuals just want to know what is going on in their neighborhood. For years there was no oil and gas activity. Now, rigs are moving in, trucks are everywhere, and pipelines are being built. The report suggests that the governmental agencies and the industry should try to improve public information on operations by putting more data on the internet.

Transparency of fracture fluid system composition Another issue was the question what are the companies pumping in the ground? Some critiques wrongly accused the industry of pumping a mixture of toxic chemicals in the ground and potentially polluting the ground water. Of course this is not true. Fracture fluids are 99.5% water and proppant (usually sand) and 0.5% chemical, most of which are either not harmful or can be found around a typical household or both. Thus, disclosure of fracture fluid composition by posting on a website was one recommendation. A website called Fracfocus.org is now being used by a majority of companies to post data on their fracture treatments online for anyone to review. The Secretary of Energy Advisory Board recently issued a new report on how to improve websites such as FracFocus.org to make it more useful to all stakeholders. The industry needs to continue to improve transparency.

Improve communication among state and federal regulators During the fact-finding portion of the study, it was clear that the federal government had several departments that wanted to regulate hydraulic fracturing and shale gas development. It was also clear that all of the oil and gas states with significant activity felt like they were doing a good job and did not need help or oversight from the federal government. These issues will likely never be solved to everyone’s satisfaction but the different regulators should cooperate as much as possible. They need to assist development and not hinder development. 30

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Protect water quality The key to protecting fresh water aquifers is wellbore integrity. Operators should use best practices to set and cement the conductor pipe, the surface casing, and all subsequent casing strings. In addition, it would be a good idea to obtain water samples from all fresh water wells in the operating area and run water analyses. The water analyses can alert the land owner or local citizens if they currently have any problems with water composition and can be used to compare with samples in the future to check for water contamination.

Fracture height growth Some critics have suggested that hydraulic fracturing can cause fractures to grow into the fresh water aquifers and that fracturing causes earthquakes. The first claim is not correct and was addressed clearly in a paper by Warpinski and colleagues (2012). The second claim is also not true except in that microseismic events do occur that we can measure and map to determine where the rock is cracking during a fracture treatment.

Improve air quality Methane emissions The industry should measure what is occurring during all phases of drilling, completing, and producing shale gas wells. If the measurements show there is no problem—that would be the best outcome. However, if fugitive methane emissions are found, the industry should develop technology to mitigate the problem.

Diesel emissions Many geographic areas have seen a marked increase in diesel emissions due to increased truck traffic and drilling activity. The industry should reduce the use of diesel fuel by converting engines to run on natural gas. This conversion is underway in many areas, like South Texas in the Eagle Ford development.

Cumulative impacts The industry should do a better job of managing cumulative impacts on communities, land, roads, and wildlife. Some residents are just overwhelmed by the increased activity in areas that have been very quiet in the past. The industry should be aware of such issues.

Organize for sharing best practices The industry has formed organizations such as the Marcellus Shale Coalition, the Eagle Ford Shale Coalition, and other groups to develop and share best practices. Hopefully, these best practices can serve as guides for other areas throughout the world as the shale gas revolution evolves.

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Essentials of Hydraulic Fracturing

Implications for the Future Without question, there is enough unconventional oil and gas to last several hundred years if the right economic and social conditions allow development. However, wells completed in unconventional reservoirs do not recover much gas per completion, so we will need to drill tens to hundreds of thousands of new wells per year. To accomplish that, we will need more rigs and equipment, such as logging trucks, cementing equipment, fracturing equipment, casing, and many other items. We will need more personnel both in the office to plan and engineer the development and in the field to do the work. The oil and gas industry is a growing industry that uses technology to improve performance. It is a global business so there is plenty of room for young professionals. We need more graduates in petroleum engineering, geology, and geophysics. The unconventional gas resource in the United States is enormous and its development is extremely important to foster economic growth. The shale gas revolution in the United States should be replicated in many other oil and gas basins in the world. Without question, shale gas can be developed in a safe and environmentally acceptable manner. The industry needs to work with state and federal regulators and NGOs to develop and use best practices. States should be the primary regulators, as most issues are local and would be best handled locally. The DOE SEAB Subcommittee report is a blueprint on what needs to be done and it can be downloaded at the DOE website: www.shalegas.energy.gov.

References Cheng, K., W. Wu, S. A. Holditch, W. B. Ayers, and D. A. McVay. 2010. “Assessment of the Distribution of Technically Recoverable Resources in North American Basins.” Paper presented at the Canadian Unconventional Resources and International Petroleum Conference, Calgary, Alberta, Canada, October 19. Daniels, J. L., G. A. Waters, J. Herve Le Calvez, D. Bentley, and J. T. Lassek. 2007. “Contacting More of the Barnett Shale through an Integration of Real-time Microseismic Monitoring, Petrophysics, and Hydraulic Fracture Design.” Paper presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, November 11–14. Dong, Z., S. A. Holditch, and D. A. McVay. 2012. “Resource Evaluation for Shale Gas Reservoirs.” Paper presented at the SPE Hydraulic Fracturing Conference in Woodlands, Texas, February 6–8. Dong, Z., S. A. Holditch, D. A. McVay, and W.B. Ayers. 2011. “Global Unconventional Gas Resource Assessments.” Paper presented at the Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, November 15. Fisher, M. K., and N. R. Warpinski. 2011. “Hydraulic Fracture-Height Growth: Real Data.” Paper presented at the SPE Annual Technical Conference and Exhibition, in Denver, Colorado, October 30–November 2. 32

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Gidley, John L., Stephen A. Holditch, Dale E. Nierode, Ralph W. Veatch, eds. 1989. “Figure 1.1.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 2. Richardson, TX: Society of Petroleum Engineers. Holditch, S. A. 2006. “Tight Gas Sands.” Journal of Petroleum Technology 58 (6): 86–93. Masters, J. A. 1979. “Deep Basin Gas Trap, Western Canada.” AAPG Bulletin 63(2): 152. Old, S., S. A. Holditch, W. B. Ayers, and D. A. McVay. 2008. “PRISE Validates Resource Triangle.” Paper presented at the 2008 SPE Eastern Regional AAPG Eastern Section Joint Meeting in Pittsburgh, PA, October 11–15. Rogner, H. H. 1997. “An Assessment of World Hydrocarbon Resource.” Annual Review of Energy and the Environment 22: 217–262. U.S. Department of Energy, Secretary of the Energy Advisory Board, Shale Gas Production Energy Subcommittee. 2011. Second Ninety Day Report. Washington, DC: U.S. Department of Energy. Warpinski et. al. 2012. SPE Production Operations 2012. 145949-PA SPE Journal Paper.

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2 Overview: Important Fracture Design Aspects This chapter focuses on post-fracture reservoir production, and on factors affecting how fractures propagate. The information herein also includes a comprehensive discussion of postfracture oil and gas production, including example calculations. The remainder of the chapter provides a general overview to introduce other aspects specifically pertinent to fracturing behavior. Later chapters provide more detail on the subjects summarized here as follows: • Rock mechanics and fracture propagation (chapter 3) • Fracturing fluid loss (leakoff ) to the formation (chapter 5) • Fracturing fluid system rheology and proppant transport (chapter 6) • Propping agents (proppants) and fracture conductivity (chapter 7) Some equations and figures contained in this chapter also reappear in the chapters designated above, along with additional discussion, figures, tables, equations, algorithms, and examples. This overview only touches on how each of the above act and interact in regard to fracture propagation.

Factors Pertinent to Fracturing Behavior and Economics Listed below are important factors that are universally applicable to all fracturing treatments. These factors apply to fracturing in both vertical and horizontal wellbores, and govern the net revenue achieved from well. Revenue stream factors depend primarily on the formation’s • Reservoir size (aerial extent, and thickness) • Hydrocarbon volume (porosity, hydrocarbon saturation) • Hydrocarbon properties (oil and/or gas viscosity, compressibility) 35

Essentials of Hydraulic Fracturing

• In situ reservoir conditions (stress, pressure, temperature) • Formation structure (rock mechanical properties, mineral content) • Formation flow properties (permeability, relative permeability, net pay thickness) • Effectively propped fracture penetration • Effective fracture conductivity from the fracture extremity to the wellbore Costs factors associated with fracture propagation behavior depend primarily on • Reservoir size (aerial extent, and thickness) • In situ rock and reservoir conditions (stress, pressure, temperature) • Formation structure (rock mechanical properties, mineral content) • Formation flow properties (permeability, net pay extent) • Rock mechanics (in situ stress profiles and mechanical rock properties), a function of matrix structure, rock composition, and mineral content • Fracturing fluid chemistry, rheology and proppant transport attributes • Propping agent attributes (type, strength, size, size distribution) • Fracturing fluid leakoff behavior (fluid loss, volumetric efficiency) • Fracture volume (penetration, vertical height, horizontal and vertical configuration), a function of rock mechanics, fluid rheology, fluid loss Obviously, there can be substantial interdependence between the factors that affect both revenue from the well after the fracture treatment and the costs to complete and stimulate the reservoir. The degree of significance and interdependence can vary widely depending upon the specific reservoir situation. For example, formation permeability combined with reservoir pore pressure impacts fluid loss behavior, which in turn affects fracture volume, which will determine fracture penetration and width. In situ stress profiles depend on the mechanical rock property, Poisson’s ratio, and reservoir pore pressure. These combined with fluid loss govern vertical fracture growth, and penetration. Fluid loss also governs achievable fracture volume. Hence, fluid loss affects fracture penetration and width, as well as the rheology (which is expressed as apparent viscosity in fracturing equations) of the fracture fluid and fracture conductivity. Fracture width and fracture height are controlled by the pressure distribution in the fracture. The elastic modulus of the rock combined with in situ stress and reservoir pore pressure affects the pressure in the fracture, which governs fracture width behavior. Fracture width, in turn, affects the volume of proppant in the fracture, which affects fracture conductivity. Fracture conductivity combined with formation permeability and fracture length penetration controls the production increase achieved from a fracturing treatment. Production increase combined with reservoir pore pressure dictates post-fracture production rate. Post-fracture oil and gas production dictates if the treatment was an economic success. Because of the wide variations and complexities encountered in nature, it is essential that the design engineer have a solid understanding of what factors are important, and where and why they are important. However, there are no situations where the above factors are not involved in any credible fracture treatment design.

36

Chapter 2

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Overview

Preliminary Post-Fracture Production Estimates The initial design step is to use pre-treatment formation evaluation data to estimate the posttreatment oil and gas production for a variety of fracture lengths and fracture conductivities. This procedure involves scoping a combination of propped fracture penetrations and fracture conductivities that optimize post-fracture production behavior. Such evaluations set the target for a treatment design that yields economically optimized results. Estimating post-fracture production may be done using one or all of the methods listed below: • Long-standing, well-established ˡˡ Folds of increase (FOI) charts for semi-steady state reservoir flow, or ˡˡ Transient reservoir flow type curve charts • Reservoir simulation software that contains algorithms for the above can be used to compute flow rate versus time for a variety of reservoir and fracture conditions. Graphical presentations that show the folds of increase in flow rate for any combination of fracture length and fracture conductivity can provide an advantage, especially for engineers new to fracture treatment design. These graphical solutions provide a visual perspective about the interdependence and relative effects of parameters, such as fracture length, fracture conductivity, and formation permeability. Hence, the discussion that follows focuses primarily on the classical charts that emerged shortly after the onset of fracturing in the 1950s, 60s, and 70s. The applicability of any of the methods is specific to two different types of reservoir behavior: • Semi-steady state flow • Transient flow These approaches can be used to determine fracture conductivity and fracture penetration design targets that optimize post-fracturing production. Design engineers, especially those who are new to fracture design, should study and use the following graphical solutions to be sure that they understand the fundamentals of reservoir behavior from a well that has been fracture treated. Once the fundamentals are understood, using a reservoir simulator to refine the results is a more preferred approach.

Essential parameters The heart of post-fracturing production increase depends on the interdependence between • Formation permeability • Effectively propped fracture penetration, i.e., from wellbore to tip (half-length) • Effective fracture conductivity KƒWƒp, where ˡˡ Kƒ = Fracture permeability ˡˡ Wƒp = Propped fracture closed width These variables apply for both semi-steady state and transient reservoir flow behavior. The importance of representative formation permeability is inherent to inferring credible targets for penetration and conductivity. 37

Essentials of Hydraulic Fracturing

Production estimates for semi-steady state reservoir flow Figure 2–1 shows five commonly used charts for predicting semi-steady state post-fracture production FOI, i.e., the ratio of production rate shortly after post-fracture cleanup to pre-fracture rate. These are comprised of developments over fracturing history made by • Prats (darcy fracture flow)—Upper left • McGuire and Sikora (darcy fracture flow)—Upper middle • Holditch (darcy fracture flow)—Upper fracture right • Tinsley and colleagues (darcy fracture flow)—Lower left • Tannich and Nierode (non-darcy fracture flow)—Lower right

Fig. 2–1. FOI charts: Prats, McGuire and Sikora, Holditch, Tinsley et al., Tannich and Nierode Source: “Figure 1.2,” “Figure 1.3,” “Figure 1.4,” “Figure 1.5,” and “Figure 15.4,” Gidley et al. 1989, 2, 318. All charts are applicable to • Single, planar fractures that propagate symmetrically about the wellbore • Fracture conductivity over the entire net pay The assumptions concerning the shape of the reservoir were • Radial reservoir flow for Prats, Tinsley, and Tannich and Nierode • Flow from a square reservoir for McGuire and Sikora and Holditch Conditions/assumptions pertinent to applying the charts are • Normalized on net pay • Fracture conductivity vertical extent equals net pay vertical extent 38

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Overview

• Semi-steady state, radial reservoir flow • No near-wellbore formation (skin) damage Results will vary among the charts because of the different assumptions made by the authors. Regardless of the differences, all provide significant value to targeting a fracture treatment design. The horizontal axes are consistent in that they include fracture conductivity, formation permeability and effectively propped fracture penetration. Prats' combines these in a single value. The others employ curves where penetration is relative to reservoir drainage radius. The vertical axes comprise post-fracture/pre-fracture production ratio functions, such that post-fracture values can be determined from known pre-fracture production rates. The charts can provide initial guidelines for determining approximate treatment size, materials (fluid systems and proppants), and other treatment variables, such as injection rates and proppant staging schedules. Prats, McGuire and Sikora, Holditch, and Tinsley et al. apply to darcy fracture flow for either steady-state or semi-steady state reservoir flow. Tannich and Nierode applies to nondarcy fracture flow, as well as semi-steady state reservoir flow. None of these graphical solutions apply to well production during transient reservoir flow. Hence, their applicability to oil formation permeability below 0.1 md and gas formation permeability below 0.01 md is questionable because it takes a long time (months or years) before wells completed in low permeability formations actually reach semi-steady state flow. Prats' approach is theoretically based. McGuire and Sikora, and Tinsley et al. are based on results from electrical similitude models. Holditch and Tannich and Nierode are developed using results from reservoir simulation models.

Insights available from semi-steady state reservoir flow FOI charts The Tinsley et al. chart in figure 2–2 is used for expanded discussion. In figure 2–2, the vertical axis (Jƒ/J) directly yields FOI of the semi-steady state productivity index before and after the fracture treatment. The productivity index is the flow rate (q) divided by the pressure drop (Δp) between the reservoir and the well bore. For millidarcy reservoirs, a well can reach semi-steady state in a matter of days or weeks. For lower permeability reservoirs, microdarcy or less, it may require months or years to reach semi-steady state flow. The horizontal axis (RC) is relative fracture capacity. The value of RC is comprised of the values of the fracture conductivity (FC), formation permeability (ki), and a constant (RCF) that includes: hf—Effectively propped fracture height hi—Net pay Re—Drainage radius S—Well spacing Curves within the chart (Xf/Re) represent ratios of propped fracture penetration (Xf ) to drainage radius (Re). 39

Essentials of Hydraulic Fracturing

Note: In figure 2–2, propped vertical fracture height (hf ) equals net pay height (hi), so the entire net pay is effectively propped. Tinsley et al. presents other charts where net pay is not totally propped. Consequences for this are obvious: lower FOI. This emphasizes the importance of treatment designs that always effectively prop the entire pay.

Fig. 2–2. Tinsley et al. FOI chart Source: “Figure 1.4,” Gidley et al. 1989, 2. In the chart, it is easily seen that as ki decreases, RC increases (to the right), and higher values of the productivity index ratio or FOIs can be achieved with deeper fracture penetrations (Xf/ Re). For RC > 100, FOI is governed primarily by fracture penetration. For RC > 500, FOI remains essentially constant, regardless of RC magnitude. However, as ki increases, RC decreases (to the left), and here, FC dominates. Note that for RC < 1, fracture penetration has little impact on FOI. In this range, maximum achievable values are FOI = 2 or lower. As a general rule of thumb for a semi-steady state reservoir flow, low-permeability formations require deeply penetrating fractures to increase the productivity index. For these low-permeability reservoirs, fracture conductivity is not as important as fracture length as long as sufficient conductivity exists for the fracture fluid to clean up in the fracture. Conversely, the optimum fracture for high permeability formations generally consists of shorter but higher conductivity fractures to provide sufficient permeability contrast with the formation. Hence, an accurate estimate of formation permeability prior to designing the fracture treatment is essential for success. Production estimates for transient reservoir flow. The charts in figure 2–1 apply only to semisteady state reservoir flow. If a reservoir exhibits transient flow over extended periods, the rule of thumb mentioned above, may not be completely applicable, but the principal of requiring deep penetrating fractures in low-permeability reservoirs remains valid. The problem is that the 40

Chapter 2

|

Overview

graphical solutions shown in figure 2–1 tend to underestimate the post-fracture behavior of a well in a low-permeability reservoir during the transient flow period. Tight (low-permeability) reservoirs can remain in transient flow for extended periods (months or years). When fractured, they can yield FOIs that are orders of magnitude higher than the figure 2–1 charts suggest. Since it is still important to determine post-fracture production behavior for a variety of fracture lengths and conductivities, the engineer must use methods for computing transient flow behavior for low-permeability reservoirs that have been hydraulically fracturetreated. These methods include analytical or finite-difference reservoir simulators, and/or dimensionless type curve charts constructed for transient flow. These type curves were computed using either analytical equations or finite-difference reservoir models. Dimensionless type curve charts, of various forms, were introduced in the early 1980s. A plethora of references pertinent to pre- and post-fracture production (both flow rate and cumulative) resides in the literature. These graphs were generated from reservoir performance computer models for a variety of boundary effects. The pertinent parameters for a typical type curve are combined into dimensionless terms for time (tD), rate (qD), or cumulative (QD), and fracture conductivity (CD) or some other developer-specified symbol. Chart displays for rates are typically in the format tD versus 1/qD, and those for cumulative formatted as tD versus QD. Both contain interior sets of CD curves. Many charts display axes consistent with reality: over time, the producing rate decreases and cumulative production increases. However, charts that do not are also relatively common. For any given type curve solution, design engineers should review the literature to be certain they understand the assumptions behind each type curve. Figure 2–3 shows examples of two such charts for inferring transient flow production over time. The upper chart applies to producing rate, the lower to cumulative production. Here the horizontal axes comprise dimensionless time tDXf, which is a function of • Real time • Formation permeability • Formation porosity • Reservoir fluid viscosity • Compressibility • Fracture penetration The vertical axes are comprised of dimensionless expressions: reciprocal rate, 1/qD (upper chart), and cumulative production. QD (in the lower chart) is a function of • Net pay • Reservoir pressure • Compressibility • Temperature • Formation volume factor (for QD, right chart) • Fracture penetration (for QD, right chart) 41

Essentials of Hydraulic Fracturing

Fig. 2–3. Transient reservoir flow, pre- and post-fracture rates (upper), and cumulative production type curves (lower) Source: “Figure 1.6” and “Figure 1.7,” Gidley et al. 1989, 2. The curves in the rate chart (top) and lower set of the cumulative chart (bottom) constitute dimensionless fracture conductivity, i.e., kƒWƒ/kXƒ, where Wƒ is the average closed fracture width. The curves in the upper set of the cumulative chart (bottom) constitute dimensionless fracture penetration, for a dimensionless conductivity = 0.2, i.e., an essentially un-propped fracture.

42

Hence, for a given set of constant formation and fracture parameters, a real-time value establishes a point on the horizontal axis. The intersection (vertically) of that point with a designated conductivity curve constitutes a corresponding value on the vertical axis. Inversion of the vertical

Chapter 2

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Overview

axis equation for that value yields the resulting producing rate, or cumulative production associated with the specified real time value. Figure 2–3 constitutes only a sampling of methods available for transient flow applications. Digital versions of both types of presentations are generally available. If not, charts can be digitized. With interpolation algorithms, rate and cumulative production streams can easily be calculated for various prospective fracture penetrations and conductivities. Again, the results can be converted to revenue streams. Many commercial models are available with analytical solutions that are easy to use to generate values of flow rate vs. time for any set of reservoir and fracture conditions. Models are also available for evaluating the effects of horizontal wells that have been fracture-treated. Such methods can also be used for both pre- and post-fracture analysis to infer fracture penetration and conductivity from production behavior. In fact, solving the inverse problem is very important to determine if the actual post-fracturing lengths and conductivities are similar to those that were designed for the well. Production folds-of-increase: semi-steady state flow for non-tight reservoirs. The following figures show five approaches used for predicting post-fracturing production FOI: • Figure 2–4 Prats • Figure 2–5 McGuire and Sikora • Figure 2–6 Holditch • Figure 2–7 Tinsley et al. • Figure 2–8 Tannich and Nierode The five different figures originate from different publications. Thus, nomenclature pertinent to parameters contained in their axes is not uniformly consistent. To address this, the parameters are identified for each figure, along with their pertinent units. Nomenclature in the figures that deviates from what is used throughout this book is indicated by the notation i.e.

Fig. 2–4. Prats, FOI chart Source: “Figure 1.2,” Gidley et al. 1989, 2.

43

Essentials of Hydraulic Fracturing

Prats, FOI chart horizontal axis (HAXIS), vertical axis (VAXIS), vertical axis intercept value (VINTERCEPT) parameters and units: HAXIS = KƒWƒp/(kXƒp) = FCD

Equation 2–1–1

VAXIS = r´w/Xƒp

Equation 2–1–2

VINTERCEPT

Per curve at HAXIS value



r´w = Xƒp 10^[A + B Log10(FCD) + C Log10(FCD)2]

Equation 2–1–3



FOI = [Log(re/rw)/Log(re/r´w)]

Equation 2–1–4

where

k

Formation permeability (md)



Kƒ, kf



Fracture permeability (md)



q

Pre-fracture producing rate



qf

Post-fracture initial producing rate



re

Reservoir drainage boundary radius (ft)



rw

Wellbore radius (ft)



r´w

Pseudo wellbore radius (ft)



Wƒp, w

Propped fracture width (ft)



Xƒp, Xf

Propped fracture penetration, i.e., half-length (ft) wellbore to propped fracture extremity

Equation 2–1–3 Coefficients for A, B, and C are functions of FCD, per table 2–1. For example, the coefficients required to calculate r´w where FCD = 0.5 reside in the left column of table 2–1, where

A = –0.7305



B =  0.7403



C = –0.1738

Accordingly, to calculate r´w where FCD = 5 the coefficients are in the table middle column, and for FCD = 50 the coefficients are in the right column of table 2–1. Table 2–1. Prats’ FOI equation constants

Coefficient A= B= C=

FCD, KƒWƒp / kXƒ, Range 0.1–1 1–10 10–100 –0.7305 –0.7325 –0.4622 0.7403 0.6867 0.1455 –0.1738 –0.3161 –0.0375

Figure 2–4, which is a single curve relation between FCD and r´w/Xƒ, is easily amenable to curve fitting for equation 2–1–3 constants A, B, and C in table 2–1. These constants apply for the 44

Chapter 2

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Overview

appropriate FCD range. Thus, it eliminates the need for determining a vertical axis intercept (r´w/ Xf ) from the intersection of the horizontal axis FCD value and the chart curve. McGuire and Sikora (figure 2–5), Holditch (figure 2–6), and Tinsely et al. (figure 2–7) contain curves pertinent to propped fracture penetration (Xƒp) as a fraction of reservoir drainage boundary. The curves in these charts have not been defined herein by algorithms similar to that presented for Prats’ approach. Hence, the charts per se require manual axes intercept-picking.

Fig. 2–5. McGuire and Sikora, FOI chart Source: “Figure 1.3,” Gidley et al. 1989, 2. McGuire and Sikora FOI chart horizontal axis (HAXIS), vertical axis (VAXIS), vertical axis intercept value (VINTERCEPT) parameters, and units: HAXIS = (12WƒpKƒ/k ) × (40A)½ = FCD

Equation 2–2–1

VAXIS = qƒ/q[7.13/(lne(0.472Xƒp/rw))]

Equation 2–2–2



Equation 2–2–3

Xƒp/re = Lf/Le

VINTERCEPT

Per Xƒp/re curve at HAXIS value

FOI = VINTERCEPT/{qƒ/q[7.13/(lne(0.472Xƒp/rw))]}

Equation 2–2–4

where

A

Well spacing (acres)



qƒ, J

Post-fracture initial producing rate 45

Essentials of Hydraulic Fracturing



q, Jo

Pre-fracture producing rate



k

Formation permeability (md)



Kƒ, kf

Fracture permeability (md)



re, Le

Reservoir drainage boundary radius (ft)



Xƒp, Lf

Propped fracture penetration, i.e., half-length (ft)



rw

Wellbore radius (ft)



Wƒp, w

Propped fracture width (ft)



Note that the natural (or Napierian) logarithm, as opposed to Log10, is integral to equation 2–2–2. The Holditch chart is similar to that of McGuire and Sikora. The axes contain identical relationships. The difference is that the curves in the Holditch chart are developed from finitedifference reservoir simulation results, whereas, those in McGuire and Sikora are based on electrical analog models.

Fig. 2–6. Holditch, FOI chart Source: “Figure 15.4,” Gidley et al. 1989, 318. Holditch, FOI chart, figure 2–6, horizontal axis (HAXIS), vertical axis (VAXIS), vertical axis intercept value (VINTERCEPT), parameters, and units:

46

HAXIS = (12WƒpKƒ/k) × (40A)½ = FCD

Equation 2–3–1

VAXIS = qƒ/q[7.13/(lne(0.472Xƒp/rw))]

Equation 2–3–2

Chapter 2



Xƒp/re = Lf/Le

VINTERCEPT

|

Overview

Equation 2–3–3 Per Xƒp/re curve at HAXIS value

FOI = VINTERCEPT/{qƒ/q[7.13/(lne(0.472Xƒp/rw))]}

Equation 2–3–4

where

A

Well spacing (acres)



qƒ, J

Post-fracture initial producing rate



q, Jo

Pre-fracture producing rate



k

Formation permeability (md)



Kƒ, kf

Fracture permeability (md)



re, Le

Reservoir drainage boundary radius (ft)



Xƒp, Lf

Propped fracture penetration, i.e., half-length (ft)



rw

Wellbore radius (ft)



Wƒp, w

Propped fracture width (ft)



Fig. 2–7. Tinsley et al., FOI chart Source: “Figure 1.4,” Gidley et al. 1989, 2. Tinsley et.al., FOI chart, figure 2–7, horizontal axis (HAXIS), vertical axis (VAXIS), vertical axis intercept value (VINTERCEPT), parameters, and units: HAXIS = RCF KƒWƒ/k

Equation 2–4–1

VAXIS = qƒ/q[7.13/(lne(0.472Xƒp/rw))]

Equation 2–4–2 47

Essentials of Hydraulic Fracturing



RCF = 0.00159[(Hƒ/hNET) × ln(re/rw) × (10/A)½]

VINTERCEPT

Equation 2–4–3

Per Xƒp/re curve at HAXIS value

FOI = VINTERCEPT

Equation 2–4–4

where

RC

Relative fracture conductivity



KƒWƒp = FC

Fracture conductivity (md-ft)

hNET, h

Net pay vertical height, i.e., thickness (ft)



Hƒp, hf

Vertical fracture propped height (ft)



q, J

Pre-fracture producing rate



qƒ, Jf

Post-fracture initial producing rate



Kƒ

Fracture permeability (md)



k, ki

Formation permeability (md)



re, Re

Reservoir drainage boundary radius (ft)



rw

Wellbore radius (ft)



A, S

Well spacing (acres)



Wƒp



Xƒp, Xf





Propped fracture width (ft) Propped fracture penetration, i.e., half-length (ft)

Fig. 2–8. Tannich and Nierode FOI chart, non-darcy fracture flow Source: “Figure 1.5,” Gidley et al. 1989, 2. 48

Chapter 2

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Overview

Tannich and Nierode, FOI chart, figure 2–8, horizontal axis (HAXIS), vertical axis (VAXIS), vertical axis intercept value (VINTERCEPT) parameters and units: HAXIS = 0.00225(Wƒpµ/k) × {ZT/[βγg(pe2 – pw2)]}½ × (2,640/re)½

Equation 2–5–1

VAXIS = qƒ/q[ 7.50/(ln(0.229re/rw))]

Equation 2–5–2

VINTERCEPT

Per Xƒp/re curve at HAXIS value

FOI = VINTERCEPT



Equation 2–5–3

where

qƒ, i.e., J´g

Post-fracture initial producing rate



q, i.e., Jg,o

Pre-fracture producing rate



k

Formation permeability (md)



Pe

Reservoir static pressure (psi)



Pw, i.e., pwf

Wellbore producing pressure (psi)



re

Reservoir drainage boundary radius (ft)



rw

Wellbore radius (ft)



T

Formation temperature (°R = 460 + °F)



Wƒp, i.e., w

Propped fracture width (ft)



Z, i.e., z

Gas compressibility factor (dimensionless)

β

Fracture non-darcy flow coefficient (atm–sec2/gm), a function of proppant size (see table 2–2)



γg

Gas specific gravity (dimensionless)



μ

Gas viscosity (cp)

The non-darcy fracture flow coefficient, β, is defined by equation 2–5–4.

β = b/(Kƒ)a

Equation 2–5–4

where

β

Fracture non-darcy flow coefficient (atm-sec2/gm)



Kƒ



Fracture permeability (darcys)



a&b



Constants depend on proppant mesh size per table 2–2.

Table 2–2 provides general β values for the listed proppant sizes. However, β values are also stress- and proppant-type dependent. Therefore, if available, published values from the proppant manufacturer, industry consortiums, or other testing services should be used.

49

Essentials of Hydraulic Fracturing

Table 2–2. Nondarcy fracture flow coefficient, beta factor equation constants Source: Cooke 1973. Proppant Mesh Size

Beta Factor, βPROP Equation Constants

8/12 10/20 20/40 40/60

a

b

1.24 1.34 1.54 1.6

3.32 2.63 2.65 1.1

Units for β in equation 2–5–1 are atm-sec2/gm. However, β values are sometimes published in other units, i.e., 1/ft, or 1/cm. If so, they must be converted to atm-sec2/gm for use in figure 2–8. Equations 2–5–5 and 2–5–6 provide conversions applicable to equation 2–5–1.

β (1/ft)/30,918,000 = β (atm-sec2/gm)

Equation 2–5–5



β (1/cm)/1,014,000 = β (atm-sec2/gm)

Equation 2–5–6

Example 2–1. FOI charts: semi-steady state flow sample calculations Consider the following data pertinent to the FOI charts: Pre-fracture production

q

=

100 BOPD

Well spacing

A

=

160 acres

Reservoir drainage radius

re

=

1,489 ft

Wellbore diameter

Dh

=

12 in.

Wellbore radius

re

=

0.5 ft

Formation permeability

k

=

1 md

In situ closure stress Formation temperature

4,900 psi Tƒ

150°F

Proppant type

Ottawa Sand

Proppant size

20/40 mesh

Proppant concentration

2.5 lb/ft2 (fracture closed)

Propped fracture width (closed)

Wƒp

=

0.273 in. = 0.02275 ft (at 2.5 lb/ft2 concentration)

Undamaged fracture permeability

Kƒ

=

80 darcys (at 150°F, 4,900 psi stress load, 50 hour data)

=

50%

=

40 darcys (proppant pack damage = 50%)

Fracture permeability damage factor

50

=

Effective fracture permeability

Kƒp

Propped fracture conductivity

KƒWƒ =

910 md-ft

Propped fracture half-length

Xƒp

1,000 ft

=

Chapter 2

Propped fracture height

Hƒp

=

|

Overview

Entire vertical net pay interval height, i.e., Hƒp/hNET = 1.0

The following shows the chart axes, curve values, resulting FOIs, and post-fracture initial producing rate calculations for the semi-steady state approaches, i.e., Prats, McGuire and Sikora, Holditch, and Tinsley et al. Prats' approach: HAXIS value = KƒWƒ/(kXƒ) = 0.91 VINTERCEPT, r´w/Xƒ = 0.173

i.e., 10^[A + B log(FCD) + C log(FCD)2]



per table 2–2 constants for FCD = 0.91

A = –0.7305 B = 0.7403 C = –1738

Pseudo wellbore radius, r´w = VINTERCEPT Xƒ = 173



FOI = qƒ/q = ln(re/rw)/ln (re/r´w) = 3.7



Initial post-fracture production, FOI q = 370 BOPD

McGuire and Sikora approach: HAXIS value = (12KƒWƒ/k) × (40/A) = 5.5 103

Applicable curve = Xƒ/re = 0.67

VINTERCEPT = (qƒ/q) × [7.13/ln(0.472 re/rw)] = 4.2

FOI = qƒ/q, VINTERCEPT/[7.13/ln(0.472 re/rw)] = 4.4



Initial post-fracture production = FOI q = 440 BOPD

Holditch approach: HAXIS value = (12KƒWƒ/k) × (40/A) = 5.5 × 103

Applicable curve = Lf/Le, i.e., Xƒ/re = 0.67

VINTERCEPT = (qƒ/q) × [7.13/ln(0.472 re/rw)] = 4.3

FOI = qƒ/q, VINTERCEPT/[7.13/ln(0.472 re/rw)] = 4.4



Initial post-fracture production, FOI q = 440 BOPD

Tinsley et al. approach: HAXIS value = (0.00159hf/hi) × (ln(re/rw) × (10/A)0.5KƒWƒ/k) = 2.89

Applicable curve = Xƒ/Re, i.e., Xƒ/re = 0.67

VINTERCEPT, qƒ/q = 3.2 51

Essentials of Hydraulic Fracturing



FOI = qƒ/q = 3.2



Initial post-fracture production, FOI q = 320 BOPD

Table 2–3 summarizes comparative results for identical input data. Obviously, the different approaches yield different results (FOIs from 3.2 to 4.4) with the resulting post-fracture initial rates ranging from 320 to 440 BOPD. Hence, it is suggested that several approaches be employed to obtain a range of prospective results. However, it is the design engineer’s discretion to determine the approach applicability. Table 2–3. Comparative FOI and post-fracture initial production rates: semi-steady state flow Approach

FOI

BOPD

Prats McGuire and Sikora Holditch Tinsley et. al

3.7 4.4 4.4 3.2

370 440 440 320

Example 2–2. Tannich and Nierode FOI Charts: Non-Darcy Fracture Flow Sample Calculations

This example for gas reservoir flow uses the same formation and pressured data as example 2–1, with the following additional data that applies to gas reservoirs, where the units for gas producing rate is expressed in thousands of cubic feet per day (MCFD).

Pre-frac producing rate

q

=

100 MCFD



Reservoir static pressure

Pe

=

3,500 psig



Wellbore producing pressure

Pw

=

3,000 psig



Gas compressibility factor

Z

=

0.862 dimensionless



Gas specific gravity

γg

=

0.65 dimensionless



Gas viscosity

μ

=

0.0534 cp



Fracture non-darcy flow coefficient β

=

b/(Kƒ)a

Per table 2–3, for 20/40 mesh proppant:

a

=

1.54



b

=

2.65



β

=

2.61 10–04 atm-second2/gm

Tannich and Nierode, FOI curve parameters: HAXIS value = 0.00216wµ/k{Z (T + 460)/[βγ(Pe2 – Pw2)]}1/2(2,640/re)1/2 = 2.21 10–7

52



Applicable curve = Xƒ/re, i.e., Lƒ/re = 0.67



VINTERCEPT = 0.750/(ln(0.229re/rw) = 4.0



FOI = qƒ/q = VINTERCEPT/[0.750/(ln(0.229re/rw)] = 3.5



Initial post-fracture production = 3.5 q = 350 MCFD

Chapter 2

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Overview

Maximum achievable semi-steady state FOI Maximum achievable FOIs are easily inferred with FOI charts. At points along the horizontal axes, a corresponding maximum vertical axis value exists. Lowering formation permeability or increasing fracture conductivity moves the horizontal axis value to the right, thus increasing FOI. Accordingly, increasing propped fracture penetration increases the corresponding vertical axis value. However, each FOI chart exhibits a maximum value for a given combination of formation permeability, fracture conductivity, and propped fracture penetration. The design engineer is constrained by formation permeability—it is what it is. Hence, reliable permeability values are essential to fracture treatment design. Also, proppant pack permeability values are subject to constraints, such as the type and size of the propping agent. However, a relatively broad range of proppants exists. Thus, there is some latitude in proppant selection. In situ stress profiles, available fracturing fluid systems and economics also govern fracture penetration and fracture width. Accordingly, the design engineer is faced with determining a fracture treatment design using available materials and treatment volumes that economically optimize treatment returns.

Post-fracture production: transient reservoir flow Figures 2–4 through 2–8 apply to only semi-steady state reservoir flow. There are no similar charts applicable to transient flow, which is exhibited in tight (low-permeability) formations. Also, FOI terminology is not commonly used for fracturing tight formations. Generally, gas reservoirs below 0.1 md and oil reservoirs below 1 md are considered low-permeability. Pre-fracturing production tests on these formations usually yield too-small-to-measure (TSTM) results or such low rates that pre-fracture productivity cannot be accurately determined. Actually, tight formations, when fractured exhibit FOIs that are orders of magnitude higher than can be achieved from semi-steady state flow formations. As stated previously in this chapter, in low-permeability reservoirs we can use transient flow solutions to estimate post-fracture production. Figure 2–9 provides an example. It is one of many dimensionless rate versus dimensionless time type curves used for transient flow. Such charts are useful for examining tight formation post-fracture production potentials, using prospective fracture penetrations and conductivity values. The chart applies to transient flow in both oil and gas reservoirs.

53

Fig. 2–9. Dimensionless rate versus dimensionless time for finite conductivity fractures: unsteady-state reservoir flow with oil and gas (after Agarwal, et al.) Source: “Figure 15.31,” Gidley et al. 1989, 330.

Chapter 2

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Overview

Example 2–3–1. Oil Reservoirs: Reciprocal Dimensionless Rate

versus Dimensionless Time Calculations

The example in table 2–4 shows post-fracture production rate prediction scenarios for different values of propped fracture penetration and fracture conductivity using figure 2–9. Here, propped fracture penetrations range from 500 to 2,500 feet, and fracture conductivity from 500 to 2,000 md-ft in an oil producing reservoir that has the formation and fluid properties listed in table 2–4. Table 2–4. Post-fracture initial oil producing rates from type curves Net Pay Formation Permeability Formation Porosity Reservoir Pressure Wellbore Pressure Avg Flowing Pressure ReservoirTemperature Oil API Gravity: Producing Gas Sp. Gr .: Producing GOR: Oil Bubble Point Pressure; Total System Compressibility Viscosity Viscosity Formation Volume Factor (STBbls/Res Bbls)

h k φ Pe Pw Pa TR

G

cT µ{Pe} µ{Pa}

100 0.01 15 5,014.65 1,014.65 3,014.65 200

ft md % psia psia psia ºF

30 0.65 100 1.0E+03 0.000012 2 2.2 1.5

ºAPI dim ft3/STBbl psi 1/psi cp cp dim

Post-Fracture Production Calculations Fracture Length

500

ft

KƒWƒ Fracture Length

1,000

ft

KƒWƒ Fracture Length

1,500

ft

KƒWƒ Fracture Length

2,000

ft

KƒWƒ Fracture Length

2,500 KƒWƒ

ft

500 1,000 2,000

md-ft md-ft md-ft

500 1,000 2,000

md-ft md-ft md-ft

500 1,000 2,000

md-ft md-ft md-ft

500 1,000 2,000

md-ft md-ft md-ft

500 1,000 2,000

md-ft md-ft md-ft

Dimensionless Time - TD (horizontal axis) 0.000264 k(md) t(hrs) tD = φ(fraction) µ{Pe}(cp) C(1/psi) Xƒ(ft) 2

Conductivity Function - Cr (chart curves) WƒKƒ(md-ft) Cr = π Xƒ(ft) k(md)

1/Dimensionless Rate - 1/q D (vertical axis) k(md) h(ft) [Pe(psi) - Pw(psi)] 1/q D = 141.3 q(BOPD) µ{Pa}(cp) (dim) Time (t) after Frac @ 15 days @ 360 hrs Cr 1/q D q (Calc'd) Chart Pick (Calc'd) BOPD tD = 9.6E-04 32 1.0E-01 86 64 9.5E-02 90 127 8.9E-02 96 tD = 2.4E-04 16 6.0E-02 143 32 5.4E-02 159 64 4.7E-02 183 tD = 1.1E-04 11 4.8E-02 179 21 4.20E-02 204 42 3.6E-02 238 tD = 6.0E-05 8 5.0E-02 172 16 4.0E-02 214 32 3.20E-02 268 tD = 3.8E-05 6 5.8E-02 148 13 3.4E-02 252 25 2.9E-02 296

Time (t) after Frac @ 30 days @ 720 hrs Cr 1/q D q (Calc'd) Chart Pick (Calc'd) BOPD tD = 1.9E-03 32 1.4E-01 61 64 1.3E-01 69 127 1.2E-01 71 tD = 4.8E-04 16 7.8E-02 110 32 7.4E-02 116 64 6.8E-02 126 tD = 2.1E-04 11 5.9E-02 144 21 5.4E-02 159 42 5.0E-02 172 tD = 1.2E-04 8 5.8E-02 148 16 4.80E-02 179 32 4.3E-02 199 tD = 7.7E-05 6 6.0E-02 143 13 4.4E-02 195 25 3.8E-02 226

55

Essentials of Hydraulic Fracturing

The scenarios provide a perspective of potential post-fracture flow rates that result from different combinations of propped fracture penetrations and conductivity. It is then up to the design engineer to select the fracturing treatment design that yields the best economic results. The scenarios selected by the engineer should span a sufficiently broad range of fracture lengths and conductivities to cover what is reasonably physically achievable, and to provide a perspective of the differences between shallow and deep fracture penetrations, and low and high fracture conductivity. In the example, producing times of 15 and 30 days after fracturing are specified as such to allow for fracturing fluid system flowback and well cleanup. This is arbitrary but can be adjusted to the field observations. Some wells clean up in a few days, while others may take a few weeks before the oil and gas flow rates are meaningful. A time, or set of times, must be established by the user depending on the field conditions. In practice, specified cleanup times after fracturing should be consistent with past experience, and/or knowledge from wells in a given field. Post-fracture production rate calculations for oil reservoirs proceed as follows: • For each propped fracture penetration (Xƒp), a dimensionless time (tD) is calculated per equation 2–6 for the specified real time (t), or times, after fracturing. tD = 0.000264kt/[φμ{Pe}cTXƒp2]

Equation 2–6

where tD

Dimensionless time

k

Formation permeability (md)

t

Time produced after fracturing (hrs)

φ

Formation porosity (fraction)

μ(Pe)

Reservoir fluid viscosity (cp) at reservoir pressure Pe(psia)

cT

Total system, i.e., rock and reservoir fluid compressibility (1/psi)

Xƒp

Propped fracture penetration (ft), wellbore to propped fracture tip (equivalent to figure 2–9 term Lf )

• For each fracture conductivity (KƒWƒ) and propped fracture penetration (Xƒp), a dimensionless fracture conductivity function (Cr) is calculated per equation 2–7.

Cr = KƒWƒ/(πXƒpk)

Equation 2–7

where

56



Cr



Dimensionless fracture conductivity function



KƒWƒ



Fracture conductivity (md-ft)



π



Pi, 3.14159265



Xƒp



Propped fracture penetration (ft), wellbore to propped fracture tip (equivalent to figure 2–9 term Lf )



k



Formation permeability (md)

Chapter 2

|

Overview

• At the intersection of each dimensionless time (tD) and dimensionless fracture conductivity function (Cr), a reciprocal dimensionless production rate (1/qD) value is determined (picked) from the vertical axis of figure 2–9. Note: The dimensionless fracture conductivity function (Cr) values, more often than not, require interpolation between the chart Cr curves in figure 2–9. • For each reciprocal dimensionless time (1/qD) value, a production rate is calculated by equation 2–8.

q = kh(Pe – Pw)/[141.3 × 1/qDμ{Pa}β)

Equation 2–8

where

q

Producing rate (BOPD)



k

Formation permeability (md)



h

Formation net pay (ft)



Pe

Reservoir pressure (psia)



Pw

Wellbore producing pressure (psia)

1/qD

Reciprocal dimensionless rate value from figure 2–9 vertical axis

μ(Pa)

Reservoir fluid viscosity (cp) at average pressure (Pa) Pa = (Pe + Pw)/2



Reservoir fluid formation volume factor (STBO/ResBO), i.e., stock-tankbarrels-of-oil per reservoir-barrel-of-oil

β

Example 2–3–2. Results, Initial Post-Fracture Oil Producing Rates after Fracturing A review of the post-fracture producing rates in table 2–4 suggests that a fracture treatment designed to achieve fracture penetrations (Xƒ) of 2,000 to 2,500 feet with fracture conductivity (KƒWƒ) on the order of 2,000 md-ft provides the more attractive post-fracture production results. One might use the same procedures to explore longer fracture penetrations and higher conductivity to investigate the potential results. The final design selection should be based on full-cycle optimum economic returns over the expected well producing life, from initial postfracture rates to the economic production rate limit.

Example 2–4–1. Gas Reservoirs: Reciprocal Dimensionless Rate

versus Dimensionless Time Calculations

The coordinates in figure 2–6 apply specifically to oil producing reservoirs. However, the same chart (and curves within) and the procedures described for oil reservoirs also apply for gas reservoirs. For gas reservoirs, equation 2–9 applies for dimensionless time, tD (horizontal axis), equation 2–10 applies for reciprocal dimensionless rate 1/qD (vertical) axis, and equation 2–11 yields post-fracture producing rates q at the specified times: tD

=

0.000264kt/[Φμ{Pe}cTXƒ2]

1/qD

=

kh(Pe2 – Pw2)/(1,424qμ{Pa}Z{Pa}T)

Equation 2–9 Equation 2–10 57

Essentials of Hydraulic Fracturing

and

q

=

kh(Pe2 – Pw2)/(1,424 × 1/qDμ{Pa}Z{Pa}T)

Equation 2–11

where tD

Dimensionless time



k

Formation permeability (md)



φ

Formation porosity (fraction)



μ{Pe}

Gas viscosity (cp) @ static reservoir pressure, Pe

cT

Total system, i.e., rock and reservoir fluid compressibility (1/psi)

Xƒ

Propped fracture penetration (ft), wellbore to propped fracture tip (equivalent to figure 2–9 term Lf )

1/qD

Reciprocal dimensionless rate (picked from the vertical axis, figure 2–9)



k

Formation permeability (md)



h

Formation net pay (ft)



Pe

Reservoir pressure (psia = 14.65 + psig)



Pw

Wellbore producing pressure (psia = 14.65 + psig)



q

Producing rate (MCFD)

μ{Pa}

Gas viscosity (cp) @ at average flowing pressure, PGa Pa =[(Pe2 + Pw2)/2]1/2



Z{Pa}

Gas compressibility factor (dim) @ at average flowing pressure, PGa



T

Absolute formation temperature (°Rankin = 460 + °F)

Example 2–4–2. Estimated Initial Post-fracture Gas Producing Rates Table 2–5 shows example 2–4 data and calculations for a gas reservoir. The formation properties are identical to those in example 2–3, table 2–4, except for the reservoir fluid properties, i.e., gas with properties listed in table 2–5. A review of the post-fracture initial gas producing rates in table 2–5 suggests, as in the oil example, that a fracture treatment designed to achieve fracture penetrations of 2,000 to 2,500 feet with fracture conductivity on the order of 2,000 md-ft provides the more attractive post-fracture production results. And, again, the final design selection should be based on full-cycle, optimum net present value (NPV) economic returns over the expected well producing life, as production rate declines from post-fracture initial producing rate to the economic production limit.

58

Chapter 2

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Overview

Table 2–5. Post-fracture initial gas producing rates from type curves Net Pay Formation Permeability Formation Porosity Reservoir Pressure Wellbore Pressure Avg Flowing Pressure

h k φ Pe Pw Pa

Producing Gas Sp. Gr .: Gas Base Pressure Gas Base Temperature

Pb Tb

Total System Compressibility Gas Viscosity Gas Viscosity Gas Compressibility Fact ReservoirTemperature

100 0.01 15 5,014.36 1,014.65 3,617.55

ft md % psia psia psia

0.65 dim 14.65 psia 60 ºF

G

cT µ{Pe} µ{Pa} Z(Pa} TR TR

2.0E-05 0.026 0.022 1.01 200 660

1/psi cp cp dim ºF ºR

Post-Fracture Production Calculations Fracture Length

500

ft

KƒWƒ Fracture Length

1,000

ft

KƒWƒ Fracture Length

1,500

ft

KƒWƒ Fracture Length

2,000

ft

KƒWƒ Fracture Length

2,500 KƒWƒ

ft

500 1,000 2,000

md-ft md-ft md-ft

500 1,000 2,000

md-ft md-ft md-ft

500 1,000 2,000

md-ft md-ft md-ft

500 1,000 2,000

md-ft md-ft md-ft

500 1,000 2,000

md-ft md-ft md-ft

Dimensionless Time - TD (horizontal axis) 0.000264 k(md) t(hrs) tD = φ (fraction) µ{Pe}(cp) cT(1/psi) Xƒ(ft)2

Conductivity Function - Cr (chart curves) WƒKƒ(md-ft) Cr = π Xƒ(ft) k(md)

1/Dimensionless Rate - 1/q D (vertical axis) k(md) h(ft) [Pe(psia) 2 - Pw(psia)2 ] 1/q D = 1,424 q(MCFD) µ{Pa}(cp) Z{Pa} TR(ºR) Time (t) after Frac @ 15 days @ 360 hrs Cr q 1/q D (Calc'd) Chart Pick (Calc'd) MCFD tD = 4.9E-02 32 5.2E-01 2,220 64 5.1E-01 2,260 127 6.0E-01 1,920 tD = 1.2E-02 16 2.9E-01 3,982 32 2.8E-01 4,124 64 2.7E-01 4,277 tD = 5.4E-03 11 2.1E-01 5,499 21 2.05E-01 5,633 42 2.0E-01 5,774 tD = 3.0E-03 8 1.7E-01 6,792 16 1.6E-01 7,217 32 1.55E-01 7,450 tD = 1.9E-03 6 1.6E-01 7,217 13 1.3E-01 8,882 25 1.2E-01 9,623

Time (t) after Frac @ 30 days @ 720 hrs Cr 1/q D q (Calc'$d) Chart Pick (Calc'd) MCFD tD = 9.7E-02 32 7.1E-01 1,630 64 7.0E-01 1,650 127 6.9E-01 1,670 tD = 2.9E-02 16 4.2E-01 2,749 32 4.1E-01 2,816 64 4.0E-01 2,887 tD = 1.3E-02 11 2.9E-01 3,982 21 2.8E-01 4,124 42 2.7E-01 4,277 tD = 7.2E-03 8 2.4E-01 4,811 16 2.15E-01 5,371 32 2.0E-01 5,774 tD = 4.6E-03 6 2.2E-01 5,249 13 1.9E-01 6,077 25 1.8E-01 6,415

Post-fracture production decline, cumulative production, present value and performance analysis The preceding discussion focused on post-fracture production rate increase from fracturing. The approaches can also be applied to production decline and cumulative production, which can be converted to revenue streams. Post-fracture production rate matching against transient flow type curves has long been used to infer fracture conductivity and effectively propped fracture penetration.

Performance analysis—effective fracture conductivity and propped fracture penetration The publications listed below, by R. G. Agarwal, R. D. Carter, and C. D. Pollack, provide useful procedures and charts for post-fracture analyses pertinent to producing rates, pressures and 59

Essentials of Hydraulic Fracturing

fracture conductivity. It is suggested that design engineers obtain and maintain both publications in their repertoire of fracture design tools. • Agarwal, R. G., R. D. Carter, and C. D. Pollack. 1979. “Evaluation and Performance Prediction of Low-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing.” Journal of Petroleum Technology 31:362–372. • Agarwal, R. G., R. D. Carter, and C. D. Pollack. 1979. “Type Curves for Evaluation and Performance Prediction of Low-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing.” Journal of Petroleum Technology 31:651–654 One caution: Tight formations require extensive time periods to develop definitive pressure distribution profiles within the reservoir. In most cases, the time to reach stabilized flow can be years, or longer. If the pressure transients are not sufficiently developed, then pressure gauge resolution is difficult to discern. Thus, early analyses of pressures can lead to incorrect estimates for the fracture conductivity or penetration, or both.

Revenue stream present value Table 2–6 shows an example of a calculated revenue stream present value, at 10% annual discount rate, for a period of N = 36 months. Production declines at a rate of 5% per month from an initial post-fracture monthly (30.4 days/month) average production rate of 500 BOPD. Net oil value is $75.00/BO after taxes, royalty and operating costs. The present value for 36 months production is $17,256,315, as compared to total income for the same period of $19,203,300. Revenue stream present values are easily determined by equation 2–12, for producing the well to the economic limit.

PVN = Σ(I = 1, N) Monthly Income/(1 + Annual Discount Rate/12)I

Equation 2–12

Semi-steady state and transient flow computer and spreadsheet programs Pre- and post-fracturing production streams and corresponding revenue streams are typically available via commercial models. However, if the design engineer chooses, they can readily be programmed on spreadsheets using the above equations. For semi-steady stat reservoir flow and a specified reservoir recovery, FOI, decline function (e.g., constant percentage, hyperbolic, etc.), cumulative production, and an associated revenue stream can easily be determined. The engineer can also calculate expected production profiles using either an analytical or numerical simulation model. The production forecast provides the initial perspective of inferred NPV for a given fracture conductivity and penetration. For transient flow, the curves in figure 2–9 were generated using an analytical reservoir model. However, if one does not have access to such a model, the curves in figure 2–9 can be digitized. Interpolation schemes, using the digitized values, may then be used to perform calculations as described in the examples.

60

Table 2–6. Production stream, monthly income, and present value for 36 months

Period Month i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Average Rate BOPD 500.0 475.0 451.3 428.7 407.3 386.9 367.5 349.2 331.7 315.1 299.4 284.4 270.2 256.7 243.8 231.6 220.1 209.1 198.6 188.7 179.2 170.3 161.8 153.7 146.0 138.7 131.8 125.2 118.9 113.0 107.3 102.0 96.9 92.0 87.4 83.0

Monthly Income $ $1,140,000 $1,083,000 $1,028,964 $977,436 $928,644 $882,132 $837,900 $796,176 $756,276 $718,428 $682,632 $648,432 $616,056 $585,276 $555,864 $528,048 $501,828 $476,748 $452,808 $430,236 $408,576 $388,284 $368,904 $350,436 $332,880 $316,236 $300,504 $285,456 $271,092 $257,640 $244,644 $232,560 $220,932 $209,760 $199,272 $189,240

Discounted Value $ $1,130,579 $1,065,173 $1,003,663 $945,522 $890,899 $839,284 $790,612 $745,034 $701,848 $661,214 $623,076 $586,969 $553,053 $521,078 $490,802 $462,389 $435,798 $410,596 $386,755 $364,439 $343,231 $323,488 $304,802 $287,151 $270,511 $254,861 $240,181 $226,268 $213,107 $200,858 $189,150 $178,321 $168,005 $158,191 $149,040 $140,367

Total

$19,203,300

$17,256,315

Essentials of Hydraulic Fracturing

Production estimates for fractures created in horizontal wellbores—massive shales, etc. In permeable formations where fracture systems propagate more or less in a planar fashion (e.g., sandstones), traditional FOI charts (millidarcy reservoirs) and transient flow approaches (microdarcy reservoirs) work well. These methods provide guidance for fracture penetration and conductivity requirements. However, in horizontal wellbores where different fracture patterns occur more frequently, and in nanodarcy formations, this is not the case. In naturally fractured reservoirs and some shale reservoirs, some believe that fracture propagation can exhibit “dendritic” (brick pile, tree-like) behavior. If this type of fracturing occurs, then the conventional FOI approaches involving penetration length and conductivity requirement do not apply. The focus then turns to a “reservoir fractured volume” requirement (an emerging term in horizontal fracturing). Many in the literature call this the stimulated reservoir volume (SRV) and the SRV is estimated using microseismic data. The fracture design and post fracture formation evaluation methods for shale gas reservoirs are evolving. The reader should continue to monitor the petroleum engineering literature to determine the best methods for design and evaluations of shale reservoirs. Regardless of fracture propagation behavior (planar or dendritic), low formation permeability translates to large fracture systems. This calls for massive treatment volumes to achieve either deeply penetrating fractures, or large values of SRV. In certain cases, fracture conductivity may not be as important as fracture system size. However, that does not imply that fracture conductivity for a dendritic system of factures is not important. Formations must have conductive fracture paths for fluids to flow to the wellbore, and the connection of the fractures to the long horizontal wellbore is extremely important. When one considers the forces and environmental issues, such as stress corrosion and unbroken fracture fluids, it may be difficult to achieve the desired fracture conductivity. For example, in reservoirs where the closure stress on the propping agent is over 8,000 psi, premium proppants, such as ceramics, should be pumped.

Formation Permeability Distribution Obviously, the preceding discussion emphasized the importance of credible formation permeability information, the importance of which cannot be overemphasized. Formation permeability has a profound effect on determining the optimum fracture length, treatment volumes, and fracture conductivity, as well as the treatment economics. The procedures for determining formation permeability are well established for clastic formations. However, determining the permeability in microdarcy and nanodarcy formations such as massive shales is much more difficult but still important for estimating post-fracture flow rates. Methods for obtaining permeability in low-permeability sands and carbonates are well proven. The procedures in shale reservoirs are not so well established. Here, discussion focuses on aspects pertinent to permeability magnitude distribution over the total net pay, which can have a major impact on treatment economics. In many cases, permeability values are calculated more often from pressure transient analysis over a specified interval than from point-wise, or interval, tests such as 62

Chapter 2

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Overview

• Laboratory cores (from point-wise tests) • Downhole “jug-type” tests (from point-wise tests) • Wellbore proximity logs (from interval tests) Pressure transient analysis provides a value that is averaged on the basis of the amount of formation that is affected by the pressure transient. For layered reservoirs, the permeability will be a weighted average of the layers. Point-wise tests (such as logs or cores) provide an estimate of permeability at the specific point where the value is measured from the core or calculated from the log. If a formation exhibits a wide permeability variance that is not identified by pressure transient data, results can be misleading in regard to fracture penetrations and conductive requirements for a treatment design. Figure 2–10 provides some insight into the layering issue. The left curve shows a gamma ray trace that indicates a formation of relatively uniform lithology. The right two curves show the • Actual permeability profile, as measured by point-wise tests, i.e., thick, very low (e.g., 0.001 md) permeability intervals, interspersed with thin layers of much higher permeability (1 to 10 md), and • Average permeability over the entire interval, determined from pressure transient analysis that implies a value in the 0.1 md range.

Fig. 2–10. Actual versus average permeability This is misleading in two respects: (1) fracture penetration requirements, and (2) economic recovery from fracturing. Interpretation of permeability = 0.1 md suggests relatively deep fracture penetration and low conductivity requirements. It also suggests a relatively thick net pay, which translates to attractive recoverable reservoir volume content. However, in practice, the thin, high-permeability intervals can be economically stimulated with much less fracture penetration and high fracture conductivity. Wellbore proximity logs provide a first-hand indication of this. Assuming vertical permeability prevails over a large areal extent, the 0.001 intervals feed the higher permeability stringers. These then serve as the primary conductive paths to an intersecting hydraulic fracture, but at a relatively low rate. In this case, the 63

Essentials of Hydraulic Fracturing

volumetric recovery and the long-term producing rates would be much less than that expected for a thick 0.1 millidarcy formation. Such situations have been encountered and companies that have accurately characterized permeability distribution in formations such as these have economically stimulated them.

Mechanical Rock Properties and In Situ Stress Rock mechanical properties are affected by both rock composition and matrix structure. These, combined with overburden confinement forces and reservoir pore pressure govern in situ stress profiles. The combined effects on fracture propagation behavior depend on their relative magnitudes and interval thicknesses. Acting in concert, they affect the following aspects of fracture propagation behaviors: • Horizontal (lateral) penetration • Width magnitudes and profiles • Post-fracture closure stress on proppant packs • Vertical growth profiles • Orientation with respect to the vertical axis • Symmetry with respect to the initiation interval • Azimuthal (compass-wise) preference • Planar versus dendritic configurations The above items, particularly penetration, width, and proppant pack stress (that impact conductivity), play major roles in post-fracture production flow rates and recoveries.

Combined force/stress balance—formation properties and in-fracture pressure The fracturing process imparts a hydraulic wedge in the formation to create fracture width. Width is created where it is easiest to do so: in the direction perpendicular to the minimum in situ stress, σMIN. The pressure in the fracture acting against in situ stress, elastic modulus, and pore pressure governs width generation. The schematic in figure 2–11 depicts the interactive behavior of prevailing forces/stresses during a fracturing treatment. Figure 2–11 shows the role of mechanical rock properties, in situ stress profiles, and reservoir pore pressure effects associated with • Overburden pressure (POVRB)—Vertical load stress • Reservoir pore pressure (Pe)—Omni-directional stress • Effective vertical stress—(POVRB – Pe) • Poisson’s ratio—a load transverse transfer factor ˡˡ First-order effect on in situ stress, second-order effect on fracture width • Elastic modulus—a rock compression factor 64

Chapter 2

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Overview

ˡˡ First-order effect on fracture width growth • Minimum in situ stress—Function of Poisson’s ratio, pore pressure, in-fracture pressure Overburden (vertical) stress (POVRB) pushes down on any given rock layer of rock due the weight of all the rocks and fluids above that layer. This downward stress is opposed by the stress created due to the reservoir pore pressure (Pe), which acts in all directions, including upwards. The resulting net effective downward vertical stress is transmitted laterally, depending upon the value of Poisson’s ratio (acting as a squash factor). In the equation used to compute the horizontal stress due to the vertical stress, the stress carried by the rock itself is computed using the expression ν/(1 – ν), where ν is the value of Poisson’s ratio. For example, consider water, which exhibits a Poisson’s ratio of ν = 0.5. If a stress is placed vertically on any liquid, a horizontal stress equivalent to the vertical stress will result.

Elastic modulus The ability to resist in-fracture pressure forces in a spring-like fashion is a measure of the stiffness of a rock. Additionally (not shown), it resists overburden loads, but the effect is relatively small, and is not included in equations pertinent to in situ stress. The width of the fracture will be a result of the pressure inside the fracture, the fracture dimensions, and the elastic modulus. The pressure inside the fracture is caused by the fluid system friction as the fluid moves down the fracture during injection. As the fracture continues to grow, the pressure inside the fracture will increase, which causes the fracture width to also increase This increase in the pressure in the fracture is opposed by reservoir pore pressure, and is affected by the elastic modulus and Poisson’s ratio. To create width, the pressure (stress) inside the fracture must exceed the minimum in situ stress resulting (σMIN). In summary, the pressure inside the fracture must be high enough to push the earth apart. Width is also affected, to a lesser degree, by inhibiting forces along the fracture perimeter, often called tip effects. Tip effects are a result of the tensile strength of the rock (not shown in figure 2–11) and a rock property called the critical stress intensity factor. These tip effects can result in higher breakdown pressures, but in most cases as the fracture becomes large, tip effects do not significantly hinder further fracture propagation. However, in rare cases where it does inhibit propagation at the fracture perimeter, as pressure inside the fracture increases the fracture width also increases (balloons), but length and height do not.

65

Overburden Pressure Po

Overburden Pressure Po

Pore Pressure – Pe

Pore Pressure – Pe

Effective Load Po – Pe

Modulus STRESS

Pore Pressure, Pe Poisson's Ratio Effect

STRESS

Modulus

Effective Load Po – Pe

Modulus

Fracturing Fluid Pressure

STRESS Pore Pressure, Pe STRESS

Poisson's Ratio Effect

Modulus

Fig. 2–11. Force balance: overburden, pore pressure, Poisson's ratio, and elastic modulus against in-fracture fluid pressure

Chapter 2

|

Overview

Basic equations and associated figures pertinent to the above parameters are introduced in this chapter to provide a general perspective of their effects on fracture propagation behavior. Some are also included in chapter 3, “Rock Mechanics and Fracture Propagation,” along with expanded discussion, additional equations, figures, tables, and example calculations.

Data sources—values for treatment design Figure 2–11 provides a perception of how the various formation properties interact in fracture propagation behavior. The following discussion explains how the design engineer can determine the values for the various rock properties and parameters required to compute fracture dimensions.

Overburden pressure The value of the overburden stress is best obtained using downhole wellbore logs for interval thickness and formation density, since the value of the overburden stress at any depth is simply the weight of all the rocks and fluids above that point. Overburden at the top of any given interval can be calculated using equation 2–13. POVRB = ΣI(1–N)[ρGRAD(I)hGROSS(I)]

Equation 2–13

where POVRB

Overburden pressure at the interval top





Number of overlying intervals

ρGRAD (I)



Average density depth gradient of the Ith interval

hGROSS(I)



Thickness of the Ith interval

N

POVRB is often calculated as the product of an assumed average ρGRAD (typically ranging from 0.9 to 1.1 psi/ft) multiplied by the total depth to the formation top. This estimate then serves as a starting point for in situ stress calculations in the underlying target fracturing interval.

Elastic modulus (E) and Poisson’s ratio (ν) These values are obtained from either: • Downhole compression and shear acoustic full-waveform logs (dynamic measurements); • Laboratory measurements on cores (static measurements); or • Published sources, obtained for a specified lithology. Dynamic measurements (full-waveform) are made using sonic signals at relatively high frequencies. Dynamic measurements can be made using sonic logs or using sonic measurements on cores in the laboratory. Static measurements are made using stress-strain tests on cores in the laboratory. Full-waveform acoustic logs provide by far the most usable data. They span all the layers of rock that are logged and evaluated. The results from the logs reflect the rock behavior under in situ confinement conditions. Additionally, the results represent a much larger formation sampling 67

Essentials of Hydraulic Fracturing

than do point-wise laboratory tests using cores. Published laboratory data is available on many rock types. However, it may or may not be reliable, depending upon the source. The use of data from a prior database should be used only as a last resort. Also, one should expect that laboratory static measurements will differ from sonic log (dynamic) derived values. To determine the correlation, cores can be tested using equipment that can simultaneously measure dynamic and static modulus in the core. Once these measurements have been made, the engineer can develop a graph or an equation to correlate the static measurements (cores) to the dynamic measurements (logs). Of course, this requires that cores be cut and evaluated on some of the first wells drilled in a play. However, once the correlation has been determined, then the design engineer can run logs to get the dynamic values and use the correlation to determine the static modulus, which is needed in the fracture design model. Elastic (Young’s) modulus and Poisson’s ratios are determined from acoustic full-waveform log velocities by equation 2–14 and equation 2–15.

E

=

CEρBULKVS2(3VC2 – 4 VS2)/(VC2 – VS2)

Equation 2–14



ν

=

(0.5Vc2 – Vs2)/(Vc2 – Vs2)

Equation 2–15

where

E

Elastic modulus (MMpsi)

CE

Unit conversion constant = 2.277335 × 10–10

ρBULK

Rock and fluid combined bulk density (lbm/ft3)

Vc

Sonic compressional wave velocity

Vs

Sonic shear wave velocity (ft/sec)



Poisson’s ratio (dimensionless)

ν

Calculated values are subject to the credibility of compressional and shear wave velocity (or sonic travel time) measurements. What is considered a “good” log may have 10%–15% measurement errors due to borehole effects and other factors. Thus, even a “good” acoustic log may not accurately represent in situ rock properties as well as we would like. However, describing the proper way to run and evaluate wireline logs is beyond the scope of this book. Suffice to say, that to design a credible fracture treatment, the design engineer requires accurate input data. Elastic modulus, which is the measure of the rock stiffness, provides resistance to fracture width growth. Thus, for higher values of moduli, the fracture widths will be smaller. Typical modulus values range from 1 to 10 MMpsi, depending on rock type (sand, shale, carbonate, etc.). Minimum values of 0.1 (coal seams) to maximum values of 15 MMpsi (dolomites) have been encountered. However, in most tight gas sands and shales, the modulus value ranges from 2–8 MMpsi. Poisson’s ratio directly affects the horizontal in situ stresses by providing a rock property that controls horizontal stresses resulting from the vertical stress. We use the relationship ν/(1 – ν) to make the conversion. Hence, higher Poisson’s ratios imply higher stresses. Typically, values of Poisson’s ratio range from 0.1 to 0.4 (dimensionless).

68

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Overburden confinement effects Laboratory measurements show that the values of both elastic modulus and Poisson’s ratio will vary depending upon the confinement stress applied to the core samples. Since the confining stress of the rocks in the ground increases with depth, it is essential the measurements be made at the confining stress that correlates with the depth of the core sample. For a given formation, the modulus increases up to a point with confinement, then decreases with further confinement because the rock fails. Modulus values can change by factors of two or more during a test as the confining stress is increased. Poisson’s ratio continually increases with confinement by a factor of 2 to 5. In both cases, it is essential that laboratory values used for treatment design conform to in situ confinement in the depth of the targeted fracturing intervals. With downhole full-waveform logs, where overburden prevails, confinement effects are integral to the measurements. Thus, confinement is not the major issue for estimates calculated from logs.

Reservoir pore pressure In fracture treatment design, the term reservoir pore pressure typically implies static pressure inside the reservoir. For a new reservoir, the pressure should be constant everywhere. However, if the reservoir has been produced, the pressure near the wellbore will be much lower than at the edge of the remote drainage boundary. For the equations in this book, Pe is the pressure at the reservoir extremity, as opposed to the average pressure distribution resulting from production. Many methods exist in the reservoir engineering arena to determine the reservoir pressure. Hence, further discussion is not warranted at this point. However, during production, pore pressure varies from the fracture vicinity to the reservoir extremity. Additionally, confinement varies, which impacts both elastic modulus and Poisson’s ratio. As the reservoir pressure declines, the value of horizontal in situ stress will also decline. This change in in situ stress distribution in the reservoir can have a dramatic effect on fracture propagation. Changes in in situ stress are especially important in cases where the degree of change varies in different layers over the target fracturing intervals. The in situ stress distribution affects both fracture widths in the target fracturing interval and vertical growth confinement.

In situ stress Fracture propagation behavior is subject to the variations in the values of σMIN between formation layers within the target fracturing interval. For a given interval, σMIN in each layer can be determined by either • Downhole point-wise measurements (in situ stress tests) in cased wells, or • Calculations using Poisson’s ratio values for each layer of rock. In situ stress test measurements provide more reliable data than those calculated from logs. Conducting stress tests is expensive compared to computing stress from logs. However, if a few in situ stress tests are run on a few wells, and the results are correlated to stresses calculated from logs, it is easy to derive a correlation between the two methods so that the correlation-adujusted log-derived values of in situ stress are more reliable. Values of overburden stress, pore pressure, and Poisson’s ratio can be used as follows to compute an in situ stress versus depth profile using equation 2–16.

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σMIN = [ν/(1 – ν)] × (POVRB – Pe) + Pe + ασT

(Equation 2–16)

where σMIN

Minimum principal horizontal stress (psi)



Poisson’s ratio (dimensionless)

ν

POVRB

Overburden pressure (psi)



Pe

Reservoir pore pressure (psi)



α

Biot’s constant (α ~ 0.7; horizontally acting σT, α ~ 1)

σT

Far-field (tectonic) stresses (psi) = Effects of thrust faults or other geologic features that affect horizontal stresses

Equation 2–14 and equation 2–15 can be used to show the relative effects that log-measured acoustic errors for the modulus and Poisson’s ratio might have on calculated in situ stress. Any errors in the measurement of the acoustic velocities directly impact the ν/(1 – ν) term. In regard to acoustic log credibility for Poisson’s ratio (per equation 2–15), obviously 10%–15% velocity errors compound the effect. The effects of the other parameters are not quantitatively direct; however, their impact is readily apparent per equation 2–16.

Combined elastic modulus and Poisson’s ratio error effects—scenario treatment designs Examination of equation 2–13, equation 2–14, and equation 2–15 yields a perspective of the combined effects that acoustic data errors can have on factors pertinent to fracture propagation behavior. In view of potential errors in the commonly used sonic logs, it is recommended that the fracture treatment design include sets of scenario designs. These scenarios proffer guidance in treatment volume requirements, and fluid system and proppant selection. This enhances the probability of arriving at an economically optimized treatment design.

In situ stress directional component magnitude differences We can express the in situ stress distribution in a given layer in three orthogonal directions. Usually the largest magnitude component acts in the vertical direction, and the two horizontal components are of unequal magnitude. However, for shallow reservoirs or reservoirs in tectonically active areas, one of the horizontal stresses could exhibit the largest magnitude. Regardless, in subsurface formations, σMAX may prevail in any direction. The minimum stress (σMIN) acts in the direction perpendicular to the other two (σMAX and σINT). However, fracturing terminology is typically in terms of a maximum (σMAX) and minimum (σMIN) principle horizon horizontal stress, with the understanding that the vertical component magnitude is greater than either of the horizontal components. The vertical component results from overburden stress offset by formation pore pressure. Horizontal stresses are impacted by the formation’s Poisson’s ratio (ν). Figure 2–12 depicts the effects of in situ stress on the following aspects of fracture propagation: • Orientation (vertical versus horizontal) • Width • Vertical growth 70

• Azimuthal (compass-wise) direction

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The arrows represent stress components. Relative size depicts relative magnitude. On the left (A), vertical fracture orientation is by virtue of the maximum stress acting vertically. On the right (C), the maximum stress acting horizontally results in a horizontally oriented fracture. In the middle of figure 2–12, vertical fracture growth is inhibited by adjacent overlying and underlying intervals with higher stresses than in the fracturing interval between them. These adjacent intervals impart confinement to vertical growth. The difference between in-fracture pressure and the opposing external in situ stress impacts width magnitude. The effect on azimuthal preference depends on the compass-wise direction of σMIN (which obviously also affects orientation).

Fig. 2–12. In situ stresses—fracture orientation, width, and vertical growth Source: “Figure 1.8,” Gidley et al. 1989, 3.

Fracture orientation Fracture orientation (horizontal versus vertical) is typically identified from fracturing gradient pressures. The fracturing pressure required to lift the overburden typically ranges from 0.9 to 1.1 psi/ft-depth. Vertically oriented fractures generally exhibit fracturing gradients ranging from 0.4 to 0.9 psi/ft-depth. The lower end (0.4 psi/ft) can be observed in some formations in basin-centered gas reservoirs with low hydrodynamic gradients. The upper end (0.9 psi/ft) is often found in deep, geopressured gas reservoirs. The values of in situ stress are easily determined from measured instantaneous shut-in pressure (ISIP) values, measured immediately after pumping shutdown either at the beginning or at the end of a treatment. ISIP values, corrected for hydrostatic column pressure, yield pressure at fracturing depth; however, the measurement made immediately after creating the fracture also provides an estimate of the fracturing gradient (in situ stress). For example, an ISIP immediately after breakdown of 0.6 psi/ft suggests a vertical fracture, whereas a value of 1.1 psi/ft indicates a horizontal fracture. The values measured at the 71

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end of a treatment will be less accurate because it will be magnified by the friction pressure in the fracture (the net fracturing pressure). Orientation may dictate both proppant-type selection and slurry proppant concentrations. Vertical fractures, where proppants tend to settle, require much higher concentrations to achieve adequate fracture conductivity than do horizontal fractures where proppant settling is not an issue.

Fracture width and height generation For a fracture to propagate, the injected fluid system must hydraulically push the formation walls apart to create fracture width. The value of the width at any point in the fracture depends on the differential pressure (net fracturing pressure, PNET) between the pressure in the fracture and the minimum in situ stress. The pressure in the fracture will be affected by the injection rate and the apparent viscosity of the fracturing fluid, which combine to create friction pressure in the fracture. The minimum value of in situ stress is affected by the overburden stress, the elastic modulus, and Poisson’s ratio. The relationship between fracture width and in situ stress is illustrated schematically in figure 2–13. The large stresses (indicated by arrow size) at the top and bottom pinch fracture width and inhibit vertical growth. In the middle layer, in situ stress is lower than in the other two layers; thus, the fracture is wider there. Also, the fracture preferentially grows downward faster than it does upwardly in this cartoon drawing because the value of in situ stress in the lower interval is smaller than the value of in situ stress in the upper interval. The relative effect of modulus on vertical growth depends on the relative thicknesses and moduli values between the layers.

Fig. 2–13. Fracture width and height versus in situ stress magnitude Equation 2–17 shows the relative effects of modulus, Poisson’s ratio, net fracturing pressure, and fracture height on fracture width. This equation was derived for Perkins–Kern–Nordgrentype (PKN-type) propagation, so horizontal fracture penetration (Xƒ) is greater than or equal to twice the vertical fracture height (Hƒ). 72

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Wƒ = CPKN(1 – ν2)HƒPNET/E

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Equation 2–17

where

Wƒ

Fracture width (inches)

CPKN

Unit conversion constant = 2.4 × 10–5



ν

Poisson’s ratio (dimensionless)



Hƒ

Fracture vertical height (ft)



E

Elastic modulus (MMpsi)

PNET

Net fracturing pressure (psi)

An equation that contains the same relative ν, E, and PNET terms, but is pertinent to the converse geometry (Hƒ > 2Xƒ, per the Geertsma and deKlerk type) is presented in chapter 3. It is obvious that modulus, as well as net fracturing pressure, directly affects fracture width. Poisson’s ratio, which generally ranges from 0.1 to 0.4, has a second-order effect. Simple calculations can easily illustrate the effects of all variables. The design engineer should run fracture models with a base set of data, and then perform sensitivity runs by varying the rock properties in a systematic manner. By doing this, the engineer will quickly learn how small changes in all the rock properties affect fracture growth and dimensions.

Leading edge fracture growth impedance If fracture growth (vertically or horizontal) is inhibited or restricted at one or more points along its leading edge, it will preferentially grow elsewhere, or stop propagating. If the fracture stops growing in length or height and pumping continues, the pressure in the fracture will increase and the fracture will balloon and the width will increase. One known inhibiting phenomena relates to fracture toughness (stress intensity factor or the similar property, rock surface energy). Its effect is more pronounced in the early treatment stages, where fractures are relatively small. Fracture edge effects are often observed during and shortly after initial formation breakdown. As fractures grow larger, the effect diminishes, but not completely. If it prevails, in-fracture pressures are higher than rheology theory predicts. Thus, fracture widths are greater than calculated. If known a priori, it can be advantageous to inject additional proppant. The result—enhanced fracture conductivity.

Vertical growth versus fracture penetration Figure 2–14 is a cartoon that illustrates the obvious effect of fracture interval height on fracture penetration for comparable injection volumes. If the vertical fracture height growth is impeded, then the fracture length will increase for a given volume of fracture fluid pumped. If the fracture height continues to grow, then the fracture length for any given volume will be less than for the height-confined case. Put another way, for a desired fracture length, the volume of fluid required will be less for the confined case. It is also clear that the cost of a fracture treatment will be a function of the volume of treatment pumped. Thus, knowing the in situ stress distribution and computing fracture height and width using that in situ distribution is of vital economic concern to the fracture design engineer. As such, it is important to obtain a priori in situ stress and rock property data pertinent to the prospective confinement intervals. 73

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Fig. 2–14. Fracture geometry: height and penetration (comparable injection volumes) Source: “Figure 1.8,” Gidley et al. 1989, 3.

In situ stress variations in layered formations Since the 1980s, experience has shown that vertically layered formations can exhibit in situ stress magnitude differentials (of varying degrees) in the various intervals. Subsequently, the industry has become aware that such phenomena are more the rule than the exception. Figure 2–15 shows data measured using in situ stress tests versus depth where the minimum in situ stress changes by large magnitudes over relatively small depth intervals. A profile such as this has a major effect on fracture propagation. Here fracture height growth depends on the vertical location of the fracture initiation (perforated) interval in relation to the in situ stress profile. For example, if a fracture is initiated through perforation at 7,900 feet, where σMIN ≈ 7,000 psi, the higher stress intervals (σMIN ≈ 8,500 psi at 7,700 and 8,000 feet) would probably confine vertical growth. With adequate confinement, significant fracture penetration could be achieved. However, if instead the fracture were initiated through perforation at 7,600 feet (σ MIN ≈ 8,000 psi), where in the overlying intervals σMIN ≈ 6,500 psi, the fracture would preferentially grow vertically upward, rather than horizontally. Additionally, fracture width in the initiation interval would decrease as the fracture progressively encountered the lower stress zones. In such instances, width at the injection point may narrow to the point that the fracture would not accept proppant at the perforations. Thus, a screen-out occurs that terminates injection.

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Fig. 2–15. In situ stress versus depth lithology and vertical fracture confinement vs. initiation point Source: “Figure 1.14,” Gidley et al. 1989, 5.

Pore pressure depletion—effect on propagation behavior Figure 2–16 shows an example of fracture propagation behavior resulting from in situ stress variations in both • Layered intervals, and • Changes caused by pore pressure depletion The information in the figure shows fracture vertical and horizontal penetrations with increasing injection volumes. The fracture is initiated through perforations in the U-Zone, at the vertical axis zero point. On the left, the T-Zone and U-Zone have essentially equal in situ stress. On the right, after pressure depletion, the T-Zone in situ stress is lower than that in the U-Zone because of 200 psi production pressure depletion over time. Prior to pressure depletion, fracture propagation is essentially radial because of nearly equivalent stresses in the two zones. Later, as pressure depletes (by production) in the T-Zone, the fracture exhibits a significantly different geometry. It breaks into the lower stress T-Zone and preferentially propagates in it, with little or no propagation in the U-Zone. 75

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Fig. 2–16. Fracture penetration geometry: in situ stress layer effects: before (left) and after (right) T-zone pressure depletion Source: “Figure 1.20” and “Figure 1.21,” Gidley et al. 1989, 6. The above case occurred in the North Sea Valhal field. Similar cases have been documented in East Texas. One of them precluded economic stimulation of a potential formation because the fracture migrated out of zone and preferentially propagated upward into a reservoir that had been partially depleted by production. In fracture computer simulation modeling, a pseudo-three-dimensional (P-3D) model is inappropriate for this case. It would yield a fracture propagation profile somewhat similar to that on the left for both cases, whereas a planar gridded three-dimensional (G-3D) model would more appropriately yield the two different profiles shown.

Relative size: formation layer thickness, horizontal regions Relative size between a fracture interval and an adjacent interval/zone governs the relative impact of the properties of the adjacent interval/zone. This observation holds for both vertical and horizontal propagation. Thus, as a fracture grows vertically and horizontally, its relative size to that of adjacent or interspersed intervals/zones suppresses effects of individual interval properties on fracture geometry. If a vertically bounding interval is much thicker than the propagating fracture vertical height, its effect is more pronounced. However, relatively thin, high-resistance intervals may have no, or little, effect. For example, a 3:1 modulus ratio between the fracture interval and an adjacent interval of equal thickness can blunt propagation into the adjacent interval. On the other hand, a 3:1 modulus ratio for an adjacent interval that is one half the fracture vertical height has much less effect. Obviously, relative effects change as fracture growth progresses. Horizontal fracture propagation is subject to the same phenomena. The same relative effects hold true for layers within the fractured interval. For example, fracture width profiles reflect weighted-average effects of individual layers that have been penetrated by the fracture. This holds where cohesion between layer interfaces prevents slippage. If slippage occurs, it may not be the case. 76

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Slippage at interfaces or high fluid-loss intervals For fractures to continue propagation across a formation interface, stresses sufficient to create width must be imparted beyond the fracture leading edge. Otherwise fracture propagation stops or penetration rate is blunted. This blunting effect can result from any of the following: • Interface slippage • Highly ductile layers • High fluid-loss zones in layers at or ahead of the leading edge Interface slippage is commonly believed to exist in highly fissured formations, or highly ductile layers. Ductile, blocky coal beds often exhibit both characteristics, vertically and horizontally. When encountered in both directions, vertically and horizontally, slippage can stop propagation. With continued injection, fracturing pressures increase somewhat rapidly if the fracture length and height quit expanding. If surface injection pressure reaches a prescribed maximum, the treatment is terminated because of working pressure limits of the tubular goods and/or the wellhead. When pressure reaches the maximum allowable surface injection pressure, we commonly call this a screen-out. Thin, highly ductile layers can totally stop vertical propagation. Thick ductile layers may not slip like a deck of cards. However, they can attenuate leading edge stress transmission that inhibits propagation. High fluid loss in faults or high-permeability zones (e.g., conglomerates) can stop or significantly reduce either vertical or horizontal propagation. Such behavior is analogous to pipe fluid flow past a perforated section. Flow exits the perforations, either partially or totally, leaving less fluid to create fracture width beyond the exit point.

Fracture azimuthal direction and symmetry Knowledge of fracture azimuth and symmetry is sometimes an important part of treatment design. This is especially so in fields where drainage patterns are not circular, such as is common for tight formations. Here, the issue is drainage interference caused by one fracture penetrating the drainage area of an offset well. Additionally, when the engineer is fracturing wells used in improved oil recovery injection or production (which may have circular drainage), the direction of the fracture may dictate the amount of fracturing fluid volume that can be injected without adversely affecting the recovery processes. It is also important in horizontal wellbore fracturing, where alignment with, or transverse to the wellbore is a factor in post-fracture production performance. Figure 2–17 depicts an aerial concept of fracture azimuth and symmetry propagation behavior relative to stress. The arrows designate directional components. Their relative arrow sizes imply relative in situ stress magnitudes. Behavior such as this adheres to the principle that fracture width generates where it is easiest to do so.

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Fig. 2–17. In situ stress effect on fracture azimuth and symmetry Several methods are available for inferring near-wellbore azimuthal propagation preference. These include point-load bifurcation tests, strain–relaxation measurements on oriented cores, borehole elliptical log surveys, etc. Far-field measurements require remote real-time mapping procedures during injection. These mapping procedures involve measurements using patterned configurations of near surface or downhole (or both) sensors. Mapping procedures commonly use acoustic sensors, high-resolution tiltmeters, electrical voltmeters, or all of them together. The stress variances, magnitude and direction, shown in figure 2–17 imply that mechanical rock properties, lithology, and geologic structure are not aerially uniform or homogeneous, which is probably the case for most wells and reservoirs. It is unrealistic to imagine otherwise in view of the plethora of formation property vertical differences revealed by downhole logs in vertical wellbores. However, there is currently little knowledge regarding formation property correlations pertinent to a priori predictions. The main reason is that there is a paucity of information about rock property and in situ stress variations beyond the wellbore. Formation properties may not be as inhomogeneous or anisotropic aerially as they are vertically. Regardless, they impact propagation behavior. Real-time mapping results indicate that fractures are more likely to conform to what is shown in figure 2–17 than otherwise. Figure 2–17 only portrays behavior in terms of stress. Other factors, such as those pertinent to relative interval size, interface boundary slippage, and high fluid-loss intervals also apply. For example, here one might suspect that a NE–SW thrust fault exists southwest of the wellbore. This could affect both azimuth and symmetry: • Azimuth by virtue of the imposed NE–SW in situ stress • Symmetry by virtue of fluid loss and/or slippage at the fault face. A priori knowledge of this may be important for future treatment designs in this area. However, remote mapping procedures are relatively costly. Therefore, it is up to the design engineer to enhance management’s awareness about the potential benefits that can be derived from it. 78

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Fracture Propagation Behavior and Patterns— Near-Wellbore and Far-Field Regions The interval extent and alignment of the perforations with respect to the minimum in situ stress azimuth and orientation will substantially affect the fracture propagation in the nearwellbore region. However, the wellbore has little impact on behavior in the far-field region away from it. Away from the wellbore, in situ stresses and the anisotropy of mechanical rock properties will control how the fracture propagates. Fracturing in horizontal wellbores has significantly increased the need to know how both the direction of the wellbore and the location of the perforations affect fracture propagation, both in the near-wellbore and far-field aspects. For horizontal wellbores, it involves aspects pertinent to directional drilling programs, wellbore isolation, and wellbore perforation interval designs.

Near-wellbore behavior During initial breakdown, the fracturing fluid system at the perforations transmits high pressure to overcome both near-wellbore in situ stress and rock tensile strength. Depending on the extent of the perforation interval, the initial propagating fractures essentially align with the wellbore. With continued propagation, these fractures seek the path of least resistance and realign accordingly, i.e., perpendicular to minimum far-field in situ stress. The distance required for realignment depends to some degree on perforated interval extent, but is typically on the order of tens of feet. In deviated wellbores (slightly or otherwise), the near-wellbore stress fields complicates the fracture growth at the wellbore. On occasion, echelon fractures can be initiated that compounds the stress field complexity. Typically, fractures do not initiate simultaneously at each perforation. Instead, one starts first, at the point of least resistance. Others sequentially initiate at points of the higher resistance as the pressure in the fracture(s) increase. Whether these fractures eventually connect and grow together or repel one another as propagation continues depends on interaction of stress fields that develop between them.

Far-field propagation behavior and patterns In many sandstone or carbonate formations, in situ stress directional magnitudes are commonly anisotropic. The differences are also commonly sufficient to dictate rather simple, planar fracture propagation that more or less follows a general azimuth. However, hydraulic fracturing treatments in horizontal wellbores drilled in shale reservoirs has resulted in fracture patterns that appear to be more complex than fractures created from vertical wells. In some tight shale formations, observations from fracture mapping measurements have indicated non-planar (dendritic) fracture propagation behavior. Inferences suggest complex patterns that we still do not completely understand. Most likely, multiple fractures are created essentially simultaneously in horizontal wells and as these fracture extend, they contact existing natural fractures that are also inflated. If the in situ stress distribution is fairly isotropic, then the propagating fractures may not have a strong preference as to direction. 79

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State of the knowledge—propagation patterns Predicting the fracture pattern of a propagating system of fractures still relies heavily on hindsight from real-time mapping results on previous fracture treatments in nearby wells. Improving technology so we can move the needle from hindsight estimates to an a priori prediction of what the fracture(s) might look like requires a comprehensive and extensive effort that may take years to develop and put into mainstream use by the fracturing engineer. The fracturing industry is progressing here with varying degrees of enthusiasm and success. However there remains a paucity of data and analyses with potential to provide insight for improving economic returns in this arena. Propagation patterns critically impact treatment design. The patterns also have a major effect on post-fracture production rates and total oil and gas recovery, which obviously translates to revenue. Retrospectively, during the first several decades of hydraulic fracturing in vertical wellbores, the industry did not completely understand the way that hydraulic fractures propagated. Progress was made when design engineers convinced management that expenditures for smarter fracturing could be the key to increasing revenue. Design engineers are encouraged to convey the need for smarter fracturing, and prospective associated economic benefits, to the appropriate parties in their organizations. The industry will benefit from more logs run and analyzed, more cores cut and analyzed, more seismic measurements, more microseismic measurements, new technologies such as fiber optics, and more sensors in the wellbore to try to determine what the fractures look like in the reservoirs. Also, more post-fracture production and pressure transient analyses will be required to compare production results with those expected on the basis of the analyses of the fractures.

Formation Composition and Temperature Formation composition (lithology) and formation temperature play important roles in the following aspects of fracture design and performance: • Damage to near-fracture face permeability • Rock mechanical properties • Fluid loss to the formation • Fluid system flow behavior and proppant transport • Fracture proppant pack conductivity Obviously, each variable must be considered individually to determine how it is or is not affected by the lithology or temperature of the formation. Again, fracture models are helpful. The design engineer can vary any of the properties in the model and determine how the change affected the fracture design.

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Formation composition and structure (lithology) Formation lithology is the term that is used to describe the mineral content of the formation. The mineral content will affect the following parameters: • Damage to near-fracture face permeability • Rock fluid flow properties • Rock mechanical properties • Fluid loss to the formation When a water-based fluid is pumped into a permeable formation, the fluid filtrate leaking off into the formation can affect the rock. If the filtrate does not contain the proper additives, such as a salt, the filtrate may damage the permeability in formations containing swellable or movable clays, such as montmorillonite or illite. Other clays, such as kaolinite, are not particularly sensitive to fracture fluid filtrate invasion. When swellable clays do exist, the use of clay-stabilizing agents in aqueous systems is recommended. Reactions between aqueous filtrate and reservoir fluids can also damage permeability near the fracture face. Examples of such damage include scale, iron, or other mineral precipitates that can plug pores. Mineralogy and granular structure will also affect rock mechanical properties, such as Poisson’s ratio (and thus in situ stress), or elastic modulus, which impacts fracture width. Grain orientation, cementation, and compaction also play a role in mechanical rock property behavior. One issue that needs to be understood is that formations with the same name in different graphical settings or at different depths may exhibit significantly different mechanical rock behavior because of mineral content. This may not be a major issue if measured values of elastic modulus and Poisson’s ratio are available. However, using published values for the “typical” rock (same name, different environment) may yield unrepresentative results. Knowledge of formation matrix structure becomes important in fluid-loss control. Homogeneous, relatively high-permeability, fractured or faulted, and vuggy (e.g., carbonate) formations respond well to particle-plugging fluid-loss control additives. However, in low-permeability formations with micro-size pores, using a fluid with high filtrate viscosity or a high liquid-droplet- interfacial tension results in better fluid-loss control than does using particulates. With micro- or nano-size pores, using particulates for fluid-loss control is akin to trying to plug a window screen with large marbles.

Formation temperature Temperature plays a somewhat minor role in rock mechanics, except in gas formations where pore pressure is temperature dependent. The reason temperature is fairly unimportant is that rock mechanics properties are usually determined from downhole logs where measurements are at in situ conditions. Also, formation temperature does not change to the degree that in-fracture fluids do, except near the fracture face where change is of little consequence. However, temperature within the fracture significantly affects • Fluid loss to the formation • Fluid rheological (viscosity) behavior • Proppant pack conductivity performance

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Figure 2–18 shows fluid system temperature behavior in a fracture during injection. The horizontal axis is normalized on fracture penetration, and 1.0 represents the fracture tip, regardless of fracture length. Formation temperature is 210°F. At the wellbore, fluid is typically near that of surface injection temperature. The curves show temperature distribution in the fracture as injection (and fracture penetration) continues from 5 to 60 minutes. As can be seen, nearly 40%–50% the fracture is below formation temperature. Essentially, fluid in half or more to the fracture is subjected to 210°F, regardless of penetration length. This directly impacts performance in those fracture portions.

Fig. 2–18. Fracturing fluid temperature versus dimensionless fracture penetration Source: “Figure 9.4,” Gidley et al. 1989, 18. Formation temperatures dictate the types of base fluids and types and concentrations of additives (e.g., gelling agents, fluid-loss agents, breakers, temperature stabilizers, etc.) needed for a given treatment. Fluids that work well at relatively low temperatures (e.g., 120°F) may totally disintegrate at 250°F. Fluids built for relatively high temperatures (e.g., 250°F) may be essentially impossible to break at 120°F. A fluid may require a high breaking agent concentration in a 180°F temperature formation and no breaker at 250°F. The use of temperature stabilizers can sometimes mitigate deleterious temperature effects. If the reservoir temperature is above 250°F–270°F, then a stabilizer should be used and guar polymers will degrade eventually, even if breaker is not used. Below 250°F, guar polymers will not degrade sufficiently to clean up completely unless breakers are used. The catch-22 is that if too much breaker is added, the gel may break too soon. Obviously, these observations apply more to linear and cross-linked gel systems. Because of gel breaking problems in low temperature reservoirs, many companies have turned more to slickwater fracture systems that have low gel concentrations. These have been used with some success in shale reservoirs. Temperature also affects fluid loss performance. For example, fluid-loss control may be acceptable in one-third of the fracture nearest the wellbore where temperatures are lower. However, as 82

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fluid temperature increases farther down the fracture, fluid-loss performance may degrade to unacceptable levels. Propping agent performance can also be affected by temperature, depending on proppant type. Sand, when exposed to high temperatures and salt water, can suffer severe degradation due to silica dissolution. Manufactured proppants (sintered bauxite, ceramics) are not as temperature sensitive. Precured resin-coated proppants are also not affected much by temperature. However, curable resin-coated proppants must be designed on the basis of reservoir temperature.

Fracturing Fluid Loss to the Formation Fluid loss occurs when the fracture fluid filtrate leaks into the permeable formation that is being stimulated. As fluid leaks off into the reservoir from the fracture, it is unavailable to contribute to further fracture propagation. Fluid loss impacts various aspects of fracturing behavior and treatment design, primarily • Treatment volume requirements to achieve a specified fracture penetration • Effective fluid system viscosity and proppant transport • Proppant concentration in a proppant-laden slurry • Proppant pack fracture conductivity • Fracture propagation blunting at one or more points along the fracture perimeter In regard to treatment volume requirements, obviously if fluid loss is high, more volume is required to create the required fracture volume than if fluid loss is low. Of course, if more fluid is required, the costs of the fluid and pumping services also increase. Fluid-loss affects fluid system viscosity by virtue of dehydrating the base fluid. This increases the concentration of the base gelling agent, and thus increases the apparent viscosity of the fluid. As to slurry proppant concentration, fluid loss increases particle fraction in the fluid system. If it increases to a sufficient degree, the resulting higher proppant concentration can lead to proppant bridging in the fracture. Counter to this, apparent viscosity increases with both system gel concentration and particle fraction, and higher viscosity creates wider fractures. Proppant pack fracture conductivity is affected by additives (polymers, cross-linkers) that affect the viscosity of the fluid, both during pumping and after they are supposed to break. Increased concentrations, by virtue of filtrate loss, can cause a decrease in fracture conductivity after fracture closure because the thick gel does not clean up. Additionally, post-fracture production carries wall-building filter cake particles into the proppant pack. Either of these can be the dominant factors in conductivity loss. Fracture propagation blunting can be caused by several fluid loss–associated conditions, including • Proppant bridging along the fracture perimeter • Attenuated stress transmission at the fracture leading edge

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Fracture width near the fracture perimeter vicinity is typically much less than in the main body. Hence, proppant bridging due to fluid loss is more pronounced in those regions. However, as fractures propagate and width increases throughout, fluids can bypass a previously bridged region. Attenuated stress transmission occurs if the propagating fracture encounters voids (e.g., fissures, faults, etc.) somewhere along its perimeter. If the attenuation is sufficient, the fluid system is no longer capable of transmitting parting pressure beyond the fracture leading edge. Highly permeable conglomerates and highly fractured or fissured intervals have been known to totally stop fracture propagation. In such cases, the fracturing fluid flows into voids, similar to fluid exiting a pipe. This can affect either vertical or horizontal fracture growth or symmetry.

Fluid loss behavior Figure 2–19 depicts fluid-loss behavior versus the square root of time. Practically all fluid systems exhibit this trend, but by varying degrees. The figure shows how the laboratory measured fluid-loss data can be graphed and used in fracture calculations by defining two variables, the • Spurt loss coefficient (the intercept) and the • Fluid loss coefficient (the line slope) Spurt-loss happens rather quickly as a filter cake builds a flow-inhibiting barrier on fracture face. In tight formations it may not be prevalent. In others it may be a significant contributor to total fluid loss. Fluid loss coefficient reflects the combined effects of flow through both the filter cake and formation matrix. The intercept determines filter cake (wall-building) volume. In practically all cases, formation matrix fluid-loss volume is linear with respect to the square root of time. The slope of that curve determines that value.

Fig. 2–19. Fluid loss behavior versus time½ Source: “Figure 8.1,” Gidley et al. 1989, 148. 84

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In the laboratory, spurt-loss and fluid loss coefficient values are obtained from measurements on cores. These laboratory tests use procedures similar to the measurements used to test fluid loss in drilling mud, using Wattman paper as the filtration medium. However, the test results can be very different depending on the pressure and temperature used to test the fracturing fluid. Laboratory testing has been essentially augmented by the advent of field data obtained from mini-frac shut-in pressure decline (SIPD) tests. These tests comprise a much larger representation of fluid loss over the target fracturing intervals than do laboratory core measurements. The results yield a total fluid loss (spurt loss and fluid loss coefficient combined) value. SIPD testing introduced a new fluid loss term to fracture treatment design: fracturing fluid efficiency (eƒ), as defined in equation 2–18. eƒ = Volume of fracture created/volume of slurry injected

Equation 2–18

eƒ values are determined via mini-frac SIPD measurements. Here, prior to a treatment, a relatively small fracture is initiated. This is followed by SIPD measurements to fracture closure. SIPD analysis yields two fluid-loss values: • Fracturing fluid efficiency • Total fluid-loss coefficient, which reflects the spurt-loss and fluid-loss coefficients combined Fluid-loss values are calculated by two methods: • Matching a set of super-position decline functions against a set of master type curves • Using the G-function approach These methods now comprise the more commonly used fluid-loss parameter in treatment design, as opposed the laboratory measured fluid loss data. Discussion and examples in chapter 5 expand on these methods.

Fluid loss control additives Fluid loss can be controlled to some degree in permeable formations. A wide variety of additives are available to control leakoff. These additives inhibit flow out of the fracture by • Particle blocking/bridging • Filtrate viscosity • Interfacial tension (capillarity) deformation forces of foams or liquid-liquid suspensions • Polymer temperature stabilization Particle blocking/bridging. Particulates impart wall-building by plugging formation matrix pores, or cracks at or beyond the fracture face. Manufactured additives comprise particle mixtures containing a wide size distribution, that either block pore entry or bridge pore throats. They are most effective when used in millidarcy permeability formations, and for plugging fractures, fissures or joints. Base-fluid thickening polymers alone retard fluid loss. 85

Essentials of Hydraulic Fracturing

However, most of these additives are not needed and may not work at all in microdarcy or nanodarcy formations. The reason relates to the relative particle size compared to formation matrix pore throat size. Even though a portion of the additive contains extremely small particles, the smallest may still be larger than pore throats in microdarcy or nanodarcy formations. Filtrate viscosity. Fluid systems with no fluid loss additive can exhibit fluid-loss control by virtue of fluid system filtrate viscosity. However, polymer gelling agent may also contribute to wall building. Laboratory tests on aqueous-based polymer gelled fluids often yield results that contain a filter cake. Interfacial tension agents. Interfacial tension agents can be used to control fluid loss. The agents help to create a liquid–liquid emulsions or dispersions, or gas–liquid foams that resist droplet or bubble deformation. Thus, the bubbles seal over micro- or nano-sized pore throats. Foams are somewhat more effective than emulsions or dispersions in the upper microdarcy range. Also, capillarity and/or relative permeability within a pore passage can restrict flow. However, neither foams nor emulsions or dispersions work as effectively as particulates do in millidarcy permeability formations. Also, foams or emulsions do not significantly control leakoff when the fracture contacts joints, fissures, natural fractures, or faults.

In situ factors affecting fluid loss behavior Primary factors that impact fluid loss behavior include • Temperature • Fluid shear • Pressure differential Fluid system polymer degradation from temperature or shear increases fluid loss, with or without fluid-loss additives. Interfacial tension forces can also deteriorate with temperature. On the other hand, shear imposed by in-fracture flow strengthens foams considerably, thus reducing fluid loss. Also, laboratory measurements have shown that fluid loss is dependent on the pressure differential between the fracture and the reservoir. However, this is yet to be fully defined for specific fluid systems, control additives, and concentrations of those additives.

Fracturing Fluid System Rheology, Viscosity, and Proppant Transport Fracturing fluid systems hydraulically push the fracture walls apart, and transport proppant throughout a fracture. Among other things, fracture fluid viscosity governs both width generation and proppant transport behavior. A broad spectrum of systems is available in this arena. These comprise a base-fluid (aqueous, hydrocarbon, liquid–liquid emulsions, liquid CO2 or nitrogen, alcohol, acid, gas-liquid foams) plus a variety of additives to enhance performance. The base-fluid with additives is collectively called the “fluid system.” 86

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Systems that contain no proppant are termed “neat” or “clean” fluids. Proppant-laden systems, called “slurries,” include both fluid and proppants. Viscosity behaviors vary significantly across the spectrum of available fluid systems, in situ conditions (temperature and pressure), in-fracture shear rates, proppant concentrations, time, etc.

Rheological properties and terminology In the fracturing world, rheology is commonly expressed in regard to parameters pertinent to apparent viscosity: • Flow behavior index (n´) • Consistency index (K´) Together they determine the apparent viscous flow behavior, per equation 2–19: µapp = 47,880K´/ỳ (1–n´)

Equation 2–19

where µapp

Fracturing fluid apparent viscosity (cp)



K´

Consistency index (rheogram – intercept)



n´

Flow behavior index (rheogram – slope)



ỳ

Shear rate (reciprocal seconds, 1/seconds)

Consistency index (K´) relates to viscosity magnitude (thickness). Flow behavior index (n´) relates to how the fluid behaves under shear. If n´ = 1, the fluid is a Newtonian fluid. The more n´ varies from 1, the more non-Newtonian or shear-dependent the fluid will act. Both n´ and K´ are unique to each fluid system and slurry. They are functions of system composition, and are time, temperature, and (for many systems) shear-rate dependent.

Shear rate effects Examination of equation 2–19 yields perceptions of how various commonly used rheology terms describe fluid system flow behavior, and the systems themselves: • Newtonian, or near Newtonian, • Power law, linear, viscous, or near-power law • Non-power law, nonlinear, viscoelastic For example, systems that are essentially unaffected by shear (e.g., water or oil) exhibit Newtonian behavior. Here, n´ ≈ 1, thus apparent viscosity is only K´ dependent. Polymer-based systems (e.g., guar, cellulose, etc.) that contain no additional thickening (cross-linking) agents, such that n´ = a constant > 0 over a wide range, behave for the most part in a power-law sense. Here equation 2–19 applies. Polymer-based systems that are thickened with cross-linking agents, emulsions, and foams are typically affected by shear, K´ = ƒ(ỳ), and n´=ƒ(ỳ). These fall in the viscoelastic, or non-power-law realm. In a sense, the description pertains to flow behavior with respect to only shear rate. However, the fracturing community commonly employs terminology pertinent to the fluid system itself, 87

Essentials of Hydraulic Fracturing

e.g., “It’s a power-law fluid.” This is attributed to available test results spanning specified, common in-fracture shear rate ranges where the fluid system exhibits, more or less, a single behavior. This is possibly to the chagrin of classical rheologists. In spite of the fact that a given fluid system exhibits multiple rheology behaviors under different shear rate ranges, the vernacular prevails, and is generally accepted by the industry. Figure 2–20 depicts an example that shows the two following aspects: • Several rheology category behaviors for a given system • Shear rate and temperature effects on apparent viscosity The chart date covers a much wider shear rate spectrum than is conventionally available per standard test procedures. The fluid system comprises an aqueous-based 40 lbm/1,000 gal (40 parts/M-gal) hydroxypropyl guar (HPG) polymer fracturing fluid with no cross-linking agent.

Fig. 2–20. Fluid viscosity versus shear rate Source: “Figure 9.8,” Gidley et al. 1989, 186. Figure 2–20 shows a range of different viscosity behaviors over shear rates of 10 < ỳ < 10 . Within that range, there are four behaviors: –2

4

• Shear rates: ỳ < 10–1 1/sec: Newtonian—No, or minimal, effect of shear rate on apparent viscosity. Apparent viscosity ≈ constant at a given temperature • Shear rates: 10–1 < ỳ < 101 1/sec: Non-power law—Logarithmically nonlinear. Apparent viscosity does not behave per equation 2–19 • Shear rates: 101 < ỳ < 102 1/sec: Near-power law—Logarithmically nearly linear. Apparent viscosity ≈ equation 2–19 • Shear rates: 102 < ỳ 1/sec: Power law—Logarithmically linear. Apparent viscosity behaves per equation 2–19 The industry has become more aware that apparent viscosity flattens to a constant viscosity as shear rate decreases. However, this behavior may or may not be incorporated in some fracture 88

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design computer models. If not, such models assume a logarithmically linear behavior throughout the entire shear range. Hence, they yield unrealistically high viscosities at lower shear rates. This results in unrealistic fracture width (Wƒ) calculations. Design engineers should be aware of such, and employ data, and models, that better represent shear effects on apparent viscosity.

Temperature effects Figure 2–20 also shows apparent viscosity degradation by temperature. As temperature increases from 80°F to 150°F, viscosity decreases accordingly. Polymer fluids will also become less viscous with time at any temperature, especially at high temperatures, as the polymers degrade. However, temperature degradation over time is not included in the figure 2–20 data. In practice, both temperature and time contribute to reduced viscosity. This is common with practically all fluid systems, by varying degrees.

Apparent viscosity effects of fracture width Viscosity directly affects net fracturing pressures, fracture width, fracture vertical growth, and proppant transport. Viscosity indirectly affects fracture conductivity, fluid leakoff, and fracture conductivity damage. This can be inferred by examining the relation between fracture width (Wƒ), apparent viscosity (µapp), injection rate (QINJ), fracture geometry parameter (Gƒ), and elastic modulus (E) for three types of fracturing theoretical approaches:

Wƒ ≈ ƒ[QINJ½(µappGƒ2/E)¼] Fracture geometry determines the parameter Gƒ in the above relation:



{

Fracture height (Hƒ)—Perkins–Kern–Nordgren (PKN)

Gƒ = Fracture penetration (Xƒ)—Geertsma–deKlerk (GdK)

Fracture radial factor (Rƒ)—Circular

Thus, regardless of the theoretical fracture propagation model equation, as µapp, QINJ, or Gƒ increases, Wƒ increases. As E increases, Wƒ decreases. The quantitative degree is attenuated by the ¼ power. Within the parameters, the impact on fracture width depends on the relative degree of change. Obviously, the design engineer controls only two of the factors, µ app and QINJ. The larger effect resides with µapp. By virtue of fluid system selection, it can be changed by orders of magnitude. In a practical sense, QINJ changes are subject to pump rate and equipment pressurelimitations. QINJ changes may be on the order of two or possibly three. However, since many fluids are shear thinning, when the injection rate increases, the apparent viscosity decreases, so the two changes tend to cancel each other. In reality, the fracture width is a function of the pressure in the fracture. Anything done to increase the pressure in the fracture will increase the width of the fracture. Interdependence also prevails. For example, fracture width, height, and QINJ determine in-fracture shear rate. This, in turn, affects µapp. µapp affects net fracturing pressure, which in turn affects fracture width. Pad injection stage—volume requirements. Pad volume requirement for the initial fracturing injection stage remains somewhat an empirical design issue, even when calculated by fracturing 89

Essentials of Hydraulic Fracturing

model simulators. The pad stage, with a neat (no proppant) fluid system, must create sufficient fracture width to allow injection of both initial and subsequent proppant-laden slurry concentrations. Considerations include • Fluid system apparent viscosity (at temperature and shear rate) • Proppant size and type • Slurry proppant concentration (i.e., particle fraction) • Fluid-loss behavior Typically, slurry concentrations immediately following the pad stage are small: 0.5–2 ppg. Subsequently, slurry proppant concentrations are gradually increased (ramped) to higher values as near-wellbore fracture width enlarges with continued injection. In vertical wells with a single vertical propagating fracture, concentrations of 6–12 ppg are feasible. In horizontal wells with multiple propagating fractures, and especially if a low viscosity fluid is used, maximum concentrations of 1–3 ppg are normally used. Volume requirements are subject to fracture height and penetration growth response to injection volume and rate. Thus, iterative calculations are required. Inherent to this are temperature and shear effects on the pad fluid system. Miscalculated pad volume results in job termination from proppant bridging in, or near, the perforations—which sometimes is a problem but can be a design goal if the engineer wants to pack the fracture with proppant near the wellbore.

Proppant concentration effect on apparent viscosity Slurry proppant concentration also affects the viscosity of the slurry itself. As proppant concentration increases, apparent viscosity increases to a higher value than that of the neat fluid system. Figure 2–21 shows how this occurs for several types of fluids. Consider the non-Newtonian, 100 S–1 curve fluid. The vertical axis is a multiplier to neat (no proppant) viscosity. The horizontal axis, particle fraction, relates to specific-gravity-adjusted proppant slurry lb/gal concentration. Consider injecting a non-Newtonian 1.1 specific gravity (spgr) fluid with 6 lb/gal slurry concentration. For 2.65 sp. gr. sand and 3.6 sp. gr. bauxite, this translates to particle fractions ≈ 0.3 and ≈ 0.2 respectively. Thus, per figure 2–21, 6 lb/gal slurry sand slurry exhibits a viscosity twice that of the neat fluid. For a sintered bauxite 6 lb/gal slurry, the increase would be 1.5 fold. Additionally, fluid loss plays a role. As the fluid system dehydrates, particle fraction increases, which increases slurry viscosity even more. Computer models used to design the treatment should incorporate viscosity adjustments for leakoff.

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Fig. 2–21. Fluid viscosity versus particle fraction Source: “Figure 9.13,” Gidley et al. 1989, 188.

Proppant transport Prior to the advent of cross-linked fluid systems, theory based on Stokes Law was considered adequate for calculating proppant transport down a fracture. However, many fluids currently in use may not transport proppants in accordance with Stokes Law. Also, Stokes Law applies for individual particle settling rates. It does not handle reduced rates caused by particle interference, i.e., “hindered” settling. Nor does it address accelerated rates for particle clumping, where the clump density to surface ratio exceeds that of a single particle. Near-perfect-transport systems. A variety of fluids are available today that exhibit “nearperfect transport.” This includes foams, emulsions, and cross-linked gels. Here, the industry is progressing in describing settling behavior, but uncertainties remain. Complexities in fracture geometry and configuration compound the issue, along with precise rheology characterization for emerging fluid systems. Equilibrium banking systems. Figure 2–22 depicts the other end of the spectrum, equilibrium banking, where proppants settle rapidly. In many shale gas and shale oil plays, operators are turning to water fracture treatments, where the fracture fluid is not viscous and exhibits poor proppant transport. In such cases, the proppants initially form banks (dunes) near the wellbore. As injection continues, proppants continually build on what has settled. Thus, the first proppant injected settles nearest to the wellbore. What is later injected, progressively settles farther away, such that proppant injected in later stages settles near the fracture extremity.

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Fig. 2–22. Equilibrium banking proppant transport Partial transport systems. There are many fluid systems with transport capabilities that lie in-between the above extremes (near-perfect and equilibrium banking). Most fluids exhibit nonpower law behavior. Here, proppant transport computations in models are subject to available technology. These may or may not adequately describe the proppant concentration throughout the entire fracture. This affects post-fracture fracture conductivity calculations. Thus, taking fracturing model results at face value is a bit risky. Transport behavior for treatment design. Significant progress has been made in transport behavior over the past several decades. This has been primarily via industry consortiums that focus on the technology. Much of the new technology is now incorporated in many fracturing design computer models. Thus, the entire industry is privy to it by virtue of widespread model use. However, there remains much to be discovered in the transport arena. The insights yielded by consortium efforts have proven well worth consortium membership costs. Hence, it behooves the design engineer to associate with future developments by them. Proppant settling effects on vertical fracture propagation. A bridging phenomenon due to proppant settling occurs at the lower fracture perimeter. This may inhibit downward propagation, and could possibly create a preference for upward growth. This bridging theory is somewhat similar to that described for fluid loss, with the exception that width growth along the bottom of the fracture is somewhat difficult to measure. Post-fracture proppant and fluid system tracer diagnostics. Proppant tracer logs provide an inference of where proppants reside in a fracture within a foot or less of the wellbore, and where fluids have preferentially entered the fracture. When designing post-fracture proppant tracer diagnostics, it is important to know when to introduce the tracer-tagged proppant during injection. Wellbore tracer logs can only sense tagged proppants within 12 to 18 inches from the wellbore. Knowing the transport characteristics of a fluid system is critical to the design.

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Propping Agents and Fracture Conductivity The inclusion of propping agents in an injected fluid constitutes the basis for the original hydraulic fracturing patent. Their function is to hold the created fracture open after injection has ceased and provide a conductive path that increases reservoir fluid flow to the wellbore. Purchasing a fracturing treatment essentially constitutes purchasing production increase, if the job is designed and pumped properly. The design involves predictions of both fracture penetration and fracture conductivity. Typically, high permeability formations that do not need deeply penetrating fractures require high fracture conductivity. This translates into smaller fluid volumes with maximum possible concentrations of stronger, larger mesh-size, high-strength proppants. Conversely, low permeability formations usually require higher treatment volumes to achieve deeply penetrating fractures, and possibly smaller mesh-size, lower strength proppants. Long-term conductive endurance at in situ conditions and fluid system related proppant conductivity damage enters the picture. Hence, proppant selection, along with minimal fluid damage becomes crucial to design. Data pertinent to this is available from all major (and many independent) pumping service companies, and via membership in industry consortiums that address this issue. The menu of propping agents, i.e., types, materials, mesh sizes, size distributions, strengths, sources, etc., has increased considerably over that previously available. This trend toward greater selection is expected to continue. The upside is the potential for improved fracture conductivity. The downside is the added effort and time involved in selection, and quality assurance requirements. Quality assurance is essential. Propping agents should be tested for quality before and after the proppant is delivered the well site and prior to injection. Samples should be caught and kept for post-fracture testing if any issues occur during post-fracture well testing and production that create suspicion that the propping agents are not performing as expected. Effective fracture conductivity (the product of fracture width and proppant pack permeability) remaining in the fracture after closure on the proppant pack depends on • Effective proppant pack permeability (at stress load, temperature, and damage factors) • Closed proppant pack width • Proppant pack location and distribution throughout the fracture The target of a treatment design is to place a sufficient quantity of the appropriate proppant throughout the effective flow portion of the fracture and adjacent to the productive interval. This pertains to proppant concentration in the slurry, fluid system transport and permeability damage attributes, and redistribution (if it occurs) of the proppant in the fracture during closure.

Proppant pack permeability In treatment design, fracture permeability values are obtained from laboratory flow measurements through proppant packs of known width. The packs are confined under stress loading, at elevated temperature, for a designated time period. Pack permeability depends on 93

Essentials of Hydraulic Fracturing

• Proppant strength, size, and size distribution (strength depends on proppant type, e.g., sand, ceramic, resin-coated sand or ceramic, etc.) • The effects of stress, temperature, time, fracturing fluid, and other damage on pack permeability Proppant permeability tests that are representative of the behavior of the propping agent under simulated reservoir conditions are difficult to run and replicate. Excellent laboratory equipment and diligent laboratory technicians who pay attention to detail are required to get repeatable results. One should also determine proppant behavior versus time, temperature, and include the effects of fracture fluid residue or unbroken fracture fluids.

Proppant type Figure 2–23 shows the effect of in situ stress and time on permeability for various proppant types. The data are for a pack concentration of 2 lbm/ft2 in the fracture, which is used for running API tests but are seldom achieved in practice. The left chart shows in situ stress effects. Time effects (at 10,000 psi) are shown on the right. The charts imply that proppant embedment fracture face (dashed curve) applies only to low-density sintered ceramics. However, it is a factor for all proppants. Embedment reduces the effective fracture flow width. This is more pronounced at low pack concentrations (1 lbm/ft2), becoming less so as concentration increases. Embedment is essentially inconsequential above 3 lbm/ft2. Note that the curves do not indicate the effects of temperature or fluid system damage.

Fig. 2–23. Fracture permeability versus proppant type, in situ stress, time Source: “Figure 6.18,” Gidley et al. 1989, 119. 94

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Several aspects are apparent in regard to pack permeability and proppant type, namely differences in • Permeability magnitude at a given stress • Rate of conductivity reduction dependence on proppant type • Effects of time on permeability magnitude for each type

Proppant size Figure 2–24, shows pack permeability (at 2 lb/ft2 area concentration) versus stress load for various proppant sizes with Ottawa or white type (excellent quality) frac sands. These range from small (70/140) to large (12/20) mesh. Data are from short-term (non-API) tests.

Fig. 2–24. Fracture conductivity versus proppant size, in situ stress, Ottawa type frac sand Source: “Figure 6.4,” Gidley et al. 1989, 112. Obviously, larger proppants exhibit higher permeability, which is true for the other proppant types. Note, the curves do not reflect degradation due to time, temperature, fluid system, embedment, stress corrosion, or a variety of other issues. Also notice the convergence in the higher stress regime (above 8,000 to 10,000 psi). This convergence is due to proppant crushing that reduces particle size in that regime, such that all 95

Essentials of Hydraulic Fracturing

initial sizes are reduced to similar sizes once the individual grains start to fail. The increased surface area of the smaller particles reduces permeability. This is more pronounced for sand than for stronger proppants, such as ceramics.

Proppant pack width Figure 2–25 shows proppant pack width versus proppant unit area concentration in a closed fracture, under stress loading (a logarithmically linear relation). The same behavior holds universally for all proppant types, by varying degrees, depending on proppant density. Notice that propped fracture width is independent of proppant mesh size. This also universally holds for all proppants. Additionally, notice that stress load (e.g., 1,000 to 13,000 psi) does not significantly affect closed width.

Fig. 2–25. Fracture propped closed width versus proppant concentration—Ottawa type sand Source: “Figure 6.5,” Gidley et al. 1989, 112.

Fracture conductivity The above parameters (pack permeability and closed fracture width) constitute the basis for predicting fracture conductivity (KƒWƒ). Whatever affects either (positively or negatively) directly affects fracture conductivity, and thus, post-fracture production and post-fracture economics. Consequently, credible knowledge of elastic moduli, Poisson’s ratio, in situ stress, net pack stress load, reservoir pore pressure, etc., is essential to treatment design. In situ stress at depth is important for proppant selection. At depths below 7,000 to 8,000 feet, in situ fracture closure stresses are typically 4,200 to 4,800 psi (but can exceed 6,000 psi). At the higher stresses, the conductivity of a fracture propped with sand can decrease to unacceptable 96

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levels over time. Here, manufactured, high-strength proppants may be warranted, even at a higher cost. Higher values of in situ stress, or low-viscosity fluid systems, can reduce fracture widths during pumping to the point that large size proppants may bridge in the fracture. Hence, smaller proppants may be required. Lower conductivities may result at low closure stress; however, smaller particles are easier to transport, so the resulting fracture may be better for stimulating the reservoir.

Net proppant pack stress load Net proppant pack stress is comprised of the prevailing in situ stress and the additional stress imposed by pack width compression on the formation. The additional pack width stress can be inferred by inverting equation 2–17 to the form: PNET = WƒCE/[CPKN(1 – ν 2)Hƒ]

Equation 2–19

where

E

Elastic modulus

WƒC

Closed fracture width

PNET

Additional pack width load stress

This can be important in treatment design. For example, consider a formation at 6,000 ft depth (overburden = 6,500 psi, pore pressure = 3,000 psi) that contains the following conditions and propped fracture configuration:

In situ stress, σMIN

=

4,000 psi



Closed fracture width, WƒC =

0.2 inches (at 2 lbm/ft2 area concentration)



Elastic modulus, E

=

6 MMpsi



Poisson’s ratio, ν

=

0.25



Propped fracture height, Hƒ =

90 ft

Per equation 2–20,

Net proppant-pack stress

≈

1,000 psi



Total proppant-pack stress

=

4,000 + 1,000 = 5,000 psi

Per figure 2–24 (for sand), fracture permeability exhibits the following values:

At 4,000 psi in situ stress

Kƒ

≈

150 darcys



At 5,000 psi in situ stress

Kƒ

≈

100 darcys

Obviously, ignoring net proppant-pack stress effects in a treatment design yields optimistic production predictions.

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Proppant distribution in vertically irregular fractures—conductivity augmentation Created fractures commonly have discontinuous surfaces. As rocks separate, the fracture surfaces contain irregularities and offset ledge edges. As proppants settle, during and after injection, these serve as collection points, possibly preventing further proppant settling. When fractures close on the propped intervals, there is a potential for small, essentially un-propped gaps throughout the vertical fracture span. Such gaps can exhibit higher conductivity than the intervals containing proppant packs. Figure 2–26 shows this, progressing from injection shut-down (left) to total fracture closure (right). The in-between period during closure from leakoff is shown in the middle. Proppant concentration is depicted by shade intensity. Darker shading implies higher concentration.

Proppant Concentration in a Fracture Segment During Closure After Closed Sequential Proppant Settling with Gaps on Fracture Ledges

Fracture Slippage Ledges

During Slurry Injection

Fig. 2–26. Proppant settling progression to fracture closure in vertically irregular fractures 98

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This is impossible to predict with current technology. Hence, it is impossible to theoretically include in treatment design. However, there have been experiences where post-fracture analysis yielded production performance well above expectations from design conductivity values (high conductivity in the open gaps of each segment). Hence, if knowledge of such occurrences is wellestablished in regard to post-fracture conductivity, omission from a treatment design may lead to uncertainty in economically optimized fracture penetration targets.

Fracture conductivity in horizontally oriented fractures For horizontally oriented fractures, the target fracture proppant concentration (CPROP) takes on a different perspective than for vertical fractures. With vertical fractures, concentration targets are usually above 2 lbm/ft2 area. For horizontally oriented fractures, it is much lower. Here, targets range from 0.05 to 0.1 lbm/ft2 area. Figure 2–27 shows an example for 20/40 mesh sand. The left and right portions of figure 2–27 are distinctively different. On the left, CPROP < 0.3 lbm/ft2 area fracture width is less than, or nearly equal to, proppant diameter. This is the monolayer range. The right portion starts at a full monolayer (0.3 lbm/ft2 area) and increases to over 5 lbm/ft2 area, forming multiple proppant layers. Here, both concentration increases and fracture width increases.

Fig. 2–27. Fracture conductivity versus proppant concentration, in situ stress Source: “Figure 1.25,” Gidley et al. 1989, 10. The monolayer range was of extreme interest in earlier fracturing periods when perceptions were that most fractures exhibited horizontally oriented propagation. This perception no longer prevails. However, formations exist where, in fact, fractures do exhibit horizontally oriented propagation. In such cases, conductivity data that addresses monolayer conductivity are beneficial to design. 99

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To the authors’ knowledge, figure 2–27 presents the only such data currently available. Thus, generation of data on other proppant types and sizes may be left to industry consortium, if such is warranted.

Fracture flow capacity—propping outside the pay Conventional algorithms pertinent to post-fracture production increase are normalized on reservoir net pay. Accordingly treatment designs focus on placing perforations and proppant in fracture portions contiguous to pay intervals. Hence, conventional treatment designs typically confine perforation extent to pay intervals, and proppant placement at or just above pay tops. However, in certain situations, it may be economically beneficial to take advantage of potential fracture flow capacity outside gross pay bounds. This involves perforating larger intervals (both above and below gross pay) and injecting sufficient proppant to create conductivity in intervals above the gross pay. Figure 2–28 portrays the conventional approach versus the propping outside the pay concept. It depicts • An in situ stress profile where during injection, the fracture extends well above and below the pay (right) • A closed fracture that is propped only to the pay top, and is connected to the wellbore only in the pay interval (A, left) • A closed fracture that is propped and connected to the wellbore, over the majority of the vertical fracture, both above and below the pay (B, middle) On the left (A), flow is limited to the pay perforations. However, additional flow capacity is available if the wellbore is connection to the fracture below the pay. This implies perforating all the way to the fracture bottom. The middle picture (B) depicts the potential for additional flow capacity both above and below gross pay by connecting the wellbore to the fracture and propping it over the entire vertical interval. The implications here are that • Perforating and propping intervals outside the pay has the potential to increase effective overall conductivity by increasing total fracture flow capacity, and • Increasing total fracture flow capacity results in higher product rates and thus, higher revenue returns The design and economic issues involved are • How far above the gross pay top should, or can, the proppant pack top lie? • The required fluid system and quantity of extra proppant to achieve that top? • Comparative production predictions between a typical and an outside the pay design

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Fig. 2–28. Propped fracture: typical and propping outside the pay design Proppant quantity is the prime focus. Fluid system volume requirements are essentially unaffected, because fracture vertical confinement is dictated by the upper and lower stress bounds. However, larger proppant quantities imply higher proppant concentrations. Thus, slurry proppant transport requirements are pertinent to fluid system selection. The process requires weighing the additional proppant and wellbore connection costs against increased revenue returns for the additional production. Pertinent, detailed examples are presented in chapter 7.

Cyclic loading on proppant Cyclic loading pertains to periodically subjecting the proppant to varying stress magnitudes. It is associated with repetitively closing and reopening wells to production, a common practice for a variety of reasons. Examination of figure 2–11, along with equation 2–16, provides a perspective of the effect of reservoir pore pressure on proppant stress load variations. Pore pressure in the fracture face vicinity increases as wells are shut-in and pore pressure builds up along the fracture. This increases stress on the proppant pack. Conversely, when wells are reopened to production, pore pressure and proppant pack stress decrease. This imparts large variations in stress magnitude. Experience has shown that cyclic stress changes can significantly reduce fracture conductivity. Attempts to mitigate this by controlled rate well shut-in and opening practices have shown to be successful. However, in some cases, after the damage is done, conductivity does not repair itself. 101

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Proppant flowback Proppant is retained in the fracture by several factors: • Compression of the fracture face on the proppant pack • Adhesion between proppant particles • Proppant bridging in the fracture during production Many practices have been employed to mitigate flow-back (if it is an issue) both during postfracture clean-up and production thereafter. This includes extending time for the fracture fluid system to close via leak-off, controlled-rate flowback procedures, controlling well production rate, use of adhesive resin-coated proppants, fluid system stranded polymers (both soluble and otherwise), etc. Success in doing so has ranged from excellent to poor, which is somewhat akin to the experience with control practices in sand producing formations.

Overview Commentary The overview presented here merely highlights a few of the various aspects affecting fracture propagation behavior. Expansion of the material in this chapter can be found in the designated pertinent chapters which present a broader, more in-depth coverage of each factor. The chapters contain the basics of hydraulic fracturing computer design models, and address both the impact of each aspect, and the interactions between them, on propagation behavior. Thus, it behooves the design engineer to attain a thorough understanding of the effects of each aspect, as well as their interactive effects. In this respect, hydraulic fracturing computer models are an invaluable asset to treatment design. However, a commonality exists between all of them, from the simplest to the most sophisticated: • None are capable of addressing the entire gamut of subsurface in situ complexities. • The results that models yield are subject to (a) the input data and (b) the sophistication level of algorithms contained in the model. As to model input data, it goes without saying—Credible representative data is essential! Admittedly, the design engineer is at the mercy of Nature’s vagaries. Design engineers have essentially no control over a remote system where in situ properties can vary widely. Also, they are faced with designing treatments using data that represents a mere fraction of that system. Additionally, both fluid systems and propping agents exhibit limited performance ranges. Also, for a given design, within those limits, available data do not typically conform exactly to design conditions. Models greatly facilitate addressing this enigma by their capacity to quickly investigate numerous input data scenarios. Doing so proffers the potential to maximize revenue for both the immediate treatment at hand, and future treatments.

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Exercises Exercise 2–1 1. True or false? A fracture will propagate perpendicular to the maximum horizontal stress. 2. True or false? It is possible to relate lithology to Poisson’s Ratio and compute the least principal horizontal stress of a rock layer in a tectonically active basin. 3. True or false? Four of the most important parameters one must know to design a hydraulic fracture treatment are the in situ stress, permeability, porosity, and water saturation of each layer of rock that might affect the fracture growth pattern. 4. True or false? Microseismic measurements and gamma ray logging of tagged fluids and proppants can both be used to estimate fracture growth patterns tens of feet from the wellbore. 5. True or false? When formations are shallow, horizontal fractures can be created, but in deeper formations, vertical fractures are to be expected. 6. True or false? The net pressure at any point (x,t) in the fracture can be related to the fracture width and the fracture height at that point (x,t) in the fracture.

Exercise 2–2 1. True or false? Reservoirs with natural fractures require fracture treatment to better connect the wellbore to the natural fractures. 2. True or false? Successful stimulation of a well in a low-permeability formation increases both the total production rate and the ultimate recovery from the well. 3. You work for XYZ Oil Company and you are given 20 wells that are not producing and need to be stimulated. Due to a limited budget, your boss asks that you evaluate each well and determine the five best candidate wells for stimulation. As such, which two formation properties are the most important to identify stimulation candidates? a) Damaged wells b) Naturally fractured wells c) Low-permeability wells d) High-permeability wells

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Exercise 2–3 Stimulation using hydraulic fracturing __________________________ reserves in high permeability reservoirs and __________________________ reserves in low permeability reservoirs. a) Increases, decreases b) Increases, doesn’t affect c) Decreases, increases d) Doesn’t affect, increases

Exercise 2–4 How many (reservoir) barrels of fluid can fit into an 80-acre, 100 ft, 30% porosity reservoir?

Exercise 2–5 A stimulation treatment is proposed for an oil well producing with an 80-acre drainage area. Preliminary assessment shows that the well is damaged with skin factor of +3 and will benefit from either matrix acidizing or hydraulic fracturing. A hydraulic fracture model built on the well predicts that a fracture half-length of 580 ft and fracture conductivity of 3,800 md-ft can be achieved if the well is hydraulically fractured. The well is completed in an undersaturated oil reservoir. We will use semi-steady state flow conditions for the calculations. The reservoir has an average bottomhole pressure of 4,360 psi and permeability of 5 md. Other well and reservoir data are also provided below. Using the provided data, calculate the potential productivity improvement if 1. Matrix acidizing completely removes the damaged skin 2. A hydraulic fracturing treatment is performed on the well What stimulation method will you recommend for this well? Data: Bottomhole temperature, T = 190°F Oil Viscosity, µ = 1.7 cp Oil formation volume factor, Bo = 1.1 rb/STB Formation porosity, φ = 0.21 Total compressibility, Ct = 1.3 ✕ 10–5 psi–1 Drainage area, A = 80 acres Well bore radius, rw = 0.328 ft Formation thickness, h = 70 ft Fracture conductivity, Wkf = 3,800 md-ft Fracture half-length, Lf = 580 ft 104

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Exercise 2–6 Given the following data, use Prat’s equation to compute J/Jo for a high conductivity fracture with a propped fracture half length of 250 ft. • Drainage area

160 acres

• Well bore diameter

8¾ inches

• Formation permeability

0.01 md

• Formation porosity

10%

• Bottom hole temperature

250°F

• Depth to the formation

10,000 ft

• Fracture conductivity

2,000 md-ft

• Gas viscosity

0.02 cp

Exercise 2–7 A gas well was fractured. Fracture and formation properties include the following:

T = 250°F

pi = 4,030 psi k = 0.1 md

µ = 0.0244 cp



φ = 0.13

cT = 9.68 × 10–5 psi–1

A = 120 acre (square)

rw = 0.328 ft

h = 58 ft (net pay and propped fracture height)

Lf = 345 ft wkf = 2,300 md-ft

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1. Use the McGuire and Sikora graph to determine the productivity-index (PI) ratio. 2. Repeat the computation except the fracture length is now 414 ft. 3. Repeat the computation except the fracture conductivity is now 2,760 ft (keep fracture length of 345 ft). 4. Briefly discuss the effects of fracture length and the fracture conductivity on the values of productivity-index ratio for this reservoir.

Exercise 2–8 Suppose we are designing a fracture treatment for a well with a formation permeability of 1.0 md and a drainage area of 320 acres. The wellbore diameter is 9.6 inches. a) Assuming a square drainage area and using the McGuire and Sikora method, how long does the fracture half-length need to be to generate a six-fold increase in semisteady state well productivity, assuming the fracture width is 0.2 inches and the permeability of the propping agent is 300 darcys? b) Assuming a circular drainage area, use the Prats method to compute the productivity index increase ratio at steady state for a fracture half-length of 800 feet and an infinite conductivity fracture.

Exercise 2–9 Using the following data and an analytical reservoir model (such as PROMAT), determine the values of skin and formation permeability that best matches the production data from the M. Jones well No. 1. After you have history matched the production data, then make five forecast 106

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computer runs using the value of the formation permeability you have just determined. For Forecast Run No. 1, use the radial flow option with the history match values of permeability and skin. For Run No. 2 use the same permeability with a skin factor of zero. For Run No. 3, use the hydraulic fracture option with a fracture length of 100 ft and a fracture conductivity of 2,000 md-ft. Run No. 4 should be made using a fracture length of 250 ft and a fracture conductivity of 2,000 md-ft. For Run No. 5, increase the fracture length to 500 ft. For all forecast runs, use a flowing bottomhole pressure of 7,000 psi for the first year then reduce the flowing bottom hole pressure to 4,000 psi for the remaining time. Determine the cumulative oil recovery at the end of 10 years. Operator Well name Location Formation Fluid type Pressure changes

Corpoven M. Jones 1 Monagas Naracual Oil Constant Pressure Steps

Oil formation volume factor Oil viscosity Oil compressibility

Formation temperature Initial reservoir pressure Net pay Wellbore radius Porosity Water saturation Water compressibility Formation compressibility Drainage area

300°F 11,500 psi 100 ft 0.35 ft 10% 20% 3.6 ✕ 10–6 psi–1 4.0 ✕ 10–6 psi–1 640 acres

1.3 rb/stb 0.8 cp 1.5 ✕ 10–5 psi–1

The following is a 30 flow test on the M. Jones well No 1. The flowing bottomhole pressure during this test was 7,000 psi.

Cumulative Time (days)

Cumulative Oil Production (stb)

1

285

2

550

3

800

5

1,300

7

1,800

10

2,500

15

3,700

20

4,850

25

6,010

30

7,150

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Exercise 2–10 The subject well is completed in the Vicksburg formation of South Texas. This formation is a low-permeability, geopressured sandstone reservoir. The following data represent the known prefracture well information. Depth

12,000 ft

Casing

5½ in., 23 lb/ft, N-80

Tubing

2⅞ in., 6.5 lb/ft, N-80 @ 11,800 ft

Hole size

8½ in.

Net gas pay

30 ft

Total porosity

15%

Water saturation

40%

Bottom hole temperature

250°F

Gas gravity

0.65 (air = 1)

Reservoir pressure

9,500 psi

Well spacing

160 acres

The Vicksburg was perforated with 2 shots/ft and after a 2% KCl breakdown treatment, the well was produced at a constant flowing bottom hole pressure of 4,000 psi for 30 days, and the following gas flow rates were measured.

Time (days)

108

Cumulative Production (Mscf)

2

1,510

4

2,745

6

3,871

8

4,990

10

6,038

12

7,097

14

8,120

16

9,120

18

10,110

20

11,114

22

12,086

24

13,030

26

13,985

28

14,953

30

15,893

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Using PROMAT, you should history match the production data to determine the most probable values of permeability and skin. Once you have determined the values of k and s, use PROMAT to forecast the values of flow rate (q) vs. time (t) for a 10-year life for a flowing bottomhole pressure of 1,200 psi if nothing is done to the well. The next step in this exercise is to determine the expected reservoir behavior if the well is fracture treated. Using a computer program (such as PROMAT, if available), generate production data for fracture lengths of 250, 500, 750, and 1,000 ft for a fracture conductivity of 500 md-ft. Repeat those runs using a value of fracture conductivity of 20 md-ft. For all runs, assume the flowing bottomhole pressure is 1,200 psi, and use a 10-year well life. Calculate the 10-year cumulative gas production for the following table.

Fracture Length (ft)

Fracture Conductivity (md-ft)

1

Radial

Radial

2

250

500

3

500

500

4

750

500

5

1,000

500

6

250

20

7

500

20

8

750

20

9

1,000

20

Run

On the basis of these result, 1. How would you assess the feasibility of fracture treating this well? 2. What appears to be the optimum fracture conditions?

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Essentials of Hydraulic Fracturing

Nomenclature Symbol

Units/Value

Description

English A

acres

ADR

fraction

CE CPKN

110

Well spacing

2.277335 = 2.4

Annual discount rate ×10–10

10–5

Unit conversion constant for equation 2–14 PKN model fracture, unit conversion constant

Cr

dim.

Dimensionless fracture conductivity function

cT

1/psi

E

MMpsi

Total system (rock and reservoir) fluid compressibility at PAVG and TABS

Elastic modulus

FC

md-ft

Fracture conductivity

FCD

dim.

Dimensionless fracture conductivity

ef

fraction

Fracturing fluid efficiency

h

ft

Formation net pay

h(Ioi)

ft

Thickness of the Ioith overburden interval

Hƒ

ft

Fracture vertical height

Hƒp

ft

Vertical fracture propped height

hNET

ft

Net pay vertical height, i.e., thickness

k

md

Formation permeability

K´

intercept

Consistency index (rheogram—intercept)

Kƒ

md

Fracture permeability

KƒWƒ

md-ft

Fracture conductivity

MNI(Im)

$US

Monthly net income for the Imth month

n´

slope

Flow behavior index (rheogram—slope)

PAVG

psia

Average reservoir pressure = (Pe + Pw)/2 semi-steady state flow = [(Pe2 + Pw2)/2]1/2 transient flow

Pe

psia

Reservoir static pressure

PNET

psi

Net fracturing pressure

POVRB

psi

Overburden pressure

PVN

$ US

Present value for N months

Pw

psia

Wellbore producing pressure

q

Pre-fracture producing rate

qƒ

Post-fracture initial producing rate

1/qD

dim.

Reciprocal dimensionless rate value picked from the vertical axis, figure 2–6

r´w

ft

Pseudo wellbore radius

re

ft

Reservoir drainage boundary radius

rw

ft

Wellbore radius

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Symbol

Units/Value

|

Overview

Description

RC

dim.

Relative fracture conductivity

T

°F

Formation temperature

TABS

°R

Absolute formation temperature = °F + 460

tD

dim.

Dimensionless time

Vc

ft/sec

Sonic compressional wave velocity

Vs

ft/sec

Sonic shear wave velocity

Wƒ

in.

Fracture width

WƒC

in.

Closed fracture width

Wƒp

ft

Propped fracture width

Xƒ

ft

Fracture penetration, wellbore to fracture tip

Xƒp

ft

Propped fracture penetration, i.e., half-length, wellbore to propped fracture extremity

Z

dim.

Gas compressibility factor

Summation Subscripts Im

Imth month

Ioi

Ioith overlying interval

Nm

Total number of months

Noi

Total number of overlying intervals

Greek µapp

cp

Fracturing fluid apparent viscosity

ỳ

1/sec

Shear rate

α

dim.

βO

STBO/ResBO

Biot’s constant (α ~ 0.7; horizontally acting σT, α ~ 1)

βPROP

atm–sec2/gm

Fracture non-darcy flow coefficient, a function of proppant size, table 2–2

γG

dim.

Gas specific gravity

μG

cp

μO

cp

Gas viscosity (cp) at PAVG and TABS

ν

dim.

Poisson’s ratio

π

3.14159263

Pi constant

ρBULK

lbm/ft3

Rock and fluid combined bulk density

ρGRAD (Ioi)

psi/ft

Average density depth gradient of the Ioith overburden interval

σMIN

psi

Minimum principal stress

σPW

psi

Proppant pack width stress

σT

psi

Far-field tectonic stresses: effects of field faults, etc.

σVToi

psi

Overburden vertical stress at the interval top

fraction

Formation porosity

φ

Oil formation volume factor at PAVG and TABS

Oil viscosity (cp) at PAVG and TABS

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Essentials of Hydraulic Fracturing

References Cooke, C. E., Jr. 1973. “Conductivity of Fracture Proppants in Multiple Layers.” Journal of Petroleum Technology 25:1101–1107 Gidley, John L., Stephen A. Holditch, Dale E. Nierode, and Ralph W. Veatch, eds. 1989. “Figure 1.2.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 2. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.3.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 2. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.4.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 2. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.5.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 2. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.6,” “Figure 1.7.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 2. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.8.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 3. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.14.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 5. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.20,” “Figure 1.21.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 6. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.25.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 10. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 6.4.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 112. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 6.5.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 112. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 6.18.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 119. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 8.1.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 148. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.4.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 18. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.8.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 186. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.13.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 188. Richardson, TX: Society of Petroleum Engineers.

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———. 1989. “Figure 15.4.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 318. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 15.31.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 330. Richardson, TX: Society of Petroleum Engineers.

113

3 Rock Mechanics and Fracture Propagation: Rock Properties—In Situ Stresses, Net Fracturing Pressures, and Fracture Geometry The importance of rock mechanics in controlling fracture propagation behavior cannot be overstated. It lies at the heart of that behavior. Credible, representative rock mechanics data pertinent to fracture treatment design is equally important. Understanding the relation between rock mechanics and propagation behavior is essential to fracture treatment design. SPE Monograph V. 12 contains comprehensive and thorough discussion about the many various aspects of rock mechanics pertinent to fracture behavior. The reader is encouraged to view the material. This chapter provides a synopsis of those aspects pertinent to treatment design, plus additional discussion and examples. The aspects covered here govern how and where fractures propagate in response to forces imposed by fluid injection. They constitute the basis for propagation behavior in all hydraulic fracturing design computer models. These aspects control fracture • Vertical height and lateral penetration dimension and profiles • Width dimensions and profiles • Volume • Azimuth and orientation Fracture treatment designs require a credible propagation simulator and accurate rock mechanics information. For hydraulic fracturing, data is required on the following for each interval or layer of rock that will affect the fracture growth: • Stratigraphy, i.e., a description of layers, or intervals, of a sedimentary sequence

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• Lithology • Rock mechanical properties ˡˡ Poisson’s ratio ˡˡ Elastic modus ˡˡ Fracture toughness • In situ stress • Net fracturing pressures • Interval interface slippage effects The above list is by no means exhaustive. Discussion in this chapter addresses individual aspects, along with the interactive effects of one parameter upon the others, and the effects imposed by fluid injection forces. Design engineers should strive to • Acquire the most credible information that is economically possible • Develop a thorough understanding of the basic concepts and the interdependencies pertinent to the interaction of all relevant parameters

Mechanical Rock Properties and In Situ Stresses in Fracture Propagation Models How rock mechanics are integrated into fracture design models may seem somewhat obscure. The complexities in some models may seem somewhat convoluted. To simplify this, two longstanding, less complicated models are used for discussions. These have been used successfully for design since the advent of fracturing models and are depicted in figure 3–1. • Perkins–Kern–Nordgren (PKN), which applies where total fracture length is greater than or equal to total fracture height • Geertsma and deKlerk (GdK), which applies where total fracture length is less than or equal to total fracture height

Fig. 3–1. Perkins–Kern–Nordgren (PKN) and Geertsma–deKlerk (GdK) models. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. 116

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These two models are computationally simplistic in that both are fixed-height models, where fractures propagate in a semi-infinite plane, with a specified constant height. Both models account only for lateral propagation. They exhibit simplistic width cross sections (e.g., width versus height). PKN width cross sections in the vertical plane are essentially elliptical; GdK width cross sections are rectangular. Penetration-wise, in the horizontal plane both exhibit essentially elliptical width versus penetrations (except at the fracture edge or tip region where a modification incorporates additional resistance). At these extremes, these models span the spectrum of fracturing behavior. Even though they are simplistic, they contain basic classical, sound rock mechanics theory, and thus, serve to provide insight about fracture propagation behavior. The PKN and GdK models apply well to planar two-dimensional (2D) fracture propagation where vertical growth is well-confined to one interval. Other fracture design models available today apply where vertical fracture growth encounters multiple intervals with different properties in each interval. These new models include the planar pseudo-three-dimensional (P-3D) model, and the gridded three-dimensional (G-3D) models. They incorporate basic rock mechanics contained in PKN and GdK, plus additional theory for vertical fracture propagation, and growth at the fracture perimeter. Most P-3D planar models partition the fracture in sliced-bread fashion, where fracture widths and heights in each slice are determined using the values of the interval’s rock mechanical properties, net fracturing pressures and in situ stress profiles. Some models incorporate a boundary integral approach. All assume that formation properties at the well-bore remain constant laterally from the wellbore to the fracture tip, and they apply to only planar fracture propagation. G-3D models, both planar and fully three-dimensional, more rigorously address changes in mechanical rock properties and in situ stress profile changes. The G-3D models are the best currently available for application to complex formations. Regardless of the model sophistication degree, data representative of the lithology, rock mechanical properties, in situ stresses, net fracturing pressures, and edge or tip region effects are essential to treatment design. In some cases all may play dominant roles. In others, possibly only a few will be dominant. It should be remembered that models are used to make decisions—such as where to perforate, what fluid system and what propping agents should be used, what volume of fluid and how much proppant is required, what injection rate is best or how to schedule injecting the propping agent? Using any credible model with representative data, and running the model with different assumptions, can give the fracture design engineer guidance when designing a fracturing treatment. Rock properties and their effects on fracture propagation behavior include the list below: • Poisson’s ratio—Primarily affects ˡˡ In situ stress profiles ˡˡ Net fracturing pressure ˡˡ Fracture width (second-order effect) • Elastic modulus—Primarily affects ˡˡ Fracture width ˡˡ Vertical or lateral growth (for interval thickness values exceeding a 3 to 1 ratio)

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• In situ stress: governed by Poisson’s ratio, overburden stress, pore pressure, and farfield tectonic stress—Primarily affects ˡˡ Fracture width ˡˡ Vertical and/or lateral growth ˡˡ Fracture azimuth (direction), orientation (vertical/horizontal), and/or symmetry • Edge, or fracture tip, effects (fracture toughness/stress intensity factor/rock surface energy), and dry zone effects, typically exhibit a second or third order effect on growth blunting at the fracture perimeter—Secondarily affects ˡˡ Fracture width ˡˡ Vertical and/or lateral growth Edge effects are sometimes not considered important to treatment design. However, in some cases they play a significant role along the fracture perimeter. The rock property that controls them is called fracture toughness or stress intensity factor, or rock surface energy. This parameter reflects propagation resistance at points along the fracture perimeter. The resistance may be different in the vertical direction than it is horizontally (laterally). In most sandstones and carbonates, after the fracture length extends some distance from the wellbore or achieves a significant vertical height, edge effects usually do not play much of a role in the fracture propagation behavior. However, in formations where natural fractures are prominent, or ones the contain butts and cleats such as coals, or where interfaces that slip are encountered, edge effects can stop or strongly retard fracture propagation. Rock composition, matrix structure, confinement forces, and pore pressure dictate rock mechanical property effects. In situ stresses are governed by rock mechanical properties, overburden loading stresses, and formation pore pressures. The combined effects on fracture propagation behavior depend on their relative magnitudes and interval thicknesses. Temperature can also play role to some degree in gas formations where pore pressure is temperature-dependent.

Mechanical Rock Properties Basic to Hydraulic Fracturing Behavior About Poisson’s ratio, elastic modulus, and fracture toughness and rock surface energy Poisson’s ratio, elastic modulus, and fracture toughness play significant roles in different ways. Elastic modulus, which can be thought of as a spring constant in the formation, dominates fracture width. Modulus can also affect vertical fracture growth in cases where large differences exist between layer thicknesses. This is especially pronounced if the intervals with higher moduli are thicker than those with lower ones, and if the layer thickness values differ by a factor greater than three times that of the target fracturing interval.

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Poisson’s ratio (similar to a squash factor) translates vertical forces to horizontal (lateral) forces. Poisson’s ratio differences between different layers of sediment affects the in situ stress profile behavior, and thus, vertical fracture growth. However, Poisson’s ratio only imparts a second-order effect on fracture width. Edge effects that resist, or blunt, fracture growth at its perimeter typically imparts a secondorder effect as compared to modulus and Poisson’s ratio. However, there have been treatments where edge effect blunting was much higher than theory indicates. The causes are not well understood, but possibly relate to • Discontinuities (e.g., cleats and butt joints in coals or other formations where interval interface slippage occurs) • High fluid-loss zones where fluids leakoff instead of transmitting parting forces • Dry zones where the fracturing fluid has not reached the fracture tip • Plugging at the tip by rock spall fragments Blocky coal formations are notorious culprits. Edge or tip region resistance results in increased pressure in the fracture. That, in turn, increases fracture width. In blocky coal formations, extremely high pumping pressures are often encountered. The consensus is that edge effects are the cause. Here very high fracture pumping pressures will result in very wide fractures, as have been seen in mineback experiments in coal seams.

Poisson’s ratio (ν) Poisson’s ratio (unit strain/unit strain) depends on rock type, composition, and matrix structure (sand, shale, carbonaceous, etc.). It converts vertical overburden loading forces transverse-wise (orthogonally) in the lateral direction by virtue of the lateral factor ν/(1 – ν). Thus, higher Poisson’s ratios imply higher lateral stresses. Table 3–1 shows typical Poisson’s ratio values ranging from 0.05 to 0.45, for various rock types, along with the lateral factor ν/(1 – ν). Minimum to maximum values of 0.04 to 0.49 have been observed, but these extremes are rare. Notice that stress loads on water (ν = 0.5) exhibit a 1:1 transverse lateral stress. Loads on cork (ν = 0.0) exhibit no transverse stress, which is what makes it a suitable material for wine bottle stoppers. Small changes in Poisson’s ratio are magnified in the lateral factor, and consequently, this impacts in situ stress. Since in situ stress is the main rock property controlling fracture height growth, small changes in Poisson’s ratio in a layer may result in somewhat large vertical growth and fracture width behavioral changes, depending on the relative magnitudes of differences between contiguous intervals. As such, design engineers need to acquire the best data rock property possible for use in the fracture treatment design process. The Poisson’s ratio data in table 3–1 represent typical, general ranges. As such, the data in table 3–1 should only be used if no other source of data is possibly available. The importance of using values representing in situ formation properties cannot be over-emphasized.

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Table 3–1. Poisson’s ratios: typical ranges and lateral stress factor

Elastic modulus (E) The elastic modulus (spring constant) effect opposes in-fracture pressure. Thus, modulus resists fracture width growth, acting against fracture widening forces created by the fracturing fluid pressure. Consequently, higher moduli imply narrower widths. Table 3–2 lists typical modulus values (dimensional units: MMpsi = 1,000,000 psi) for various rock types (sand, shale, carbonaceous, etc.), ranging from 1 to 10 MMpsi. Minimum to maximum values of 0.1 to 15 MMpsi, respectively, have been observed, but these are rare. As with the values listed in table 3–1, the elastic moduli data in table 3–2 represent typical general ranges. Accordingly, these data should only be used if no other data is available. Again, the importance of using values that actually represent in situ formation properties cannot be over-emphasized.

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Table 3–2. Elastic moduli: typical ranges

Fracture edge or tip effects: classic rock mechanics and other Two factors have been identified that increased resistance to fracture growth at the fracture’s edge or tip • Theoretical rock mechanics ˡˡ Stress intensity factor (KIC) or fracture toughness (Tƒ), or an analogous effect ˡˡ Rock surface energy (Seƒ, or γ) • Nontheoretically described ˡˡ Dry zone along the fracture edge where the fracture is essentially a crack that is too small for invasion by the fracturing fluid ˡˡ Excessive fluid-loss zones ˡˡ Interface slippage between layers or intervals Any one or all can increase fracture propagation pressure requirements. Stress intensity factor (akin to fracture toughness) and the corresponding parameter rock surface energy theoretically characterize forces required to extend a fracture along its perimeter from one point to the next. They reflect growth resistance at the fracture edge relative to its existing size. Their dimensions (units) are: stress intensity factor or toughness (psi-√in), and rock surface energy (ergs/cm2). Their effects are typically of significantly lower order than those of elastic modulus or Poisson’s ratio. However, they can impact the net pressure requirements for a fracture of given size to propagate further. They usually diminish as fracture extent becomes larger. One analogy is that a tree log becomes easier to split as the split grows larger. Similarly, as a fracture enlarges, the resistance at its perimeter decreases. Typically, they occur in the early stages when fracture length or height is relatively small.

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Other nontheoretically described causes (and often obscure) can result in very high net fracturing pressures, and relatively little propagation at the fracture edge. This sometimes results in shorter, wider fractures. Typically, they are not well known a priori. However, if they are, the knowledge can be used to enhance fracture width and thus, conductivity. Even though toughness is a second-order resistance to fracture growth, it is a factor in propagation behavior, and should be included in treatment design. Increases in edge or tip region effects result in increases in fracture extension pressure. Knowledge of edge effects can be used advantageously. If fracture growth vertically or laterally) is restricted in one place or direction, it will try to grow wider. Resistive edge or tip region effects along the upper, lower, or lateral edges of the fracture can impede fracture growth. Higher resistance at the edge tends to increase width. This can be beneficial because it allows the injection of additional propping agents which, in turn, increase fracture flow capacity. Typically, stress intensity factor or toughness, and rock surface energy data are obtained from published sources. Measuring them is a painstaking laboratory endeavor. Hence, a paucity of data exists for use in specific fracture treatment designs. Also, published values seldom appear in consistent units across the different sources. Consequently, conversion from one set of units to another is often required. Equations 3–1 and 3–2 provide this. KIC = Tƒ = 0.2389591[SeƒE × 106/(1 – v2)]0.5

Equation 3–1

and Seƒ = 17.51269 KIC(1 – v2)/(E × 106)



Equation 3–2

where: KIC

Stress intensity factor (psi-√in)



Tƒ

Fracture toughness or stress intensity factor (psi-√in)



Sef

Rock surface energy (104 ergs/cm2)



E

Elastic modulus (MMpsi)



v

Poisson’s ratio (dim.)

Values for KIC usually range from 500 to 2,000 psi-√in, and those for Seƒ from 50,000 to 250,000 ergs/cm2. They are confining pressure dependent. Thus, in deep formations where in situ stresses are high, data from tests at atmospheric conditions can be low (by factors of 20 to 30). Edge effect resistances are calculated by equations 3–3 through 3–6. Notice that their effects differ between vertical and horizontal growth because of their relation to fracture dimensions. Toughness edge effect growth resistance:

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PEDGE (psi) = KIC/(π2Xƒ)0.5

Equation 3–3

PEDGE (psi) = KIC/(πHf )0.5

Equation 3–4

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Surface energy edge effect growth resistance: PEDGE = [5.710145 × 104SeƒE/(1 – v2)/(π2Xƒ)]0.5

Equation 3–5

PEDGE = [5.710145 × 104SeƒE/(1 – v2)/(πHƒ)]0.5

Equation 3–6

where PEDGE



Magnitude of pressure growth resistance at the fracture edge

KIC



Stress intensity factor (psi-√in.)

Seƒ



Rock surface energy (104 ergs/cm2)



E



Elastic modulus (MMpsi)



v



Poisson’s ratio (dim)



Xƒ



Fracture lateral penetration, i.e., half-length (ft)



Hƒ



Fracture vertical height (ft)

Table 3–3 shows examples of the edge or tip region resistance for equations 3–3 thru 3–6. These provide insight about the effects of relative Xƒ and Hƒ values. The table for each set shows how lateral and vertical effects relative to fracture penetration changes at a given point during propagation. The upper portions of each set depict a fracture growing laterally at a constant height. The lower portions are for a fracture growing vertically at a constant lateral penetration. The resulting pressures at each point along the fracture perimeter add to the total pressure in the fracture during propagation. The two sets show the effects of modulus and Poisson’s ratio in the process. One can infer the changes in resistance as a fracture grows out of one interval and into another with different rock properties. Table 3–3. Toughness and surface energy edge or tip region resistance to lateral and vertical height growth for different fracture geometries

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Poisson’s ratio and elastic modulus laboratory measurements Elastic modulus and Poisson’s ratio data are obtained by two methods: • Laboratory stress–strain measurements on core samples, and • Sonic log wire line well surveys, i.e., acoustic measurements of compressional (p-wave) and shear (s-wave) travel times. Travel times are converted to sonic velocities by the distance between the sonic sources and detectors. Laboratory tests can obtain both elastic modulus and Poisson’s ratio from the same test. The procedures are basically as follows: • Installing high-resolution strain gages on a core sample to measure strains in the x, y, and z directions • Placing the sample in a high-pressure test cell • Confining the sample with internal cell pressure • Subjecting the sample to a series of load stresses at the sample ends with a piston • Measuring the triaxial (x, y, and z) strain displacements at each corresponding piston stress load Figure 3–2 shows an example of a laboratory stress–strain measurement for Poisson’s ratio and elastic modulus on a rock core sample (“Figure 3.10,” Gidley et al. 1989, 62). Here, a cylindrical core sample is confined under pressure in a test cell and subjected, to a series of axial compressional stress loads on the sample’s ends. Strain gages measure triaxial, orthogonal (x, y, z) displacements resulting from the axial load to generate stress–strain behavior. Poisson’s ratio and elastic modulus are determined from the initial (tangent) slopes, near zero strain. These tangent values translate the laboratory data on small core sample to in situ behavior in the much larger formation. The volumetric tangent value determines the elastic modulus. The lateral and axial tangent slopes determine Poisson’s ratio. For those interested, SPE Monograph V. 12 contains detailed discussion.

Fig. 3–2. Laboratory stress–strain core data for calculating Poisson’s ratio and elastic modulus. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. 124

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Confining pressure effects on Poisson’s ratio and elastic modulus. Both Poisson’s ratios and elastic moduli are confining-pressure-dependent. An example is shown in figure 3–3. Poisson’s ratio (chart b) continually increases from lower to higher values as confinement increases. The behavior generally trends logarithmically with confinement, and can vary by factors of five or more from low to high confinement. Thus, knowledge of the test confinement magnitude is essential because of Poisson’s ratio effect on in situ stress behavior. Relatively small erroneous Poisson’s ratio values magnify errors in calculated in situ stress values. Elastic modulus (chart a) generally trends as follows: (1) lower values at lower confinement, (2) increasing to a peak value with increasing confinement, then (3) decreasing with further confinement increases. Moduli can vary by factors of two or more for a rock at different confinement. Thus, it is important to know the moduli test confinement conditions because of the modulus impact on fracture width. Erroneous elastic moduli values yield linearly erroneous fracture width calculations. Poisson's ration (chart b) continually increases with confining stress.

Fig. 3–3. Poisson’s ratio and elastic modulus versus confining stress. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. Sonic log measurements of Poisson’s ratio and elastic modulus. Poisson’s ratio and elastic modulus are also determined from acoustic measurements of compressional (p-wave) and shear (s-wave) velocity. Measurements can be done in the laboratory on samples, but more commonly in situ stress is calculate from acoustic wave train (sonic) logs in openhole wellbores. Sonic log tools generate p- and s-waves and measure the travel time difference (Δt) between a source and sensor. The distance between the two determines velocity. These are then used to calculate both Poisson’s ratios and elastic moduli. There can be differences between laboratory-measured Poisson’s ratio and elastic modulus values (termed “static” in the figure), and those determined by openhole acoustic wave train sonic log measurements (termed dynamic). Figure 3–4 shows the differences for elastic moduli. The correspondence is widely scattered, especially for foliate (thin-layer) rocks. For other rocks, the mean shows that dynamic measured elastic moduli run about 85% of statically measured values. Correspondence for Poisson’s ratio measurements is not available in SPE Monograph V. 12. However, by virtue of Hooke’s Law, an estimated difference would be about one-half that observed for elastic moduli. These differences are sufficient to affect calculated stress profiles and fracture width calculations.

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Also, laboratory test data, such as that shown in figure 3–2, represents only a small fraction of the formation. They cannot provide the coverage expanse of wire line sonic log surveys. Sonic log surveys measure a broader sampling, but they have problems that don’t occur under laboratory controlled conditions. With sonic logs, shear waves are attenuated by wellbore fluids (e.g., mud, liquid). Thus, the measurements are suspect. In boreholes containing foams or gasses, sonic logs are ineffective for s-wave data, and possibly for p-waves. Regardless, acoustic wave train sonic logs provide the most credible source available for representative in situ formation Poisson’s ratio and elastic modulus values.

Fig. 3–4. Laboratory static versus dynamic measurements of elastic modulus. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. Poisson’s ratio and elastic modulus are calculated from sonic log compressional (p-wave) and shear (s-wave) velocities by equations 3–7 and equation 3–8 respectively (ref: Equation 3.42, and Equation 3.44,” Gidley et al. 1989, 68). Most sonic logging services convert the measured Δt source-to-sensor arrival times to velocity, and can output the data digitally in spreadsheet format. Here, the data is averaged over specified intervals. Some services advertise calculated in situ stress and fracture heights. If these are used, the fraction design engineer is encouraged to work closely with the logging service to ensure that credible associated reservoir pressure data is properly employed. Poisson’s ratio. Poisson’s ratios are calculated from sonic log compressional (p-wave) and shear (s-wave) velocities by either equation 3–7–1, or its equivalent equation 3–7–2.

ν = 0.5(VC2 – 2VS2)/(VC2 – VS2)

Equation 3–7–1



ν = (0.5RV2 – 1)/(RV2 – 1)

Equation 3–7–2

where 126

ν

Poisson’s ratio (dim.)

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VC

Sonic compressional wave velocity (ft/sec) = 106/ΔtC

VS

Sonic shear wave velocity (ft/sec) = 106/ΔtS

ΔtC

Sonic compressional wave arrival time (micro-secs/ft)

ΔtS

Sonic shear wave arrival time (micro-secs/ft)

RV

= VC/VS = ΔtS/ΔtC

Elastic modulus. Elastic (often called Young’s) moduli (E) are calculated from sonic log compressional (p-wave) and shear (s-wave) velocities by equation 3–8, or equation 3–9 which yields equivalent results. These are derived from Hook’s law relation between Poisson’s ratio and elastic modulus, i.e., E = 2G(1+ν), where G is a shear modulus rock property. In English units the equations are:

E = 4.3378 × 10–10ρBULK(1 + ν)Vs2

Equation 3–8



E = 2.1689 × 10–10ρBULKVS2(3VC2 – 4VS2)/(VC2 – VS2)

Equation 3–9

where

E

Elastic modulus (MMpsi)

ρBULK

Rock and fluid combined bulk density (lbs/ft3)

VC

Sonic Compressional wave velocity (ft/sec) = 106/ΔtC

VS

Sonic Shear wave velocity (ft/sec) = 106/ΔtS

ΔtC

Sonic Compressional wave arrival time (micro-secs/ft)

ΔtS

Sonic Shear wave arrival time (micro-secs/ft)



Poisson’s ratio (dim.)

ν

Inferring shear wave travel times from p-wave sonic logs. Shear (s-wave) data was not available from older sonic logs (prior to the mid-1960s), which only measured compressional (p-wave) values. Occasionally these older logs may be the only resource available. In such cases, s-wave data can be estimated from equations 3–10. This is possible using independent p-wave data sources from nearby surrounding intervals and shales. The inference comes from observations that equations 3–10 prevails for a large population of formations. Hence, if only compressional (p-wave) data is available, and travel time data can be obtained for the matrices of a formation and surrounding shales, then shear wave travel times can be inferred by equations 3–10–1 and 3–10–2. ΔtS-EST = ΔtC-MEAS[1.5 + (ΔtC-MATRIX/ΔtC-SHALE)φ/(1 – φ)]

Equation 3–10–1

ΔtC-MATRIX = ΔtSAND%SAND + ΔtSHALE%SHALE + ΔtLIME%LIME

Equation 3–10–2

where ΔtS-EST



Estimated shear wave travel time (micro-secs/ft)

ΔtC-MEAS



Measured compressional wave travel time (micro-secs/ft) 127

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ΔtC-MATRIX

Computed matrix compressional wave travel time from laboratory data (micro-secs/ft)

ΔtC-SHALE

Compressional wave travel time in adjacent shales (micro-secs/ft)

φ Porosity Such values should be used as a last resort, and with caution. Parametric studies should be made to investigate how variances in calculated Poisson’s ratios and elastic moduli affect in situ stress, fracture width profiles, or fracture height growth. Poisson’s ratio and elastic modulus from other correlations. Poisson’s ratio. Poisson’s ratio can be calculated, if independent in situ stress data is available (e.g., from point- or intervalwise microfrac, minifrac, etc., tests). Discussion later in this chapter lists sources/methods for obtaining point- or interval-wise in situ stress values. Such data is at localized sections in the wellbore, rather than over the larger span offered by sonic log surveys. However, Poisson’s ratio values at such local sections may provide some insight into either (a) the correlation (equation 3–11), and or (b) properties in the fracture target interval vicinity. In such cases, the equation for calculating Poisson’s ratio, which is an inversion of the conventional in situ stress equation, is

ν = (σMIN – Pe – ασT)/(σMIN + σVToi – 2Pe – ασT)

Equation 3–11

where

ν

Poisson’s ratio (dim)

σMIN

Minimum principal stress (psi)

σvToi

Overburden vertical stress at the interval top (psi)



Pe

Reservoir pressure (psi)



α

Biot’s constant (α ~ 0.7; for fracture design typically α = 1.0)

σT

Far-field stress: effects of far-field faults, mountains, etc. (psi)

Elastic modulus. Figure 3–5 and figure 3–6 also provide other sources for inferring elastic modulus from older sonic logs where shear data is not available. Figure 3–5 yields inferences of elastic modulus from sonic log p-wave correlations. It shows elastic moduli for sand, dolomite, and lime formations based on compressional wave acoustic travel time. Figure 3–6 shows modulus as a function of formation porosity. Data from either figure 3–5 and or figure 3–6 are last resort sources. They come from days preceding the advent of wave-train logging services, and efforts to cope with the lack of better sources, using relative large populations of diverse formations. However, from time to time, design engineers face situations where current data is unavailable. If such data are employed, error scenarios should be investigated for use in treatment design.

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Fig. 3–5. Elastic modulus versus p-wave acoustic travel time Source: “Figure 1.2,” Halliburton 1986, 13.

Fig. 3–6. Elastic modulus versus porosity Sources: Hall 1953; Craft and Hawkins 1959.

Essentials of Hydraulic Fracturing

Example 3–1. Nine-Interval Example: Poisson’s Ratio and Elastic Modulus

Calculated from Acoustic (Sonic) Wave Train Logs

An example, hereafter referred to as the nine-interval example, that include calculations for Poisson’s ratios, elastic moduli, in situ stresses, in-fracture pressures, net fracture pressures, fracture heights, and widths is used throughout the chapter. The example includes tables that are easily developed in spreadsheet format. It is suggested that tables such as these be set up on design engineers’ computers as a part of their standard tools for treatment design. Such spreadsheet-formatted tables are quite helpful for (1) averaging log data over specified intervals, (2) investigating the effects that various parameters have on fracture propagation behavior, and (3) conducting error scenarios that address data verity. Table 3–4 lists interval-averaged sonic log data over each of the nine intervals or formations. The porosity, density, and arrival time (Δt) values are from direct measurements between the sensor and the sources. Velocities are calculated by the relation, velocity (feet per second) = 106/ΔtS (micro-seconds/foot). Poisson’s ratios and elastic moduli are determined from equation 3–7 and equation 3–9, respectively. Table 3–4. Poisson’s ratios and elastic moduli calculated from acoustic wave train logs Depth From To ft ft 0 7,800 7,800 8,000 8,000 8,200 8,200 8,400 8,400 8,500 8,500 8,600 8,6008,800 8,800 8,900 8,900 9,000 9,000 9,100 9,100 12,000

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Rock Type Overburden Shale Shale Shale/Lime Lime Lime/Sand Sand–Pay Sand/Dolomite Dolomite Dolomite Shale Shale

Log Sonic ∆t Sonic Poisson’s Elastic Bulk Arrival Velocity Porosity Grad’nt Ratio Modulus Density μ-sec/ft feet/sec φ v E % gms/ lbs/ psi/ft Compr Shear Compr Shear dim. 1/psi ∆tc ∆ts Vc Vs cm3 ft3 30.0 30.0 30.0 25.8 25.0 21.8 18.0 15.4 17.0 23.8 25.0

2.540 158.5 2.122 132.4 2.122 132.4 2.212 138.0 2.268 141.5 2.298 143.4 2.334 145.7 2.476 154.5 2.527 157.7 2.326 145.1 2.183 136.2

1.101 88.8 184.8 11,261 5410 0.3500 0.919 88.8 184.8 11,261 5410 0.3500 0.919 88.8 184.8 11,261 5410 0.3500 0.958 73.3 134.6 13,652 7431 0.2895 0.983 60.7 100.1 16,461 9990 0.2084 0.996 63.9 108.0 15,642 9263 0.2299 1.012 64.6 107.8 15,483 9279 0.2198 1.073 62.0 103.5 16,141 9663 0.2207 1.095 58.5 93.8 17,092 10661 0.1815 1.008 68.7 117.7 14,560 8495 0.2420 0.946 85.1 159.1 11,758 6285 0.3000

2.852 2.382 2.382 4.475 7.773 6.893 6.968 8.019 9.644 5.924 3.186

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Example 3–2. Error Scenarios: Nine-Interval Example—Poisson’s Ratios and Elastic Moduli Calculated from Sonic Logs

Even though acoustic wave train logs are considered relatively reliable sources for Poisson’s ratio and elastic modulus values, errors in determining travel times can occur. Small errors may seem somewhat unimportant; however, they can translate into larger ones for calculated Poisson’s ratio and elastic moduli values. Compressional (p-wave) measurements are less subject to error than shear (s-waves). Shear waves are more attenuated by borehole fluids than p-waves, and thus more difficult to ascertain. Neither can be accurately detected in wellbores containing foams or gases. Wave travel time accuracies of 90% to 95% are considered good for acoustic logs. Consistent errors in both p- and s-wave travel times (e.g., ±10% in both ΔtC and ΔtS) are not reflected in calculated Poisson’s ratios. However, they do affect elastic modulus value calculations. When the errors are different between p- and s-wave travel times, both Poisson’s ratio and elastic modulus calculations are affected. The examples in table 3–5 and table 3–6 show the effect for shear (s-wave) errors of ±5 and ±10% (i.e., from what would be considered good log data). Here, the compressional travel times shown in table 3–4 represent true values for the formation. However, the s-wave travel times are only 90% to 95% accurate. It is obvious that “good” log data translates into some relatively large errors in Poisson’s ratios and elastic moduli. The effect of these errors on subsequent calculations for in situ stress and fracture width are shown later in this chapter. Table 3–5. Poisson’s ratio errors resulting from ±5% and ±10% errors in ∆t shear Depth From To ft ft

Rock Type

0 7,800 Overburden 7,800 8,000 Shale 8,000 8,200 Shale 8,200 8,400 Shale/Lime 8,400 8,500 Lime 8,500 8,600 Lime/Sand 8,6008,800 Sand–Pay 8,800 8,900 Sand/Dolomite 8,900 9,000 Dolomite 9,000 9,100 Dolomite Shale 9,100 12,000 Shale

ν TRUE Value 0.350 0.350 0.350 0.290 0.208 0.230 0.220 0.221 0.182 0.242 0.300

±5% ∆t Shear Error @ Minus 5% % ν Value Diff 0.328 –6 0.328 –6 0.328 –6 0.256 –12 0.155 –26 0.182 –21 0.169 –23 0.171 –23 0.121 –33 0.197 –18 0.268 –11

@ Plus 5% % ν Value Diff 0.368 5 0.368 5 0.368 5 0.316 9 0.249 20 0.267 16 0.258 18 0.259 17 0.227 25 0.277 14 0.325 8

±10% ∆t Shear Error @ Minus 10% % ν Value Diff 0.301 –14 0.301 –14 0.301 –14 0.212 –27 0.083 –60 0.118 –49 0.102 –54 0.103 –53 0.038 –79 0.138 –43 0.227 –24

@ Plus 10% % ν Value Diff 0.382 9 0.382 9 0.382 9 0.338 17 0.281 35 0.296 29 0.289 31 0.290 31 0.263 45 0.304 26 0.345 15

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Table 3–6. Elastic moduli errors resulting from ±5% and ±10% errors in ∆t shear Depth From To ft ft

Rock Type

0 7,800 Overburden 7,800 8,000 Shale 8,000 8,200 Shale 8,200 8,400 Shale/Lime 8,400 8,500 Lime 8,500 8,600 Lime/Sand 8,6008,800 Sand–Pay 8,800 8,900 Sand/Dolomite 8,900 9,000 Dolomite 9,000 9,100 Dolomite Shale 9,100 12,000 Shale

E TRUE Value 2.85 2.38 2.38 4.48 7.77 6.89 6.97 8.02 9.64 5.92 3.19

±5% ∆t Shear Error @ Minus 5% E % Value Diff 3.11 9 2.60 9 2.60 9 4.83 8 8.23 6 7.34 7 7.40 6 8.52 6 10.14 5 6.33 7 3.44 8

@ Plus 5% E % Value Diff 2.62 –8 2.19 –8 2.19 –8 4.14 –7 7.29 –6 6.44 –7 6.52 –6 7.50 –6 9.09 –6 5.52 –7 2.95 –8

±10% ∆t Shear Error @ Minus 10% E % Value Diff 3.39 19 2.83 19 2.83 19 5.19 16 8.60 11 7.74 12 7.77 12 8.95 12 10.46 8 6.70 13 3.71 17

@ Plus 10% E % Value Diff 2.41 –15 2.02 –15 2.02 –15 3.84 –14 6.81 –12 6.00 –13 6.09 –13 7.00 –13 8.52 –12 5.14 –13 2.73 –14

In Situ Stress The most important data for successfully designing a fracture treatment is knowledge of the in situ stress profile for all of the formation layers or intervals that will affect fracture growth. One might wonder “How did we successfully do fracturing treatments years ago, without considering stress profiles?” The answer is that we just thought we were doing well. With stress data, we would have done better. During the 1950s, 1960s, and most of the 1970s, hydraulic fracturing consisted of small treatments performed on relatively high permeability reservoirs or to remove formation damage. Also, there was not an industry-wide awareness of how in situ stress magnitudes can significantly change from one formation to the other. However, once the industry started pumping larger treatments (i.e., massive hydraulic fracturing both vertical and horizontal wellbores) trying to propagate and prop open deeply penetrating fractures, the importance of fracture height growth relative to penetration, and treatment costs became apparent. The need for more accurate in situ stress data also became clearer. A massive (volume-wise) hydraulic fracturing (MHF) treatment can cost as much or more than all the drilling and other completion costs combined. Thus, in situ stress and in situ stress profiles have become an essential part of hydraulic fracturing treatment design. The list below summarizes the aspects of in situ stresses that affect fracture propagation: In situ stress directly affects fracture • Orientation (i.e., vertical, slanted, horizontal) • Azimuth (i.e., compass direction) and symmetry about the wellbore • Vertical height growth • Vertical and lateral penetration profile 132

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• Width and cross-sectional shape • Effectively propped conductivity Pertinent parameters also include overburden stresses that are related to • Depth • Formation interval thickness • Rock properties • Density, porosity, Poisson’s ratios, elastic moduli, edge or tip region effects • Fluid density • Porosity • Reservoir pressures For many situations, fractures will usually propagate into overlying and underlying intervals. It is not common, but does occur, that a fracture will be totally confined by an interval or zone. If so, it is often due less to factors directly related to in situ stress, and more to those related to the blunting effects of edge or tip region conditions, such as • Excessive fluid loss, resulting from ˡˡ Highly permeable zones ˡˡ Conglomerates ˡˡ Joints ˡˡ Fissures ˡˡ Fractures ˡˡ Faults ˡˡ Vugs • Formation interface slippage barriers which may be caused by plastic deformation The magnitudes of in situ stresses can vary widely, both vertically and laterally. There is a paucity of information about lateral variations (i.e., those away from the wellbore). However, variations between vertically separated intervals can, and should, be determined because they can significantly affect vertical fracture propagation.

The relation of rock mechanics and in situ stresses to fracture propagation geometry Fracture geometries can vary considerably from the configurations shown in figure 3–1. Discussion in chapter 1 alludes to some common variations. These can be a result of encountering • Rock property and stress variations both laterally and vertically • Permeability and porosity variations • Irregular growth confining barriers • High fluid-loss intervals (e.g., highly permeable fractured, faulted, or conglomerate zones) • Fracture edge or tip region growth restrictions 133

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Such effects may or may not be sufficient for the geometry to diverge significantly from the textbook image that it defies reasonable expectations from design efforts. Extending this to penetration in very complex lithologies can result in extremely unusual geometries and configurations of the fracture, including • Bimodal • Echelon • Multi-stranded • Non-planar • Asymmetrical • Non-uniform cross-sectional Situations such as these may yield some disappointing surprises from a design. It is now possible to map dynamic fracture penetration and height growth during a treatment. However, the high cost of making such measurements currently discourages widespread application of the technology. Also, inferences of vertical growth are obtainable from post-fracture investigations (however, such investigations may not be practiced on a regular basis, as should be the case). These processes usually include • Post-fracture logs or surveys on candidate or nearby wells • Temperature surveys • Fluid tracer surveys • History matching with computerized dynamic fracturing simulators It is well known that measurements made in the wellbore will only sample the temperature, radioactivity, or chemistry within a few inches to a foot away from the wellbore. As such, temperature surveys or fluid tracer surveys only show where the fluid exits the wellbore and many times do not provide credible information on fracture height. Regardless, these approaches can provide insight about fracturing vertical growth behavior.

In situ stress and fracture azimuth (compass direction) and symmetry about the wellbore As previously mentioned, in situ stress directly affects fracture orientation (i.e., vertical, slanted, horizontal). It also affects fracture azimuth (compass direction) and symmetry about the wellbore. Figure 3–7 shows an aerial view of the effect of lateral in situ stresses on (a) the direction fractures follow and (b) their symmetry about the wellbore during propagation. This presumes that overburden loading effects a vertical stress (not shown) that exceeds both orthogonal lateral (horizontal) stresses (σMIN and σMAX). Arrows represent relative in situ stress magnitudes, and their directions. As to azimuth, again, fracture width occurs where it is easiest to do so. This is perpendicular to the minimum lateral in situ stresses (σMIN-1 and σMIN-2), and thus parallel to the maximum lateral stress (σMAX) direction. Fracture azimuths vary from field to field, and can change from well to 134

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well in a given field. If faults exist in one portion of a field, locally imposed tectonics can alter the σMAX direction away from that observed in other areas or wells. As to symmetry about the wellbore, it is probable that varying degrees of minimum in situ stress magnitudes will occur away from the wellbore vicinity. Figure 3–7 shows two magnitudes, where σMIN-2 is greater than σMIN-1. Here, more width, and thus length, is created in the vicinity of σMIN-1 than in the σMIN-2 vicinity. This asymmetric behavior has been observed from fracture mapping measurements in several different fields. It can be more the rule, than the exception.

Fig. 3–7. Effect of in situ stress magnitude and direction on fracture azimuth and symmetry

In situ stress and rock property effects on fracture lateral penetration and cross-section profiles In situ stress relative magnitude differences between vertical intervals governs fracture propagation from interval to interval. Additionally, relative interval thickness is also a factor. The effect of in situ stress differences in foliated (thin-layered) rocks acts differently in controlling propagation than in thick intervals. In foliated rocks, the fracture may see a composite, average in situ stress effect, rather than that of each individual layer. Figure 3–8 and figure 3–9 are examples of in situ stress and rock property effects on fracture penetration profiles and width cross-sections. Figure 3–8, from a pseudo-three-dimensional (P-3D) model, shows penetration and width (on the lower right) for the in situ stress profile (on the left) versus depth. The lowest stress lies between 6,910 and 7,005 feet. The larger stress (3,900 psi) above 6,900 feet strongly inhibits upward fracture growth. This forces downward growth into the lower stress intervals. Fracture downward growth rate gradually decreases through the lower intervals, 7,005 to 7,110, reaching its lowest rate below 7,110 feet where underlying in situ stress is 3,350 psi. Figure 3–8 also indicates a bullet-nosed penetration versus height profile. This is somewhat suspect, and is possibly a result of model construction inherencies. More sophisticated models, e.g., G-3D, would more likely show a stair-step fracture profile below 7,000 ft, and most likely not a bullet nose configuration.

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6,800

Depth (feet)

6,900

7,000

7,100 Fracture Width Shade Code 0 0.1 0.2

7,200 2,500

3,250 In Situ Stress (psi)

4,000

125

250 Penetration (feet)

375

500

Fig. 3–8. P-3D fracture profile simulation versus in situ stress profile Figure 3–9 shows several very different fracture cross-sections. It compares examples of fractures in a typical sand formation (A) with that of actually observed in several coal formations. Cross sections (B), (C), and (D) came from actual mineback and borehole photography observations. The blocky, butt and cleat nature of coal, the existence of interface slippage, and the nearly equal lateral σMIN and σMAX stress values result in significantly different propagation behaviors than typically are expected in sandstone, carbonaceous, or shale formations. Cross sections (B) and (C) demonstrate interval interface slippage. Cross sections (C) and (D) suggest that rock tensile strength prevails over lateral σMIN:σMAX ratios. Other formations such as diatomites, softer chalks, and shales can exhibit these types of behavior. Only a few current fracture propagation models can predict representative fracturing behavior in formations such as these, be they coals or otherwise.

Fig. 3–9. Comparative fracture cross sections: sand (A) and coals (B, C, D) 136

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Bimodal fracture propagation. Figure 3–10 shows a snapshot (at a given injection volume) of bimodal fracture propagation, i.e., two single fractures, initiated at, and propagating from different depths in the wellbore. The practice of creating bimodal fractures is somewhat common in the industry. It sometimes encompasses several intervals (more than two), with different distance spans between the perforated (or open hole) initiation points. The practice often employs limited entry approaches, where high injection rates impose sufficiently high wellbore pressures to exceed fracture parting pressures at all perforations.

Fig. 3–10. Bimodal P-3D fracture profile simulation versus in situ stress profile (courtesy of Schlumberger) Also, unplanned bimodal fractures can occur in open hole fracturing (i.e., with no casing across the target interval), where a fracture first initiates at the lowest in situ stress point; then, as wellbore pressure increases, another fracture initiates at some other remote depth in the secondlowest in situ stress point. If the wellbore pressure is sufficiently high, separate fractures will sequentially initiate in other intervals. Whether separate fractures that initiate at different depths eventually join into one fracture, or continually propagate separately depends on their alignment with each other, and the distance between them. Fracture alignment is affected by wellbore alignment with vertical stress. Essentially no wellbores are perfectly vertical. Fractures initiated at separate wellbore intervals relatively quickly align with the prevailing in situ stress field as they propagate vertically beyond the perforated intervals. Hence, separate bimodal fractures may be laterally offset from each other as they propagate vertically. Rock mechanics theory, supported by laboratory experiments, indicates that internal wellbore pressure during fracture initiation aligns the fracture with the wellbore until it progresses into the region where formation in situ stresses dominate propagation. Thus, created fractures start contiguously aligned to the wellbore over the initiation interval span, then reorient according to the prevailing formation in situ stress. 137

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For example, consider a wellbore, such as that shown in figure 3–11, with a hole deviation of ±3° from vertical, two 50-foot perforated intervals, separated by a 200-foot span, and a truly vertical in situ stress. Fractures usually follow the wellbore angle over the perforated interval. Then, after propagating vertically a short distance (e.g., 10 feet) beyond the perforations, they will bat wing to a vertical alignment. At those points (10 feet above and below the perforation) the fractures will laterally offset the wellbore. For this example, the offset is about 0.5 feet.

Fig. 3–11. Vertical fracture extent inference in non-vertical wellbore Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. Lateral spans between bimodal fractures are easily calculated. With equal upward and downward growth from each fracture, by the time their edges reach each other, the calculated lateral span between them is four feet. If there is an upward/downward growth rate ratio of 3:1, the lateral span between the upper and lower fracture is seven feet. If wellbore deviation is ±5°, the lateral distances are seven feet for equal upward/down vertical growth rate, and 11 feet for an upward/down vertical growth rate of three. This deviation also affects fracture height diagnostics using wellbore tools, because these tools are limited to radial sensing distances of 1½ to 2 feet away from the wellbore. Hence, the tools cannot sense a fracture that is farther away from the wellbore than that.

138

Figure 3–12, showing fracture cross-sections, depicts the scenarios of whether or not the fractures will seek each other and join as one, or repel each other and propagate separately. This depends on the stress fields generated at the fracture edges during propagation, their vertical heights, and the lateral span between them. If the lateral span is relatively small (such as that shown on the left) they will more likely join. However, as the lateral span increases (as shown on the right) so does the probability of separate propagation. Here, stress interference is more complex. Predicting whether or not they join, or propagate separately, requires a theoretical approach not found in many existing models. In some models that are proclaimed to have bimodal capabilities, whether fractures join or repel is designated by the user. In these cases the results should be taken with skepticism.

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The same concepts described above apply to propagation predictions for multiple (three or more) echelon fractures, as shown in the figure 3–13 cross sections. If the fractures are closely spaced the left scenario will not happen; instead, the right scenario will prevail. Here, the stress interference between the center fracture and the two outside fractures blunts the center fracture vertical growth. The other two will preferentially grow as shown. Again, judgment calls by a model user can be seriously misleading.

Fig. 3–12. Bimodal fracture vertical propagation: cross sections—alignment-complementing stresses versus interfering stresses

Fig. 3–13. Echelon vertical fracture propagation: cross sections—stress interference effects 139

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Minimum principle in situ stress Knowledge of minimum principle in situ stress (σMIN) and its profile is essential to treatment design. It dictates fracture width and height profiles, pumping pressure requirements, pad volume requirements, total treatment volumes, fluid and proppant selection and fracture conductivity. As shown in figure 2–11, chapter 2, in situ stresses result from the combined effect of overburden formation vertical stress loads, Poisson’s ratios, reservoir pore pressure, and far-field tectonics. Equation 3–12 determines theoretical magnitudes: σMIN = ν/(1 – ν) × (σvToi – Pe) + Pe + ασT

Equation 3–12

where σMIN

Minimum principal stress (psi)



Poisson’s ratio (dim.)

ν

σvToi

Overburden vertical stress at the interval top (psi)



Pe

Reservoir pore pressure (psi)



α

Biot’s constant (α ~ 0.7, typical H F value α = 1.0)

σT

Far-field stress: effects of far-field faults, mountains, etc. (psi)

In equation 3–12, Poisson’s ratio and formation pore pressure are the dominant factors. Differences between adjacent intervals determine whether a fracture will be confined to, or propagate across, interval boundaries. Poisson’s ratio data is more pertinent to in situ stress profiling than to fracture width (Wƒ) calculations where it plays a second-order role. In regard to pore pressure, a reduction in reservoir pressure may sometimes be beneficial to vertical fracture confinement (thus extending lateral penetration) and to increasing fracture width. Cases have been cited where taking advantage of this has resulted in deeper fracture penetration, higher conductivity and consequently, higher production folds of increase (FOI). Far-field stresses pertinent to σT result from the effects of thrust or drop faults, and/or nearby mountains that impart lateral stresses in a fracturing locale. They usually do not play a significant role in fracture behavior other than that reflected in the azimuthal direction preference that a propagating fracture follows. If they are large enough to affect a treatment design, they should be taken into account. However, to quantify the effect takes a considerable number of precise in situ stress measurements in a large number of wells between the fracture candidate and the far field source. It is not a common practice, and thus processes for doing this are not discussed.

In situ stress equations from sonic logs Example 3–3. Nine-Interval Example: In Situ Stress Profile Calculations for Layered Formations

Consider the formation intervals with formation densities, Poisson’s ratios and elastic moduli previously calculated by sonic logs in the nine-interval example (table 3–4), and the associated formation density and reservoir fluid properties listed in table 3–7. 140

Table 3–7. Reservoir fluid properties Depth From ft

To ft

0 7,800 7,800 8,000 8,000 8,200 8,200 8,400 8,400 8,500 8,500 8,600 8,600 8,800 8,800 8,900 8,900 9,000 9,000 9,100 9,100 12,000

Rock Type Overburden Shale Shale Shale/Lime Lime Lime/Sand Sand–Pay Sand/Dolomite Dolomite Dolomite Shale Shale

Fluid Composition (%)

Fluid Densities/Gravities Brine

Oil

Combined Fluid

Gas

Brine

Oil

Gas

Sp Gr

ºAPI

Sp Gr

Sp Gr Air=1

Temp ºF

Z Factor

Relative Volume

Sp Gr Water=1

Sp Gr

psi/ft

100 100 100 95 95 95 15 95 95 90 90

0 0 0 0 0 0 85 0 0 0 0

0 0 0 5 5 5 0 5 5 10 10

1.005 1.005 1.005 1.006 1.007 1.008 1.009 1.010 1.011 1.012 1.013

10 10 10 25 25 25 30 35 35 40 40

1.000 1.000 1.000 0.904 0.904 0.904 0.876 0.850 0.850 0.825 0.825

– 0.700 0.680 0.680 0.680 0.680 0.650 0.640 0.640 0.620 0.620

– 173 175 178 179 181 182 184 186 187 205

– 0.807 0.807 0.853 0.878 0.905 0.933 0.944 0.953 0.974 1.024

– 0.00514 0.00516 0.00493 0.00485 0.00480 0.00473 0.00466 0.00461 0.00456 0.00402

0.000 0.176 0.170 0.178 0.181 0.183 0.178 0.178 0.180 0.176 0.199

1.005 1.005 1.005 0.965 0.966 0.967 0.896 0.968 0.969 0.928 0.932

0.435 0.435 0.435 0.418 0.418 0.419 0.388 0.419 0.420 0.402 0.403

Essentials of Hydraulic Fracturing

The data in 3–7, combined with the Poisson’s ratios calculated from measured p-wave and s-wave shear Δts values in table 3–4 and equation 3–12, provide the in situ stress values for each interval shown in table 3–8. Here, depths, formation density, and fluid gradients (psi/ft) determine overburden pressures at interval tops and bottoms. Equation 3–12 determines the corresponding in situ stresses. Table 3–8. Overburden, pore pressure, and stress calculated from sonic log data Depth From ft

To ft

0 7,800 7,800 8,000 8,000 8,200 8,200 8,400 8,400 8,500 8,500 8,600 8,600 8,800 8,800 8,900 8,900 9,000 9,000 9,100 9,100 12,000

Overburden Rock Type Overburden Shale Shale Shale/Lime Lime Lime/Sand Sand–Pay Sand/Dolomite Dolomite Dolomite Shale Shale

Pressure

Stress

@Top Grad @Bot @Top Grad @Bot @Top Grad @Bot psi psi/ft psi psi psi/ft psi psi psi/ft psi 0 7,165 7,349 7,533 7,724 7,822 7,922 8,124 8,231 8,341 8,441

0.919 7165 0 0.435 3,394 0 0.919 7349 3,394 0.435 3,481 5,424 0.919 7533 3,481 0.435 3,568 5,563 0.958 7724 3,425 0.418 3,509 5,099 0.982 7822 3,512 0.418 3,554 4,621 0.995 7922 3,558 0.419 3,600 4,832 1.011 8124 3,337 0.388 3,414 4,628 1.072 8231 3,690 0.419 3,732 4,946 1.094 8341 3,736 0.420 3,778 4,733 1.007 8441 3,618 0.402 3,658 5,125 0.945 11182 3,671 0.403 4,841 5,715

0.695 0.695 0.695 0.638 0.567 0.591 0.563 0.604 0.569 0.595 0.636

5,424 5,563 5,703 5,226 4,678 4,891 4,741 5,006 4,790 5,185 7,558

Figure 3–14 shows the in situ stress profile for table 3–8, spanning the intervals of interest in the vicinity of the pay sand. Here we see two potential upper and lower confining boundaries for vertical fracture growth. An upper boundary exists at 8,400 feet and a stronger one at 8,200 feet. There is a lower boundary at 9,000 feet with a stronger one at 9,100 feet. Vertical fracture growth across these boundaries at 8,400 and 9,000 ft depends on the net fracturing pressure (in-fracture pressure during pumping minus interval in situ stress). The relative in situ stress differences between the intervals, rather than the absolute stress values, are the determining factors pertinent to vertical fracture growth. Thus, for this example, during pumping, the fracture would not likely be confined to just the pay sand very long. It would very quickly break out into the adjacent intervals immediately above and below it, and grow upward and downward until confined by the stronger stress bounds above and below.

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In Situ Stress (psi) 4,500 8,000

4,750

5,000

5,250

5,500

5,750

6,000

Shale

8,200

Depth (feet)

8,400 8,600

Sand Pay 8,800 9,000 9,200

Shale @

ts TRUE

Fig. 3–14. In situ stress versus depth calculated from sonic log data @ ∆ts true

Example 3–4. Nine-Interval Example: Error Scenarios in In Situ Stress Calculations from Sonic Logs

As previously stated, sonic log output that represents within ±10% truth-case p-wave and s-wave arrival times is considered industry-wide to be good data. Table 3–5 gives the resulting Poisson’s ratio for the errors in each interval. Figure 3–15 reflects the effects on calculated in situ stress for each interval for ±10% error in only the s-wave, Δts, data and zero error in the p-wave data). As can be seen, the differences between calculations with true Δts and those with erroneous data are significant. However, these differences may not critically affect treatment design. Again, the stress differentials between the intervals govern vertical fracture growth. For this case, even with the 10% Δt error, sufficient stress differential exists for fracture confinement. The barrier at 8,400 feet poses a differential of 535 psi between the pay sand interval and the barrier. The next barrier above that, at 8,200 feet, has a 975 psi differential. Hence, for a fracture to break into the interval above 8,200 feet would require net fracturing pressures on the order of 975 psi. To do so would yield fracture widths greater than 2.5 inches. It may not be possible to find a fracturing fluid that could create 143

Essentials of Hydraulic Fracturing

widths of that magnitude. Thus, for this example, sonic log errors are not a serious concern in regard to fracture vertical growth. However, as shown later in this chapter, sonic log errors can significantly affect fracture width. In Situ Stress (psi) 4,500

3,500 8,000

5,500

6,500

7,500

8,200

Depth (feet)

8,400

8,600

Sand Pay 8,800

9,000

9,200

@

ts Error 10% LOW @

@

ts TRUE

ts Error 10% HIGH

Fig. 3–15. Comparative in situ stress profiles at true ∆t and ±10% errors in ∆t shear

In situ stress measurements Very accurate, pin-point data can be obtained using microfrac pump-in or shut-in pressure tests through casing perforations over relatively small intervals that are isolated mechanically. Figure 3–16 shows an example of the wellbore configuration for performing these tests.

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Fig. 3–16. Downhole wellbore configuring for microfrac in situ stress measurements. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. The test procedure involves • Isolating very small intervals in the wellbore with packers; • Pumping small volumes of fluid (20–40 gallons) to breakdown the formation and gain fluid exposure to the fracture faces; • Dropping the mandrel (with a high resolution pressure gage hanging below it) in the nipple to close the interval from the rest of the well bore; • Keeping the mandrel seal closed with pressure above it; • Recording the pressure decline in the interval as fluid leaks off into the formation, allowing the fracture to close; and • Analyzing the results and determining a value for in situ stress. Figure 3–17 is a composite of SPE Monograph V. 12, Figs. 3.2 and 3.3. It shows examples of microfrac test data. The peaks of the curves show the breakdown that creates the fracture. The steep decline starts when the mandrel is set. The flattening portion is the pressures where the fracture is closing. This is where one must interpret the pressure at which the fracture is actually closed (the closure pressure), which is considered the in situ stress pressure. Usually the tests involve several (three to five) repeated pump-in and pressure-decline measurements to arrive at a result where the interpreted fracture closure pressure remains essentially unchanged, and further decline is due to porous matrix flow.

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Essentials of Hydraulic Fracturing

Fig. 3–17. Ideal and typical stress-test data from microfrac breakdown tests Source: “Figure 3.2” and “Figure 3.3,” Gidley et al. 1989, 59

In situ stress versus depth profiles Figure 3–18 shows the results of microfrac tests (stress magnitude versus depth in various formations) in the Mesa Verde group at the DOE Multi-Well Experiment (MWX) Site in Rifle, Colorado. These data were obtained with precise microfrac tests at various points in the wellbore. Here, small fluid volumes were injected to create micro-sized fractures in the formation. After injection stopped, pressure decline versus time behavior provided the fracture closure pressure (σMIN) data. These tests were a significant revelation to the industry. Prior to their emergence, it was commonly perceived that in situ stress consistently increased with depth. However, the figure 3–18 data refutes that perception. Also, notice the large differences in stress magnitude over some relatively small vertical intervals. Subsequently, throughout the industry, similar tests have revealed that stress profiles such as shown in figure 3–18 are more often than not the norm. This type of profile has a major effect on vertical fracture propagation. It depends on the fracture initiation (perforated) interval. If the perforated interval is between zones of sufficiently higher stresses, the fracture will be well-confined. If it were not, the fracture would grow out of zone, possibly screening out as upward or downward growth continued. The reason 146

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for screen-out is that fracture width in the perforated interval would decrease as the fracture progressively encountered lower stress zones, which would result in narrowing fracture width at the perforated interval to the point where it would not accept proppant.

Fig. 3–18. Microfrac tests in situ stress results versus depth and lithology. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. Other observations about fracture vertical growth yield different perspectives related to where the perforations are made and what would happen as a result. Consider perforating a 100-foot interval and fracturing at other sections of the column: • For the interval 7,400–7,500, the fracture would grow unconfined vertically upward; • For the interval 7,650–7,750, the fracture would grow unconfined vertically upward, and would most likely eventually screen out; • For the interval 7,850–7,950, the fracture would be highly confined within the interval from 7,800–8,000; and • For the interval 8,050–8,150, the fracture would grow rather quickly into the upper interval 7,800–8,000, and would screen out shortly after it broke into that upper interval. 147

Essentials of Hydraulic Fracturing

Consider another case where two 100-foot intervals are perforated and fracked simultaneously, in this case, the 7,450–7,500 and the 7,650–7,750 ft intervals. Here the fracture would probably never initiate in the lower interval. The easiest place for it to go is in the upper interval, i.e., 7,400–7,500 ft. Hence, in situ stress profiles play a dominant role in fracture propagation behavior. They affect (1) fracture vertical growth, (2) fracture width, and thus, conductivity, (3) fracture lateral penetration, (4) fracture symmetry about the injection interval, (5) fracture azimuthal component and (6) occasionally the location of the perforated interval. Also, the in situ stress profile impacts on fracture geometry and conductivity governs the selection of proppants, fluids, and pumping prognoses requires that it be well defined. Thus, fracture design engineers should be acutely aware that vertical fracture confinement or growth, and screen-out potential is highly dependent on a formation’s in situ stress profile, and the point(s) at which the well is perforated.

Other methods for obtaining in situ stress profiles: Microfrac or minifrac tests Microfrac tests are both time-consuming and costly, but the lack of knowledge about stress behavior in formations can be exponentially more costly than the tests. It can have a drastic effect on the economic outcome of a fracturing job. What to do? Consider the following two options: • Pre-fracture minifrac pump-in, shut-in, or pressure-decline tests • Sonic (p-wave, s-wave) log data calibration, using data from either microfrac or minifrac tests on only a few wells in the formation. Minifrac tests through casing perforations, whether they be total interval, or over small or large intervals that are isolated mechanically, have become a standard practice. They are typically done without isolating the perforated interval (which is required for microfrac tests). They employ somewhat larger injection volumes than do the microfrac tests. Minifrac tests are usually executed in conjunction with and prior to the regular fracture job. Most tests are performed only on the fracture candidate formation. However, they can also be done in other adjacent zones if there is no danger of compromising the treatment of the candidate formation by perforating other zones in the well. A major advantage of minifrac tests is that they also yield an estimate of fracturing fluid efficiency and a value for fluid-loss coefficient, which is very important data for fracture treatment design. The tests are described in chapter 5, “Determining Fluid-Loss Behavior.”

In situ stress correlations: measured versus sonic-log-calculated values A correlation may exist between sonic log calculated in situ stresses and measured microfrac or minifrac tests. If a suitable correlation exists for a given stratigraphy, it greatly enhances the in situ profiling requirements for a treatment design. However may be some cases where a suitable correlation does not exist. Figure 3–19 is a composite of SPE Monograph V. 12, Figs. 1.15 and 1.16. It shows two very different cases. The left figure shows a very good correlation between the microfrac test stress data and the calculated sonic log values. Here, the correlation exists for both sand and shale in different fields from Wyoming to Texas. Even though the sonic log values were lower than those 148

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measured by the microfrac tests, the relationship between the two showed that the sonic data could be adjusted to obtain representative in situ stress values for a large spectrum of fracture design.

Fig. 3–19. Measured microfrac test in situ stress versus calculated in situ stress correlations Source: “Figure 1.15” and “Figure 1.16,” Gidley et al. 1989, 69. The other case is not so, as shown in the right figure. Here, no meaningful correlation exists for the available data. Hence, it may be necessary to expand the number of microfrac or minifrac tests over a larger stress range. Even if this is done, the results may not be definitive. If they are not, the sonic log data should be considered suspect, and the design engineer must resort to using only microfrac or minifrac tests.

Net Fracturing Pressure Net fracturing pressure (PNET) is defined as the pressure in the fracture during pumping (Pƒ) minus the in situ stress (σMIN): PNET = Pƒ – σMIN

Equation 3–13

where PNET

Net fracturing pressure (psi)



In-fracture pressure during injection (psi)

Pƒ

σMIN

In situ stress (psi)

Note that net fracturing pressure is often loosely referred to as net pressure at the wellbore where pressures (PƒW) are physically measured. Thus, it is often expressed as such. However, 149

Essentials of Hydraulic Fracturing

net pressure applies to all point in the fracture where in-fracture pressures (Pƒ) result from the fracturing fluid friction exists at those points.

Net fracturing pressure versus pumping time log-log charts (Nolte-Smith plots). Net fracturing pressure analysis revolutionized how the industry designs and evaluates fracture treatments. It was one of the more important technology improvements leading to the success of massive hydraulic fracturing in tight gas sands. The use of the Nolte-Smith plots has evolved as an important and integral part of fracturing treatment design, as well as real-time and post-fracture analysis. It provides significant insight about dynamic fracture propagation during a treatment, and is useful to corroborate post-fracture geometry (fracture width, and vertical and lateral penetration) investigations. It also provides a perception of fracture width development during a treatment, and can provide insight about edge effects. Many techniques involving net pressure behavior analysis before, during, and after fracturing can be used to estimate some of the important data requirements for either designing a treatment, or gaining some understanding of fracturing behavior in a particular formation. These techniques can provide useful information about • In situ stress or fracture closure pressure • Fracture propagation behavior • Fluid-loss behavior or fluid fracturing efficiency Figure 3–20 is a composite of SPE Monograph V. 12, Fig. 1.58, by Nolte and Smith, and SPE Monograph V. 12, Fig. 1.59, by Conway et al. The net fracturing pressure for both charts is based on pressure measured at the wellbore (PƒW).

Fig. 3–20. Net fracturing pressure versus time (log coordinates) for inferring fracture propagation behavior: wellbore configuration (left), per Nolte (middle), per Conway types (right) Source: “Figure 1.58” and “Figure 1.59,” Gidley et al. 1989, 25, 26. 150

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On the left (Nolte-Smith), the figure shows how a log-log chart of net fracturing pressure versus pumping time behavior can yield insight about fracture geometry growth development during a given treatment. The Nolte-Smith type designation on the left applies to specific phases that can occur during a fracturing treatment. On the right (Conway et al.) are examples from a large sampling of typically observed fracturing behaviors that occurred throughout treatments from start to finish. The Conway et al. type designation refers to categories of behavior types within a particular behavior grouping, where the interpretation suggests that several different Nolte-Smith type behaviors occurred during the treatment. The left portion of the Nolte-Smith chart shows one of several possible methods for measuring pressure in the wellbore during pumping (PƒW). Here, PƒW is determined using a tubing dead string filled with an incompressible fluid of known density. The value for PƒW is determined by adding the hydrostatic tubing column pressure in the dead string to the measured surface pressure (Pt). Other methods, such as placing a pressure gage at the bottom of the tubing are commonly used. Nolte-Smith type charts. A very important aspect of these tests is to eliminate potential data distorting factors such that PƒW accurately reflects pressure at the injection point. One approach is to use a known-density brine in the dead string and to keep the string clear of gelled fluid. Another is to placing a bottomhole pressure gage at the bottom of the dead string, at a point near the perforations. Perforation friction effects can be eliminated by using a high density of large diameter holes to mitigate friction. Engineers should never rely on PƒW values calculated using dynamic pipe friction algorithm, especially for proppant-laden slurries. This has been emphasized several times by actual tests that compare measured PƒW values with algorithm calculated values. Algorithm calculated values can be very erroneous. Even though some pumping service companies claim otherwise, technology does not yet exist to yield reliable results, so such data are not only highly suspect, they can be extremely misleading. The Nolte-Smith chart depicts the four behavior types described below: • Nolte-Smith Type I: PNET increasing on a positive 1/4 slope with time. This slope suggests a highly confined vertical fracture where there is practically no, or minimal, height growth. Here, the lateral fracture penetration rate greatly exceeds that of the vertical growth rate. The fracture is a container with a constant, very slow horizontal growth and possibly minimal leakoff. • Nolte-Smith Type II: PNET remaining relatively flat. For the pressure to remain flat, either there is some slow and stable vertical height growth, or the fracture is now leaking at some point, which means fluid loss has increased. • Nolte-Smith Type III: PNET increasing on a positive 1/1 slope with time. Here, there is no lateral penetration and no vertical height growth. Edge effects dominate the behavior. The fracture is not growing in length or height. Instead, it is ballooning, which means the fracture width is growing. As a corollary, a 1/1 slope in well testing is attributed to fracture storage. • Nolte-Smith Type IV: PNET decreasing on a negative 1/1 slope with time. The most likely cause of a sudden pressure drop is rapid, unstable vertical height growth. The fracture is predominantly growing vertically upward, or downward. The vertical growth rate greatly exceeds that of the lateral fracture penetration rate.

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Essentials of Hydraulic Fracturing

Conway et al. categories. The right portion of figure 3–20 (Conway et al.) depicts groups of wells that behave similarly. The categories designated here refer to wells grouped by similar behavior. Notice, that propagation behavior does not exhibit the sequence described by Nolte-Smith. Rather, they exhibit several Nolte-Smith behaviors throughout the treatment. The four Conway et al. category types are: • Conway et al. category I Well: Nolte-Smith Type II behavior throughout (some vertical height growth, slow and stable), ending with Nolte-Smith Type III behavior. • Conway et al. category II Well: Initially Nolte-Smith Type II behavior: ˡˡ Highly confined vertical fracture length, practically no growth. The lateral fracture penetration rate greatly exceeds that of the vertical growth rate. ˡˡ Then Nolte-Smith Type IV behavior (unstable vertical height growth). The fracture is predominantly growing vertically upward, or downward. The vertical growth rate greatly exceeds that of the lateral fracture penetration. ˡˡ Then Nolte-Smith Type III behavior (no lateral penetration or vertical height growth). The fracture is not extending at its perimeter. It is ballooning. Fracture width is becoming larger and larger, ending with a screen-out. • Conway et al. category III Well: Initially Nolte-Smith Type IV behavior (unstable vertical height growth). ˡˡ Here, the fracture is predominantly growing vertically upward, or downward. The vertical growth rate greatly exceeds that of the lateral fracture penetration rate until it eventually starts to screen out, ending with a screen-out. • Conway et al. category IV Well: Initially Nolte-Smith Type I behavior (highly confined with lateral penetration). ˡˡ Then, several Nolte-Smith Type III and Type IV behaviors as the fracture encounters and breaks through barriers. ˡˡ For the most part, the fracture is not extending at its perimeter. It is ballooning. Fracture width is becoming larger and larger, ending with a screen-out. Many treatments have exhibited a Nolte-Smith behavior sequence from start to finish. However, if, and only if, fracture height remains constant throughout pumping will, PNet increase by a 1/4 slope relation when fracture penetration (Xƒ) continue increasing, which means that the fracture is following a PKN behavior (constant height). When fracture height (Hƒ) does not remain constant, and grows more rapidly than fracture penetration (Xƒ), PNET will decrease in proportion to the change (Xƒ/Hƒ). Here the fracture is following more closely to GdK geometry where height growth is greater than lateral penetration. If a fracture stops growing both vertically and horizontally, it will grow wider. However, many treatments have also exhibited the Conway et al. category IV behavior where fractures break through a series of confinement barriers, thus indicating different Nolte-Smith type behaviors during propagation. The relation between the wellbore pressure during pumping (PƒW), fracture dimensions (height, length, and width), and the formation rock property’s Poisson’s ratio (ν) and elastic modulus (E), plus the additional forces due to the edge or tip-region effects can be analyzed by observing the net fracturing pressure (PNET) behavior with time. The interaction of all these factors provides an inference of fracture geometry behavior from measurements of wellbore pressure during pumping. 152

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Nolte-Smith charts are commonly available from all fracturing service companies during a treatment. They can be displayed in real-time, and they provide a perspective of fracture geometry growth behavior as the treatment progresses. However, they are only valid if the pressure at or very near to the injection point is accurately measured. If the pressure is calculated from fluid friction algorithm equations and surface measured pressures be very wary of the interpretations about fracturing behavior. Other uses for Nolte-Smith plots. If one or two parameters are known from experience with a given formation (interval), such as formation-effective leak-off zone height and/or elastic modulus, pertinent fracturing equations can provide considerable insight about other parameters. This is because of the relative interactive effects between: • Formation-effective leakoff zone height • Formation-effective elastic modulus • Fracture vertical height • Fracture width For example, if zone leakoff height, elastic modulus and fracture vertical height are known, fracture width at the wellbore can be calculated.

Limitations to net fracturing pressure analyses As with the fracturing propagation models, these techniques are based on theoretical approaches As such, they are sometimes bound by the confines of the theory basic to the technique. The complexities of nature which, more often than not, far exceed the bounds of theory, the techniques alone may not provide answers to some of the quandaries that have been encountered. Nevertheless, the Nolte-Smith charts provide significantly helpful tools for enhancing our fracturing design capabilities.

In Situ Stress and Net Fracturing Pressure Effects on Fracture Height, Width, Penetration, and Volumetric Propagation Geometry Bounding interval height and fracture lateral penetration It is clearly understood that propagating fractures follow the path of least resistance. If initiated at a point where in situ stresses are lower than the stresses in surrounding intervals, propagation into those higher stress zones is inhibited. If initiated in a layer where the value of in situ stress is higher than those in surrounding intervals, the fracture will migrate to those lower stress intervals. The rate of migration depends on the relative differences in in situ stress magnitudes between where the fracture is initiated and where it is going (and obviously the hydraulic pressures within the fracture that are forcing it to propagate). Figure 3–21 shows the obvious effect of fracture interval height on fracture penetration for comparable injection volumes. The value of the in situ stress in the bounding layers controls

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vertical fracture height. The vertically confined fracture height results in deeper penetration than the vertically extensive height. Conversely, injection volume requirements to achieve comparable fracture penetrations for the vertically extensive case are much larger than for the confined case. This emphasizes the need to obtain a priori in situ stress and rock property data pertinent to confinement intervals. Knowledge of fracture height also applies to economics. It may not be economically feasible to fracture the vertically extensive cases that require high costs for large volume treatments.

Fig. 3–21. Fracture geometry: height versus penetration (comparable injection volumes)

Calculating Fracture Height with In Situ Stress Profile Data Figures 3–22 and 3–23 demonstrate ways to investigate questions about how far a fracture will propagate vertically into contiguous intervals. These figures apply to simple three-interval cases. Figure 3–22 applies for symmetric cases where the in situ stresses in the bounding overlying and underlying intervals are equal. Figure 3–23 is used for asymmetric cases where the in situ stresses in the overlying and underlying intervals are different. Examples are discussed thoroughly in SPE Monograph V. 12; however, the processes as described therein require (a) calculating horizontal axis values, (b) manually picking points from specified curves that correspond to the horizontal axis values, and (c) picking points on the vertical axis that correspond to the curve-picked points. Also, the examples start by specifying a fracture vertical height, and the question is what is the in-fracture pressure associated with that height? 154

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The examples given in what follows show the inverse approach where in-fracture pressure is specified, and the question is what is resulting vertical fracture height for that pressure? This approach uses the same charts that are contained in SPE Monograph V. 12, i.e., figures 3–22 and 3–23. These examples also employ algorithms that eliminates manual curve-point picking. The method uses equations and algorithms for calculating: (a) curve points that correspond to horizontal axis values and (b) vertical axis (fracture height) values that correspond to those curve points. Additionally the method provides for interpolation to address conditions that are not shown per se in figures 3–22 and 3–23. Details for using the method and creating a spreadsheet program to do so are contained in appendix A. This significantly facilitates and expedites utilizing the data available in the figures. The two figures are based on fundamentally sound rock mechanics theory. As such, the method for using them serves as a springboard for creating computerized rock mechanics models that incorporate calculations for fracture widths and volumes as well as fracture height. This can also be readily done on a spreadsheet platform. Detailed instructions for doing so are contained in appendix B. Examples of using the algorithm approach are presented later in this chapter.

Fig. 3–22. Fracture penetration versus in situ stress in-fracture pressure function—symmetric case. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. 155

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Fig. 3–23. Fracture penetration versus in situ stress, in-fracture pressure function—asymmetric case Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. Equation 3–14 determines the relative fracture height growth into the σ2 upper and lower layers relative to the height of the σ1 layer, using A, B, and C coefficients in table 3–9.

hs/h = A + BΔσƒ/Δσ + C(Δσƒ/Δσ)2

Equation 3–14

where:

hs/h

Relative fracture height (dim.)



Δσƒ/Δσ (σ2 – Pƒ)/(σ2 – σ1)

σ2

In situ stress in upper and lower bounding layers (psi)



In-fracture pressure during injection (psi)

Pƒ

σ1

In situ stress in fracture interval (psi)

Table 3–9 coefficients came from least square regression of digitized values for the Kic = 0, all σ2 – σ1 curve in figure 3–22. Appendix A contains additional tables for calculating coefficients that apply to all curves contained in both figure 3–22 and figure 3–23, plus algorithms 156

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that account for the effects of KIC as well as algorithms for interpolation. Note: the coefficients are range specific to the figure 3–22 horizontal axis value (σ2 – Pƒ)/(σ2 – σ1). Using an Excel spreadsheet “VLOOKUP” function that keys on the “From” column values, lookup indices of 3, 4, and 5 for coefficients A, B, and C. Note: table 3–9 applies only to the Kic = 0, all σ2 – σ1 curve in figure 3–22. There are six other tables in appendix A for other conditions. Table 3–9. Equation 3–14 coefficients (σ2 – Pƒ)/(σ2 – σ1)

Equation 3–14 Coefficients

∆σƒ/∆σ Range From To 0.0001 0.1000 0.1375 0.1655 0.2142 0.3000 0.3760 0.5060 0.6280 0.8700 0.9500

0.1000 0.1375 0.1655 0.2142 0.3000 0.3760 0.5060 0.6280 0.8700 0.9500 1.0000

A

B

C

10.008 –4.1684 –6.8462 5.0580 2.9964 2.0501 2.0375 1.3227 0.88727 1.6479 0.0020

–83.852 143.21 132.62 –30.172 –12.650 –6.5907 –6.4478 –3.3460 –1.8901 –3.4935 –0.00200

137.68 –715.28 –496.64 52.408 15.540 5.8567 5.5662 2.2278 1.0135 1.8515 0.00000

Example 3–5. Vertical Fracture Height Calculations, Symmetric In Situ Stress Barriers Case

This example shows a comparison between results using the approach described in the SPE Monograph V. 12, with the results obtained using equation 3–14. The example uses the same SPE Monograph V. 12 symmetric case example data. Thus, the calculations should be comparatively easy to follow. Both sets of calculations (Monograph V. 12 and equation 3–14) using figure 3–22 (symmetric case) are shown in table 3–10, for net fracturing pressures from 100 to 400 psi, and the following conditions:

h = 50 feet

Height of σ1 interval

σ1 = 3,000 psi

In situ stress in the lowest in situ stress interval

σ2 = 3,500 psi

In situ stress in the bounding intervals (above and below)

KIc = 0 psi√in

Stress intensity factor in σ1 interval (use figure 3–22 chart curve: KIc = 0, and All σ2 – σ1)



In-fracture pressure

Pƒ = psi

PNET = Pƒ – σ1

Net fracturing pressure

Table 3–10 shows the stepwise calculations, column by column, to determine total fracture height for the above conditions. It also shows the comparative results for curve-picked hs/h 157

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values with those calculated by equation 3–14. Obviously, the two approaches yielded close results. However, using equation 3–14 is a much quicker exercise. Table 3–10. Height growth into symmetric in situ stress barriers

Example 3–6. Vertical Fracture Height Calculations, Asymmetric In Situ Stress Barriers Case

This example employs the approach implied by figure 3–23. It applies to a three-interval asymmetric case where the target fracturing interval exhibits the lowest in situ stress, the underlying interval contains the greatest in situ stress, and the overlying interval in situ stress magnitude is in-between the other two. As with example 3–5, it compares results obtained for both the SPE Monograph V. 12 non-symmetric hand-picked-curve case approach and the algorithm approach using equation 3–14. Again, the same example case data is used so that the reader may compare the results between the two approaches. Calculations using figure 3–23 data (asymmetric case) are shown in table 3–11, for the same conditions used in figure 3–22 (net fracturing pressures from 100 to 400 psi), for the following conditions:

h = 50 feet

Height of σ1 interval

σ1 = 3,000 psi

In situ stress in the lowest in situ stress interval

σ2 = 4,000 psi

In situ stress in the bounding underlying interval

σ3 = 3,500 psi

In situ stress in the bounding overlying interval

KIc = 0 psi√inches

Stress intensity factor in σ1 interval

σ3 – σ1 = 500 psi

Minimum in situ stress difference

σ2 – σ1 = 1,000 psi

Maximum in situ stress difference

Again, the two different approaches yielded reasonably close results.

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Table 3–11. Height growth into asymmetric in situ stress barriers

Comparison between the symmetric and asymmetric case results Figure 3–24 depicts the resulting total fracture height versus net fracturing pressure (PNET) for both examples. In the symmetric case (solid curve), height growth is vertically symmetric, equally upward and downward, about the low in situ stress interval. If fracturing pressures were to reach or exceed the bounding interval in situ stress (3,500 psi), the fracture would not propagate laterally, only upward and downward. In the asymmetric case (dashed curve), the fracture grows upward faster than downward. Growth is relatively small at low net fracturing pressures. As fracturing pressure increases toward the bounding interval with the lower in situ stress (3,500 psi), vertical height increases rapidly. If fracturing pressures were to reach or exceed 3,500 psi, the fracture would not propagate laterally, only upward. The lower bounding interval (in situ stress = 4,000 psi) would not allow downward growth.

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160

Tota l Fracture Height, Hƒ (feet)

140 120 100 80 60 40

Symmetric Case

20 0

Asymmetric Case 0

200

400

600

Net Fracturing Pressure, Pƒ – 1 (psi)

Fig. 3–24. Fracture height versus net fracturing pressure—asymmetric and symmetric barrier cases Application of figure 3–23 where the overlying interval exhibits the maximum in situ stress. Figure 3–23 applies to an asymmetric case where in situ stress in the overlying interval is less than that in the underlying interval. Thus fracture vertical growth is preferentially upward. However cases do exist where the overlying interval has the higher stress, and consequently downward growth dominates. The figure 3–23 still applies for the upside down case by always assigning σ2 the largest stress value, even though it occurs in the overlying interval. Merely apply the approach accordingly for the high- and low-stress intervals. Then, for graphic display, turn the image upside down. Fracture height versus in-fracture pressure for multiple (more than three) intervals. Computations for cases with additional intervals (more than three) are a bit more complex. They are discussed in SPE Monograph V. 12. However, the three-layer examples shown here suffice for initial investigations, and can be readily programmed in a spreadsheet. For more complex systems, fracturing simulator models are suggested. Hence, discussion pertinent to four or more intervals is not presented. Algorithms for four or more intervals are integral to several pseudothree-dimensional (P-3D) models. However, the reader is cautioned that other P-3D models (without that capability) do not credibly address the four or more interval cases. Figure 3–25 shows an example from SPE Monograph V. 12 where a very credible model was used to calculate the fracture height profile. It shows fracture height through five layers of different in situ stresses, as in-fracture pressures increases from the fracture tip to the wellbore. Here, the fracture tip has zero in-fracture pressure. At the wellbore the pressure is 800 psi.

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Fig. 3–25. Fracture height versus fracturing pressure—asymmetric barriers case. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. Conceptually, the depiction in figure 3–25 can be inverted to show what a fracture height versus length profile generated with a gridded three-dimensional (G-3D) model would look like. This is shown in figure 3–26. The fracture profile is quite different from the bullet-nosed profile generated with the P-3D shown in figure 3–8. Obviously, the G-3D model better represents fracturing behavior better than does a P-3D model.

Fig. 3–26. Fracture height versus penetration—asymmetric barriers case This case shown in figure 3–26 demonstrates how fracture geometry is governed by the interaction of in situ stress profiles and pressure in the fracture during treatment. Note that 161

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figure 3–26 shows only one snapshot in time. Also, that it is for a given fracture fluid system slurry, leakoff behavior, and injection volume at that single point in time. The display would be different for smaller, or larger, injection volumes. The picture would probably change if the in-fracture pressure profile changes because of the different friction behaviors exhibited by different fracturing fluid system, or with different proppant concentrations that affect rheology (viscosity) behavior. Obviously, a different stress profile would also present a different picture. If the rock mechanics were different. The list goes on, but figure 3–26 provides one image of how in situ stress profiles interact with fracturing fluid systems, and how mechanical rock properties govern fracture geometry propagation behavior.

Pore Pressure Effects on In Situ Stress and Fracture Propagation Behavior Restructuring equation 3–12 to form equation 3–15 shows another perspective of the relation between in situ stress and reservoir pore pressure (Pe). The relation is by the factor (1 – Cν ) shown in equation 3–16 that reflects in situ stress changes (ΔσMIN) resulting from pore pressure changes (ΔPe).

σMIN = Cν × σvToi + Pe(1 – Cν ) + ασT

ΔσMIN = ΔPe(1 – Cν )

Equation 3–15 Equation 3–16

where: σMIN

Minimum principal stress (psi)

Cν

ν/(1 – ν)



Poisson’s ratio (dim.)

ν

σvToi

Overburden vertical stress at the interval top (psi)



Pe

Reservoir pore pressure (psi)



α

Biot’s constant (α ~ 0.7, for typical fracture design α = 1.0)

σT

Far-field stresses (psi): Effects of far-field faults, mountains, etc.

Hence, changes in ΔPe can result in changes in σMIN and thus, changes in fracture propagation behavior. Two examples are shown from the Carthage Gas Unit field, Texas, and one from the Valhall field, Norwegian North Sea. Both come from extensive fracturing model studies of reservoir pressure depletion effects on in situ stress profiles, and the resulting effects on fracture propagation. The studies were done after the initial fields had been producing for several years, the reservoirs were partially depleted, and • New intervals were completed in near proximity to producing intervals, • Previously completed, producing wells were refractured, or • Infill wells were completed in the partially depleted reservoir. The lithologies of the two formations are quite dissimilar, but the effects of pore pressure depletion on propagation geometry are very consistent. 162

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Example 3–7. Carthage Gas Field, Texas, Scenario 1: Pore Pressure Depletion and In Situ Stress

Figure 3–27 shows the reservoir pore pressure, in situ stress, and fracture propagation profiles at (1) initial reservoir pressure and (2) after pore pressure had depleted in two zones over various portions of the field. As can be seen at initial reservoir pressure, there were no stress-confining intervals above the fracture initiation point. Consequently, fractures propagated upwardly more than laterally. After the producing interval pore pressures were reduced due to partial depletion, a differential stress of 400 to 600 psi was measured in the fracture treated zones. These differential values of in situ stress resulted in strongly confined fractures for both new infill wells and refractured wells. Fracture penetrations for the same volume treatments were longer in the partially depleted case than for the initial pore pressure case.

Fig. 3–27. Effect of pore pressure depletion on fracture propagation geometry 163

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The longer propped fractures increased resulting post-fracture production. Treatments in the partially depleted wells outperformed the wells that were fracture-treated when the reservoir was at initial pore pressure. There are two probable reasons: (1) deeper fracture penetrations from vertical height growth confinement, and (2) wider fractures generated in the lower stress intervals, which increased fracture conductivity. These combined yielded higher producing rates, even though reservoir pressure had been partially depleted by production from the reservoir. However, there can be a downside to fracture treating a layer after it is partially depleted: the treatment could experience very high leakoff. However, in this case, high fluid leakoff was not an issue. Figure 3–28 shows a different Carthage Gas Unit field scenario. Here, a prospective interval is in the near vicinity of, and underlying, a pressure-depleted interval. It had not been fractured when the overlying upper interval was at initial reservoir pressure. Consequently, when fracturetreated, the initiated fracture propagated into the overlying lower stress interval, instead of propagating laterally into the prospective interval. Post-fracture production results were dismal. The resulting fracture had very limited penetration in the new prospective interval, and some added flow capacity to the wellbore for the overlying interval. Essentially, reserves from the lower prospective interval were forever lost.

Fig. 3–28. Effect of pore pressure depletion on fracture propagation geometry—lower interval fracture treatment

Example 3–8. Carthage Gas Field, Texas, Scenario 2: Pore Pressure Depletion and In Situ Stress

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Figure 3–29 shows the reservoir pore pressure, in situ stress, and fracture propagation profiles at initial reservoir pressure and after pore pressure had depleted by 400 psi. As can be seen at initial reservoir pressure, there were no stress-confining intervals above the fracture initiation point. Consequently, fractures propagated upwardly more than laterally. Partial depletion

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imposed differential stresses of 200 psi in intervals both above and below the fracture initiation points. These relatively small differentials inhibited vertical growth rate considerably. Both fracture penetration and propped fracture widths for the same volume treatments were greater in the partially depleted case than in the initial pore pressure case.

Fig. 3–29. Effect of pore pressure depletion on fracture propagation geometry 165

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Example 3–9. Valhall Field, Norwegian North Sea: Fracture Vertical Propagation and Pore Pressure Depletion

This example comes from the Norwegian Valhall field, located offshore in the North Sea, where the incompetent T-zone chalk formation had to be stimulated by perforating and initiating a fracture in the underlying competent U-zone formation. Without this practice, if the T-zone were perforated and stimulated, the chalk formation itself would produce into the wellbore, and flow to surface. With the initial in situ stress profile, the fracture would grow upward from the U-zone into the overlying T-zone, and deposit proppant in the T-zone, thus creating a conductive path for T-zone production through the proppant-packed fracture to perforations in the U-zone. A successful fracture treatment design was developed to do this, and was used in many Valhall wells. After several years of production, an infill development program was started. The previously successful fracture design was used to fracture the first infill well. Attempted fracturing treatments using the same size proppant (10/20 mesh) screened out three successive times. Further investigations suggested that the in situ stress (closure pressure) in the T-zone had declined by approximately 200 psi because of reservoir pressure decline in the infill area. Fracture stimulation computer models implied that this change in closure pressure had a dramatic effect on fracture propagation behavior. Figure 3–30 shows the in situ stress profiles for (A) initial reservoir pressure and (B) after partial pressure depletion (drawdown). At initial reservoir pressure, the T-zone and U-zone have essentially equal in situ stress gradients. After pressure drawdown, the T-zone in situ stress was approximately 200 psi lower than that in the U-zone. This relatively small change in stress may not seem consequential, but it resulted in a significant change in fracture propagation behavior.

Fig. 3–30. Valhall Field in situ stress profile at initial reservoir pressure and after partial depletion. Copyright 1989, SPE. Reproduced with permission of SPE. Further reproduction prohibited without permission. 166

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Studies, using a G-3D computer model, implied that 200 psi reduction in closure pressure had a dramatic effect on fracture propagation width behavior. Figure 3–31 is a composite of SPE Monograph V. 12, Figs. 1.21 through 1.23. It shows the computer model simulation results for two cases: • Case A, on the left, at initial reservoir in situ stress conditions, and • Case B, on the right, after a 200 psi in situ stress reduction in the T-zone In figure 3–31, the top portion shows fracture height versus length profiles at designated injected fluid volumes. The middle portion shows fracture width versus height profiles at the wellbore for the stated injection volumes. The bottom portion shows the calculated fracture widths at both the perforations and the maximum fracture width (wherever it occurred in the fracture) as a function of injection volume. Figure 3–31 shows computed fracture penetration and width profiles for the respective stress conditions. The figure displays profiles for various volumes injected through perforations in the U-zone at the vertical axis zero point. Prior to pressure drawdown, fracture propagation was essentially radial. Later, as pressure depleted in the T-zone, fractures exhibit significantly different geometries. They quickly break out of the lower U-zone, and migrate into the lower stress T-zone. Then, as injection continues, the fracture propagates primarily in the T-zone, with little or no propagation in the U-Zone. The critical issue, per fracture width, is that at the perforation injection point the width was not sufficient to accept the 10/20 size proppant used in the treatment. For Case A, the fracture propagated in both the U-zone and the T-zone throughout the entire treatment. Its width, both at the perforations and at its widest point, kept increasing with continued fluid injection. In Case B, when the fracture broke upward into the T-zone (after injection 200 bbls), its width at the perforations dropped back to about 0.1 inch. Throughout the entire 1,800 barrels injected, the fracture width at the perforations stayed at about 0.1 inches, even though its maximum width at the fracture center in the T-zone eventually exceeded 0.25 inches as pumping continued. This suggested that for both cases, during early injection stages, fracture width at the perforations was large enough to accept the 10/20 mesh-size proppant which was standard for the early treatments. For Case A, it kept widening at both the perforations and the fracture center. Thus, there was no problem. But for Case B when the width reduced to 0.1 inches, the fracture became too narrow to accept the 10/20 mesh-size proppant, hence the treatment screened out. To remedy this, the fracture design was modified to pump a smaller proppant, 20/40 size, which theoretically should pass through a 0.1 inch wide fracture. The remedy was successful, and the screen-out problem disappeared. An interesting note—the quantitative fracture width calculations by the computer simulator were actually close enough to reality to provide guidance in arriving at a solution to the problem.

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Fig. 3–31. Valhall Field, comparative fracture geometries at initial reservoir pressure (left) and after partial depletion (right) Source: “Figure 1.21,” “Figure 1.22,” and “Figure 1.23,” Gidley et al. 1989, 8, 9.

Computer model applications The examples pertinent to figure 3–27 thru figure 3–31 illustrate the benefits of using a more sophisticated three-dimensional hydraulic fracturing models and rock mechanical property data and credible in situ stress profiles. A P-3D model is inappropriate for this study. It would yield Case-A type behavior very well, but not Case-B behavior. Only a G-3D model can address Case B propagation. This emphasizes the need to use models that best represent in situ fracture propagation behavior. 168

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Interval Interface Slippage, Ductility and Fluid-Loss Confining Effects To continue propagation across a boundary or interface, stresses that create width must be imparted to rock ahead of the fracture’s leading edges. If that does not occur, fracture propagation stops. Fracture blunting can result from any of the following: • Slippage between interfaces • Ductile layers • High fluid loss adjacent to the fracture interval Interface slippage is common in highly fissured or blocky coal beds. It occurs both vertically and laterally. When encountered, either or both fracture vertical and lateral propagation can stop. If both stop and injection continues, fracturing pressures increases. This often results in premature termination of injection (screen-out) to keep from bursting the injection tubulars. Ductile shale layers that slip do not allow the fracture to exert stresses beyond the fracture edge. If encountered they can totally stop or strongly inhibit further fracture propagation. However, this may not result in screen-out. Vertical propagation stops, but the fracture may continue lateral propagation. Conversely, if lateral propagation stops, a fracture will preferentially grow vertically. High fluid loss in faults or high permeability leakoff zones (e.g., conglomerates) can also stop either vertical or lateral propagation. If they don’t totally stop it they can reduce propagation rate significantly. The behavior is analogous to pipe fluid flow encountering a leak somewhere along a pipe. Beyond the leak-point there is less fluid flowing.

Fracture Width During a fracturing treatment the injected fluid hydraulically wedges formation walls apart to create width. The in-fracture pressure acting against the in situ stress, formation modulus and pore pressure dictates fracture width. This is conceptually depicted in figure 3–32 where the interval opposing force magnitudes (primarily from stress) are indicated by arrow size. Here, the fracture is widest in the lowest stress interval. The larger in situ stresses above and below that interval govern fracture vertical growth, and the fracture tends to grow more downward than upward. Cohesion at the interval interfaces also affects the width profile shape. Fracture vertical growth confinement increases fracture horizontal penetration as injection continues. If there is both vertical and horizontal confinement, the fracture will widen (balloon) with continued injection. Fracture width plays a major role in fracture conductivity which, in concert with fracture length, dictates post-fracture production rate and thus, economic returns. Hence, knowing the effect of in situ stress on width is essential to fracture treatment design.

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Fig. 3–32. Fracture width and height versus in situ stress magnitude The relation between fracture width, elastic modulus, Poisson’s ratio, and in situ stress is given by equation 3–17. It applies for two different theoretical approaches—PKN, and GdK.

Wƒ = (CMODEL[1 – ν 2]Dƒ × PNET)/E

Equation 3–17

where

Wƒ

CMODEL



Conversion constant (depending on PKN or GdK)

CPKN

2.4 10–5 , the conversion constant, PKN

CGdK

4.8 10–5 , the conversion constant, GdK

ν

DƒMODEL



Fracture width (in.)

Poisson’s ratio (dim) Model fracture dimension (depending on PKN or GdK)

DƒPKN

PKN fracture height, Hƒ (ft)

DƒGdK

GdK fracture penetration, Xƒ (ft)

E

PNET

Elastic modulus (MMpsi) Net fracturing pressure = Pƒ – σMIN (psi)



Pƒ

σMIN

In-fracture pressure during injection (psi) Minimum principal stress (psi)

Obviously, elastic modulus (E) and net fracturing pressure (PNET) are the primary width governing factors. In situ stress, does not appear per se in the width equation; it is embedded net fracturing pressure (PNET). Poisson’s ratio, which generally ranges from 0.1 to 0.4 (maximum 0.5), has a second-order effect. Simple calculations quickly bring the relative governing effects of the above parameters into perspective. Note: The PKN approach bases fracture width on fracture height (Hƒ). The GdK approach bases width on fracture penetration (Xƒ). 170

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Also notice: Rock tensile properties (stress intensity) do not appear in equation 3–17. These only impact the fracture edge or tip region. However, they become important if they are sufficiently large enough to inhibit or stop propagation at the fracture edges, and thus cause net pressure to increase, which causes the fracture to widen. Equations 3–18 and 3–19 incorporate the rheological effect of dynamic fracturing fluid behavior on width during pumping. Here, fluid system apparent viscosity and injection rate replaces Poisson’s ratio and net fracturing pressure in equation 3–17. Structuring the equation to express the PNET effect in terms of a rheological form, i.e., viscosity (µapp) and injection rate (BPM), yields different equations for the PKN and GdK fractures. Fracture Width While Pumping—PKN geometry model: Wƒ = f {[(µapp × QINJ × Hƒ2)/(E]1/4}



Equation 3–18

Fracture Width While Pumping—GdK model:

Wƒ = f {[(µapp × QINJ × Xƒ2)/(Eƒ)]1/4}

Equation 3–19

where

Wƒ

Fracture width



Hƒ

Fracture height



Xƒ

Fracture penetration (half-length)



E

Elastic modulus

QINJ

Fracturing injection rate

µapp

Fracturing fluid apparent viscosity

Fracture width (Wƒ) calculations where Xƒ > Hƒ/2, the PKN approach yields more credible Wƒ results. Where Xƒ < Hƒ/2, the GdK formulation is more credible. In cases where Xƒ ≈ Hƒ/2, then WƒPKN = WƒGdK. The message here is: Use models based on PKN theory where fractures might penetrate laterally faster than they grow vertically. Vice versa, for those based on the GdK theory. This is important for determining the initial pad injection stage to create sufficient width to accept proppant. During the stage, fracture behavior usually exhibits GdK behavior. If this is ignored, fracture width calculations may yield misleading results. The examples that follow (3–10, 3–11, and 3–12) use the in situ stress profile shown in figure 3–14 to demonstrate the relation between in-fracture pressure, net fracturing pressure, and fracture widths. Example 3–10 includes cases where slippage does and does not occur at interval interfaces. Example 3–11 discusses the hydrostatic column pressure effects attributed to proppant-laden slurry density. Example 3–12 addresses the effects that sonic log shear wave velocity errors can have on calculations of fracture width.

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Example 3–10. Nine-Interval Example: In-fracture Pressures, Net Fracturing Pressures and Fracture Width

This example here and those that follow relate to the figure 3–14 in situ stress profile per table 3–8. This example compares fracture widths that result from three different mid-pay-depth in-fracture pressures of 5,000, 5,500 and 5,900 psi. Such pressures result from the interaction of fluid rheology, injection rate, and fracture geometry. As the fracture extends, wellbore injection pressure (PƒW) increases due to fluid friction in the fracture. Also, fluid loss to the formation results in higher viscosities that increase friction and thus, in-fracture pressure. Here, the focus is on the effect of in-fracture pressures on fracture width. In this example the entire section from 8,200 to 9,100 ft is subjected to fracturing pressure. Figure 3–33 shows the net fracturing pressure versus depth. Interval pressures, which occur at different depths, are adjusted for hydrostatic fluid pressures within the fracture, referenced to the mid-pay sand depth. The fracturing fluid system is comprised of a 6 lb/gal proppant-laden slurry of 2.65 specific gravity sand in a 1.01 specific gravity fluid. The slurry hydrostatic gradient of the 27.2% particle fraction slurry is 0.630 psi/ft. Thus, the net pressure slopes versus depth gradient slopes are less steep than the in situ stress slopes versus depth slopes shown in figure 3–14. Pore pressure which also increases with depth also plays a role in this behavior. Table 3–12 lists fracture widths at the midpoint of each interval, as calculated by equation 3–16. Negative net pressures imply insufficient in-fracture pressure to create fracture width. At 5,000 psi in-fracture pressure, only three intervals exhibit fracture width greater than 0.25 in. The fractured intervals span from 8,400 to 9,000 feet depths. As pressure increases to 5,500 psi, the fracture widens. At an in-fracture pressure of 5,900 psi, width in the intervals increases, and the fracture grows upward to 8,200 feet. However, the width above 8,400 ft is very narrow. This is a relatively typical scenario of fracture geometry progression as in-fracture pressures increase. Net Fracturing Pressure (psi) 8,000

0

500

1,000

1,500

8,200

Depth (feet)

8,400 8,600

Sand Pay 8,800 9,000 9,200

@ 5,000 psi

@ 5,500 psi

@ 5,900 psi

Fig. 3–33. Comparative net fracturing pressures, for in-fracture pressures at mid-pay 172

Table 3–12. Interval midpoint fracture widths at mid-pay in-fracture pressure = 5,000, 5,500, and 5,900 psi Mid-Pay In-Fracture Pressure Depth From ft To ft 0 7,800 8,000 8,200 8,400 8,500 8,600 8,800 8,900 9,000 9,100

7,800 8,000 8,200 8,400 8,500 8,600 8,800 8,900 9,000 9,100 12,000

Formation Overburden Shale Shale Shale/Lime Lime Lime/Sand Sand–Pay Sand/Dolomite Dolomite Dolomite Shale Shale

Poisson’s Elastic DEPTH Stress Ratio Modulus @ Depth v dim. E 1/psi ft psi – 0.350 0.350 0.290 0.208 0.230 0.220 0.221 0.182 0.242 0.300

– 2.382 2.382 4.475 7.773 6.893 6.968 8.019 9.644 5.924 3.186

– 7,900 8,100 8,300 8,450 8,550 8,700 8,850 8,950 9,050 9,150

– 5,494 5,633 5,162 4,650 4,861 4,685 4,976 4,761 5,155 6,637

5,000 psi

5,500 psi

Press Net Frac Frac 1n Frac Press Width psi psi in – – 998 4,496 4,622 1,011 868 4,294 4,842 193 4,905 44 5,000 315 5,095 118 5,158 396 5,221 65 5,284 1,353

– – – – 0.398 0.10 0.72 0.24 0.67 0.17 –

5,900 psi

Press Net Frac Frac Press Net Frac Frac 1n Frac Press Width 1n Frac Press Width psi psi in psi psi in – 4,996 5,122 4,794 5,343 5,406 5,500 5,595 5,658 5,721 5,784

– 498 511 368 693 545 816 619 896 565 853

– – – – 1.43 1.26 1.87 1.23 1.51 1.51 –

– – 5,396 98 5,522 111 5,194 32 5,743 1,093 5,806 944 5,900 1,216 5,995 1,018 6,058 1,296 6,121 965 6,184 453

– – – – 2.90 2.80 3.58 2.61 2.81 3.31

Essentials of Hydraulic Fracturing

Fracture width profile with interval interface slippage. Figure 3–34 shows the Nine-Interval Example, fracture half-width versus depth profile, at the same mid-pay pressures (5,000, 5,500 and 5,900 psi) for the case of no (zero) cohesion between interval interfaces. Here, the intervals act independently, somewhat comparable to a deck of cards. The profile closely resembles that shown in figure 3–33 for net fracturing pressure. Admittedly, this is not common, except for coal, diatomite, or soft shale formations, but it can be encountered in some fracturing candidates. Interface slippage exaggerates the effects of interval properties on fracture width. Fracture Half–Width (inches) 8,000

0

0.5

1

1.5

2

8,200

Depth (feet)

8,400 8,600

Sand Pay 8,800 9,000 9,200 @ 5,000 psi

@ 5,500 psi

@ 5,900 psi

Fig. 3–34. Comparative fracture widths with interval interface slippage Fracture width profile with no interval interface slippage. Figure 3–35 shows the fracture half-width versus depth profiles for the three pressures. This profile includes cohesion between the intervals (no slippage at the interval interfaces). This is typical for most formations. Interface cohesion imparts stiffness to the entire fracture system, such that the rock properties of each interval affect the fracture width behavior of contiguous intervals.

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Fracture Half–Width (inches) 8,000

0

0.5

1

1.5

2

8,200

Depth (feet)

8,400

8,600

Sand Pay 8,800

9,000

9,200 @ 5,000 psi

@ 5,500 psi

@ 5,900 psi

Fig. 3–35. Comparative fracture widths for cohesion between rock intervals—no interval interface slippage

Example 3–11. Nine-Interval Example: Effect of Fluid System Density on Fracture

Width Profile

The hydrostatic column density of a fracturing fluid system opposes in situ stresses in a fracture, thus affecting net fracturing pressure, which in turn, affects fracture width profiles. Fluid density, proppant density, and slurry concentration govern hydrostatic column density. Obviously, the effects are more pronounced in vertically extensive fractures. However, it can be critical for less extensive ones if the stress differences that control downward growth are small. Figure 3–36 shows this for the following fluid systems, where the base fluid specific gravity (spgr) is 1.01: • With no proppant, hydrostatic gradient = 0.437 psi/ft • With 6 lb/gal, 2.65 spgr proppant, slurry hydrostatic gradient = 0.630 psi/ft • Width 12 lb/gal, 3.65 spgr proppant, slurry hydrostatic gradient = 0.888 psi/ft To provide a sharper, and somewhat exaggerated, perspective of fluid system density effects on fracture width, figure 3–36 depicts a case with interface slippage. Here, we are seeing fracture width differences on the order of 0.5 inches between the scenarios. The case for interface cohesion, with no slippage between the intervals, would exhibit lesser degrees of effect on fracture width. Regardless, they can be significant. Hydrostatic pressure materially impacts net fracturing pressure, especially in vertically extensive fractures. 175

Essentials of Hydraulic Fracturing

Fracture Half–Width (inches) 0.4 8,200

0.5

0.7

0.6

0.8

0.9

1

1.1

1.2

Depth (feet)

8,400

8,600

Sand Pay 8,800

9,000

9,200

With No Proppant

With 6 PPG, 2.65 Sp.Gr., Proppant

With 12 PPG, 3.65 Sp.Gr., Proppant

Fig. 3–36. Fracturing fluid proppant-slurry density effects on fracture width—interval interface slippage for in-fracture pressure at 8,400 feet = 5,500 psi

Example 3–12. Nine-Interval Example—Error Scenarios for Fracture Widths Calculated from Sonic Log Data

Table 3–13 and table 3–14 show mid-interval fracture width differences between those calculated for true ΔtS versus those calculated with ±5% and ±10% ΔtS sonic log errors. Both are for interval interface slippage. Admittedly, this exaggerates the differences over the more representative and common no interval interface-slippage case. The exaggerated data are shown to make the point that what is considered relatively good log data (±5% to 10% ΔtTRUE) can result in significant differences between true in situ width behavior and that calculated from sonic log data. The effect is also dependent on net fracturing pressure, as shown by comparing table 3–13 data for the mid-pay in-fracture pressure of 5,500 with table 3–14 data for the mid-pay in-fracture pressure of 5,900. Figure 3–37 shows the fracture width versus depth profile for the 5,900 psi mid-pay in-fracture pressure. Obviously, significant differences can result if the log Δt S do not reflect true rock properties. An example of the effect of such errors on net fracturing revenue is presented in chapter 10.

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Table 3–13. Fracture width errors resulting from ±5% and ±10% errors in ∆t shear 5,500 psi in-fracture pressure at mid-pay 5,500 psi In-Frac Pressure @ Mid-Pay Depth From ft

To ft

Rock Type

0 7,800 Overburden 7,800 8,000 Shale 8,200 8,400 Shale/Lime 8,400 8,500 Lime 8,500 8,600 Lime/Sand 8,600 8,800 Sand–Pay 8,800 8,900 Sand/Dolomite 8,900 9,000 Dolomite 9,000 9,100 Dolomite Shale 9,100 12,000 Shale

Fracture Width Errors Resulting from Errors in ∆t Shear

±5% ∆t Shear Error ±10% ∆t Shear Error Wƒ True Wƒ % Wƒ % Wƒ % Wƒ % Value Value Diff Value Diff Value Diff Value Diff – – 1.84 1.62 2.40 1.58 1.94 1.94 –

– – 1.97 1.58 2.51 1.66 2.27 1.86 –

– – 7 –2 5 5 17 –4 –

– – – – 0.24 – – – –

– – – – –90 – – – –

– – 3.24 2.92 3.96 2.88 3.44 3.48 –

– – 76 81 65 82 77 79 –

– – – – – – – – –

– – – – – – – – –

Table 3–14. Fracture width errors resulting from ±5% and ±10 errors in ∆t shear 5,900 psi in-fracture pressure at mid-pay 5,900 psi In-Frac Pressure @ Mid-Pay

Fracture Width Errors Resulting from Errors in ∆t Shear ±5% ∆t Shear Error

Depth Rock Type From ft To ft 0 7,800 Overburden 7,800 8,000 Shale 8,200 8,400 Shale/Lime 8,400 8,500 Lime 8,500 8,600 Lime/Sand 8,600 8,800 Sand–Pay 8,800 8,900 Sand/Dolomite 8,900 9,000 Dolomite 9,000 9,100 Dolomite Shale 9,100 12,000 Shale

±10% ∆t Shear Error

Wƒ @ Minus 5% @ Plus 5% @ Minus 10% @ Plus 10% True Value Wƒ % Diff Wƒ % Diff Wƒ % Diff Wƒ % Diff Value Value Value Value – – 2.90 2.80 3.58 2.61 2.81 3.31 –

– – 3.00 2.71 3.65 2.64 3.11 3.17 –

– – 3 –3 2 1 11 –4 –

– – 1.09 0.67 1.47 0.78 1.37 0.70 –

– – –62 –76 –59 –70 –51 –79 –

– – 4.23 4.02 5.06 3.84 4.26 4.74 –

– – 46 43 41 47 52 43 –

– – – – 0.04 – – – –

– – – – –99 – – – –

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Essentials of Hydraulic Fracturing

0.0 8,200

0.5

Fracture Half-Width (inches) 1.0

1.5

2.0

2.5

Depth (feet)

8,400

8,600

Sand Pay 8,800

9,000

9,200

@ ∆ts Error 5% LOW @ ∆ts Error 5% HIGH @ ∆ ts TRUE

@ ∆ts Error 10% LOW @ ∆ ts Error 10% HIGH, σmin > Pƒ, Wƒ = 0

Fig. 3–37. Fracture widths at true ∆t shear and ∆t shear errors of ±5% and ±10% in.—5,900 psi in-fracture pressure at mid-pay—with interval interface slippage

Fracture Volume Calculations from Width, Height, and Lateral Penetration Equations 3–20 through 3–22 yield fracture volumes for three simplistic fracture geometries. Even though the geometries are simplistic, the equations provide easy, quick, ballpark estimates of fracture volumes for specified fracture dimensions: Wƒ, Hƒ, and Xƒ. They can be helpful for quickly approximating treatment volume requirements, which can be done by dividing the proposed fracture volume (Vƒ) by fracturing fluid efficiency. Vƒ = ⅓πWƒHƒXƒ

Ellipsoidal Geometry (ELL)

Equation 3–20

Vƒ = 2 ⁄ 5πWƒHƒXƒ

PKN Geometry

Equation 3–21

Vƒ = ½πWƒHƒXƒ

GdK Geometry

Equation 3–22

where:

178

Vƒ

Fracture volume (ft3)

π

Constant: pi = 3.14159263

Wƒ

Fracture width (ft)

Hƒ

Fracture height (ft)

Xƒ

Fracture penetration.

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Fracturing in Horizontal Wellbores In regard to fracturing in horizontal wellbores, the basic theory and principles pertinent to rock mechanics, in situ stress, net fracturing pressure, etc., apply the same as in vertical wellbores. Their effects on fracture propagation behavior are independent of borehole angle and configuration after the fracture has propagated beyond the wellbore influence. This distance is usually less than twice the length of the perforated section, or the isolated portion of the initiation interval. Beyond that distance formation parameters alone dictate fracture vertical and horizontal growth resistance, fracture patterns, orientation, azimuth, interface slippage. However, the formations typically fractured via horizontal wellbores (e.g., massive shales) can be significantly different than those typically fractured via vertical wellbores (e.g., sandstones and carbonates). For example, horizontal maximum and minimum in situ stress differentials in shales may not be as great as they are in sandstones or carbonates, or the fissure patterns may be significantly different, ductility varies. There are several possibilities causing the differences. Also, knowledge of vertically layered formation data profiles is more difficult to ascertain via horizontal wellbores. Regardless, the basic principles governing fracture propagation do not change. As fractures propagate beyond the wellbore, far-field conditions and properties control their behavior.

Hydraulic Fracturing Studies with a Quasi Three-Dimensional Rock Mechanics (Q-3D-RM) Spreadsheet Model Prior discussion focused primarily on the qualitative and quantitative effects of individual mechanical rock properties, in situ stress, and pore pressure pertinent to fracture width and height growth. What follows are examples of the types of fracture behavior perspectives that design engineers can obtain by using a quasi three-dimensional rock mechanics (Q-3D-RM) spreadsheet model. This type of model uses prescribed wellbore injection pressure as a base reference. Specified retained friction gradient (retained-ΔPƒΔXƒ) profiles simulate the combined effects of fluid viscosity and injection rate on in-fracture pressure profiles from the wellbore to the fracture tip. What is presented here demonstrates a few of the types of scenario studies that can be done relatively quickly with such an approach. Appendix A addresses algorithms for readily calculating fracture vertical height growth into upper and lower bounding intervals. These are based on data shown in figure 3–22 (reference SPE Monograph V. 12, Figures 3.17 and 3.18, p. 70) and figure 3–23. The underlying theory behind the curves in these figures is integral to many sophisticated commercial hydraulic fracturing design models. The approach in appendix A provides a relatively quick and simple way of using a spreadsheet to calculate vertical growth caused by in-fracture pressure. The Q-3D-RM model is described in appendix B. This includes pertinent equations, algorithms, composition and structure of the model, and sufficient descriptive detail for design engineers, if they wish, to build such a model for their own use. It also contains templates, tables, and some calculated results applicable to the graphical displays for the case examples shown 179

Essentials of Hydraulic Fracturing

here. Design engineers who wish to create their own model will find instructions for doing so in appendixes A and B. Having a Q-3D-RM type of model at their fingertips gives design engineers the ability to quickly and interactively scope a wide variety of the many parameters pertinent to fracturing behavior. The examples below yield perspectives of the types of information that can be studied. They also show the combined effects of rock mechanical properties, in situ stresses, fluid flow resistance, etc., on fracturing propagation behavior.

Examples of fracturing behavior scenario studies using a Q-3D-RM spreadsheet model For these examples figure 3–38 depicts the conceptual interval layering, i.e., three intervals with unique properties, and an in-fracture pressure that is the same across all intervals. Interval numbers are consistent with those shown in figure 3–23, and presented in appendices A and B. In the discussion here they are referred to according to their relative depths as follows: interval 3—upper, interval 1—middle PAY, interval 2—lower.

Interval 3: Pe3, ν3, σ3, E3, KIC3 ► ◄ Pƒ Interval 1: Pe1, ν1, σ1, E1 ► ◄ Pƒ Fracture Pressure Interval 2: Pe2, ν2, σ2, E2, KIC2 ► ◄ Pƒ Fig. 3–38. Q-3D-RM model interval layering Table 3–15 contains the input “base case” data for the Q-3D-RM spreadsheet model examples that follow. The examples show propagation behavior, and the degree of effects that deviations from base case fracture treatment design parameter values can have on that behavior. The base case data comprises a 1,000-ft-long fracture in a 100-ft-thick formation at 8,000 ft depth, with different rock mechanical properties and in situ stresses in each of the three intervals. The 4,400 psi in situ stress in the middle PAY interval dictates the 4,400 psi in-fracture pressure at the fracture extremity. The specified wellbore injection pressure of 5,100 psi is maintained throughout the treatment duration. The retained ΔPƒ/Xƒ values in each segment are estimates of what might typically occur from fluid temperature and time exposure and fluid-loss effects throughout the fracture. Fluid viscosity typically declines because of temperature increase in the first one-half of the fracture, then remains essentially constant for a while, and finally degrades rapidly near the fracture extremity because of time exposure. The retained-ΔPƒ/Xƒ profile in table 3–15 does not change. It applies whether the total fracture length is 100, 500, or 1,000 ft. A fracturing fluid efficiency (i.e., the ratio of created fracture physical volume to total slurry injected volume) of 20%, is considered reasonable for a 1,000 ft long fracture.

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Table 3–15. Base case fracture design data

Example 3–13. Fracture Progression with Continued Injection Figure 3–39 shows width cross-sections at the wellbore and fracture height versus length profiles at 300, 600, 800, and 1,000 ft as the fracture progresses with continued injection. The legend shows the associated well injection pressures and injection volumes at each length. Notice that the height versus length profile is “trumpet-shaped” as shown in figure 3–26. This is consistent with portrayals for gridded three-dimensional (G-3D) higher-end models, as opposed to the “bullet-shaped” profiles shown in figure 3–8 that are often exhibited by some three-dimensional fracturing (P-3D) simulator models. Also notice (1) the vertical asymmetry where upward fracture growth is more pronounced than downward growth because the in situ stress in the lower interval exceeds that of the upper interval by 400 psi, (2) the in situ stress profile significantly affects fracture width cross-section configuration, (3) fracture height does not begin to increase until the fracture length exceeds approximately 500 to 600 ft, (4) as the fracture approaches 900 to 1,000 ft, fracture width growth at the wellbore accelerates, and (5) as shown in the legend, the degree of difference in the wellbore injection pressures and injection volumes at the different fracture lengths, (i.e., at Xƒ = 300 ft, PƒWELL = 4,610 psi, VINJ = 11 Mgal; as the fracture progresses to Xƒ = 1,000 ft, wellbore injection pressure (PƒW) increases to 5,100 psi, and VINJ = 128 Mgal).

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Width @ Well vs. Depth 7,900 (4)

7,950 Vertical Depth (feet)

Vertical Depth (feet)

7,950

(3)

7,975 8,000 8,025 (1)

(2)

Width (inches)

(1)

8,050

8,100 0.3

VƒINJ: 11 Mgal VƒINJ: 44 Mgal VƒINJ: 79 Mgal VƒINJ: 128 Mgal

8,025

8,100 0.1

Pƒ: 4,610 psi, Pƒ: 4,820 psi, Pƒ: 4,960 psi, Pƒ: 5,100 psi,

8,000

8,075

–0.1

@ Xƒ = 300 ft, @ Xƒ = 600 ft, @ Xƒ = 800 ft, @ Xƒ = 1,000 ft,

7,975

8,075

8,125 –0.3

(1) (2) (3) (4)

7,925

7,925

8,050

Fracture Vertical vs. Horizontal Profile

7,900

8,125

(2)

(3)

(4)

Sand Pay

0

200

400

600

800

1,000

Horizontal Distance from the Wellbore (feet)

Fig. 3–39. Wellbore fracture width and height versus length profiles as the fracture length increases with continued injection

Animated fracture progression displays Once algorithms and chart displays for calculations pertinent to figure 3–39 have been developed, spreadsheet macros can be readily constructed to display animated fracture progressions. This provides design engineers a convenient tool to enlighten, and possibly amuse, their colleagues, managers, clients, students, etc., about progressing fracture propagation behavior.

Example 3–14. Fracture Profiles at Different Well Injection Pressures Figure 3–40 shows (1) width cross-sections at the wellbore and (2) fracture height versus length profiles after the fracture has reached a total length of 1,000 ft for well injection pressures of 150 psi above and below the 5,100 psi. Wellbore injection pressures relate primarily to injection rate fracturing fluid viscosity where perforation and/or near-wellbore restrictions are minimal. Here, there are no perforation friction, nor near wellbore restrictions. Hence, the fracture behavior is related to only viscosity. The legend shows the associated injection pressures and injection volumes. Notice that (1) fracture height growth predominantly occurs within 100 to 200 ft from the wellbore; beyond that it is essentially confined to the middle PAY interval; (2) as wellbore injection pressures approach the upper interval 5,375 psi in situ stress, height growth accelerates; and (3) relatively small injection pressure increases result in relatively large injection volume requirements, i.e., at PƒWELL = 4,950 psi, VINJ = 96 Mgal; whereas, at PƒWELL = 5,250 psi, VINJ = 160.8 Mgal.

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Width @ Well vs. Depth 7,850

7,850

(1)

Vertical Depth (feet)

Vertical Depth (feet)

(2)

8,000 (3)

8,050 8,100 8,150 -0.3

Rock Mechanics and Fracture Propagation

Fracture Vertical vs. Horizontal Profile

7,900 7,950

|

7,900

(1)

7,950

(2)

(1) @ Pƒ: 5,100 psi, VƒINJ: 128 Mgal (2) @ Pƒ: 5,250 psi, VƒINJ: 178 Mgal (3) @ Pƒ: 4,950 psi, VƒINJ: 96 Mgal

(3)

8,000

Sand Pay

8,050 8,100 8,150

-0.1 0.1 0.3 Width (inches)

0

200 400 600 800 Horizontal Distance from the Wellbore (feet)

1,000

Fig. 3–40. The effect of wellbore injection pressure on wellbore fracture width and height profiles versus length profiles

Example 3–15. Three Scenarios of Mechanical Rock Property Effects on Fracture Propagation Behavior and Injection Volume Requirements

Figure 3–41 depicts the comparative effects of deviations from the base case in mechanical rock properties on wellbore width profiles for Poisson’s ratio, ν, elastic modulus, E, and stress intensity factor, KIC . Wellbore height and width profiles yield some perspectives about fracture geometry that governs injection volume requirements. In each scenario, only one parameter is changed at a time. The other parameter values remain as shown in table 3–15. Width @ Well vs. Depth

Width @ Well vs. Depth 7,850 (1)

(1) ν3 = 0.24 (2) ν3 = 0.26 (3) ν3 = 0.28

8,000

(2)

(3)

8,050

7,850 (1) Kic3 =

0, KIC2 =

0

(2) Kic3 = 1,000, KIC2 = 500 (3) Kic3 = 4,000, KIC2 = 2,000

7,900 Vertical Depth (feet)

7,950

(1) E3 = 4, E1 = 3 (2) E3 = 5, E1 = 4 (3) E3 = 6, E1 = 5

7,900 Vertical Depth (feet)

Vertical Depth (feet)

7,900

7,850

Width @ Well vs. Depth

7,950 (1)

8,000 (2)

8,050

7,950 8,000

(2)

(1)

(3)

8,050

(3)

8,100

8,100

8,150 -0.3

8,150 -0.3

-0.1 0.1 Width (inches)

0.3

8,100

-0.1 0.1 Width (inches)

0.3

8,150 -0.3

-0.1 0.1 Width (inches)

0.3

Fig. 3–41. Rock property effects on wellbore fracture width. Left: Poisson’s ratio; middle: elastic modulus; right: stress intensity factor.

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Essentials of Hydraulic Fracturing

Poisson’s ratio, ν This relates to the left chart in figure 3–41, where only the upper interval Poisson’s ratio, ν3, is changed. The changes are relatively small in value, i.e., ±0.02 units. An increase in ν3 from 0.26 to 0.28 causes an increase in situ stress, σ3, from 5,375 to 5,575 psi. This reduces both wellbore fracture width and height in the upper interval. However, it reduces injection volume requirements by less than 3 Mgal. A decrease in ν3 from 0.26 to 0.24 decreases upper interval in situ stress to a value of 5187 psi, which allows the fracture to grow vertically 150 ft. Injection volume requirements are increased by 14 Mgal. However, the major issue is that the fracture confining stress (5,187 psi) is only 87 psi above injection pressure. Further decreases in upper interval Poisson’s ratio would drop in situ stress levels below injection pressure, causing unstable vertical upward growth. Thus, a design engineer must ensure that Poisson’s ratio values used for design accurately reflect resident in situ values.

Elastic modulus, E The middle chart in figure 3–41 shows the effects of changed elastic modulus values in both the upper and middle PAY intervals. Here, modulus is changed by ±1 MMpsi in both intervals. Current theoretical approaches for calculating fracture height growth suggest that elastic modulus is not a major fracture height factor, especially for modulus ratios (confining/fracturing interval) less than 3. However, modulus plays a major role in fracture width, which in turn, affects fracture volume. A decrease of 1 MMpsi in both E3 and E1, results in an increase to injection volume requirements by 40 Mgal. Whereas, a modulus increase of 1 MMpsi reduces injection volume requirements by 22 Mgal. However, a 128 Mgal treatment that was designed to create a 1,000 ft fracture for E3 = 5 and E1 = 4 MMpsi where the true formation values are 1 MMpsi lower would result in a total fracture length (Xƒ) of only 700 ft. This may significantly affect post-treatment production. As with Poisson’s ratio values, accurate mechanical rock property data that reflect in situ values is essential to fracture treatment design.

Stress intensity factor, KIC (fracture toughness) As can be seen in the chart on the right of figure 3–41, stress intensity factor values do not significantly affect this particular case. Significant KIC changes in both the upper and middle PAY intervals (i.e., factors of four on the high side and zero values on the low) resulted in minimal effects on wellbore fracture width or height. The same held true for injection volume requirements. However, in cases where fracture confinement by virtue of in situ stress differentials between intervals is not of the magnitude in this example, stress intensity factor may play a more 184

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significant role. Hence, KIC scenarios should be include in all fracture designs to determine if it is important to the design

Example 3–16. Fracturing Fluid Rheology, Fluid Loss, Fracture Penetration, and Proppant Transport Scenarios

Even though the following discussion is preliminary to what is contained in chapters 5, 6, and 7, it is presented here to demonstrate the utility of a Q-3D-RM model. The interaction of rheology, fluid loss, and proppant transport with rock properties and in situ stresses is integral to fracture treatment design. As previously discussed, fracturing fluid apparent viscosity typically changes because of many factors as the fluid progresses toward the fracture tip. Fluid degradation and the effects of fluid loss and proppant concentration dictate these changes. This example compares the results of two cases where fluid performance deviates from expected behavior. Rock mechanical properties and in situ stresses are those listed in table 3–15. The left chart in figure 3–42 shows the different retained-ΔPƒ/Xƒ input data profile for each case. Retained-ΔPƒ/Xƒ at any point along the fracture between the wellbore and the fracture tip is represented as a percentage of the friction gradient ΔPƒ/Xƒ that prevails at the wellbore. It corresponds to a percentage of the effective viscosity of a fluid entering the fracture at the injection point. Case 1 applies where the effective fluid behavior is below expectations. Viscosity is lower than indicated from laboratory data, and fluid loss is significantly more pronounced. Case 2 is for a fluid where viscosity meets expectations, but encounters unexpectedly high fluid loss. This fluid loss increases both thickening agent concentration and proppant concentration that, in concert, cause an increase in viscosity. 100%

In-Fracture Pressure Pƒ, psi

80% % Retained ΔPƒ/ΔXƒ

5,050

Base Case Case 1 Case 2

60%

40%

20%

0%

Base Case Case 1 Case 2

4,950 4,850 4,750 4,650 4,550 4,450 4,350

0

0.2

0.4

0.6

0.8

Relative Fracture Point, X/Xƒ

1

0

0.2

0.4

0.6

0.8

1

Relative Fracture Point, X/Xƒ

Fig. 3–42. Retained ΔPƒ/ΔXƒ and in-fracture pressure, Pƒ, versus relative fracture point: Base Case, Case 1, and Case 2

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Essentials of Hydraulic Fracturing

The right chart reflects the resulting fracturing pressures at points in the fracture relative to total fracture length. Under these conditions total fracture lengths differ from case to case because of the different friction gradient profiles. These differences cause different fracture segment pressures, and thus different segment widths, heights and volumes. Base Case total fracture length is 1,000 ft. For Case 1 it is 950 ft. Case 2 has a much shorter total length, i.e., 510 ft, because of the high leakoff. Also, the lower fluid efficiency of Cases 1 and 2 (12% versus Base Case 20%) affects the final results. Table 3–16 contains the comparative case data. Note the significantly different segment pressures between the cases in segments 5 through 10. Here, these differences imply different fracture widths, heights, and volumes for each segment. Table 3–16. Example 3–18 Base Case, Case 1, and Case 2 results summary: segment mid-point distance from the well, retained-ΔPƒ/ΔXƒ, ΔPƒ/ΔXƒ value, Pƒ and fracturing fluid efficiency

The example is predicated on maintaining identical injection volumes (122 Mgal) and well injection pressures (5,100 psi) for each case. This requires a double-parameter-back-solving (Excel’s Goal Seek) approach. Here, fracture length is iterated until injection pressure is satisfied; then, iterated again until injection volumes match. Repetitive double-parameter-back-solving procedures are required until both injection pressure and volume match Base Case values. Figure 3–43 shows (a) the fracture length and height profile, and (b) proppant transport width limits for a 12/18 mesh size proppant in each of the three example cases. The solid and dashed curves in figure 3–43 represent vertical and horizontal fracture extent. The circular dots represent points in the fracture where width is less than 0.13 inches, and thus vertical or horizontal proppant transport beyond those points because the fracture width decreases. For all cases, the proppant would vertically span the entire net pay. Achieved fracture heights are essentially the same for all cases. However, fracture lengths and proppant transport width limits are not. 186

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Fracture Edges and Proppant Limits: Vertical vs. Horizontal Profiles 7,900

Proppant Limits (P-B) Base Case (P-1) Case 1 (P-2) Case 2

7,925 Vertical Depth (feet)

7,950 7,975

Fracture Edges [F-B] Base Case [F-1] Case 1 [F-2] Case 2 [F-2]

8,000 8,025

(P-1)

8,050

[F-1]

[F-B]

(P-B)

Sand Pay

(P-2)

8,075 8,100 8,125 0

200

400

600

800

1,000

Horizontal Distance from the Wellbore (feet)

Fig. 3–43. Fracture height-length and proppant limit profiles Proppant transport limits were specified as the point in the fracture where fracture width is less than 2.5 times the largest diameter (DPROP-MAX) particle in the proppant mixture. The factor 2.5 is an arbitrary rule-of-thumb value that depends on, among other things, proppant mesh size. The 2.5 factor is a reasonable value for this example. For a 12/18 mesh proppant, DPROP-MAX = 0.052 inches, which yields a proppant transport width limit, WƒPROP-LIM = 0.13 inches. Obviously, the Base Case offers the more desirable total fracture length. However, proppant transport is limited to about 650 ft. The Case 1 fracture extends horizontally to 950 ft, but beyond 400 ft the fracture width is too narrow to transport 12/18 mesh proppant much beyond about 400 ft. For Case 2, the fracture length is only a little over 500 ft, but because the in-fracture pressure is relatively high near the fracture tip, the 12/18 mesh proppant can be transported to about 400 ft. Obviously, the Base Case fluid would yield a more effectively propped fracture length than either the poorly performing Case 1 fluid or the Case 2 event where the fluid encounters high fluid-loss zones during fracture propagation.

Q-3D-RM spreadsheet model utility Examples 3–13 through 3–16 show only a few of the many scenario studies possible by using a Q-3D-RM spreadsheet model. Even though such a model is not as sophisticated as many commercial gridded or pseudo-three-dimensional models, it contains well-established fracture design theory and equations. The model provides qualitative—and possibly quantitative— perspectives of different outcomes resulting from changing different design parameters. This allows design engineers to quickly and interactively investigate, among other things: • which design parameters require high degrees of accuracy 187

Essentials of Hydraulic Fracturing

• wellbore injection pressure limits that keep vertical fracture growth within desired limits • injection volume requirements for effectively propped fracture penetration • what types of fluids potentially offer the more desired propagation behavior • what proppant mesh sizes provide the more effectively propped fracture These types of spreadsheet models can be constructed according to the design engineer’s preferences and needs. Templates, figures, and tables can be developed accordingly. Macro activated animated fracture growth progressions can be displayed. Case design data can be stored for quick import to input data templates. Hence, design engineers are encouraged to develop their own Q-3D-RM model.

Summary of Data Acquisition Pertinent to Mechanical Rock Properties, In Situ Stresses, and Net Fracturing Pressures As discussed in this chapter, the values of elastic modulus, Poisson’s ratio, and in situ stress for all layers of rock that are affecting the fracture propagation are essential to computing fracture widths, lengths, heights, and volumes in treatment design. The best available data possible should be obtained. Hence, design engineers should specify that acoustic wave train logs be run on all exploratory and development wells that are potential fracture treatment candidates until sufficient data has been developed to adequately describe in situ stress profiles, (in situ stress versus depth) for candidate formations.

Possible data sources for mechanical rock properties • Standard sonic, acoustic wave train (p-wave, s-wave) logs • Websites for rock properties (U.S. government and university laboratories, etc.) • Fracturing service companies • Industry consortiums • Estimates from data base information for similar rock types • Table 31 and Table 32, SPE Monograph V. 12 • Laboratory tests on cores from candidate or nearby wells These provide helpful insight into how rock mechanical properties, in situ stresses, and net fracturing pressures interact in fracture geometry propagation behavior.

Procedures for data acquisition There are numerous ways of determining in situ stress in subsurface formations. Some, such as calculations from lithology, provide only an inference. Others, such as microfrac tests, yield very 188

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reliable data. The methods or data sources for determining or inferring in situ stress and stress profiles include those primarily applicable over multiple intervals, but also to single intervals: • Microfrac pump-in and shut-in pressure tests through casing perforations over multiple relatively small intervals that are mechanically isolated • Calculations from openhole, wireline, and acoustic wave train surveys (compressional and shear wave velocity logs, etc.) • Calculations of an inferred profile from lithology and rock properties • Minifrac breakdown, shut-in pressure decline, tests, through casing perforations; either total interval, or over small or large intervals that are isolated mechanically • Minifrace pump-in and flowback through casing perforations, either total interval, or over small or large intervals that are isolated mechanically • Openhole instrumented borehole pressure and deformation-response tests • Openhole, isolated interval (with openhole expandable straddle packers) formation breakdown tests • Openhole mechanical (or sonic) borehole ellipticity measurements during drilling or completion operations prior to setting casing • Openhole, bottomhole, packed off (drill stem test) fracturing, followed by oriented coring of the fractured formation below • Pumping step rate injection formation pressure parting tests through casing perforations • Instantaneous shut-in pressures observed during initial breakdown pumping operations of a fracturing treatment • Casing shoe breakdown tests during drilling operations • Databases on fields of similar lithology

Methods for obtaining bottomhole pressure data during testing • Wireline downhole pressure gages • Retrievable downhole pressure gages • Downhole interval isolation methods • Dead string or casing annulus surface readout

Methods for analyzing pressure or pressure versus time data • Pumping pressure versus time/volume plots • Nolte-Smith plots • Shut-in and pressure decline tests • Microfrac or minifrac calibration tests

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Essentials of Hydraulic Fracturing

References to comprehensive full-scale field research programs • Department of Energy (DOE): Multi-Well Experiment (MWX), Piceance Basin, Rifle, Colorado • Gas Research Institute: Staged Field Experiments Nos. 1–4, Cotton Valley and Travis Peak formations, East Texas

Methods for developing in situ stress profiles • Calculation of an inferred profile with equation 3–12, using formation layer thicknesses, porosities, rock densities, pore fluid densities, Poisson’s ratios, and pore pressures • Measured stress from acoustic wave train surveys (over the entire well or only from selected intervals) • Stresses from minifrac or microfrac tests • Credible correlations between measured and sonic log calculated values

Cautions about step-rate, pump-in, flowback, instantaneous shut-in, and other data sources Step-rate tests and pump-in and flowback tests have the danger of unreliable precision. Shut-in pressure decline tests at the end of a fracturing treatment are affected by the proppant pack in the fracture. These mask the true closure stress value. Instantaneous shut-in pressures observed during initial breakdown pumping operations of a fracturing treatment or at the end of a treatment reflect the pressure of an open rather than a closed fracture. Openhole, isolated interval (with openhole expandable straddle-packers) formation breakdown tests are often masked by the expandable straddle-packers creating near-wellbore fractures during setting. Openhole, bottomhole, packed-off (drill stem test) fracturing, followed by oriented coring of the fractured formation below can yield fracture azimuth information. If the azimuths of the fractures throughout a core are predominantly all in the same direction, there is some comfort that this reflects the general azimuthal directions of the major and minimum principal stresses.

Exercises Exercise 3–1 Given the following data for a shale reservoir, • bulk density: 2.3 g/cc • compressional travel time: 95 μsec/ft • shear travel time: 190 μsec/ft • overburden pressure: 1.1 psi/ft • pore pressure: 0.45 psi/ft 190

• tectonic gradient: 0.1 psi/ft

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Compute the following values: (1) Poisson's ratio, (2) shear modulus, (3) Young's modulus, (4) bulk modulus, and (5) minimum horizontal stress gradient.

Exercise 3–2 Rock properties calculations Given:

Compressional-wave velocity

= 13,150 ft/sec



Shear-wave velocity

= 8,200 ft/sec



Bulk density

= 2.44 g/cc



Overburden stress gradient

= 1.05 psi/ft



Average depth of formation

= 10,000 ft



Reservoir pressure

= 5,000 psi



Biot’s constant

=1

Compute the following mechanical properties for this formation: (1) minimum in situ stress, (2) Young's modulus, (3) Poisson's ratio, (4) shear modulus, and (5) bulk modulus.

Exercise 3–3 A well is drilled in a complex, layered formation. The following data were obtained from the well logs.

(g/cc)

ρb

∆tc (μsec/ft)

∆ts (μsec/ft)

Shale

2.30

95

190

8,200–8,250

Siltstone

2.51

70

119

3

8,250–8,290

Sandstone

2.42

76

122

4

8,290–8,310

Shale

2.30

95

190

5

8,310–8,400

Sandstone

2.42

76

122

6

8,400–8,600

Siltstone

2.51

70

119

7

8,600–8,800

Shale

2.30

95

190

Depth (ft)

Lithology

1

8,000–8,200

2

Zone

Assume that the overburden stress gradient is 1.0 psi/ft and the average reservoir pressure gradient in all layers is 0.5 psi/ft. Compute the least principal horizontal stress (omin) gradient using the poro-elastic equation. Also compute the stress in each layer based upon the midpoint depth of each layer. After you have computed the stresses, also compute the values of Young’s modulus, E, and shear modulus, G, for each layer. 191

Essentials of Hydraulic Fracturing

After computing the stresses using only log data, a series of in situ stress tests were pumped in Zones 5, 6, and 7. The following pressure data were measured during the pressure falloff portion of the stress tests.

Time (sec)

Zone 5 Pressures

Zone 6 Pressures

Zone 7 Pressures

0

6,200

6,800

7,050

1

6,000

6,600

7,000

2

5,920

6,525

6,990

3

5,855

6,465

6,980

4

5,800

6,405

6,970

5

5,735

6,360

6,950

7

5,670

6,295

6,935

9

5,600

6,220

6,920

11

5,535

6,165

6,910

15

5,420

6,075

6,900

20

5,300

5,950

6,875

25

5,160

5,850

6,850

30

5,050

5,705

6,835

45

4,700

5,225

6,515

60

4,440

4,895

6,150

Graph the pressure falloff data and determine the fracture closure stress and fracture closure time for zones 5, 6, and 7. Use these results to adjust the stresses in all seven layers.

Exercise 3–4 The (a or b?) model implicitly assumes that the fracture height is relatively large compared with its length, while the (a or b?) model implicitly assumes that the fracture length is the infinite dimension. (Insert a and b as applicable.) a) GdK/PKN b) PKN/GdK

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Exercise 3–5 Nolte-Smith Graph, Figure 3–20 In Situ Stress Tests

7,500 7,000

Pressure

6,500 6,000 5,500 5,000 Zone 5 Zone 6 Zone 7

4,500 4,000

0.0

1.0

1.4

1.7

2.0

2.2

2.6

3.0

3.3

3.9

4.5

5.0

5.5

6.7

7.7

SQRT Time

In the Nolte-Smith paper “Interpretation of Fracturing Pressures,” JPT, 1981, they described four fracture growth modes. Briefly answer the following questions about that paper (25 words or fewer for each answer). a) What is the significance of Mode I growth? b) What are the two main reasons that lead to Mode II growth? c) What is the main cause of Mode III growth? d) What is the main cause of Mode IV growth?

Exercise 3–6 This following graph shows the bottomhole pressure (BHP) that was recorded during a minifracture test in Well A that was conducted prior to a fracturing treatment.

193

Essentials of Hydraulic Fracturing

P1

BHP, psi

P2

P5

P3 P4

Time 1. Select the correct answer. The objective of the mini-fracture test is to estimate: a) In situ leak-off and closure pressure b) Permeability and porosity c) Water saturation and lithology d) Shale volume 2. Define the pressure points P1, . . ., P5 in the figure above.

Exercise 3–7 Fracture Orientation Prior to pumping a fracture treatment, an openhole logging suite was run that included an induction, density, neutron, gamma ray, four-arm caliper, and inclinometer. The interval to be perforated was from 8,853 ft to 8,887 ft. Integration of the density log from surface to 8,853 ft showed an overburden of 9,023 psi. The caliper showed borehole breakout in the north-south axis of the hole. The minimum horizontal stress at 8,870 ft was measured to be 5,132 psi. What is the most probable initial orientation of a hydraulic fracture in the described zone? a) Vertical and in the north-south direction b) Vertical and in the east-west direction c) Horizontal and in the north-south direction d) Horizontal and in the east-west direction e) Not enough information is provided

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Nomenclature Symbol

Units/Value

Description

English Cb Cν

1/psi dim.

DƒMODEL DƒGdK DƒPKN E G Hƒ Hs/h K Pe PEDGE

ft ft ft MMpsi MMpsi ft dim.

Pƒ PNET QINJ Rb

psi psi bbl/min dimensionless

Sef ΔtC ΔtC-MATRIX

104 ergs/cm2 micro-secs/ft micro-secs/ft

ΔtC-MEASURED ΔtC-SHALE ΔtS ΔtS-EST Tƒ VC Vƒ VS Wƒ Xƒ

micro-secs/ft micro-secs/ft micro-secs/ft micro-secs/ft psi-√in. ft/sec ft3 ft/sec in. ft

Bulk compressibility Poisson’s overburden to horizontal stress transfer = ν/(1 – ν) Model fracture dimension (depending on PKN or GdK) GdK geometry fracture penetration = Xƒ PKN geometry fracture height = Hƒ Elastic modulus Shear modulus Fracture vertical height Relative fracture height Bulk modulus Reservoir pressure Magnitude of pressure growth resistance at the fracture edge In-fracture pressure during injection Net fracturing pressure = Pƒ – σMIN Fracturing injection rate Compressional-wave/shear-wave velocity ratio Shear-wave/compressional-wave travel time ratio Rock surface energy Sonic compressional wave arrival time Computed matrix compressional wave travel time from laboratory data Measured compressional wave travel time Compressional wave travel time in adjacent shales Sonic shear wave arrival time Estimated shear wave travel time Fracture toughness Sonic compressional wave velocity = 106/ΔtC Fracture volume Sonic shear wave velocity = 106/ΔtS Fracture width (in.) Fracture penetration (half-length)

dim. dim. lbm/ft3

Relative stress (σ2 – Pƒ)/(σ2 – σ1) Poisson’s ratio (dim.) Rock and fluid combined bulk density

psi psi

Greek Δσƒ/Δσ ν ρBULK

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Essentials of Hydraulic Fracturing

Symbol

Units/Value

σ1 σ2 σMIN σT

psi psi psi psi

σVToi φ µAPP

psi fraction cp

Description In situ stress in fracture interval In situ stress in upper and lower bounding layers Minimum principal stress Far-field stresses (psi): Effects of far-field faults, mountains, etc. Overburden vertical stress at the interval top Porosity Fracturing fluid apparent viscosity

Constants CMODEL CGdK CPKN g α π

10–5

4.8 × 2.4 × 10–5 32.2 ft/sec2 Biot’s const. Pi const.

Conversion constant (depending on PKN or GdK) Conversion constant, GdK Conversion constant, PKN Gravitational acceleration α ~ 0.7; for fracture design typically α = 1.0) 3.14159263

References Craft, B. C., and M. F. Hawkins. 1991. “Figure 3.16.” In Applied Petroleum Reservoir Engineering, 132. Englewood Cliffs, NJ: Prentice Hall, Inc. Gidley, John L., Stephen A. Holditch, Dale E. Nierode, and Ralph W. Veatch, eds. 1989. “Figure 1.13.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 4. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.14.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 5. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.15,” “Figure 1.16.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 5, 6. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.17.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 6. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.19.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 7. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.20” and “Figure 1.21.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 8. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.21,” “Figure 1.22,” and “Figure 1.23.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 8, 9. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.58” and “Figure 1.59.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 25, 26. Richardson, TX: Society of Petroleum Engineers. 196

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———. 1989. “Figure 2.7.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 44. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 3.2” and “Figure 3.3.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 59. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 3.10.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 62. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 3.11.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 63. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 3.13.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 67. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Equation 3.42” and “Equation 3.44.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 68. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 3.17.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 70. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 3.18.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 70. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 3.20.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 71. Richardson, TX: Society of Petroleum Engineers. Hall, Howard N. 1953. “Compressibility of Reservoir Rocks.” Journal of Petroleum Technology 5:17–19. Halliburton Co. 1986. “Figure 1.2.” In The fracbook II: Design/data manual for hydraulic fracturing, 13. Duncan, OK: Halliburton Services.

197

4 Fracturing Fluid Systems Fracturing fluid systems refers to the entire mixture of base fluids plus all its additives that are pumped into a well during a hydraulic fracturing treatment. These systems have the following basic purposes: • To drive a hydraulic wedge into a formation so as to create, widen, and extend a fracture by forcing subsurface formation intervals to part • To transport and distribute proppants in that fracture so that when fluid injection has stopped and the fracture closes on the proppant, a permeable pack remains as a conductive path for the broken fracture fluid, such that reservoir fluids are able to flow from the formation into the fracture and then to the wellbore. Fracturing fluid systems have continually emerged and evolved throughout hydraulic fracturing history, and this evolution will continue in the future. These systems consist of a base fluid plus performance enhancing additives. Typically, the base fluids that can be chosen are • Aqueous liquids (fresh water or brine) • Non-aqueous liquids (hydrocarbons, liquefied CO2) • Liquid/liquid emulsions—(aqueous/hydrocarbon) • Liquid/gas foams—(liquids foamed with air, CO2, or N2 gas) All of these fluid systems must be tailored for the specific situation concerning reservoir temperature, pressure, pumping time, shear while flowing in the fracture, and contact with formation minerals. Additionally, their viscosity must break (reduce to a lower value) at a prescribed time so that after injection ceases they will flow back to the wellbore (cleanup) and leave the injected proppant in the fracture. Additives serve a plethora of fluid system performance-enhancing functions, not only tailored for the reservoir but also to protect the well completion equipment from corrosion and erosion. Primary additives create a fluid system that provides adequate viscosity to create fracture width and transport the proppant down the fracture, while concurrently exhibiting minimal fluid loss (leakoff ) to the formation. Supplementary additives address specific aspects (e.g., bacteria 199

Essentials of Hydraulic Fracturing

growth, formation damage, pipe friction, temperature corrosion, adverse reactions with formation minerals) pertinent to in situ conditions and target formations. Every fracturing pumping service company has its own fluid system formulations, and along with each, a trademarked name. Some formulations are essentially identical across the industry. Different trademarked names identify each service company’s products, even though the some of the formulations are common throughout the industry. Most service companies offer their own trade secrets, but few if any trade secrets really give any one company much of a competitive advantage outside of marketing. As patents and licenses expire, especially for high performance products, those products are quickly adopted industry-wide. Incremental changes in both base fluids and additives are constantly occurring. New and improved products continually emerge, while some existing ones may disappear. Some that disappear re-emerge with improvements. For example, in the 1950s, oil-based fluids were commonly used. In the 1960s, many treatments were essentially water fracture treatments, using water with only a friction reducer and possibly one or two additives (potassium chloride and a bacteria). Water fracture treatments were phased out in favor of gel-thickened fluids. In the 1970s, crosslinked fluids or foam fracture fluids were commonly used. However, in the 2010s, water fracture treatments have made a comeback and are used in many treatments for deep, low-permeability shale reservoirs. Both the physical and chemical properties of additives also change as technology improves. For example, the industry has moved from powdered additives to liquid concentrates. There are also new or improved gelling agents introduced to the industry regularly. Because of these dynamics, what is presented here cannot forecast new product availability a year from the date these pages are viewed. The same may hold for product manufacturers and pumping service companies, or their identities. This book describes generic fluid systems with the goal of helping design engineers choose the most appropriate system for their wells. To decide the exact fluid and combination of additives, design engineers should work closely with their service company engineers to determine the appropriate fluid system and pumping schedule. It is important that design engineers know what additives are being recommended, exactly what each additive is supposed to do, and determine if each additive is really necessary. Most fracturing products are derived from natural materials. Service companies will often obtain some basic products, raw materials, or certain chemicals from common suppliers. However, each major service company has repositories of common or trade secret formulations or processing refinements. Figure 4–1 shows the evolution of a fracturing fluid system from the beginning. It began with gasoline, thickened with napalm gel (in the center), then grew to early aqueous systems, and now continues to environmentally green fluids. The circularity implies emerging, diminishing, and possibly re-emerging popular use over fracturing history.

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Fig. 4–1. The circular world of emerging and re-emerging fracturing fluid systems Also, new additives have been developed to improve overall fluid system performance. As previously stated, the menu shown in figure 4–1 and material lists contained there will add new items as time progresses. Thus, keeping current on available systems and additives requires continual interaction with pumping service companies and product manufacturers.

Design Engineer and Service Company Engineer Interaction As service companies innovate and compete, they are constantly introducing new fluids and additives. The wide spectrum of fluids may make selecting the appropriate fluids for a treatment a somewhat daunting task. Thus, when doing so, a good approach is to provide the service company with the following: • Information on the reservoir properties of the candidate formation and the layers of rock above and below the target zone (permeability, in situ stress, reservoir pressure, etc.), • Existing downhole conditions and the number of rock layers and formation types that will affect fracture growth (depth, temperature, etc.), • Proposed or existing wellbore configurations, • How many stages will be required, • If applicable, how the injection will be diverted for multiple intervals, and • Expected effective propped fracture penetration and fracture conductivity. Once the service company receives and considers the required information, the design engineer should request that the service company propose the fracturing fluid system(s) that best applies. However, the design engineer is ultimately responsible for knowing how fluid systems behave pertinent to a fracturing candidate well, and the potential effects that the target formation 201

Essentials of Hydraulic Fracturing

characteristics have on fluid system behavior. As such, both the service company engineer and the design engineer should eventually come to a consensus on the fluids and additives needed for a specific treatment. The discussion here provides, in a general sense, insight about • Base fluids and total fluid system (i.e., base fluid plus additives) components • Behavior(s) of various types of fluids and additives • Factors that affect the behavior of the fluids • The degrees of how they do so Hopefully this chapter will serve as guidance for design engineers to interact with service companies to select the appropriate fracturing fluid system for the candidate fracturing formation. Awareness of behavior(s) is essential to this. It serves as the basis for questions to ask, things to point out, etc., that are associated with service company proposals.

Fracturing Fluid System Requirements A fracture fluid system that is acceptable for a given treatment should be able to do the following: • Create a fracture and drive a hydraulic wedge to force the target formation to part so that the fracture is wide enough to allow for transport of proppants along the fracture, and create the desired fracture conductivity; • Maintain sufficient rheology (i.e., apparent viscosity) throughout the treatment to adequately carry proppants into and along the entire fracture; • Partially seal the fracture walls to minimize fluid loss into the permeable formation and thus maximize fracturing fluid efficiency, i.e., the volume-of-fracture-created/ volume-of-slurry-injected ratio; • Break (i.e., reduce fluid system viscosity) at the end of injection (pumping) to the degree that the broken fluid can flow back through the created fracture and residual proppant pack and into the wellbore, leaving a conductive flow path remaining in the fracture; and • Minimize pumping hydraulic horsepower requirements when flowing down tubulars and throughout the fracture. In hydraulic wedging, for a fracture to extend, fracture width must increase. This happens when the pressure inside the fracture (net pressure) increases, which is due to either friction pressure drop or growth-resistive effects along the fracture edge. Fluid friction pressure drop is the dominant cause. Edge resistance is a secondary phenomenon that occurs by virtue of edge or tip region resistance along the fracture perimeter. Edge resistance, with continued fluid injection, results in fracture ballooning. However, this effect diminishes as fractures enlarge. The two phenomena, friction and edge resistance, in concert constitute forces that generate fracture width. The friction pressure in the fracture always affects the net pressure. Tip effects may or may not be present in a particular reservoir depending on the rock properties. 202

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Selecting a Fracturing Fluid System Considerations for selecting a fracturing fluid system include the following aspects: • Fluid flow rheology effects (here the term “rheology” implies both apparent viscosity and the elastic properties of the fluid) ˡˡ In the tubular goods, and for cased completions, through perforations ˡˡ Along the fracture ˡˡ During proppant transport along the fracture • Fluid loss to the formation • Fracture closure pressure on the injected proppant • Flowback out of the fracture after injection has stopped These considerations require the design engineer to take into account how the in situ conditions (in-situ stress profiles, reservoir pressure, and temperature), formation characteristics (e.g., permeability, mineralogy, fissures, natural fractures, etc.), and exposure time to the fluid, temperature, etc., affect the above aspects.

Fracturing fluid system selection considerations Many factors impact fluid system performance, including • Chemical composition (base fluid, and additives) • Formation temperature • Exposure time in the fracture (during and subsequent to injection) • Shear and turbulence during injection (down tubulars, through perforations, in the fracture) • In-fracture pressure of compressible systems—hydrocarbons, foams, emulsions) • Formation lithology and mineralology • Reservoir fluid composition Detailed discussion of fluid selection considerations is presented in SPE Monograph V. 12, Appendix B, “Selection of Water-, Non-Water-, or Acid-Based Fracturing Fluids” and in many other SPE papers published since SPE Monograph V. 12 was printed. When selecting fracturing fluid systems for a treatment, the following aspects must be considered: • On-site safety involved in preparing and pumping the fluid systems on site (this is the prime consideration all the time but especially when pumping flammable fluids) • Effect of fluid system cost on potential economic returns from the treatment • Logistics involved in preparing the fluid systems on site • Effects of fluid loss to the formation in determining types of fluids, types, and concentrations of fluid loss control agents, treatment volumes, and fluid and proppant staging to achieve the desired effective fracture penetration and conductivity (see chapter 9 for more detailed discussion)

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• Types and volumes of fluids, proppant concentrations, and staging required to effectively transport the desired types and sizes of proppants along the entire fracture to achieve the necessary in situ proppant distribution and the desired fracture conductivity • Potential degree of proppant pack conductivity damage by the gelling agents and fluid loss additives in the fracturing fluid (see chapter 7 for more detailed discussion) • Potential degree of fracturing fluid filtrate damage to formation permeability in the vicinity of the fracture face • Proppant transport behavior down the tubulars, through the perforations and throughout the fracture • Pumping hydraulic horsepower requirements, and tubular or wellhead pressures resulting from fluid or slurry flow down the tubulars and through the perforations • Effects of heat transfer and fluid temperature on fluid effective viscosity, fluid loss, and proppant transport in the fracture to determine the appropriate fluid, gel loading, and fluid or proppant staging requirements • Methods and additives to control fluid rheology and friction in the fracture to provide sufficient pressure to attain the desired fracture width at various points throughout the fracture (see chapter 10 for more detailed discussion) • Additives necessary to enhance fluid cleanup without flowing proppant back into the wellbore • Potential environmental impacts resulting from the fluid system

Good fluid system characteristics. Fracturing fluid systems that have the following characteristics are good prospects for treatments: • Can be safely mixed and pumped on site • Are economically cost-feasible • Can be easily, quickly, and efficiently mixed or prepared on site • Exhibit low formation damage effects • Exhibit low proppant pack conductivity damage • Exhibit reduced flow friction down the tubulars and through casing perforations • Yield effective viscosity behavior that provides sufficient friction pressure to attain desired widths throughout the fracture (net fracturing pressure) • Exhibit good proppant transport down the tubulars, through the perforations, and to the extremities of the fracture • Exhibit low fluid loss for both the pad and the proppant-laden slurry • Maintains adequate viscosity during treatment, resisting degradation due to temperature, shear, and time • Exhibit good breaking control and minimal shear strength after breaking 204

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• Exhibit good post-fracture cleanup behavior • Exhibit characteristics that minimize effects on the environment (ideally zero effects) Many fluid systems are available that have the some of the above characteristics, but no fluid can meet every desirable characteristic. Determining those characteristics that best apply to a given situation requires that all parties involved understand both the nature of the target formation and the expectations for a treatment. The various phenomena that affect fracturing fluid system performance, and the degree of their effects, are presented in chapters specifically pertinent to those phenomena. Some relate to the fluid systems themselves. Others result from physics-related aspects of fluid systems flowing at elevated temperatures in a fracture where in-fracture pressures exceed formation pressures. What is presented next is an overview of the results of industry-wide efforts to improve fluid system performance under in-fracture conditions for a wide variety of different types of formations.

Types of Fluid Systems Table 4–1 lists the following commonly used fracturing fluids included in SPE Monograph V. 12. Detailed, in-depth coverage of fluid system types, components, additives, etc., is presented in the SPE Monograph V, 12, Appendix A, “Typical Products Available From Service Companies.” Significant additional supplementary information is available in John Ely’s book Stimulation Engineering Handbook (1994). It is a valuable addition to a design engineer’s resources. Polymers for freshwater-based or brine-based fluids include guar gum, guar derivatives such as hydroxypropyl guar (HPG), or cellulose gelling agents like hydroxyethyl cellulose (HEC) or carboxymethyl-hydroxyethyl cellulose (CMHEC). Polymer water-in-oil emulsions are generated with guar or HPG polymer to viscosify the water. As shown in table 4–1, the specific hydrocarbon–water ratio is 2:1. Petroleum distillates are typically high gravity (40+ ºAPI) condensates. Gelled HCl implies various concentrations (10% to 15%) of hydrochloric acid, typically gelled with Xanthan polymer solutions. The remaining items in the table are sufficiently identified. Note: Current fluid system component concentrations are now expressed by the term ppt, parts-per-thousand. The term results from the emergence of liquid concentrates that replaced previously used powders, where concentrations were expressed in lb/1,000 gal, or lb/Mgal.

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Essentials of Hydraulic Fracturing

Table 4–1. Commonly used fracturing fluid systems Water-based polymer solutions Natural guar gum (guar)* HPG* HEC Carboxymethyl HEC* Polymer water-in oil emulsions 2/3 hydrocarbon** + 1/3 water based polymer solution† Gelled hydrocarbons Petroleum distillate, diesel, kerosene, crude oil Gelled alcohol (methanol) Gelled CO2 Gelled acid (HCl) Aqueous foams Water phase–guar, HPG solutions Gas phase–nitrogen, CO2 Source: “Table 1.3,” Gidley et al. 1989, 12. *Can be crosslinked to increase viscosity. **Petroleum distillate, diesel, kerosene, crude oil. †Usually guar or HPG.

Additional fluid systems that have emerged Subsequent to publication of the SPE Monograph V. 12 and Ely’s book, additional types of system have evolved that supplement those listed in table 4–1. Improvements to existing systems, or newly developed systems that are available as of this book’s publication include: • Improved cellulose • Improved guars (modified, derivatized, recyclable) • Cross-linked oils • Environmentally green, or recyclable • Gelled CO2 and methanol • Hydrocarbon foams • Hydrocarbon in water emulsions • Liquid CO2 (not gelled) • Polymer-free • Surfactant aqueous-system viscosifiers • Water in hydrocarbon • Xanthan polymer • Designer systems (e.g., hairy stranded) This greatly increases the menu of available fracturing fluid systems. Major pumping service companies typically offer the entire menu. However, independent local service companies may 206

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not provide the entirety. Trade names are unique to each company, even though compositions may be identical. The menu spans an extremely broad spectrum of applications. It is beyond the scope of this book to cover detailed information about each product or each service company’s fluids. Resources for specific applications, product behavior, and associated limitations lie primarily within the service companies. Hence, the company that offers a product is the primary information resource for that product’s applicability and behavior. What follows provides an overview of generalities about this. Environmental safety has become a part of the design engineer’s fluid system selection process. Service companies typically stay abreast of this. All must maintain Material Safety Data Sheets (MSDS) on their products. Thus, they can provide these resources for the design engineer.

Fluid System Databases Recently, the industry has started using a database called FracFocus.org to enter all the information on fracture treatments and make it available to the public. The companies typically list all the chemicals pumped and the quantities of each chemical. They may also include all the additives by product name. However, to protect any trade secrets, the companies do not have to list which chemical is in which product. So the recipe of any company’s “secret sauce” can remain confidential. FracFocus.org is a sincere effort on the part of the oil and gas industry to let the public know what is being pumped into each and every well. Ideally, the fluids will become greener as the industry tunes its business to the expectations of the public.

Base Fluid System Components Viscosity building agents Viscosity control starts with the base fluid system shown in table 4–1 and the additional list. Here, concentrations of the base fluid constituents play a major role in system viscosity. The amount of polymer added to the fluid (measured in ppt) will control the base gel viscosity. Then the base gel viscosity can be increased by adding cross-linkers that link the long chain polymers into extremely large networks. Cross-linking affects the friction in the fracture which increases the dynamic fracture width and the propped fracture width, as well as proppant transport and placement capabilities. The results: higher fracture conductivities, thus higher initial post-fracture producing rates, assuming these cross-linked fluids break and clean up. If the bottomhole temperature is less than 250°F, and breakers are not added to the polymer systems correctly, then the polymers may not break on their own and the fluid may not clean up from the fracture. Even if some of the fluid breaks and the well appears to be stimulated, the literature suggests that portions of the fracture away from the well bore could stay partially plugged with gel for many years. Typically, guar or cellulose derivatives (polysaccharides) constitute the primary gelling agent for building apparent viscosity in aqueous-based fluid systems. The polymer concentration in 207

Essentials of Hydraulic Fracturing

these fluids span a range from 5 to 80 ppt of aqueous liquid. Concentrations of 5 to 10 ppt, called “slickwater” systems, are more common currently than in the past. Slickwater offers reduced pipe friction and low proppant-pack damage benefits. Currently, mid-range concentrations of 15 to 40 ppt are commonly used. Higher concentrations (above 50 ppt) are not currently used by the industry. Gel concentrations have been reduced in recent years for the following reasons: • Better mixing and chemical advancements make it easier to cross-link gel concentrations as low as 15 ppt; • More companies are using slickwater treatments to fracture-treat shales using horizontal wellbores; and • More companies are concerned with recent research that shows the yield strength of partially broken gel may severely hinder fracture fluid cleanup. Hydrocarbon-based fluids and others with no thickening agent may exhibit sufficient viscosity behavior to serve specific applications. However, these oil-based fluids are not used very often and are under scrutiny by the environmental community.

Cross-linked: aqueous-based systems Cross-linkers work by activating the bonds of the long chain polymers (guar) and converting the fluid to a system with a 3D molecular structure. These super-high molecular weight structures provide rheological properties that significantly (and concurrently) enhance fracture width creation, proppant transport, fluid loss reduction, and pipe friction reduction. Typically, crosslinkers convert fluid systems from power law to non-power law behavior. When converted, the fluids exhibit viscoelastic character, rheologically speaking, that improves performance. Cross-linker activation is often temperature sensitive. Figure 4–2 shows applicable temperature ranges (the dark segments) for cross-linked, aqueous-based fracturing fluid systems. It is a modified version of the SPE Monograph V. 12, Fig 9.21. There are two modifications, and a caution, to the SPE Monograph V. 12 figure: 1. Errata in SPE Monograph V. 12, Fig. 9.21: aluminum and antimony (III) are interchanged, as appropriately shown in figure 4–2. 2. New borates: figure 4–2 reflects expanded temperature range applicability for new and improved borate (boron) cross-linked systems. 3. Caution: Consult governmental regulations prior to using heavy metal cross-linkers, i.e., zirconium, titanium (IV), chromium (n+), antimony (V), and antimony (III). These may be subject to governmental controls. At temperatures below the indicated ranges, fluid systems either do not activate satisfactorily, or experience breaking (viscosity reduction) difficulties. Non-activation yields insufficient rheological behavior. Ineffective breaking results in excessive proppant volume backflow into the wellbore during post-fracture cleanup. Typically, these non-breaking difficulties are not readily mitigated by chemical breaking agents. At temperatures above the indicated range, fluid system apparent viscosity falls below that required for desired fracture width generation, or effective proppant transport. 208

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Fig. 4–2. Applicable cross-linker temperature ranges for fracturing fluid systems Source: “Figure 9.21,” Gidley et al. 1989, 194.

Improvements to base system polymers and cross-linkers Improvements in both base fluid gelling polymers and cross-linkers have reduced the lower polymer concentration limit requirements for cross-linker activation. Currently, polymer concentrations in the 10 to 15 ppt range can be effectively cross-linked. Prior to this, lower limits ranged from 20 to 25 ppt. Viscoelastic (cross-linked) systems exhibit a memory phenomenon, i.e., rheological performance depends on both the system’s prevailing thermal and mechanical (shear) energy and its prior temperature and shear history. Appropriately predicting fluid behavior requires comprehensive testing procedures that are rigorously followed by the laboratory technician. How to properly test cross-linked fluids to obtain correct and reproducible values of apparent viscosity is discussed in SPE Monograph V. 12, Chapter 9. Sadly, those procedures have not become standard practice industry-wide. Current standard procedures ignore it. Hence, the rheological behavior predicted by computerized hydraulic fracturing simulators may not adequately reflect in situ performance. Both thermal energy and mechanical forces affect fluid cross-linker performance. Typically, at low temperatures, molecular bonding is enhanced (however, some require elevated temperatures to activate). As temperature increases, bonding tendencies decrease. Mechanical energy (fluid shear) acts commensurately. In borate (boron) cross-linked systems, hydrogen molecular bonding affects the cross-linking, which affects viscosity enhancement. Here, if bonds are broken, they typically re-heal much faster than those of heavier metal cross-linkers, such as titanium IV (titinate). Once broken (e.g., by high shear downpipe or through perforations), heavy metal bonds may not re-heal within a sufficient time frame to perform effectively in the fracture.

Hybrid systems Hybrid systems, sometimes called pseudo-hybrids, are comprised of low (10–15 ppt) polymers or cross-linked polymers containing high breaker concentrations, such that they exhibit low friction in the fracture and apparent viscosities near that of fresh water or brine. 209

Essentials of Hydraulic Fracturing

Hydrocarbon-based systems With hydrocarbon-based systems, aluminum phosphate esters and sodium bicarbonate (NaCO2) powder are common viscosifiers. However, NaCO2 acts as both a viscosifier or a breaker. It also is a fluid-loss control agent. Viscosity is highly sensitive to NaCO2 concentration. Either over- or under-treating can reduce viscosity significantly. NaCO2 is also sensitive to the base hydrocarbon type (e.g., summer diesel, winter diesel, kerosene, lease crude, etc.). Different base hydrocarbons behave differently. Ignoring this can yields disastrous results. Hence, both preliminary testing on the specific chosen hydrocarbon-based fluid and well-site quality control are essential to ensure viscosity performance.

Emulsions—hydrocarbon in aqueous polymers, and aqueous polymers in hydrocarbon Hydrocarbon in polymer emulsions (two-thirds hydrocarbon, one-third gelled aqueous) are more common than the reverse (more aqueous polymer than hydrocarbon). The interfacialsurface phenomena of emulsions yields excellent fracture width, fluid loss (in tight formations), proppant transport, temperature stability, and formation damage benefits. Emulsion viscosity is sensitive to proppant mesh size. Small-sized proppants (70/140, 100 mesh, etc.) exhibit large surface-area-to-mass ratios. This exacerbates aqueous adherence to proppant surface, thus dehydrating the aqueous portion from the system. The result is viscosity increase, primarily observed by extreme friction loss in the tubulars. If it occurs, one remedy is to (a) stop blending proppant, (b) reduce injection rate to reduce wellhead injection pressure, (c) continue injection to clear the slurry out of the pipe, and (d) resume the treatment with either a lower small-proppant concentration or larger proppants.

Foamed systems Foams (mixtures of a gas phase, a liquid phase, and a surfactant) exhibit high viscosity that results in adequate fracture width, low fluid loss (in tight formations), adequate proppant transport, good cleanup due to the gas phase, and minimal formation damage. Foams can be generated with aqueous or hydrocarbon as the base fluid. Air, nitrogen (N2), or carbon dioxide (CO2) is used as the gas phase. However, air is not applicable for creating foams with hydrocarbon liquids because of the potential flammability danger. Gas–liquid phase interfacial forces and the volume of gas in the foam determine system viscosity. These are subject to surfactant chemistry and foam quality (percent gas), in concert with foam generation shear rate. Typical foam qualities range from 85% to 95%; the higher qualities yield higher viscosity. However, qualities exceeding 97% to 98% may result in a mixture of liquid droplets and gas discontinuities in the mixture. The downside of foamed fluids are depth limitations (low density requires high wellhead injection pressures), temperature sensitivity, and requisite use of mechanical proppant concentrators to achieve high proppant concentration. So there is a practical limit to the use of nitrogen foam— usually around 10,000 ft due to high surface injection pressures. However, if foam is generated using water and CO2, the depth limitation can be extended as CO2 foam systems can possibly be denser than water when compressed at high pressures. 210

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Surfactant-based system Surfactant-based liquid systems exhibit minimal formation damage potential. However, they do not typically yield sufficient apparent viscosity (fluid friction flow resistance) to create wide fractures. Screen-outs (injection termination due to proppant bridging in the fracture) have occurred, even with large pad (neat fluid) stages. This is because the width of the created fracture was insufficient to accommodate proppant injection. Hence, prior to using surfactant-based liquids, rheological tests are required to determine maximum proppant size limits. Hydraulic fracturing computer simulators are essential to investigate the performance of such fluids.

Fracturing Fluid System Performance Control Agents Table 4–2 is a composite of the SPE Monograph V. 12, Tables 1.4 and 7.5. Table 4–2 (left) shows a list of 22 various functions or types for fluid system additives. Table 4–2 (right) shows materials used to mitigate fracturing fluid loss to the formation for water- and oil-based fluids. Table 4–2. Fracturing fluid system additives Typical Functions or Types of Additives Available for Fracturing-Fluid Systems Antifoaming agents Bacteria-control agents Breakers for redicing viscosity Buffers Clay-stabilizing agents Crosslinking or chelating agents (activators) Defoamers Demulsifying agents Dispersing agents Emulsifying agents Flow-diverting or flow-blocking agents Fluid-loss-control agents Foaming agents Friction-reducing agents Gypsum inhibitors pH-control agents Scale inhibitors Sequestering agents Sludge inhibitors Surfactants Temperature-stabilizing agents Water-blockage-control agents

Fluid-Loss Additives Oil Based Adomite Mark II Silica flour Adomite aqua Lime powder Sodium bicarbonate powder N2 /CO2 100-mesh salt or sand

Water Based Silica flour Adomite aqua Mixture gum and oil-soluble resin Mixture gum and talc 1% to 5% diesel 0.05% to 1% aromatics and surfactant N2 /CO2 100-mesh sand, oil-soluble resin, salt,   or benzoic acid

Source: “Table 1.4” and “Table 7.5,” Gidley et al. 1989, 12, 142. 211

Essentials of Hydraulic Fracturing

Base fluids alone (containing none of the listed items) address some of the listed functions, such as fluid loss or temperature control. Some gelling agents (polymers, thickeners, etc.) that are used to make the fluid more viscous also act to reduce the fluid loss, reduce the friction in the pipe, or any combination of these functions. Obviously, the list of potential additives suggests a wide variety of applications. Typically, agents for killing bacteria, breakers for reducing viscosity, stabilizing clay, cross-linking the polymers, controlling fluid loss, reducing friction, and stabilizing polymers at high temperatures represent typical uses of additives. Not all additives contained in the list are used concurrently in the same system. Some are counter-active (e.g., anti-foaming agents and defoamers, demulsifying agents and emulsifying agents, etc.). Others may overlap to some degree (e.g., gypsum inhibitors and scale inhibitors). Hence, design engineers should understand the use of each additive and design a fluid system using only the additives that are essentially needed for the treatment. The fracturing service industry has a wide variety of choices when addressing needs for a particular situation. Interaction with the service company engineer is essential to selecting the correct additives for a given treatment. As with all aspects of the oil and gas industry, environmental considerations are at the forefront of planning. Choosing a fluid that will be easy to recover and dispose of or recycle is important in developing reservoirs that must be fracture treated.

Fluid-loss control agents Fluid-loss agents (table 4–2, right) span the requirements for both aqueous- and hydrocarbonbased systems. Adomite products (Aqua and Mark II) are long-standing in the industry. They consist of a wide range of particulate sizes consisting of silica flour, barite, ground polymers, etc.). As previously stated, sodium bicarbonate powder is also a commonly used agent for hydrocarbon-based systems. Interfacial tension agents that have emerged as fluid loss are not shown (except for N2, CO2, and surfactants). However, liquid/liquid interfacial tension control agents have been found to exhibit excellent fluid-loss control in tight formations. Fluid-loss control plays an essential (extreme) role in fracture treatment design in permeable reservoirs. The importance cannot be overemphasized in reservoirs where the treatment is dominated by leakoff. Fluid loss must be considered when estimating values of • Initial pad (neat) fluid injection requirements to achieve sufficient fracture width to accept proppants • Fracture volume created relative to the fluid and proppant slurry injected • Treatment fluid costs (treatment net dollar returns) Fluid filtrate that leaks from the fracture into the reservoir during injection typically occurs through the following different paths: • Permeable formation matrix pores • Formation joints and fissures • Natural fractures and faults 212

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The following types of fluid loss to a formation constitute significantly different types of flow paths: (1) porous or permeable matrix, (2) miniscule slots, and (3) small to large slots. Thus, they require significantly different means of mitigating fluid loss, such as fluid viscosity, wall-cake formation, pore plugging, slot bridging, or plugging. The components in some fluid systems may, by their nature, be sufficient for adequate fluid loss control. Gelled and cross-linked systems concurrently invoke viscosity and wall-cake pore plugging. These mechanisms work well in low- to medium-permeability formations where pores are large enough for them to be effective. In lower permeability (tight) formations with microsized pores, these mechanisms do not work well. This is akin to trying to plug a window screen with large marbles (it does not happen). Tight formations require interfacial forces, as provided by emulsions and foams, or materials that resist spherical deformation and thus retard pore entry. The phenomena here is plugging via micro-size droplet- or bubble-surface deformation. High interfacial surface tension forces, inherent with micro-size droplets or bubbles, strongly resist deformation. The droplets or bubbles tend to remain spherically shaped. The fracture-to-formation pressure differential deforms them so that they exhibit a very effective resistance to pore entry. If forced totally into a micro-pore, contact with rock compounds the resistance by virtue of three component (two different fluids and rock) interfacial forces. Small to large slots require mixtures of small to large granules for effective plugging.

Breakers for reducing viscosity Temperature alone, acting over time, may or may not satisfactorily break many of the fluid systems. If the bottom hole temperature is above 250°F, the high concentrations of guar polymers will eventually degrade, but maybe not enough to clean up completely. Below 250°F, those guar polymers may not sufficiently break because of temperature. Thus, breakers are needed for cleanup, even at high temperatures, and are often needed to accelerate temperature breaking effects. New and improved fluid system breakers are continually being introduced by the fracturing service companies. In the past, breaking behavior was so difficult to control that certain design engineers purposely avoided using them (which may have been a mistake in hindsight). Instead, they designed fluid systems where temperature alone affected breaking. Additional compounds or applications currently available include • Molecularly focused enzymes or esters that attack particular polymers—designer breakers • Encapsulated compounds that release upon encapsulation dissolution or crushing by fracture closure • Breaker-impregnated ceramic proppants that release breakers by dissolution out of the proppant pores The above breaker types provide significant advantages that enhance treatment design in activation time and breaker distribution in the fracture. Their activation is significantly more dependable. Many cause less proppant pack permeability damage than earlier breakers. Fracturing service companies are very much on top of new developments, and some have substantial research efforts directed at improved breaker types.

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Bacteria control agents Bacteria control is especially important in aqueous-based systems that rely on polymers for increasing viscosity. Biocide compounds (e.g., glutaraldehyde, bromo-nitro-propanediol, etc.) formulate various bacteria control agents. Current primary use is to prevent anaerobic bacteria activity that generates hydrogen sulfide (H2S) in oil-bearing formations. If this is not controlled it can result in severe pipe corrosion and potential environmental health hazards. Biocides are also needed in the fluid system to kill resident bacteria that destroy (by eating) guar polymer. If the bacteria are not killed before gelling, the fluid viscosity is reduced and it might be impossible to cross-link the fluid (should one desire to do so). Past biocide use was directed at bacteria growth in base fluid mixing tanks that would destroy the polymer content. However, the emergence of liquid concentrate gelling on the fly (i.e., in the blender tub) has decreased this concern somewhat. Aqueous liquids delivered to the well site pose bacteria contamination concerns. Water from city water sources will have fewer bacteria than water obtained from ponds, lakes, or rivers, but all water from any source can have bacteria. Another common source of bacteria would be water or gel left over in frac tanks delivered to the wellsite. Hence, it is always necessary to assure that both the water and the tanks do not pose contamination potentials that compromise the performance to the fracturing fluid system. The service company should always run tests to determine the type of bacteria in the water and use an appropriate bactericide to kill the bacteria prior to gelling the fluid for the treatment. The public is very concerned with the chemicals being used by the oil and gas industry. However, bactericides are commonly used in most households, so if they are used correctly, there should be no problem. The industry is also working to find better, more environmentally friendly ways to kill bacteria in the oilfield.

Temperature-stabilizing agents In concert with previous statements about fluid loss, the components in some base fluid systems provide adequate temperature behavior control. If not, service companies maintain a repertoire of temperature-stabilizing agents. Methanol (MEOH) is a common one. Temperature stabilizers are essentially oxygen scavengers. Oxygen tends to break down the polymers and cross-linked molecular chains at high temperatures. Removing the oxygen helps to stabilize the gel and/or cross-linking. Proper use of temperature stabilizers can significantly prolong fluid effectiveness during a treatment.

Diverting agents These products are used to try to prevent or inhibit fluid systems from going where they should not. Their primary use is to mitigate • Flow through extraneous perforations • Excessive vertical (up or down) fracture growth • Fluid thievery by high-permeability zones 214

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Table 4–3 shows a wide variety of diverting agents. Their function is to plug off flow at some point, and divert it elsewhere. This requires an aggregation of plugging agents in a particular portion of the flow path, but not others. Sealing off extraneous perforations with ball sealers in the pipe is more effective for than trying to divert flow inside a fracture. Fracture flow diversion has been achieved for certain situations, but some design engineers consider such attempts as a last resort at the best. Proppant settling during injection is effective in mitigating downward fracture growth. Some success has been seen for inhibiting upward growth (in certain cases), using mixtures of a wide range of proppant sizes (e.g., 10% 100 mesh and 90% 20/40 mesh, etc.). However, diverting flow within the fracture itself is, at best, difficult. Table 4–3. Fracturing fluid system diverting agents Coarse rock salt Graded rock salt Graded paraformaldehyde Flake benzoic acid (fine and coarse) Graded oil-soluble resin (low temperature) Graded oil-soluble resin (high temperature) Ball sealers Solution of benzoic acid in alcohol or hydrocarbon* Unibeads (was beads) Crosslinked polymers Slurries of oil-soluble resins* Mixture of karaya and oil-soluble resin Karaya powder* Graded naphthalene Oil-external emulsion High-concentration linear gel Oyster shells Polymer-coated sand Buoyant particles High-quality foams Flake boric acid Source: “Table 7.6,” Gidley et al. 1989, 142. *Primary function in matrix application.

Decision Flowcharts to Facilitate and Accelerate Fluid System Selection Selecting the fluid system best suited for a specific fracturing treatment design is typically a repetitive process that requires several (sometimes many) iterations to arrive at a decision. Decision flowcharts are quite useful in this arena. They provide guidelines that aid and accelerate the selection process. Such charts are typically somewhat general in that they apply to a relatively wide span of parameters pertinent to a large number of formation types. However, the span has limits. 215

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Figure 4–3 is an example of a decision chart that is constructed for tight gas sands. Similar charts can also be developed for other applications, such as massive shales, and millidarcy or darcy formations. Many service companies, including those outside the major category, have such charts available, and use them for recommending applicable fluid systems and additives. Sometimes, they rely more heavily on them than is beneficial to their customers. Four examples of decision charts, with detailed explanations, are contained in SPE Monograph V. 12, Appendix B. Examples 4–1 and 4–2 show similar uses for decision flowcharts. 200 ℉ & < 270 ℉

High

High BHP

BHP Many

N2 Foam

>270℉

Natural Fractures Strong

Lower Barrier

Weak

Upper Barrier Moderate

Weak

Payzone

Low

Strong

Thin Payzone 100 2. a second regression on coefficients from the first regression over two parsed temperature ranges: T = 60°F to 100°F and T = 100°F to 150°F The resulting coefficients and equation 6–23 yield representative apparent viscosity values at all test points, as well as others over the entire span of the shear rate and temperature test range. µAPP(ý, T) = 10^[AýT + BýTlog(ý) + CýTlog(ý)2]

Equation 6–23

where: µAPP(ý, T)

Apparent viscosity at ý and T (°F)



ý

Shear rate data (sec–1)



T

Temperature (°F)

AýT, BýT, and CýT

Multiple regression coefficients (shear rate, temperature)

Equation system 6–24 is the logarithmic version of equation 6–23: log(µAPP) = AýT + BýTlog(ý) + CýTlog(ý)2

Equation 6–24

The first regression, viscosity versus shear rate, yielded coefficients Aý, Bý, and Cý for the three parsed regions ý ≤ 1, 1 ≤ ý ≤ 100, and ý > 100. Note the log-log relationship. Equations 6–24–1 through 6–24–3 are consistent with equations 6–17–1 through 6–17–3: Σlog(µAPP)

322

= AýN + Bý Σlog(ý) + Cý Σlog(ý)2

Equation 6–24–1

Σ[log(ý)log(µAPP)] = AýΣ log(ý) + BýΣ log(ý)2 + CýΣ log(ý)3

Equation 6–24–2

Σ[log(ý)2log(µAPP)] = AýΣ log(ý)2 + BýΣ log(ý)3 + CýΣ log(ý)4

Equation 6–24–3

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Fracturing Fluid System Rheology and Proppant Transport

The differences in variables are listed below, with variables from equations 6–17–1 through 6–17–3 coming first and those from equations 6–24–1 through 6–24–3 second:

N

= Number of data sets in the system of equations



Y

= log(µAPP)



X

= log(ý)

The second regression calculations are done on each coefficient from the first regression (Aý, Bý, and Cý) versus temperature over parsed temperature regions T = 60°F to 100°F, and T = 100°F to 150°F. For brevity's sake, equations 6–25–1 through 6–25–3 are pertinent only to the Aý coefficient. The same approach applies to the other coefficients Bý and Cý. = ATN + BTΣT + CTΣT 2

ΣAý

Equation 6–25–1

Σ[TAý] = ATΣ T + BTΣT2 + CTΣT3

Equation 6–25–2

Σ[T2Aý] = ATΣ T2 + BTΣT3 + CTΣT4

Equation 6–25–3

Table 6–18 lists the results for determining coefficients AýT, BýT, and CýT applicable to the entire data set in figure 6–20, i.e., shear rates from ý = 0.01 sec–1 to ý = 5000 sec–1, and temperatures from T = 60°F to T = 150°F. Table 6–18. Constants for determining coefficients pertinent to equation 6–24 Shear Rate Range: ý < 1 sec–1 Temperature: 60°F to 100°F AýT BýT CýT

1 2 3

AT

BT

2.862E+00 –8.823E–02 6.316E–02

–4.495E–03 –3.282E–04 –2.009E–03

Temperature: 100°F to 150°F

CT

AT

–1.324E–05 1 3.021E+00 –8.253E–03 4.56E–06 2 –3.924E–01 5.509E–03 1.199E–05 3 –2.156E–01 3.316E–03 –1 Shear Rate Range: 1≤ ý ≤ 100 sec

Temperature: 60°F to 100°F AýT BýT CýT

1 2 3

AT

BT

2.862E+00 –7.650E–02 –1.840E–01

–4.498E–03 –2.174E–03 1.881E–03

CT

AT

1 2 3

BT

–1.322E–05 1 3.018E+00 –8.191E–03 2.202E–05 2 –1.297E+00 2.054E–02 –1.101E–05 3 2.816E–01 –6.870E–03 Shear Rate Range: ý > 100 sec–1

AT

BT

CT

3.258E+00 –6.872E–01 2.799E–02

–9.021E–03 5.736E–03 –1.087E–03

5.195E–05 –5.269E–05 1.097E–05

CT 8.464E–06 –2.339E–05 –1.338E–05

Temperature: 100°F to 150°F

Temperature: 60°F to 100°F AýT BýT CýT

BT

CT 8.188E–06 –8.303E–05 2.994E–05

Temperature: 100°F to 150°F 1 2 3

AT

BT

CT

–4.136E–01 1.723E+00 –3.705E–01

6.223E–02 –4.239E–02 6.988E–03

–2.935E–04 1.875E–04 –2.993E–05 323

Essentials of Hydraulic Fracturing

Focusing on only one temperature (T = 80°F) at shear rate ý = 40 sec–1 (shear rate parse: 1 ≤ ý ≤ 100, temperature parse: T = 60°F to 100°F) AýT, BýT, and CýT are AýT

= 2.862 – 0.004498T – 0.00001322T2



= 2.862 – 0.004498 × 80 – 0.00001322 × 802





= 2.418

BýT

= –0.07650 – 0.002174T + 0.00002201T2



= –0.07650 – 0.002174 × 80 + 0.00002201 × 802



= –0.1095

CýT

= –0.1840 + 0.001881T – 0.00001101T2



= –0.1840 + 0.001881 × 80 – 0.00001101 × 802



= –0.1039

Viscosity is then calculated at shear rate ý = 40 sec–1 (per equation 6–24): µAPP(ý,T)

= 10^[AýT + BýTlog(ý) + CýTlog(ý)2] (per equation 6–24)

µAPP(40,80) = 10^[2.418 – 0.1095log(40) – 0.1039log(40)2]

= 94.6 cp

Thus, equation 6–23 can be used to compute apparent viscosity for this fluid over any temperature and shear rate combination within the range shown in figure 6–20. However, figure 6–20 does not address the effects of time on apparent viscosity. Such information would significantly enhance the data set utility.

Carreau model fluid approach Carreau model fluids are types of generalized Newtonian fluids where effective viscosity, µEFF(γ), depends upon shear rate, γ. Figure 6–20 reflects this behavior. Some fracture design models incorporate Carreau model behavior for viscosity calculations. If the design engineer does not have access to a model with the capability to calculate µEFF(γ) (which in this case is used as apparent viscosity, µEFF), it can be calculated using equation 6–26. µEFF(γ) = µINF + (µ0 – µINF)[1 + (tγ)2][(n´ – 1)/2] where:

324

µEFF(γ)–

Apparent (effective) viscosity (Pa-sec)

µINF

Viscosity at zero shear rate (Pa-sec)

µ0

Viscosity at infinite shear rate (Pal-sec)

tR

Fluid system relaxation time (sec)



n´

Fluid system flow behavior (power law) index



γ

Shear rate (sec ) –1

Equation 6–26

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Fracturing Fluid System Rheology and Proppant Transport

At low shear rates (γ < 1/t), Carreau fluid behaves as a Newtonian fluid and at high shear rates (γ > 1/t), it behaves as a power-law fluid. Note: equation 6–26 is expressed in cgs units, or Pascalseconds. Thus, viscosity values that are expressed in centipoise must be converted accordingly (1.0 cp = 0.001 Pa-sec) for use in equation 6–26. Assuming that the T = 150°F is in accord with the curve in figure 6–20 and the 40 ppt, noncross-linked HPG fluid system, where an estimate for n´ is approximately 0.7, and the following values apply, equation 6–26 yields µEFF(γ-10, T-150°F, tR-1) = 0.055 Pa-sec = 55 cp: µINF

= 110 cp at γ = 0.1 sec–1 = 0.11 Pa-sec

µ0

= 0.5 cp at γ = 100,000 sec–1 = 0.006 Pa-sec

tR

= 1 sec, an estimate for a non-cross-linked gelled system



n´

= 0.7, an estimate for a non-cross-linked HPG system at 150°F



γ

= 10 sec–1

Note: The results were calculated using figure 6–20 values for µINF (110 cp) and µ0 (0.5 cp), and estimates for tR (1 sec) and n´ (0.7). Thus, a comparison with calculated µEFF (55 cp) at 10 sec–1 is not a valid comparison. However, the difference between the figure 6–20 µAPP value (65 cp) at T = 150°F and γ = 10 sec–1 and the calculated µEFF value (55 cp) is somewhat surprisingly close. To use equation 6–26, one must have the values for µINF, µ0, and tR at the applicable temperature from the service company for their fluid systems, an industry fracturing fluid rheology consortium, or laboratory testing services.

Example 6–6. In-Fracture Apparent Viscosity Profile: Effects of Scenario on Equation 6–31 Calculations of Figure 6–2 Apparent Viscosity Data

The coefficients in table 6–19 and equation 6–23 provide the opportunity to examine in-fracture apparent viscosity profiles from the wellbore to the fracture tip. This is useful when addressing viscosity effects on fracture propagation and possibly proppant transport. This example is a hypothetically constructed scenario, somewhat analogous to example 6–4, that provides a snapshot profile at some distance, X, from wellbore to fracture tip at distance Xƒ, and shows that • Temperature increases from 80°F at the wellbore to 150°F at the fracture mid-point, X/Xƒ = 0.5. • Shear rate decreases somewhat uniformly from 200 sec–1 at the wellbore to 5 sec–1 at the fracture tip, X/Xƒ = 1. • The fluid system contains no proppant. Thus, there is no particle concentration viscosity enhancement. Apparent viscosities are calculated from the data in table 6–19 using equation 6–23. Table 6–19 lists the calculated results of combined shear rate and temperature effects on apparent viscosity. The figure 6–21 vertical axis commonly reflects apparent viscosity (cp), shear rate (sec–1), and temperature (°F) value profiles along the fracture from wellbore to fracture tip. Interestingly, figure 6–21 shows viscosity increasing along the fracture beyond X/Xƒ = 0.45. Here, decreasing shear rate dominates viscosity behavior. In this scenario, increased viscosity in 325

Essentials of Hydraulic Fracturing

the fracture extremity would enhance fracture width generation. However, note that the effect of fluid system dehydration from fluid loss that would increase in-fracture polymer concentration, and thus viscosity is not considered in the table 6–19 data. The table reflects only the effects of temperature and shear rate. Table 6–19. In-fracture temperature, shear rate, and apparent viscosity versus dimensionless fracture penetration for a 40 ppt, non-cross-linked HPG fluid system Dimensionless Temperature Fracture °F Penetration X/Xƒ 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

80 89 98 105 115 125 135 145 150

Shear Viscosity Rate cp sec–1 200 190 180 165 155 145 130 120 110

42.3 40.4 38.5 38.3 37.1 35.4 34.0 31.5 30.6

Dimensionless Temperature Fracture °F Penetration X/Xƒ 0.45 0.50 0.55 0.60 0.70 0.80 0.90 1.00

150 150 150 150 150 150 150 150

Shear Viscosity Rate cp sec–1 100 90 80 60 40 20 10 5

31.8 33.1 34.6 38.4 44.1 54.4 65.0 75.3

200

Temp (ºF), Shear Rate (1/sec), Viscosity (cp)

180 160 140 120

Temperature

100

Viscosity

Shear Rate

80 60 40 20 0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Dimensionless Fracture Penetration – X/Xƒ

Fig. 6–21. In-fracture temperature, shear rate, and apparent viscosity profiles for a 40 ppt, non-crosslinked HPG fluid system 326

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Fracturing Fluid System Rheology and Proppant Transport

Apparent Viscosity of Foam Fluid Systems Foam systems are typically constructed with either nitrogen or, for relatively low pressure treating, CO2. Some foam systems can yield superior performance over liquid systems for certain applications, primarily fluid loss and proppant transport. For other applications, such as deep wells and high temperatures, this may not be so. Foam fluid systems exhibit some behaviors similar to liquid systems, and some that are very different due to foam compressibility. Because of this, design engineers should work closely with the service companies when designing foam fracturing treatments. Some attractive benefits of foam systems over liquid systems exhibit: • Higher fracturing fluid-loss efficiency • Lower damage to near-wellbore formation permeability • Better proppant transport capabilities • Equivalent or better fracture width generaton • Shear enhanced viscosity • A shear sensitivity On the downside, as compared to liquid systems, foam systems: • Require higher wellhead injection pressures, and are therefore are not attractive for deep wells • Require special blending concentrators to achieve proppant concentrations that are easily blended in liquid systems • Have poorer temperature stability • Are not foam at extremely high qualities, e.g., above 96% to 98 %. Figure 6–22 is a composite of SPE Monograph V. 12, Figures 9.34 and 9.35. It shows the apparent viscosity behavior of foam systems versus foam quality (the fraction or percentage of gas in the mixture) at various shear rates. The left chart (Figure 9.34) is a water–nitrogen mixture. The right chart (Figure 9.35) is a system created with 40 ppt HPG, not cross-linked. Both data sets are for ambient temperature behavior. Notice that • The water-nitrogen foam (left chart) requires at least 50% nitrogen to develop viscosity • The higher the foam quality, the higher the viscosity • Higher shear rates significantly degrade apparent viscosity performance of the mixtures • Viscosity behavior is amenable to regression approaches for calculating behavior

327

Essentials of Hydraulic Fracturing

Fig. 6–22. Foam system viscosity versus foam quality (percent gas) Source: “Figure 9.34” and “Figure 9.35,” Gidley et al. 1989, 199. Figure 6–23 shows n-Prime and K-Prime behavior for a water–nitrogen foam system versus temperature at qualities ranging from 55% to 75%. It can be seen that • n-Prime and K-Prime behaviors are consistent with those of liquid systems, i.e., n-Prime increases and K-Prime decreases as temperature increases. Hence, temperature degrades viscosity. • Higher foam quality enhances both n-Prime and K-Prime behavior. • n-Prime and K-Prime behaviors of foam, being consistent with liquid systems, are amenable to regression approaches for developing behavioral equations.

Fig. 6–23. Foam system n-Prime and K-Prime versus temperature for various percentages of gas foam quality Source: “Figure 9.38,” Gidley et al. 1989, 201.

328

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Fracturing Fluid System Rheology and Proppant Transport

Not shown are the effects of pressure. Pressure affects bubble size and temperature affects interfacial tension forces. This will affect viscosity to some degree. Hence, it is important that test procedures span the applicable in-fracture pressure, temperature and shear rate ranges for a specified treatment design.

Fluid System Apparent Viscosity Increase due to Proppant Concentration In proppant-laden slurries, the proppant concentration (particle fraction) of the slurry increases the apparent viscosity of the slurry above that of a neat fluid that contains no proppant. This occurs for both laminar and turbulent flow. For example, in-fracture, laminar flow sand concentrations of a 5 lb/gal slurry causes a 2.2-fold viscosity increase. At 10 lb/gal slurry, the increase is 5.4-fold. Thus, the in-fracture viscosities calculated from n-Prime, K-Prime, and shear rate values using equation 6–16 are µAPP = CµK´/ỳ (1-n´)

(per equation 6–16)

These viscosity values must be adjusted to account for in-fracture particle concentrations at various points along the fracture. What is presented here pertains to in-fracture laminar flow. Turbulent pipe flow is addressed in the section “Tubular Friction Loss during Injection.” Proppant concentrations are typically expressed in terms of lb/gal of slurry or lb/gal of liquid. Viscosity concentration relationships are based on particle fraction. Equation 6–27 and equation 6–28 convert the term lb/gal (slurry or liquid) to particle fraction, FP. FP = SPPG/(8.331gPROP)

Equation 6–27

FP = [LPPG/(8.331gPROP)]/[1 + (LPPG/(8.331gPROP))]

Equation 6–28

where: FP

Particle fraction (dim.)

SPPG

Proppant concentration (lb/gal slurry)

LPPG

Proppant concentration (lb/gal liquid)

gPROP

Proppant specific gravity

Figure 6–24 reflects regression fitting of data in SPE Monograph V. 12, Figures 9.13 and 12.10. This yields equations 6–29 and 6–30 for the effects of proppant concentration on relative viscosity, µREL. Here, µREL = µSLURRY/µNEAT, where µSLURRY is the proppant-laden slurry viscosity, and µNEAT is the viscosity of the fluid system containing no proppant.

329

Essentials of Hydraulic Fracturing

Relative Visscosity: µ-Slurry/µ-Neat

8.0 7.0

RC LW: spgr. 2.10

Eq. 6-29 Extrap'd

Sand: spgr. 2.65

Eq. 6-29 Extrap'd

Int Wt: spgr. 3.20

Eq. 6-29 Extrap'd

Bauxite: spgr. 3.65

Eq. 6-29 Extrap'd

Sand: Eq. 6-30

6.0 5.0 4.0 3.0 2.0 1.0

0

2

4

6

8

10

12

Proppant Concentration (lb/gal-Slurry)

Fig. 6–24. Relative viscosity versus proppant concentration Source: “Figure 9.13” and “Figure 12.10,” Gidley et al. 1989, 188, 254. Equation 6–29 applies to all proppants. It yields viscosity ratio values based on particle fraction, as determined from proppant specific gravity obtained using equation 6–27 or equation 6–28: µREL = 1 + 1.076FP + 19.15FP2

Equation 6–29

where FP is determined by either equation 6–27 or 6–28 per terminology, i.e., lb/gal slurry (SPPG) or lb/gal liquid (LPPG). Equation 6–30 applies only to sand: µREL = 10^(1.44FP)

Equation 6–30

However, notice that equation 6–30 yields values closer to those calculated by equation 6–29 for intermediate weight ceramic that has a specific gravity (gPROP) of 3.20 than those equation 6–29 yields for 2.64 specific gravity sand. Hence, the authors suggest using equation 6–29 for relative viscosity. Figure 6–24 shows five relative viscosities versus lb/gal slurry. Four are calculated and extrapolated beyond the SPE Monograph V. 12, Figure 9.13 data limit by equation 6–29. Here the designations are • RCLW: Resin coated, light weight ceramic, gPROP = 2.10 • Sand, gPROP = 2.65 330

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Fracturing Fluid System Rheology and Proppant Transport

• Int. Wt.: Intermediate weight ceramic, gPROP = 3.20 • Bauxite: Sintered bauxite, gPROP = 3.65 The fifth (curve legend: for any sand, equation 6–30) is calculated only for sand using equation 6–30. Comparative behavior of SPE Monograph V. 12, Figure 12.10 data, which spanned proppant concentrations from SPPG = 0 to SPPG = 12, with extrapolated SPE Monograph V. 12, Figure 9.13 data, justifies extrapolation beyond the Monograph Figure 9.13 data limits. For an example of the dependence of relative viscosity on proppant specific gravity, at 5 lb/gal slurry proppant concentration, consider: • Resin-coated, lightweight ceramic with a gPROP of 2.10 yields µREL = 2.87 • Sand with a gPROP of 2.65 yields µREL = 2.23 • Intermediate-weight ceramic with a gPROP of 3.20 yields µREL = 1.88 • Sintered bauxite with a gPROP of 3.65 yields µREL = 1.69 Apparent viscosity increase due to proppant concentration is integrated into most fracturing computer models. However, it is wise for design engineers to inquire as to whether it is or is not.

Small-sized proppants or particles in emulsion and foam fluid systems— effect on apparent viscosity Small-sized proppants such as 70/140 mesh, 100 mesh, silica flour, or other similar size particulates are typically used for fluid-loss control or as diverting agents. Particles of such size used with aqueous-hydrocarbon emulsions or aqueous-based foams can effect a significantly increase fluid system apparent viscosity. The reason is that molecular attraction between the proppant or particle and water, i.e., very small particles capture water from foams or emulsions. This tightens the interfacial effects of the fluid system, thus increasing its viscosity. Such behavior can result in orders of magnitude viscosity increases. The magnitudes of degree have not been well established by laboratory or field tests. However, the effect has been observed during treatments that exhibit extremely high pipe friction when 70/140 mesh, 100 mesh, silica flour stages are injected. The remedy is to reduce or eliminate concentrations of the small particles, until the problem disappears.

Fluid system apparent viscosity increase due to fluid loss As previously discussed pertinent to figure 5–19 in the section “Fluid System Viscosity Increase by Virtue of Fluid Loss” in chapter 5. Fluid loss can also dehydrate the fluid system, thus increasing its effective apparent viscosity in the fracture. The reader is directed to this section for pertinent details. Unfortunately, the degrees of increase have not been well established by extensive testing. This encourages engineers to design fluid systems so as to minimize fluid-loss behavior. Some more sophisticated fracture design models account for viscosity increase due to fluid loss. This is another aspect that design engineers should inquire about.

331

Essentials of Hydraulic Fracturing

Fracturing fluid system rheology data files Design engineers’ personal rheology files Examples 6–3 through 6–6 provide various processes for developing algorithms and equation coefficients to calculate the in-fracture rheology behavior of a given system at any point in the fracture from wellbore to tip. The examples presented were created via spreadsheet programs. However, other platforms are amenable to the same processes. Prior discussion suggested constructing template files for • Charting data behavior • Determining appropriate coordinate relationships (rectangular, semi-log, log-log) • Specifying region parses • Calculating equation coefficients • Error analysis Additional suggestions pertain to constructing library files for results from processed data. Such files are invaluable resources when conducting fracture treatment designs. Aspects important to the construction include • Quick search and retrieval of the desired fluid system or systems • Flags to automatically determine pertinent coordinate relationships • Automatic designation of specified parsed regions • Automatic reference to parsed region lookup • Automatic charting and output templates Such construction may not fall within the direct purview of a design engineer, per se. It may be provided by computing support staff, or by outside services. However, it behooves the design engineer to be directly involved in providing guidance such that the results are user-friendly and expeditiously applicable.

Templates for n´ and K´ data input to hydraulic fracturing design simulators Many hydraulic fracturing computer design models address rheology over the entire fracture temperature, time, and shear rate spectrum. Some may not. Those that do typically contain builtin resource libraries, with algorithms that import a specific fluid system’s rheology-pertinent data as well as other design data, e.g., fluid loss, etc. In this regard, processes such as those presented in examples 6–3 through 6–5 are amenable to creating templates that are import-compatible with a specific model. Hence, such processes provide the capability of adding new fluid systems or upgrading what resides in a computer model built-in fluid system resource library.

332

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Fracturing Fluid System Rheology and Proppant Transport

Hydraulic Horsepower Injection Requirements Hydraulic horsepower (HHP) is important to several aspects of hydraulic fracturing treatment design. These include • Pumping hydraulic horsepower unit charges, i.e., $/HHP • The number of in-service pumps required for a treatment • The number of on-site stand-by pumps required for a treatment Either of the equivalent expressions below is commonly used to calculate hydraulic horsepower:

HHP = QINJPW-INJ/40.8

Equation 6–31–1



HHP = 0.02451QINJPW-INJ

Equation 6–31–2

where:

HHP

Hydraulic horsepower

QINJ

Total wellhead injection rate (bbls/min)

PW-INJ

Wellhead, surface injection pressure (psi)

Pumping hydraulic horsepower unit charges Hydraulic horsepower unit charges typically are based on the maximum HHP that occurs over a defined time interval (possibly very short) during a treatment, as opposed to an average for the entire treatment. This often occurs at the end on injection, during displacement of the fracturing fluid system by a neat fluid that has a lower density than the proppant-laden slurry, which results in higher injection pressures. Foam fluid systems, being less dense, require higher HHP than aqueous- or hydrocarbon-based systems.

Number of in-service pumps required for a treatment Fracturing pumps each have maximum horsepower, pump rate, and pressure limits. Standard practice for in-service pumping is to employ them somewhat below these limits. Hence, the total number of in-service pumps required for a fracturing treatment is total HHP requirements/ HHP-per-pump. This affects the number of in-service pumps required for a treatment, and thus charges.

Number of on-site standby pumps required for a treatment High fluid system volume fracturing treatments require long injection times. This, combined with high surface pressure injection requirements, erodes pump performance. Hence, to maintain continuous injection, a sufficient number of standby pumps are required as replacements for poor- or nonperforming in-service pumps. This adds to total pumping charges.

333

Essentials of Hydraulic Fracturing

Wellhead surface injection pressure Per equation 6–31, wellhead surface injection pressure is integral to hydraulic horsepower. It comprises factors pertinent to different aspects of fracturing treatment design. Equation 6–32 determines wellhead injection pressure. PW-INJ = σMIN + PNET + ΔPPERFS + ΔPTUBULARS – PCOL

Equation 6–32

where: PW-INJ

Wellhead, surface injection pressure (psi)

σMIN

In situ minimum stress, i.e., fracture closure stress (psi)

PNET

Net fracturing pressure (psi)

ΔPPERFS

Perforation friction loss (psi)

ΔPTUBULARS Tubulars, pipe or annulus, friction loss (psi) PCOL

Fluid-proppant slurry hydrostatic column pressure (psi).

Obviously, a number of different factors impact PW-INJ by varying degrees. In regard to fluid system rheology, these factors comprise flow rate in both the fracture and the tubulars, plus those listed below. Accordingly, each is affected by various parameters as indicated in the listing: • Net fracturing pressure (psi) –– Fluid system rheology indices: n-Prime and K-Prime –– Slurry proppant concentration –– In-fracture shear rate, temperature, and time • Perforation friction loss –– Slurry specific gravity –– Perforation diameter (in.) –– Number of perforations • Tubulars, pipe or annulus, friction loss –– Tubular hydraulic diameter (pipe, annulus, or manifolded) –– Flow regime, i.e., laminar or turbulent • Fluid-proppant slurry hydrostatic column pressure –– Fluid system density –– Proppant density and concentration (particle fraction)

Example 6–7. Calculations for Components of Wellhead Surface Injection Pressure Throughout the remainder of the discussion on wellhead surface injection pressure, aspects pertinent to each term in equation 6–32 are presented, along with example calculations. The aspects affecting net fracturing pressure are contained in chapter 3 and previous discussion in this chapter. This example omprises the remaining terms in the equation, i.e., ΔPPERFS, ΔPTUBULARS, and PCOL. The examples are sequenced in accordance with their position in the equation, left to right: 334

Example 6–7–1

Perforation friction loss—ΔPPERFS

Chapter 6

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Fracturing Fluid System Rheology and Proppant Transport



Example 6–7–2

Tubulars, pipe or annulus, friction loss—ΔPTUBULARS



Example 6–7–2f

Hydrostatic column pressure—PCOL

In equation 6–32, values for in situ stress, σMIN, and net fracturing pressure, PNET, are σMIN = 3,900 psi PNET = 500 psi Therefore, PW-INJ = σMIN + PNET + ΔPPERFS + ΔPTUBULARS – PCOL becomes PW-INJ = 3,900 + 500 + ΔPPERFS + ΔPTUBULARS – PCOL = 4,400 + ΔPPERFS + ΔPTUBULARS – PCOL psi



As each term in equation 6–32 is calculated, the pertinent parameters for that term are introduced, and then used in addressing subsequent terms. Thus equation 6–32 is reiterated as the discussion progresses, and the progression provides a perspective of the relative impact of each term on the final results for PW-INJ, and consequently, HHP requirements for the same given set of conditions. The following data are used, as pertinent to the respective term, throughout example 6–7.

Tubing description

4½ in. OD, 13.5 lb/ft



Casing description

8⅝ in. OD, 49.00 lb/ft



Injection rate, QINJ

50 bbls/min



Tubular length, ∆L

6,000 ft



Fluid system

50 ppt WG-11, 2% KCl, specific gravity = 1.013



Proppant type

Sintered bauxite, specific gravity = 3.65



Perforated interval

50 ft



Shots/foot

4



Number of perforations

200



Perforation diameter, OD

0.5 in.

Perforation friction loss during injection Perforation friction is estimated per equation 6–33. ΔPPERF = QPERF2gSLURRY/(CPERFdPERF4)

Equation 6–33

where ΔPPERF

Friction loss across one perforation (psi)

QPERF

Flow rate through one perforation (bbls/min)

gSLURRY

Slurry specific gravity (dim.)

CPERF

Perforation coefficient (range: 0.2 to 0.5, typically = 0.4 (dim.)

dPERF

Perforation diameter (in.) 335

Essentials of Hydraulic Fracturing

The term “estimated” is used because over an entire perforated interval, the following may prevail: • Ineffective gun performance (e.g., gun is not centralized in the casing, the perforated hole edges are burred, inadequate perforation gun power, gun charge misfire) • CPERF value is a guess (range: 0.2 to 0.5, typically = 0.4) (dim.) • DPERF values may vary over a perforated interval, i.e., DPERF may = 0.5 inches over some sections and 0.3 or 0.7 (due to erosion) over others

Perforation programs It is suggested that design engineers use an approach that minimizes perforation friction. That is, create a sufficient number of perforations of sufficient hole size, such that they mitigate potential detrimental effects on fluid system rheological performance. This is especially important when using fracturing fluid systems (both neat and proppant-laden) that are shear-sensitive. One suggestion for non-limited-entry designs is to keep total perforation friction below a specified maximum. One of the authors has found that a maximum perforation friction value of 20 psi seems plausible. Granted this is arbitrary and is based on experience as opposed to in-depth research by that author. For limited-entry designs, it is essential to maintain a guaranteed wellbore pressure inside the pipe that is several hundred psi above the highest expected formation break-down or formation parting pressure. Precise calculation of perforation friction may not yield the desired results. Perforation erosion can significantly enlarge hole diameter. It it does, per equation 6–33, limitedentry treatments may not perform as designed.

Fluid system specific gravity Equation 6–33 requires a fluid system gSLURRY value. Equation 6–34 determines this: gSLURRY = (1 – FP)gFLUID + FPgPROP

Equation 6–34

where gSLURRY

Fluid system specific gravity (dim.)

FP

Proppant particle fraction (fraction)

gFLUID

Neat fluid system specific gravity (dim.)

gPROP

Proppant specific gravity (dim.)

FP = SPPG/(8.331gPROP)

(per equation 6–27)

or FP = [LPPG/(8.331gPROP)]/[1 + (LPPG/(8.331gPROP)]

(per equation 6–28)

where

336

FP

Particle fraction (fraction)

SPPG

Slurry proppant concentration (lb/gal slurry)

LPPG

Liquid proppant concentration (lb/gal liquid)

gPROP

Proppant specific gravity (dim.)

Chapter 6

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Fracturing Fluid System Rheology and Proppant Transport

Example 6–7–1. Perforation Friction: Number of Shots, Perforation Size Consider a QINJ rate of 50 bbl/min, a NPERF of 200, and a slurry concentration where SPPG = 8 lb/gal slurry. The pertinent data are QPERF = QINJ/NPERF = 50/200 = 0.25 bbls/min/perforation CPERF 0.4 gPROP 3.65 FP

= SPPG/(8.331gPROP)



= 8/(8.331 × 3.65)



= 0.2631

gSLURRY = (1 – FP) gFLUID + FPgPROP

= (1 – 0.2631)1.013 + 0.2631 × 3.65



= 1.707

(per equation 6–27)

(per equation 6–34)

Example 6–7–1a. Calculated Total Perforation Friction ΔPPERF = QPERF2gSLURRY/(CPERFdPERF4)

= [(0.25)21.707]/[0.4(0.5)4]



= 4.3 psi

(per equation 6–33)

Example 6–7–1b. Calculated Minimum Number of Shots (dPERF = 0.5 inches) to

Keep Total Perforation Friction below a Specified Maximum, ΔPPERF-MAX, or 20 psi. Inverting equation 6–33 yields equation 6–35 for the number of total shots (N):

NPERF = (QINJ/dPERF2)[gSLURRY/(CPERFΔPPERF-MAX)]1/2

= [50/(0.5)2][1.707/(0.4 × 20)]1/2



= 92.4 shots

Equation 6–35

For the 50-foot perforated interval, perforating density = 1.85 shots/ft, which suggests a minimum density of 2 shots/ft.

337

Essentials of Hydraulic Fracturing

Example 6–7–1c. Calculated Minimum Dperf with 200 Shots to Keep Total

Perforation Friction below 20 psi.

Inverting equation 6–33 yields equation 6–36 for dPERF: dPERF = (QINJ/NPERF)1/2[gSLURRY/(CPERFΔPPERF-MAX)]1/4

= (50/200)1/2[1.707/(0.4 × 20)]1/4



= 0.340 inches

Equation 6–36

This suggests a minimum perforation size of 0.375 inches; however, in concert with the basic data for these examples, and rounding ΔPPERF to 4 psi, equation 6–32 PW-INJ = σMIN + PNET + ΔPPERFS + ΔPTUBULARS – PCOL becomes PW-INJ = 3,900 + 500 + 4 + ΔPTUBULARS – PCOL

= 4,404 + ΔPTUBULARS – PCOL psi

Tubular Friction Loss during Injection Wellbore tubular configurations Tubular friction loss refers to friction loss occurring during injection down any of the following wellbore configurations: • Tubing (pipe) • Casing (pipe) • Annulus (between tubing and casing) • Manifolded flow (simultaneous down tubing and annulus) Tubular friction is a relatively large component of equation 6–32. As such, it is an important issue in fracture treatment design.

Hydraulic diameter Friction calculations in conduits require prescribing “diameter” that affects conduit flow, i.e., a hydraulic diameter (DHYD). For any closed conduit, DHYD is defined as the 4 × flow area/wetted flow perimeter. In rheology technology, DHYD applies to all flow configurations: circular, elliptical, rectangular slots (including narrow slots, such as fractures), squares and other polygons.

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For circular pipes with an internal diameter (dI): DHYD

= 4π(dI/2)2/(πdI)



= dI2/dI



= dI

Thus, for tubing, and casing DHYD-TBG

= tubing internal diameter (IDTBG)

DHYD-CSG

= casing internal diameter (IDCSG)

For annuli, with tubing of external diameter (dO) inside of casing of internal diameter (dI) DHYD

= [4π(dI/2)2 – 4π(dO/2)2]/(πdI + πdO)



= 4π[(dI/2)2 – dO/2)2]/π(dI + dO) = dI – dO



= (dI2 – dO2)/( dI + dO)



= (dI + dO) (dI – dO)/( dI + dO)



= dI – dO

DHYD-ANN

= casing internal diameter (IDCSG) minus tubing external diameter (ODTBG).

In practice, tubing couping diameter, which is larger than that of the tubing body is typically ignored for flow calculations.

Friction gradient data Charts such as figure 6–25, or data pertinent to them, provide resources for tubular friction gradient data. The chart shows both pipe and annulus (Halliburton 1986, 20) friction gradients (psi/100 feet) as a function of injection rate (bbls/min) for a series of tubing and casing sizes. Such data is available in various forms from pumping service companies for all of their fluid systems, and include many pipe or annulus configurations at any injection rate. Figure 6–25 is specific to Halliburton’s 50 ppt WG-11, 2% KCl neat (no proppant) fluid system. The left portion of each chart (slope ≈ 1/2) applies to laminar flow. The right portion (slope ≈ 1) is for turbulent flow. The slope change points (breakpoints) designate flow regime transition from laminar to turbulent flow. In regard to the breakpoints, a few service companies provide charts and data that depict less sharp laminar-to-turbulent flow regime transitions. Discussion with providers of such data suggest that this is an algorithm convenience for use in fracturing computer simulation models. These algorithms do not reflect the more representative sharper break points behavior as shown in figure 6–25, and measured over the years for many fluids. The algorithms presented in example 6–7–2 better represent actual behavior than do the convenience algorithms. Data such as those shown in the charts are commonly available for most fracturing fluid systems. They are quite reliable. Additionally, they have been used with confidence for many years. These data come from • A plethora of tests on different fluid systems, for different pipe sizes and annular configurations 339

Essentials of Hydraulic Fracturing

• Highly instrumented tests in relatively long vertical pipe sections • Each major pumping service company, current and past

Fig. 6–25. Tubing and annulus differential friction pressure (psi/100 feet) versus flow rate (barrels/minute) for a Halliburton 50 ppt WG-11, 2% KCl fluid system Source: “Figure 2.11” and “Figure 2.12,” Halliburton 1986, 5.

Developing equations for computing tubular friction from six data points Even though the charts in figure 6–25 contain several tubing, casing, and annular sizes, they are somewhat limited in regard to the many pipe sizes and annulus configurations used for treatment design. However, with only six data points for pipe configurations and six for annulus configuration, algorithms can be readily constructed that provide tubular friction gradients for a specific fluid system with any tubular configuration and any set of tubular sizes. These then allow the design engineer quick access for application to their specific well tubular configuration, regardless of tubular sizes. The algorithms can then be used for flow down • Tubing (pipe) • Casing (pipe) • Annulus (between tubing and casing), or • Manifolded flow (simultaneous down tubing and annulus) 340

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The charted data in figure 6–25 are used as the example for instructions pertinent to constructing algorithms pertinent to practically all fluid systems.

Example 6–7–2. Equations for Pipe and Annulus Flow Friction Gradients for a Halliburton 50 ppt WG-11, 2% KCl Fluid System

Notice in figure 6–25, the nearly parallel behavior between different pipe and annulus sizes for both laminar and turbulent flow. Also notice the near-linearity of slope breakpoints where flow regimes transition from laminar to turbulence. Practically all fracturing fluid systems exhibit this behavior. This affords ready construction of pipe and annulus friction loss equations, with a small data set, that apply to an extensively large menu of fluid systems and tubular configurations. Table 6–20 lists data for each pipe and annulus size and configuration in figure 6–25. The critical points denoted by arrows in figure 6–25 are listed in table 6–21 and table 6–22 for pipe and annular flow, respectively. The tables contain axes-value and break points for all pipes shown in the figure. However, only the table-highlighted sizes (white text on black) are required to construct pertinent equations that yield flow friction gradients for any pipe size or set of annulus sizes. Table 6–20. Tubular friction pressures at flow rates 50 ppt WG-11, 2% KCl

Pipe and Annular Flow Friction Pressure P/ L ( psi/100 ft ) and Injection Rate Q ( bbls/min ) Halliburton 50-ppt WG-11, 2% KCL

Annulus

2.375 2.875 2.375 2.875 2.375

@ Chart @ Chart Break Points Right Axis Q P/ L Q P/ L BPM psi/100 ft BPM psi/100 ft 2.2 17 61 1000 2.9 14 96 1000 4.4 10 100 457 6.3 7.4 100 215 7.9 6.3 100 135 9.2 5.5 100 101 16.0 3.6 100 34 23 2.6 100 16 37 1.8 100 6

Pipe DHYD in

A B C D E F G H I

1.380 1.610 1.995 2.441 2.764 2.992 4.000 4.892 6.366

@ Chart Left Axis Q P/ L BPM psi/100 ft 1 13.0 1 9.1 1 5.6 1 3.6 1 2.7 1 2.2 1 1.2 2.0 1 8.0 1

Chart

Pipe

@ Chart

DHYD in

Left Axis Q P/ L

Break Points Q P/ L

1.625 2.017 2.517 3.491 3.991

1 1 1 1 1.4

12 15 20 29 34

Csg ID Pipe OD Annulus in in Code 4.000 4.892 4.892 6.366 6.366

Pipe Flow

Chart Pipe Code

A B C D E

Annular Flow

5.1 3.3 2.1 1.1 1

@ Chart

14.0 9.9 7.0 4.3 3.5

@ Chart Right Axis Q P/ L 100 100 100 100 100

181 97 51 20 13

Source: “Figure 2.71,” Halliburton 1986, 20.

341

Essentials of Hydraulic Fracturing

Table 6–21. Data points for developing pipe friction equations for different pipe sizes Pipe Flow Friction-Chart Construction from 6 Data Points P/ L (psi/100 feet) versus Rate, Q (BPM) Halliburton 50-ppt WG-11, 2% KCL Chart Break Points

Chart Left Axis DHYD-L in @ QCHRT-L = 1 BPM 1.380 @ QCHRT-L = 1 BPM 4.000

P/ LCHRT-L psi/100 ft 13.0 1.2

D HYD-BP Q CHRT-BP in BPM 1.380 2.2 6.366

37

Chart Right Axis

P/ L CHRT-BP psi/100 ft 17

DHYD-R in 1.995

1.8

6.366

P/ LCHRT-R psi/100 ft 457 @ QCHRT-R = 100 BPM 6.0

@ QCHRT-R = 100 BPM

Table 6–22. Data points for developing annulus friction equations for different pipe and casing sizes Annular Flow Friction-Chart Construction from 6 Data Points P/ L (psi/100 feet) versus Rate Q (BPM) Halliburton 50 ppt WG-11, 2% KCL Chart Left Axis DHYD-L P/ LCHRT-L in psi/100 ft @ QCHRT-L = 1 BPM 1.625 5.1 @ QCHRT-L = 1 BPM 3.491

1.1

Chart Break Points D HYD-BP Q CHRT-BP P/ L CHRT-BP in BPM psi/100 ft 1.625 12 14 3.991

34

3.5

DHYD-R in 1.625

Chart Right Axis P/ LCHRT-R psi/100 ft 181 @ QCHRT-R = 100 BPM

3.991

13

@ QCHRT-R = 100 BPM

The data listed in tables 6–21 and 6–22 comprise the extremity points for first-order (linear) behavior on log-log coordinates. The left-axis ΔP/ΔL, break point and right-axis ΔP/ΔL values are defined in terms of pipe diameter, or annulus hydraulic diameter, by expressions in the form ΔP/ΔL = 10^[A + Blog(DHYD)]



Equation 6–37

where ΔP/ΔL

Tubular (pipe or annulus) friction pressure gradient (psi/100 feet), at QINJ or breakpoint QINJ (bbls/min), as pertinent



Constants developed using table 6–21 and table 6–22 data

A&B

DHYD

Pipe or annulus average hydraulic diameter (in.) For pipe flow: DHYD = Avg. pipe internal diameter, IDPIPE For annulus flow: DHYD = IDCSG – ODTBG

The relationship is logarithmically linear between D HYD and ΔP/ΔLCHRT-AXIS for both the chart’s left and right vertical axes, as well as the DHYD and ΔP/ΔLBP for the chart breakpoints. Thus, determining the constants A and B is straightforward. They are calculated by solving twopoint, equation sets of linear-logarithmic data, converted to exponential form for the left axis, break point, and right axis.

Example 6–7–2a. Tubing Flow Equations for Left Axis, Breakpoint, and Right

Axis Values in a 50 ppt WG-11, 2% KCl fluid system

From table 6–22 data, equations 6–38–1 through 6–38–4 define the • left axis flow rate (QCHRT-L) and tubular friction gradients (ΔP/ΔLCHRT-L),

342

• breakpoint flow rate (QCHRT-BP) and breakpoint tubular friction gradient (ΔP/ΔLCHRT-BP), and

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• right axis flow rate (QCHRT-R) tubular friction gradient (ΔP/ΔLCHRT-R) in terms of tubular DHYD for figure 6–25. Left chart axis: QCHRT-L

= 1(bbl/min)

ΔP/ΔLCHRT-L = 10^[1.430 – 2.264log(DHYD-TBG)](psi/100 feet)

Equation 6–38–1

Chart laminar-turbulent breakpoints: QCHRT-BP

= 10^[0.08419 – 1.846log(DHYD-TBG))] (bbls/min)

ΔP/ΔLCHRT-BP = 10^[1.441 – 1.469log(DDHYD-TBG))] (psi/100 feet)

Equation 6–38–2 Equation 6–38–3

Right axis: QCHRT-R

= 100 (bbls/min)

ΔP/ΔLCHRT-R = 10^[3.780 – 3.734log(DHYD-TBG)](psi/100 feet)

Equation 6–38–4

Table 6–23 shows the six chart points calculated for a 2.441-inch pipe ID by equations 6–38–1 through 6–38–4. These compare well with the table 6–20 values. Table 6–23. Pipe-flow rate versus friction: chart data points for 2.441inch ID pipe in a Halliburton 50 ppt HPG, 2% KCl neat fluid system Pipe Flow:

P/ L Friction versus Rate Q Curve Data Points for a Specified Pipe Size from 6-Point Constructed Chart Data Halliburton 50-ppt WG-11, 2% KCL Specified Q P/ L Pipe BPM psi/100 ft ID 1 3.6 Chart Left Axis Point 6.305 7.4 Chart Break Point in 2.441 100 215 Chart Right Axis Point

Example 6–7–2b. Annular Flow Equations for Left Axis, Breakpoint, and Right Axis Values in a 50 ppt WG-11, 2% KCl fluid system

Applying the same approach for annular flow, using equations developed from table 6–20, equations 6–39–1 through 6–39–4 then define the left axis annulus friction gradient, breakpoint flow rate and annulus friction gradient, and right axis annulus friction gradient in terms of annulus hydraulic diameter. Left chart axis, at QINJ = 1 bbls/min: ΔP/ΔLCHRT-L

= 10^[1.131 – 2.006 × log(DHYD-ANN)] psi/100 feet Equation 6–39–1 343

Essentials of Hydraulic Fracturing

Chart laminar-turbulent break points: QBP

= 10^[0.8348 – 1.159log(DHYD-ANN)] bbls/min

Equation 6–39–2



= 10^[1.472 – 1.542log(DHYD-ANN)] psi/100 feet

Equation 6–39–3

ΔP/ΔL

Right axis, at QINJ = 100 bbls/min:

ΔP/ΔL

= 10^[2.876 – 2.931log(DHYD-ANN)] psi/100 feet

Equation 6–39–4

Table 6–24 shows the six chart points calculated for a 2.375-inch OD tubing in 4.862-inch ID casing annulus. These compare well with the table 6–21 values. Table 6–24. Annular-flow rate versus friction: chart data points for 2.517-inch hydraulic diameter annulus in a Halliburton 50 ppt HPG, 2% KCl neat fluid system Annular Flow: P/ L Friction versus Rate Q Curve Data Points for Specified Annulus ID and Pipe OD from 6-Point Constructed Chart Data Halliburton 50-ppt WG-11, 2% KCL Hydraulic Q P/ L Annulus Data DHYD BPM psi/100 ft Csg ID Pipe OD (ID - OD) 1 2.1 Chart Left Axis Point in in in 19.9 7.1 Chart Break Point 4.892 2.375 2.517 100 50 Chart Right Axis Point

Tubular friction gradient data for all tubular configurations Figure 6–26 shows the algorithm-calculated pipe and annulus friction gradients versus injection rate calculated for all tubulars listed in table 6–21 and table 6–22, per the above approach. Average accuracy between calculated and table 6–21 values is 99.4%, with a standard deviation of 0.8%. Thus, this 6-point approach provides the advantageous capability for calculating friction gradient data for any pipe size or tubing–casing annulus configuration for a specific fluid system. Hence, design engineers are not limited to what is available in charts, tables, or data supplied by pumping service companies. An additional advantage is that data storage requirements, such as those shown in tables 6–22 and 6–23, are much less than would be required for a large set of tubulars.

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Q vs. ∆P/∆L Chart Calc'd with 6-Points – Pipe Flow

Q vs. ∆P/∆L Chart Calc'd with 6-Points – Annular Flow

A

1,000

B

1000 A 4.000''/2.375''

A 1.380''

D 2.441''

D

Pipe Friction, ∆P/∆L (psi/100 ft)

E 2.764'' F 2.992''

E F

G 4.000'' H 4.892'' I 6.366'' Break Pt

G H 10

I

1

1

10

100

C 4.892''/2.375'' D 6.366''/2.875''

Pipe Friction, ∆P/∆L (psi/100 ft)

C 1.995''

100

B 4.892''/2.875''

C

B 1.610''

E 6.366''/2.375''

A

Break Pt

B

100

C

D E 10

1

1

10

100

Injection Rate, Q (BPM)

Injection Rate, Q (BPM)

Fig. 6–26. Pipe and annulus friction versus injection rate, constructed from six chart data points for a Halliburton 50 ppt HPG, 2% KCl neat fluid system

Example 6–7–2c. Tubular Friction Gradient Data for Tubular Configurations not Shown in Figure 6–25

Tubular friction gradient data such as shown in the legend of figure 6–25 and the corresponding data in table 6–20 often contain only a limited number of tubing and casing configurations. Note that for this example, neither the described tubing nor casing data is contained in the legends of either figure or the table. However, friction gradient can be calculated for other tubing and casing sizes pertinent to any given fluid system, in this case Halliburton 50 ppt WG-11, 2% KCl. These data can be used to address any of the above tubulars, using DHYD . Consider the following configuration for this example: QINJ: 50 bbls/min Tubing/casing (pipe/annulus) configurations: Tubing description

4½ in., 13.5 lb/ft

Tubing ID (DHYD-TBG)

3.920 in.

Tubing OD

4.500 in.

Casing description

8⅝ in., 49.00 lb/ft

Casing ID (DHYD-CSG)

7.511 in.

Annulus description

4½ in., 13.5-lb/ft tubing in 8⅝ in., 49.00-lb/ft casing

Annulus (DHYD-ANN)

3.011 in. (casing ID – tubing OD = 7.511 in. – 4.500 in.)

Equations 6–38–1 through 6–38–4 determine the chart relative QCHRT versus ΔP/ΔLCHRT values for the above tubular configurations: • Left axis • Laminar-turbulent breakpoint

345

Essentials of Hydraulic Fracturing

• Right axis Thus, the chart relative values can be calculated as follows for the various tubular configurations: • Equations for the tubing relative chart data, where DHYD-TBG = 3.920 in.: Left axis, where QCHRT-L

= 1 bbl/min:

ΔP/ΔLCHRT-L

= 10^[1.430 – 2.264log(DHYD-TBG)]



= 10^[1.430 – 2.264log(3.920)]



= 1.22 psi/100 feet

Laminar-turbulent breakpoints: QCHRT-BP

= 10^[0.08419 – 1.846log(DHYD-TBG)]



= 10^[0.08419 – 1.846log(3.920)]



= 15.1 bbls/min

ΔP/ΔLCHRT-BP

= 10^[1.441 – 1.469log(DHYD-TBG)]



= 10^[1.441 – 1.469log(3.920)]



= 3.71 psi/100 feet

Right axis, where QCHRT-R = 100 bbls/min: ΔP/ΔLCHRT-R

= 10^[3.780 – 3.734log(DHYD-TBG)]



= 10^[3.780 – 3.734log(3.920)]



= 36.7 psi/100 feet

• Equations for the tubing–casing annulus relative chart data, where DHYD-ANN = 3.011 in.: Left axis, where QCHRT-L

= 1 bbl/min:

ΔP/ΔLCHRT-L

= 10^[1.131 – 2.006log(DHYD-ANN))]



= 10^[1.131 – 2.006log(3.011)]



= 1.48 psi/100 feet

Laminar-turbulent breakpoints: QCHRT-BP

= 10^[0.835 + 1.159log(DHYD-ANN)]



= 10^[0.835 + 1.159log(3.011)]



= 24.5 bbls/min

ΔP/ΔLCHRT-BP

= 10^[1.441 – 1.469log(DHYD-ANN)]



= 10^[1.441 – 1.469log(3.011)]



= 5.87 psi/100 feet

Right axis, where QCHRT-R = 100 bbls/min:

346

ΔP/ΔLCHRT-R

= 10^[2.876 –2.931log(DHYD-ANN)]



= 10^[2.876 –2.931log(3.011)]



= 29.7 psi/100 feet

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Equations for injections down casing are equivalent to those for injections down tubing. Thus, equations for casing-relative chart data, where DHYD-ANN = 7.511 in.:

Left axis, where QCHRT-L

= 1 bbl/min

ΔP/ΔLCHRT-L

= 10^[1.430 – 2.264log(DHYD-CSG)]



= 10^[1.430 – 2.264log(7.511)]



= 0.280 psi/100 feet

Laminar-turbulent breakpoints: QCHRT-BP

= 10^[0.08419 – 1.846log(DHYD-CSG)]



= 10^[0.08419 – 1.846log(7.511)]



= 50.2 bbls/min

ΔP/ΔLCHRT-BP



= 10^[1.441 – 1.469log(DHYD-CSG)]



= 10^[1.441 – 1.469log(7.511)]



= 1.42 psi/100 feet

Right axis, where QCHRT-R ΔP/ΔLCHRT-R



= 100 (bbls/min): = 10^[3.780 – 3.734log(DHYD-CSG)]



= 10^[3.780 – 3.734log(7.511]



= 3.24 psi/100 feet

Summary of relative chart data for Halliburton 50 ppt WG-11, 2% KCl at 50 bbls/min fluid system The injection rate QINJ = 50 bbls/min is above the breakpoint rates (QCHRT-BP) for both tubing and annulus (between tubing and casing) flow. For casing, QINJ is a fraction below QCHRT-BP. Hence, the pertinent relative chart data points for the Halliburton 50 ppt WG-11, 2% KCl at 50 bbls/min are Tubing:

Breakpoint: QCHRT-BP = 15.1 bbls/min, and ΔP/ΔLCHRT-BP = 3.71 psi/100 feet



Right axis: QCHRT-R = 100 bbls/min, and ΔPΔP/ΔLCHRT-R = 36.7 psi/100 feet Tubing–casing annulus:



Breakpoint: QCHRT-BP = 24.5 bbls/min, and ΔP/ΔLCHRT-BP = 5.87 psi/100 feet



Right axis: QCHRT-R = 100 bbls/min, and ΔP/ΔLCHRT-R = 29.7 psi/100 feet Casing:



Left axis: QCHRT-R = 1 bbl/min, and ΔP/ΔLCHRT-R = 0.280 psi/100 feet



Breakpoint: QCHRT-BP = 52.2 bbls/min, and ΔP/ΔLCHRT-BP = 3.24 psi/100 feet

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Essentials of Hydraulic Fracturing

Example 6–7–2d. Comparison of Total Friction Losses Between Injection Down 6,000 ft of Tubing versus Manifolded Tubing-and-Annulus for the Halliburton 50 ppt WG-11, 2% KCl at QINJ = 50 bbls/min

Given the option and casing strings that can withstand fracturing pressures, design engineers prefer fracturing down casing. Doing so minimizes wellhead injection pressure, and thus HHP, which in turn reduces pumping charges. However, for this example, a tubing string is part of the treatment. Reasons for this can vary. One is to measure bottomhole treating pressure at various times during the treatment. With a tubing string in the well, it is possible to temporarily divert injection to either the tubing or to the annulus (as the “hot” string), and use the other as a “dead” (no-flow) string for downhole pressure measurement pertinent to net fracturing pressure calculations (as discussed in chapter 3). Then manifolded injection can be resumed, which reduces surface injection pressure, until a subsequent downhole pressure measurement is scheduled. For this example the perforation interval top is at 6,000 ft depth. Thus, both tubing and casing) length, ΔL = 6,000 ft. Note also that casing ID is uniform over the entire 6,000 ft. This is typically not the case. Casing strings are usually designed with higher weights, lb/ft, in upper sections for added tensile strength, and in lower sections for added collapse resistance. This results in different casing IDs throughout the entire string (a more complex issue). However, that is not the case here. Casing ID remains constant, at 7.511 in. The scenarios focus on injection down (a) only the tubing and (b) manifolded injection simultaneously down both the tubing and the annulus between the tubing and casing. • Injection down tubing where DHYD-TBG = 3.920 in. Relative tubing chart data slope ΔP/ΔL calculations ΔP/ΔLTBG = [log(ΔP/ΔLCHRT-R) – log(ΔP/ΔLCHRT-BP]/[log(QCHRT-R) – log(QCHRT-BP)]

= [log(36.7) – log(3.71)]/[log(100) – log(15.1)]



= 1.212 psi/100 feet at 1 BPM

Equation 6–40

Tubing friction gradient at 50 bbls/min injection rate is ΔP/ΔLTBGG = 10^{log(ΔPCHRT-BP) + ΔP/ΔQTBG[log(50) – log(QCHRT-BP)]}

= 10^{log(3.71) + 1.212[log(50) – log(15.1)]}



= 15.84 psi/100 feet

Equation 6–41

Total tubing friction pressure for 6,000 feet for Halliburton 50 ppt WG-11, 2% KCl at QINJ = 50 bbls/min is ΔPTBG

= ΔP/ΔL × ΔL/100



= 15.84 × 6,000/100



= 950 psi

Equation 6–42

• Injection Down Manifolded Tubing and Annulus. Manifolded flow calculations require that pressure at the tubing exit point is equivalent to annulus pressure at that same point. The fact that flow rates in the tubing and annulus are usually not the same must be addresses. This requires iterative solution by varying tubing (QTBG) and 348

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annulus (QANN) flow rates such that total tubular friction ΔPTBG = ΔPANN for their respective flow rates. This is readily achieved with spreadsheet macros, such as Excel’s Goal Seek macro, or its equivalent in other spreadsheets. Pertinent data and calculations: QINJ

= QTBG + QANN = 50 bbls/min

QANN

= 50 – QTBG bbls/min

DHYD-TBG

= 3.920 in.

ODTBG

= 4.500 in

DHYD-CSG

= 7.911 in

DHYD-ANN

= 3.011 in.

ΔP/ΔLANN

Relative annulus chart data slope

ΔP/ΔLANN calculations are ΔP/ΔLANN

= [log(ΔPCHRT-R) – log(ΔPCHRT-BP]/[log(QCHRT-R) – log(QCHRT-BP)]



= [log(29.7) – log(5.87)]/[log(100) – log(24.5)]



= 1.153 psi/100 feet

(per equation 6–40)

The equation for tubing friction pressure gradient at QTBG rate is ΔP/ΔLTBG

= 10^{log(ΔPCHRT-BP) + ΔP/ΔQTBG[log(QTBG) – log(QCHRT-BP)]}



= 10^{log (3.71) + 1.212[log(QTBG) – log(15.1)]}

Equation 6–43

The equation for annulus friction pressure gradient at QANN rate is ΔP/ΔLANN

= 10^{log(ΔPCHRT-BP) + ΔP/ΔQANN[log(QANN) – log(QCHRT-BP)]}



= 10^{log(ΔPCHRT-BP) + ΔP/ΔQANN[log(QINJ – QTBG) – log(QCHRT-BP)]}



= 10^{log (5.87) + 1.153[log(50 – QTBG) – log(15.1)]}

Equation 6–44

Determining manifold friction pressure gradient (ΔP/ΔLMAN) requires that the friction pressure gradient difference (ΔP/ΔLDIFF) is zero: ΔP/ΔLDIFF = ΔP/ΔLTBG – ΔP/ΔLANN

Equation 6–45

= 0 (or very small)

Iterating QTBG values for equation 6–43 and equation 6–44 that satisfy equation 6–45 yields, at ΔP/ΔLDIFF = –6 .7 × 10–6 QTBG

= 25.6 bbls/min

QANN

= 24.4 bbls/min

ΔP/ΔLMAN = 5.79 psi/100 ft Total manifolded tubing–annulus friction pressure for 6,000 feet for Halliburton 50 ppt WG-11, 2% KCl at QINJ = 50 bbls/min is ΔPMAN

= ΔP/ΔL × ΔL/100



= 5.79 × 6,000/100



= 347 psi

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Essentials of Hydraulic Fracturing

Observation: If there were not the requirement to measure bottomhole treating pressure at various times during the treatment, and the casing was capable of withstanding downhole pressures at all points, the treatment could be pumped down casing. Here the total friction component per equation 6–32 would be only 12 psi. At 50 BPM injection rate, the HHP component per equation 6–31–1 would be 14.7 HHP. That constitutes a difference of 1,150 HHP between tubing and casing injection. At a unit cost of $6.00/HHP, this would add $6,900 to the treatment cost to acquire good BHP data. However, the information gained from the bottomhole treating pressures could possibly be worth 100 times the HHP costs.

Commentary on tubular friction loss during injection Pipe and annular friction pressure data for practically all fracturing fluid systems are spreadsheet amenable to the approach described in example 6–7. It is a useful approach for determining friction loss when existing data is limited to only a few pipe sizes, and does not contain data pertinent to the fracture treatment tubular configuration of a specific design. As previously stated, casing strings are usually designed with different casing IDs throughout the entire string. Thus, the above process and algorithms require segmenting ΔLs of various segments with different DHYDs, and then adding the ΔPs over the total ΔL. This is easily accomplished using segmented spreadsheet calculations. Also, such segmenting and algorithms are integrated with many hydraulic fracturing design treatment simulators. However, it behooves design engineers to be able to confirm simulator calculations.

Friction Loss (Turbulent Tubular Flow)— Proppant-Laden Slurries Friction pressure multipliers Most fracturing treatment injection rates are high enough to induce turbulent flow in the tubulars. Proppant concentration increases tubular friction in turbulent flow. This is because particle momentum plays a primary role in energy loss in the turbulent regime. It significantly exceeds that of the apparent viscosity, µAPP. Proppant concentration (particle fraction), and proppant and fluid system density are the primary factors in turbulent flow friction loss. Proppants, being the higher density component of proppant-laden slurries, dominate the effect. Approaches to address proppant-laden slurry employ friction loss multipliers. Total friction pressure is then determined by the product of the friction loss multiplier and the neat fluid system apparent viscosity. Friction pressure for proppant-laden slurries can sometimes be a dominant factor pertinent to total treatment costs. This is because service company pumping costs are based on maximum HHP charges. Pipe friction contributes to this, per equation 6–32 (PW-INJ = σMIN + PNET + ΔPPERFS + ΔPTUBULARS – PCOL). However, friction pressure is offset by hydrostatic column pressure. Hydrostatic column pressure increases with proppant density and concentration. This reduces PW-INJ pressures. 350

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Usually, maximum HHP occurs during pad or flush displacement injection (which contains no proppant). Pad and displacement fluids exhibit significantly lower hydrostatic column pressures and thus require higher wellhead injection pressures than do higher density proppant-laden slurries. However, if the pad or displacement fluid is liquid and the base proppant laden stages are foam with low proppant density and low concentration, maximum HHP may occur during those stages What is presented here is a synthesis of approaches that should be, for the most part, sufficient for design. If not, the reader is directed to SPE Monograph V. 12, Chapter 9, pages 189–192. The referenced section comprises lucid, comprehensible, in-depth discussion, equations and examples covering the issue. In this book, comprehensive reiteration of that referenced is essentially redundant. Example calculations are presented. One addresses non-cross-linked, aqueous-based, proppant-laden slurries. The other covers non-cross-linked, hydrocarbon-based slurries. Approaches for cross-linked slurries are not presented per se. However, in view of the system density dominance over apparent viscosity, the non-cross-linked approaches should adequately represent the effects for cross-linked slurries. Important cautionary advice: For proppant-laden slurries and neat polymer-thickened fluid systems, if bottomhole pressure treating data are required for net fracturing pressure analyses, they should be obtained via bottomhole measurement rather than from surface injection pressures and friction loss calculations. Technology for calculating reliable slurry bottomhole pressures is yet to be developed. Using the calculation technology that is currently available can yield seriously misleading results.

Friction pressure multipliers—non-cross-linked, aqueous-based, proppantladen slurries Figure 6–27 shows SPE Monograph V. 12 Figure 9.17, which accounts for friction pressure multiplier versus proppant concentration for 40 and 50 ppt HPG fluid systems in turbulent flow at 26 bbls/min for a 2⅜-inch tubing/5½-inch casing annulus wellbore configuration. Typically, during a fracturing treatment, injection down tubulars (pipe, annulus) exhibits turbulent flow. Here slurry density dominates fluid viscosity friction loss behavior. This is obvious in equation 6–46 that describes the friction pressure multiplier behavior shown in figure 6–27 (“Equation 9.30,” Gidley et al. 1989, 190).

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Essentials of Hydraulic Fracturing

Fig. 6–27. Friction pressure multiplier versus proppant concentration, turbulent annular flow, 26 bbls/min, 23/8 inch tubing in 5½ inch casing, HPG fluid system Source: “Figure 9.17,” Gidley et al. 1989, 190. FM-AQ = µREL0.2ρREL0.8 = ΔPSL/ΔPNF

Equation 6–46

where FM-AQ

Friction pressure multiplier for aqueous fluid systems (dim.)

µREL

Relative viscosity, µS/µN (dim.)

µS

Slurry viscosity (cp)

µN

Neat system viscosity (cp)

ρREL

Relative density, ρSL/ρNF (dim.)

ρSL

Slurry density (lb/ft3)

ρNF

Neat system density (lb/ft3)

ΔPSL

Slurry friction loss (psi)

ΔPNF

Neat system friction loss (psi)

Figure 6–28 depicts the digitized data in figure 6–27 converted to proppant particle concentration (as opposed to lb/gal slurry). Thus, it applies to all proppants including sand, resin-coated sand, sintered bauxite, and other ceramics at a tubular flow velocity of 77.25 ft/sec. Equation 6–47 extends the data beyond the figure 6–27 9-lb/gal slurry sand concentration to an equivalent of 12-lb/gal slurry.

352

Chapter 6 | Fracturing Fluid System Rheology and Proppant Transport Friction Pressure Multiplier–Aqueous–Base Data @ 75 ft/sec Tubular Velocity

Friction Pressure Multipliier

2.0

1.8

1.6

1.4

1.2

1.0

Data

0

0.1

0.2

0.3

Eqn. 6-42

0.4

0.5

0.6

Proppant Particle Fraction Fig. 6–28. Base friction pressure multiplier versus slurry proppant fraction: non-cross-linked aqueous proppant-laden slurries at 75 feet/sec velocity Equations 6–47 and 6–48 extend the application for general use by fluid velocity adjustment via flow rate and tubular DHYD. VT = [5.615QINJ/60]/[π(DHYD/24)2]

Equation 6–47

where VT

Velocity in the tubular (ft/sec)

QINJ

Injection rate (bbls/min)

DHYD

Tubular diameter, IDPIPE or DHYD, annulus (in.)

FM-AQ

= 1 + (VT/FM-BASE)1.668FP = 1 + (VT/77.25)1.668FP

Equation 6–48

where FM-BASE

Base friction pressure multiplier at 77.25 ft/sec velocity down tubulars

FP

Proppant particle fraction, FP = SPPG/(8.331gPROP)

SPPG

Proppant concentration (lb/gal slurry)

gPROP

Proppant specific gravity (dim.)

(per equation 6–27)

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Example 6–7–2e. Friction Loss Multiplier and Tubular Pipe Friction Loss: 8-lb/gal

Sintered Bauxite

Friction loss multipliers for slurry flow apply to flow down pipe (tubing or casing), annulus, and manifold tubing–annulus. The approach to pipe flow is relatively straightforward. Manifold flow is a bit more involved. It requires integrating equation 6–46 for VT and equation 6–48 for FM-AQ into tubing flow equation 6–43 to calculate ΔP/ΔLTBG and into annulus flow equation 6–44 for ΔP/ΔLANN, and then iterating on injection rates QTBG and QANN (where QANN = QINJ – QTBG) so that the products of FM-AQ-TBGΔP/ΔLTBG = FM-AQ-ANNΔP/ΔLANN. Step-by-step details are only given for the pipe (tubing or casing) wellbore configurations. However, for brevity’s sake, only calculated results are shown for manifold flow.

Pipe (tubing or casing) friction loss multipliers Here the example, and those that follow, focuses on injection down tubing. The value for tubing friction loss gradient from example 6–7–2d is ΔP/ΔLTBG = 15.84 psi/100 feet

(per equation 6–41)

Thus, calculations for tubing flow provide a perspective of maximum HHP requirements. Thus, for the neat Halliburton 50 ppt WG-11, 2% KCl fluid system, ΔPTBG – 950 psi

(per equation 6–42)

Using this neat fluid system data for the same proppant-laden system loaded with 8-lb/gal slurry sintered bauxite, the friction loss multiplier (FM-AQ) is calculated using tubing velocity (VTBG) and FP as follows: VTBG

= [5.615QINJ/60]/[π(DHYD-TBG/24)2]



= [5.615 × 50/60]/[π(3.920/24)2]



= 4.559 ft/sec

FP

= SPPG/(8.331gPROP)



= 8/(8.331 × 3.65)



= 0.2631

FM-AQ-TBG

= 1 + (VTBG/77.25)1.668FP



= 1 + (4.559/77.25)1.668 × 0.2631



= 1.317

The ΔPSLURRY for 8-lb/gal slurry with sintered bauxite is ΔPSL

= ΔPTBGFM-AQ



= 950 × 1.317



= 1,251 psi

Hence, the value of equation 6–32 354

PW-INJ

= σMIN + PNET + ΔPPERFS + ΔPTUBULARS – PCOL

(per equation 6–47)

(per equation 6–27)

(per equation 6–48)

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becomes PW-INJ

= 3,900 + 500 + 4 + 1,251 – PCOL



= 5,655 – PCOL psi

This compares to the neat fluid system pressure of PW-INJ

= 3,900 + 500 + 4 + 950 – PCOL



= 5,354 – PCOL psi

Manifold tubing—annulus friction loss multipliers pertinent to slurries The calculated value for manifold friction loss gradient from example 6–7–2d (ΔP/ΔLMAN = 8.35 psi/ft), where ΔP/ΔLDIFF ≈ zero (0) psi/ft, applies only to the neat fluid system. For slurries, the different hydraulic diameters, DHYD-TBG = 3.920 in. and DHYD-ANN = 3.011 in., and different flow rates, QTBG = 29.5 bbls/min and QANN = 20.5 bbls/min yield different VTUBULAR velocities, and therefore different friction loss multipliers: FM-AQ-TBG and FM-AQ-ANN. For slurries, this changes the ΔP/ΔQ and ΔP/ΔL values. Manifold slurry flow requires integrating VTBG and FM-AQ-TBG into ΔP/ΔLTBG equations and VANN and FM-AQ-ANN into ΔP/ΔLANN equations, and then iterating QTBG until ΔP/ΔLTBG ≈ ΔP/ΔLTBG, as is shown for neat fluid systems. The equations pertinent to tubing are ΔP/ΔQTBG = [log(ΔPCHRT-R) – log (ΔPCHRT-BP]/[log(QCHRT-R) – log(QCHRT-BP)] (per equation 6–40) ΔP/ΔLTBG = 10^{log(ΔPCHRT-BP) + ΔP/ΔQTBG[log(QTBG) – log(QCHRT-BP)]} (per equation 6–43) VTBG = [5.615QINJ/60]/[π(DHYD-TBG/24)2]

(per equation 6–47)

FM-AQ-TBG = 1 + (VT/FM-BASE)1.668FP

(per equation 6–48)

The equations pertinent to the annulus are ΔP/ΔQANN = [log(ΔPCHRT-R) – log (ΔPCHRT-BP]/[log(QCHRT-R) – log(QCHRT-BP)] (per equation 6–40) ΔP/ΔLANN = 10^{log(ΔPCHRT-BP) + ΔP/ΔQANN[log(QANN) – log(QCHRT-BP)]} (per equation 6–43) VANN = [5.615QINJ/60]/[π(DHYD-ANN /24)2]

(per equation 6–47)

FM-AQ-ANN = 1 + (VT/FM-BASE)1.668FP

(per equation 6–48)

Iteration such that FM-AQ-TBG × ΔP/ΔLTBG ≈ FM-AQ-ANN × FM-AQ-ANN yields (for injecting 8 lb/gal slurry, sintered bauxite at 50 bbls/min): QTBG

= 27 bbls/min

QANN

= 23 bbls/min

ΔP/ΔLMAN = 7.22 psi/100 ft, and for ΔL = 6,000 ft ΔPMAN

= 433 psi 355

Essentials of Hydraulic Fracturing

This compares to the neat fluid calculations in example 6–7–2d: QTBG

= 25.6 bbls/min

QANN

= 24.4 bbls/min

ΔP/ΔLMAN = 5.79 psi/100 ft

ΔL

= 6,000 ft

ΔPMAN

= 347 psi

Example 6–7–2f. Hydrostatic Column Pressure Hydrostatic column pressure (PCOL) is determined by equation 6–49: PCOL = 0.434 gCOL∆LCOL

Equation 6–49

where PCOL

Hydrostatic column pressure (psi)



∆P/∆L gradient of a 1.0 specific gravity column fluid (psi/ft)

0.434

gCOL

Specific gravity of the column fluid

∆LCOL

Vertical (true vertical) tubular column span (ft)

Here the PCOL values are compared between the neat fluid system and the 8 lb/gal slurry system where gFLUID

1.013 as stated in the example 6–7 basic data set

gSLURRY

1.707 as calculated in example 6–7–1

∆LCOL

6,000 ft

Thus, for the two columns, PCOL-NEAT

= 0.434gFLUID∆LCOL



= 0.434 × 1.013 × 6,000



= 2,638 psi

PCOL-SLURRY = 0.434gSLURRY∆LCOL

= 0.434 × 1.707 × 6,000



= 4,445 psi

Example 6–7–g. Summation of Wellhead Injection Pressure and Hydraulic

Horsepower

This compares the neat versus slurry and tubing versus manifold wellhead injection pressures and hydraulic horsepower requirements for QINJ = 50 bbls/min. • Injection down tubing –– Wellhead injection pressure • PW-INJ 356

= σMIN + PNET + ΔPPERFS + ΔPTUBULARS – PCOL (per equation 6–32)

• PW-INJ-NEAT = 3,900 + 500 + 4 + 1,251 – 2,638

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= 3,017 psi • PW-INJ-SLURRY = 3,900 + 500 + 4 + 1,251 – 4,445 = 1,210 psi –– HHP for the neat fluid and the slurry: • HHP = QINJPW-INJ/40.8

(per equation 6–31)

• HHPNEAT = QINJPW-INJ-NEAT/40.8 = 50 × 3,017/40.8 = 3,697 hhp • HHPSLURRY = QINJPW-INJ-SLURRY/40.8 = 50 × 1,210/40.8 = 1,483 hhp Thus, for 4.500 inch tubing pumping a 50-ppt WG-11, 2% KCl, non-cross-linked fluid system with 8-lb/gal sintered bauxite slurry at 50 bbls/min results in 1,807 psi lower wellhead surface injection pressure, and requires 2,214 less hydraulic horsepower than for the neat fluid system. • Injection down manifolded tubing and annulus –– Wellhead injection pressure • PW-INJ

= σMIN + PNET + ΔPPERFS + ΔPTUBULARS – PCOL (per equation 6–32)

• PW-INJ-NEAT = 3,900 + 500 + 4 + 347 – 2,638

= 113 psi • PW-INJ-SLURRY = 3,900 + 500 + 4 + 433 – 4,445



= 392 psi –– Hydraulic horsepower for the neat fluid and the slurry, i.e., • HHP

= QINJPW-INJ/40.8

• HHPNEAT

= QINJPW-INJ-NEAT/40.8



= 50 × 2,113/40.8



= 2,589 hhp • HHPSLURR

(per equation 6–31)

= QINJPW-INJ-SLURRY/40.8



= 50 × 392/40.8



= 480 hhp

The results calculated in the previous examples demonstrate the wide variations that fluid system rheology and wellbore configuration can cause in wellhead injection pressure and horsepower for a fracturing treatment. They also provide a perspective of the relative impact that each parameter has on the requirements for a treatment. Admittedly, rheology calculations are tedious and somewhat arduous. However, as mentioned previously, such calculations can be done easily using spreadsheets. Once these have been constructed, the tedium disappears, and leaves design engineers a menu of utilities that are essential to designing fracturing treatments, and easily and quickly checking results from fracturing treatment design models. 357

Essentials of Hydraulic Fracturing

Application restrictions pertinent to friction loss multipliers for non-crosslinked, aqueous-based fluid systems The above discussion pertains to the turbulent vertical flow down tubulars in non-crosslinked, aqueous proppant-laden slurry. The discussion pertinent to this implies that the approaches presented here not be reliably applicable to cross-linked systems. Additionally, these approaches are restricted to vertical (or near vertical) flow. They should not be used for nonvertical applications.

Friction loss multipliers: non-cross-linked, hydrocarbon-based proppant-laden slurries A previous example introduced friction loss multipliers for aqueous-based fluid systems. Here, the discussion pertains to hydrocarbon-based systems. As with aqueous-based systems, the multipliers are applicable only to turbulent flow. Figure 6–29 shows SPE Monograph V. 12 Figure 9.16, which shows friction pressure multiplier versus proppant concentration for crude oils (with gravities from 10° to 60°API) at 30 bbls/min down 5½-inch casing. This has similar application to that of figure 6–28 for aqueous based systems. Figure 6–30 depicts data in figure 6–29 converted to proppant particle concentration (as opposed to lb/gal slurry). It applies to all proppants including sand, resin-coated sand, sintered bauxite, and other ceramics at a tubular flow velocity of 25 ft/sec. It also extends the proppant concentration range.

Fig. 6–29. Friction pressure multiplier versus proppant concentration, turbulent casing flow, 30 bbls/min, down 5½-in. casing, 10°–60° API crude Source: “Figure 9.16,” Gidley et al. 1989, 190.

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Friction Pressure Multiplier–Hydrocarbon–Base Data @ 25 ft/sec Tubular Velocity 2.2

Friction Pressure Multiplier

2.0 1.8 1.6 1.4 1.2 1.0

0

0.1

0.2

0.3

60ºAPI Data

Eq. 6-48

50ºAPI Data

Eq. 6-48

40ºAPI Data

Eq. 6-48

30ºAPI Data

Eq. 6-48

20ºAPI Data

Eq. 6-48

10ºAPI Data

Eq. 6-48

0.4

0.5

0.6

Proppant Particle Fraction Fig. 6–30. Base friction pressure multiplier versus slurry proppant particle fraction for 10°–60°API hydrocarbon proppant-laden slurries at 25 ft/sec velocity Equation 6–50 extends (by inference) the data beyond the figure 6–29, 9 lb/gal slurry sand concentration to an equivalent of 10 lb/gal slurry. Additionally, it can be applied to any tubular velocity where the slurry exhibits turbulent flow. As with aqueous proppant-laden slurries, application is limited to vertical (or near vertical) flow. The divisor (i.e., “25”) in equation 6–50 derives from the base rate of 25 bbls/min for the figure 6–29 data. FM-OIL = A + VT/25(BFP + CFP2)

Equation 6–50

where FM

Friction pressure multiplier for oil at velocity VT (dim.)

VT

Tubular velocity, per equation 6–46 (ft/sec)

FP

Proppant particle fraction

The equation coefficients A, B, and C are

A

= 0.9999 – 1.570 × 10–4 × °API + 2.678 × 10–6 × °API2



B

= 2.171 + 2.231 × 10–2 × °API – 5.308 × 10–5 × °API2



C

= –1.301 – 4.739 × 10–3 × °API – 1.956 × 10–4 × °API2

Application of equation 6–50 to hydrocarbon-based proppant-laden slurries is identical to the approach presented in example 6–7–2e. 359

Essentials of Hydraulic Fracturing

Warning about calculating downhole wellbore injection pressure from surface pressure measurements: As discussed in chapter 3, net fracturing pressure versus pumping time log-log charts (Nolte–Smith Plots) provide significant insight about dynamic fracture propagation during a treatment. The warnings in that section, and previous statements in this chapter, are re-emphasized that downhole injection pressure values that are calculated have a very high probability of being significantly different from what actual measurements would yield. If high precision bottomhole pressure treating data are required for proppant-laden slurries (and even gelled fluid systems), they should be obtained using bottomhole measurement rather than from surface injection pressures, fluid system densities (neat and proppant-laden), and friction loss calculations. The technology for calculating reliable slurry bottomhole pressures is yet to be developed. Using what is currently available can yield seriously misleading results.

Proppant Transport Proppant transport is important throughout all aspects of a fracturing treatment, including: • Through surface equipment—blending equipment, pumps, manifolds, injection lines, wellhead equipment • In tubulars (pipe, annulus)—vertical, inclined, horizontal • Through perforations • In-fracture flow transport (aspects: proppant placement, fracture conductivity)

Fracturing treatment screeouts Screen-out usually terminates the fracturing treatment. Fracture treatment proppant aspects typically focus primarily on in-fracture proppant transport pertinent to maximizing fracture conductivity. However, ensuring that proppant-laden slurries enter the fracture is equally important. Screen-outs in surface equipment may, or may not, permanently terminate a treatment. If they do, and remedial measures are employed within a suitable time frame, the effect is usually only a temporary interruption. Surface equipment screen-outs usually happen suddenly. Blender screen-outs typically result in interruptions. However, a screen-out in a pump or between the pump and the perforation usually results in equipment rupture that terminates the job. Screen-outs at the perforations often occur less suddenly. These can occur by gradual proppant build-up in the tubulars until perforation flow is no longer possible. This is indicated by rapidly increasing surface pressures, but does allow time to cease injection before exceeding surface equipment pressure limits. In-fracture screen-outs, as discussed in the chapter 6 section “Fracture Propagation Geometry Inferences from Net Fracturing Pressure Behavior,” are indicated by gradually increasing surface pressures that allow adequate time to adjust the fluid system or injection rate or stop injection before reaching down-hole or surface equipment pressure limits.

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Transport through surface equipment Proppants can screen out in the surface equipment. Events that are easily preventable, such as those listed below, can and have happened. • Blenders have proppant concentration limits, and can be overloaded by the proppant feeders. • Improperly configured blender-to-pump manifold piping can starve liquid in one or more pumps, and overload proppant particle fraction limits in others. • Pumps also have proppant concentration limits (especially for larger mesh, low density proppants). If the pump head proppant particle fraction limits are exceeded, the head will rupture. Confirm these limitations with the pumping service company. • Pump valves can clog. • Sharp turns in lines to the wellhead can plug at high injection rates, or can take fluids from the downstream slurries because of fluid/proppant momentum differences. • Restrictions in piping below the wellhead can cause plugging. • Proppant-laden slurries exiting from a smaller to larger diameter pipe exhibit excessive turbulence that can cut through casing below the injection tubing exit point. This is exacerbated for slurries of ceramics and sintered bauxite. Any of the above can terminate a job. Some can be extremely dangerous. They can be prevented by proper planning.

Through tubulars and perforations Down vertical tubulars and through perforations Proppant transport problems down vertical tububulars and through perforations are relatively rare. One possibility is where wellhead injection rate is reduced to the point that proppant fall rates exceed fluid velocity. Here, proppant can gradually build up in the wellbore and eventually cover the perforated interval, thus blocking flow. Another may occur if tubular diameters are small and leaks develop in the tubular string. This could possibly dehydrate slurry liquid concentration to the point that particle fractions exceed effective transport limits. At typical injection rates, proppant momentum significantly exceeds that of the slurry liquids. At the perforations there is a right angle change in flow direction. When the slurry turns the corner at the perforations, liquid/particle momentum differences and turbulence may cause temporary changes in slurry particle fractions. Thus, proppant accumulation continues building in the wellbore below the bottom perforation until equilibrium is reached. Often, post-frac wellbore proppant tops are measured to depths somewhat below (e.g., 10 to 20 feet) the bottom perforation. Proppant buildup accumulation in the pipe precludes obtaining post-frac behindthe-pipe proppant survey data below the wellbore proppant top.

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Essentials of Hydraulic Fracturing

The effect of tubular shear rate on some fluid systems can be dramatic. Those most sensitive to it include: • Foam systems • Highly loaded polymer systems cross-linked with heavy transition metals such as –– Titanium –– Chromium –– Zirconium Foams can be severely changed (either degraded or tightened) by shear, depending on the foam type. Highly loaded polymer systems cross-linked with heavy transition metals are also severely affected by shear, but in a different way. The very strong cross-linking bonds formed by these systems can be broken under high shear, and take a long time to heal. Hence, the fluid system that exits the surface injection pump may be much different, rheologically, than the system that ends up in the fracture. Borate cross-linkers are hydrogen bonded, and thus are not as severely affected by shear. If the hydrogen bonds are broken, borate cross-linked fluids heal rather quickly. Hence, they are usually not as subject to shear degradation as foams or heavy transition metal cross-linked systems. Non-cross-linked system in-fracture performance generally adheres to the behavior described in equation 6–16 in regard to shear effects.

Inclined or horizontal tubulars These configurations need to be seriously addressed by design engineers. Separation of the proppant from the fluid system can occur by gravity segregation. Here there is possibility that the fluid system will override or partially override the wetted proppant aggregate. This is aggravated by • Large diameter proppants • Density and/or apparent viscosity differences between the wet proppant aggregate and the fluid system (proppant concentrations exhibit an apparent viscosity multiplier in slurries) • Density and/or apparent viscosity differences between one fluid system and another • The angle of inclination of the tubulars Proppant transport in horizontal (as well as vertical) tubulars is better understood than that for inclined tubulars. Proppant transport problems in horizontal or inclined pipes effects fracturing fluid displacing and flushing operations. Over long intervals proppant can aggregate along the lower side of the tubulars. This reduces the effective tubular flow cross section, which increases flow friction effects. When flushing at the end of the job, care must be taken to avoid unintentional overflushing. Unintentional over-flushing can move proppant out and away from the wellbore. This can seriously reduce near-wellbore fracture conductivity. 362

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Proppant Transport In Fractures Perceptions of proppant transport in vertical fractures In-fracture proppant transport focuses on proppant placement to maximize fracture conductivity. Perceptions of fluid system proppant transport characteristics include: • Equilibrium banking (poor transport, maximum proppant settling rates) • Good proppant transport • Excellent to near-perfect transport Figures 6–31 through 6–33 depict perceptions of transport and settled proppant beds during a treatment. These range from equilibrium banking, to good, to near perfect transport. It is unrealistic to expect fluids that are sometimes called perfect transport fluids (essentially no proppant settling from wellbore to fracture tip) to exhibit such behavior throughout the entire vertical fracture. However, near perfect transport can be achieved in portions of the fracture, with appropriate fluid systems. Generally speaking: • Non-gelled or low gel concentration fluid systems exhibit equilibrium banking transport • Non-cross-linked fluid systems exhibit poor to good transport behavior • Cross-linked fluid systems exhibit very good to near perfect transport • Emulsions and foam systems exhibit excellent to near perfect transport

Poorest proppant transport—Equilibrium banking proppant transport fluid systems Figure 6–31 depicts equilibrium banking where proppant settling rates are high. This occurs when using low viscosity fluid systems with low drag coefficient fluids (e.g., gasses, water, brine, low polymer- concentration, non-cross-linked, etc.). Here proppants settle rapidly after entering the fracture and form a settled bed at the fracture bottom. Subsequent slurry injection continually forms a dune-like proppant bed pattern. Thus, what initially enters the fracture is deposited nearest to the wellbore and proppants injected later are continually deposited further away from the wellbore. When using tracers for post-frac proppant bed surveys, it is necessary to inject tracers in both early and late injection stages to ensure a sense of the entire proppant bed.

363

Essentials of Hydraulic Fracturing

Fig. 6–31. Equilibrium banking proppant transport

Good proppant transport fluid systems Figure 6–32 shows experimental proppant transport observations in a macro-scale (20-feet long, 1-foot tall) parallel-plate fracture simulated apparatus with no fluid loss occurring (Gidley et al. 1989, 22). The apparatus includes • Proppant-slurry blending • Transport through perforations • Transport observations near the test cell exit

Fig. 6–32. Good proppant transport fluid systems—four distinct domains Source: “Figure 1.53,” Gidley et al. 1989, 22.

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Observations were made via an optical window near the end of the fracture. Even though the results are qualitative as opposed to quantitative, they provide a perspective of the behavior of a good transport fluid system. By virtue of the proppant concentration through the optical window, this investigation identified four distinct proppant transport domains: 1. Settled bank: No movement. The slurry above is passing over it (per equilibrium banking) 2. Bed load: proppant is crawling or rolling over the settled bank 3. Fluidized layer: proppant is settling 4. Turbulent transport: no proppant settling (perfect transport)

Best proppant transport—excellent to near-perfect proppant transport fluid systems Figure 6–33 depicts proppant transport for excellent to near-perfect transport fluid systems. Here, with low proppant settling rates, the majority of what first enters the fracture is transported farthest from the wellbore. Settled bed height magnitudes as shown at the bottom of the figure may be exaggerated for these systems. Near perfect proppant transport fluid systems exhibit very small bed heights.

Fig. 6–33. Excellent to near perfect proppant transport

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Essentials of Hydraulic Fracturing

Laboratory Proppant Transport Testing Developments After 1990 Subsequently, the results of several types of laboratory equipment pertinent to proppant transport have been developed. This has greatly improved the industry’s perception and understanding of proppant transport behavior. Large-scale laboratory proppant transport testing. For example, a large-scale, high-pressure simulator (HPS), residing at the Well Construction Technology Center, University of Oklahoma, has been employed by various industry consortiums for proppant transport studies on many fluid systems. Its details are as follows: • Dimensions: length: 9.3 feet; height: 7 feet • Service rating: 1,200 psi, 250°F • Platen sections: 12, 4 horizontal by 3 vertical, each 28-inches square, with 1-inch thick interchangeable rock faces of desired permeability and texture • Platen width—each variable, 0 to 1.25 inches • Proppant concentration in each platen measured by 121 (11 × 11) fiber-optic LED light intensity sensors • Inlet, exit perforation configurations are variable, and can be up to 11 equally spaced • Pre-test fluid system and slurry blending operate per field practices Other smaller scale equipment has been developed that provides the industry the ability to investigate the many different factors affecting proppant transport. An example of a test in a 9-platen (3 × 3) configuration, simulating proppant transport in a 7-foot × 7-foot × 0.375-inch-wide fracture is shown in figure 6–34. Test conditions were • Injection: 30 gal/min for 10 minutes • Slurry: 40 ppt, non-cross-linked HPG 6 lb/gal 20/40 mesh sand • Temperature: Not specified Sand concentration listed for each platen section in figure 6–34 (14-inch settled bed height, and top to bottom increasing sand concentration) indicates a behavior similar to that described per figure 6–32. Tests with such equipment expand significant insight about proppant transport behavior, especially for viscoelastic (cross-linked) fluids. Bench-scale proppant transport test equipment. Figure 6–35 depicts a schematic of a proppant viscometer that employs a Fann Model 50 type viscometer where the bob is replaced by a spindle with flags and flags are installed on the cup walls. This allows investigation of a fluid’s viscoelastic (cross-linked) effect on proppant settling by virtue of volume-average viscosity (VAV) determined from volume-average shear rate versus volume-average shear stress measurements. Such studies have identified factors, previously not considered, pertinent to proppant transport behavior. 366

Fig. 6–34. Proppant transport profile: 30 gal/min injection for 10 minutes, 40 ppt non-cross-linked HPG 6 lb/gal 20/40 mesh sand Source: Subhash, Asadi, and Lord 2001.

Fig. 6–35. Proppant viscometer shaft and cup Source: Harris, Morgan, and Heath 2005.

Essentials of Hydraulic Fracturing

Vertical-fracture proppant transport theories Theory basic to proppant transport in vertical fractures began with Stokes’ law, per the general expression in equation 6–51. In view of the facts below, parameter units and conversion constant values are omitted in equation 6–50: 1. Design engineers seldom perform proppant transport calculations per se. 2. Stokes’ law is not strictly applicable for the majority of fracturing fluids currently in use. Regardless, it is mentioned to provide a general perspective of parameter relativity, being that: • Proppant diameter is a major factor in settling velocity. • Vertical settling velocity increases as Δρ increases, and decreases as µN increases. VZ = CdPROP2Δρ/µN

Equation 6–51

where VZ

Vertical proppant settling velocity



Unit conversion factor

C

dPROP

Proppant average diameter

Δρ ρPROP – ρNF ρPROP

Proppant particle density

ρNF

Neat fluid system density

µN

Neat fluid system viscosity

Subsequently, laboratory experiments have indicated that Stokes’ law and power-law related approaches do not adequately reflect proppant transport behavior. Some of the reasons for this are that Stokes’ law does not account for: • Proppant particles clumping together—this increases mass/surface area density • Hindered settling—particles bumping into one another • Velocity variations—vertically, laterally • Fluid loss to the formation –– Viscosity increase—by gel liquid dehydration into formation matrixes, into fissures, etc. –– Fracture wall filter cake effects on velocity • Viscosity variations, viscous fingering • Dependence on viscoelastic fluid parameters G prime (G´) and G double prime (G´´) and thermal and mechanical (shear) history that are not available from typical laboratory tests • The existence of non-vertical fractures • Irregular fracture walls—width variations, ledges, etc. • Fluid system uniqueness 368

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• Proppant/fluid system reactions—chemical, interfacial, etc., effects proppant-type/ fluid-system Each fluid system at in situ conditions (proppant type, proppant concentration, temperature, shear, and time) exhibits unique proppant transport behavior. Recent findings suggest that proppant type has a major effect on proppant transport. Chemical, interfacial, etc., interaction between proppant and fluid system affects transport behavior. Studies with the figure 6–35 proppant viscometer identified significant differences in transport slurry viscosities because of different cross-linker and breaker reactions between the proppants and fluid systems. Additionally, fluid rheology tests are typically conducted at shear rates exceeding what typically occurs in a fracture during proppant transport. Thus, using n-Prime, K-Prime, viscosity, etc., values from such tests may not reflect proppant transport behavior for a lower shear rate environment. Consequently, researchers have developed adaptations to Stokes’ law, or pertinent theoretical approaches to address some of the aspects listed above. Much work remains to be done in order to bring the proppant transport learning curve to a comfortable level industry-wide.

Computer simulator, vertical fracture proppant transport calculations Some fracturing models ignore proppant transport. Others employ a fall rate factor, input by the frac design modeler for a given fluid system. This adjusts Stokes’ law proppant calculated settling rates by that factor. More sophisticated models contain complex algorithms. Design engineers are left to inquire as to whether or not such algorithms reside in their models of choice, and if so, what they entail. In models that do address proppant transport, the pictures displaying proppant concentrations and distribution in the fracture are impressive. However, the reader is cautioned about taking model results at face value. Some may be more valid than others. None address all of the issues listed above. The problem is not as much with the models themselves as it is with the lack of definition and understanding about the behavior of fluid systems commonly used today. Models can be quite helpful to design engineers. However, model calculations rely on the rheological data input. Thus, it is necessary that this input be as representative as possible.

Proppant transport in horizontally oriented fractures Proppant transport is not, in itself, the issue in horizontally oriented fractures. Here, the key factor is horizontal proppant distribution. There is a paucity of research in this area, primarily because of the limited percentage of wells where horizontally oriented fractures occur. In the event that one is faced with the situation, primary considerations to be addressed include (1) the rapid slurry velocity decline from the wellbore to the slurry penetration radius, and (2) viscous fingering of slurry. To mitigate potentially detrimental effects, design engineers are left with few options.

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Desktop estimates: proppant transport-related fracture conductivity Design engineers are seldom called upon to perform proppant transport calculations. These are better left to computer fracture design models. However, model fracture conductivity calculations should be confirmed to be within a reasonable degree of one's expectations. In this regard, the reader is directed to the discussion and examples in the chapter 7 section Closed/Healed Fracture Width versus Proppant Concentration in the Fracture Charts for comparison.

Fluid System Pumping, Staging, and Scheduling Considerations When designing fracturing treatment, the following list serves as a guide for discussion points between design engineers and service companies. These are particularly pertinent to developing fracturing treatment pumping schedules, i.e., • How much (pad, slurry, flush) of what (fluids, proppants) should be pumped • What should be the composition of each stage –– Fluid system type, gel loading –– Proppant type, size, concentration • At what injection rates should each stage be pumped • What wellhead surface pressures should be expected for each stage • How should the tubulars be flushed at the end of the job The discussion considerations and points include: • Rheological behavior –– Down tubulars and through perforations • Shear effects • Temperature effects –– Along/in the fracture ·· Temperature effects ·· Shear effects ·· Time • Proppant transport • Slurry - proppant concentrations • Fluid loss dehydration • Fracturing-fluid/formation interaction • Formation damage considerations –– Chemical –– Interfacial tension

370

• Fracturing-fluid/proppant-pack interactions –– Gel-plugging

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• Breaking/cleanup behavior • Other chemical requirements • Chemical loading/mixing scheduling/timing

Flowback—Fluid System Recovery and Cleanup Enhancement In tight formations (both gas and oil) the capillary pressure effects of low-permeability micropores can have a significant effect on both long-term fracturing fluid recovery and on short-term post-frac production cleanup.

Short-term cleanup Short-term cleanup or flowback can be enhanced by energizing fluids with nitrogen or carbon dioxide, usually in the later injection stages (even in the displacement stage at the end of the job). This provides a lower density energized fluid that will cause faster flowback. Some of the cautionary issues include • Calculating and pumping displacement volumes, so as not to overflush the neat displacement fluids past the perforations and into the fracture such that it reduces near-wellbore fracture conductivity • It requires a relatively quick turnaround to bring the well back on production, so that the energized fluid does not dissipate into the formation. • The fracture closure techniques used to allow the formation to lock the proppant pack in place must minimize the flowback that would carry proppant out of the fracture There are many ways to address these issues. Hence, design engineers should always discuss them with the fracturing service companies when selecting and designing fracturing fluid systems for candidate wells.

Long-term recovery enhancement Capillary pressure Fluid-rock interfacial tension capillary forces act rather quickly to imbibe fracturing fluids into the formatting porous matrix. They can hold them there for long periods. In microdarcy to nanodarcy formations, capillary pressures can have psi values anywhere from a thousand to ten thousand and beyond. It may take months, possibly years, until pressure differentials between the reservoir and the fracture are sufficient to overcome capillary forces and unblock those pores to allow reservoir fluid flow. Mitigation can sometimes be partially achieved by adding surfactants (of which there are several) to fluid systems. There is no one single recipe for this. It depends on the chemistry of the fluid system, formation mineral content, pore throat size, pore configuration, etc. It is definitely an agenda item on the design engineer’s discussion list with the service company. 371

Essentials of Hydraulic Fracturing

Clay swelling Other phenomena, such as clay swelling mitigation, also need to be addressed. For many formations the addition of 2% to 3% potassium chloride (KCl) to a fluid system will mitigate clay swelling sufficiently (more than five percent is often a waste of money). Kaolinite clays are relatively benign. However, montmorillonites, smectites, vermiculites, etc., can have a negative impact. Mitigation requires the addition of various clay stabilizers to the fracturing fluid system. Again, this is definitely an agenda item on the design engineer’s discussion list with the service company.

Mitigating Microcrack Gumming in the Formation Microdarcy and nanodarcy formations (e.g., shales, coals, diatomites, silicious formations, etc.) can exhibit a maze of fractures or microcracks that are offshoots from the dominant fracture system. Also, in others, it is possible that auxiliary fractures will open near the wellbore when net fracturing pressures reach relatively high levels. Upon fracture closure after a fracturing treatment, these network offshoot fractures that have been invaded by fluid systems will, in effect, be formation permeability barriers. There will be fluid system gelling agent trapped in the closed microcracks. Mitigating this requires selecting as low a gel loading as possible that will still create the fracture width and proppant transport necessary for the treatment. This also applies to the minimization of fracture conductivity damage by fracturing fluid systems.

Summary of Considerations for Fluid System Flow Behavior and Proppant Transport Design engineers should be aware of the sensitivities innate to prospective fluid systems that are being considered for a specific fracturing treatment. They must ensure that these systems contain the requisite component recipes to yield the required performance at in-fracture conditions throughout the fracturing treatment entirety. This includes an awareness of the effects of overloading or under-loading additives, as well as the potential of detrimental additive counteractions. Laboratory viscometer and field-conducted pipe-flow tests remain the only resources for fluid behavior. Depending on the quantity of test data available, and their time, temperature, and shear rate spans, these may or may not sufficiently characterize fluid behavior. Charting behavior (n-Prime, K-Prime, viscosity, etc.) versus time, temperature, shear rate, etc., provides invaluable fluid system performance perspectives about applicable ranges. Second-order regression (multiple regression) over parsed spans (if necessary) provides a means for developing equations that describe fluid behavior over wide ranges of time, temperature, and shear rates. Regression results typically provide advantages regarding data 372

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storage requirements, incorporation in algorithms, exportation to fracturing computer design models, etc. The variety of available fluid systems (e.g., aqueous, hydrocarbon, emulsions, foams, etc.), both non-cross-linked and cross-linked (with an overabundance of different cross-linkers), plus the many options for additives (temperature stabilizers, fluid-loss control agents, etc.) results in a plethora of different rheological behaviors. Hence, design engineers must consider the following aspects: • Flow patterns –– Laminar –– Turbulent –– Plug –– Wall shear • Flow types/rheograms –– Power-law ·· Newtonian ·· Near Newtonian ·· Non-Newtonian –– Non-power-law –– Shear rate region differences • Behavior in pipes • Behavior through perforations • In-fracture effects on rheological behavior of –– Temperature –– Time –– Shear –– Proppant concentration –– Fluid loss dehydration –– Wall-building behavior

Data and Information Resources (Hard Copy, Website, etc.) • Professional society publications (SPE technical journals, monographs, books, etc.) • Industry periodicals (Oil & Gas Journal, Petroleum Engineer, etc.) • Service company technical publications • Industry consortium membership • Independent laboratories • Laboratory test reports: Published, unpublished (government, industry, etc.) • Post-frac penetration and conductivity analysis 373

Essentials of Hydraulic Fracturing

Exercises Exercise 6–1 Given the following information, calculate the shear rate and the apparent viscosity of the fracturing fluid for each of the five cases below.

Injection Rate (bpm)

Fracture Width (in.)

Fracture Height (ft)

n

ka

1

10

0.5

100

0.7

0.025

2

10

0.5

100

0.6

0.025

3

10

0.5

100

0.5

0.025

4

20

0.5

100

0.5

0.025

5

30

0.5

100

0.5

0.025

6

30

0.5

200

0.5

0.025

7

30

0.5

300

0.5

0.025

8

30

0.7

300

0.5

0.025

9

30

0.9

300

0.5

0.025

10

30

0.5

200

0.5

0.025

11

30

0.5

200

0.5

0.04

12

30

0.5

200

0.5

0.06

13

30

0.5

200

0.5

0.1

14

30

0.5

200

0.5

0.2

Case

In one typewritten page or less on letter size paper, discuss the following three items. 1. The effects of n and ka on the values calculated for apparent viscosity. 2. The effects of injection rate on the values of apparent viscosity. 3. The effects of fracture width and height on the values of apparent viscosity.

Exercise 6–2 The formation temperature for a prospective fracturing treatment is 310°F. Set up a spread to calculate an in-fracture temperature profile from the wellbore to the fracture extremity using the Biot, Massey, and Medlin (BM&M) approach for any wellbore temperature and any formation temperature, and any time.

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Exercise 6–3 For a wellbore injection temperature of 90°F and any formation temperature, create a chart of wellbore to fracture extremity profile (wellbore to the fracture extremity) after 1. 30 minutes of injection 2. 4 hours of injection

Exercise 6–4 The table below contains rheology parameters, n-Prime and K-Prime laboratory values for two fluid systems being considered for the treatment. The data spans tests from 200°F to 325°F over a 6-hour period 1. Create charts for the n-Prime and K-Prime laboratory values in a format similar to figure 6–13. 2. Set up spreadsheet multiple regression processes similar to those shown in tables 6–4, 6–5, 6–6, 6–7, and 6–8, with charts similar to figures 6–11, for calculating n-Prime and K-Prime using coefficients and algorithms per equations 6–17, 6–18, and 6–19. 3. Calculate n-Prime and K-Prime at the following conditions at any in-range temperature a. 30 minutes b. 1 hour at c. 1.5 hours at d. 2 hours at e. 3 hours at f. 4 hours at 4. Calculate apparent viscosities for these times and temperatures at shear rates of 20, 60, and 100 1/sec, and then chart the results. Composition & Conc's (%, ppt or lbs/Mgal) Gelling Agent

X Link

Type Conc.

Type

Laboratory Test Data

Tested Thermal Stabilizer @ Shr Type Conc. Type Conc. Temp. Rate ºF 1/s

Rheology: 1 - Time ( hrs ) t-1 Flow Consistency @ Index Index ºF n' K'

Time, n' & K' @ Temp & Shear 2 - Time ( hrs ) 3 - Time ( hrs ) t-2 Flow Consistency t-3 Flow Consistency @ Index Index @ Index Index ºF n' K' ºF n' K'

MY-T-GEL HT - WG-19 Guar Guar Guar Guar Guar Guar

60 60 60 60 60 60

Titanate Titanate Titanate Titanate Titanate Titanate

HPG HPG HPG HPG HPG HPG

60 60 60 60 60 60

Titanate Titanate Titanate Titanate Titanate Titanate

MEOH MEOH MEOH MEOH MEOH MEOH

5 5 5 5 5 5

Gel-Sta Gel-Sta Gel-Sta Gel-Sta Gel-Sta Gel-Sta

10 10 10 10 10 10

200 225 250 275 300 325

Gel-Sta Gel-Sta Gel-Sta Gel-Sta Gel-Sta Gel-Sta

10 10 10 10 10 10

200 225 250 275 300 325

170 170 170 170 170 170

0.05 0.05 0.05 0.05 0.05 0.05

0.61 0.62 0.62 0.6 0.56 0.475

0.115 0.101 0.105 0.120 0.013 0.170

3 0.61 3 0.62 3 0.65 3 0.6575 2.9 0.675 1.6 0.6175

0.107 0.083 0.057 0.031 0.004 0.013

6 6 6 6 5.8 3.2

0.62 0.63 0.69 0.715 0.79 0.76

0.100 0.068 0.031 0.008 0.001 0.001

0.200 0.280 0.230 0.200 0.200 0.180

3 3 3 3 3 1.25

0.100 0.180 0.130 0.070 0.016 0.013

6 6 6 6 6 2.5

0.58 0.52 0.57 0.63 0.80 0.80

0.050 0.130 0.070 0.022 0.002 0.001

VERSAGEL HT - WG-11 170 170 170 170 170 170

0.05 0.05 0.05 0.05 0.05 0.05

0.48 0.48 0.50 0.50 0.50 0.51

0.53 0.50 0.52 0.57 0.65 0.65

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Essentials of Hydraulic Fracturing

5. Calculate the in-fracture, laminar flow friction pressure multiplier for a proppant-laden slurry for an aqueous based fluid containing 8.0 SPPG (lb/gal slurry) of sand with specific gravity 2.65. 6. What is the proppant concentration in terms of LPPG (lb/gal liquid) for an aqueous based fluid containing 8.0 SPPG (lb/gal slurry) of sand with specific gravity 2.65? 7. Using the data in table 6–20, set up a spreadsheet to calculate ΔP/ΔL for any tubing or casing size, or any tubing-casing annular configuration.

Nomenclature Symbol

Units/Value

Description

English CPERF

dim.

Perforation coefficient {range: 0.2 to 0.5, typically = 0.4}

DHYD

in.

Pipe or annulus average hydraulic diameter

dPERF

in.

Perforation diameter

dPROP

in.

Proppant average diameter

FM

dim.

Friction pressure multiplier for oil at velocity VT

FM-AQ

dim.

Friction pressure multiplier for aqueous fluid systems

FM-BASE

dim.

Base friction pressure multiplier at 77.25 ft/sec velocity

FP

fraction

Proppant particle fraction

gCOL

dim.

Specific gravity of the column fluid

gFLUID

dim.

Neat fluid system specific gravity

gPROP

dim.

Proppant specific gravity

gSLURRY

dim.

Slurry specific gravity

Hƒ

ft

Fracture height

HHP

hhp

Hydraulic horsepower

K´

dynes/cm2

Fracturing fluid consistency index (rheogram intercept)

∆LCOL

ft

Vertical (true vertical) tubular column span

LPPG

lb/gal-liquid

Proppant concentration

n´

dynes/cm2/sec-1

Fracturing fluid flow behavior index (rheogram slope)

OINJ

bbls/min

Injection rate

psi

Fluid-proppant slurry hydrostatic column pressure

PNET

psi

Net fracturing pressure

PW-INJ

psi

Wellhead, surface injection pressure

ΔP/ΔLTBG

psi/100 feet

Tubular (pipe or annulus) friction pressure gradient

ΔPNF

psi

Neat system friction loss

ΔPPERF

psi

Friction loss across one perforation

ΔPPERFS

psi

Perforation friction loss

PCOL

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|

Fracturing Fluid System Rheology and Proppant Transport

Units/Value

Description

ΔPSL

psi

Slurry friction loss

ΔPTUBULARS

psi

Tubular, pipe or annulus, friction loss

QINJ

bbls/min

Total wellhead injection rate

QPERF

bbls/min

Flow rate through one perforation

SPPG

lb/gal-slurry

Proppant concentration

T(X)

°F

Temperature at point X

TD

dim.

Dimensionless temperature at point X in the fracture

TR

°F

Reservoir temperature

TW

°F

Wellbore temperature at the injection point (i.e., perf’ns)

VTUB

ft/sec

Velocity in a tubular

Wƒ

in.

Fracture width

X

either t, T, or ý

Independent variable (either t, T, or ý.)

XD

dim.

Dimensionless fracture penetration

Xƒ

ft

Total fracture penetration

Y

either n´, K´, or µAPP Dependent variable (either n´, K´, or µAPP)

t

VZ

Time

Vertical proppant settling velocity

Greek µAPP

cp

Apparent viscosity

µAPP(ý, T)

cp

Apparent viscosity at ý and T(°F)

µNF

cp

Neat fluid system viscosity

µREL

dim.

Relative viscosity

µSL

cp

Slurry viscosity

ý

sec-1

Shear rate

ρNF

lb/ft3

Neat fluid system density

ρREL

dim.

Relative density

lb/ft3

Slurry density

σMIN

psi

In situ minimum stress (i.e., fracture closure stress)

dynes/cm2

Shear stress applied on a fracturing fluid system

ρPROP ρSL τ

Proppant particle density

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Essentials of Hydraulic Fracturing

Resources American Petroleum Institute. 1998. API RP 39: Recommended Practices for Standard Procedures for Evaluation of Hydraulic Fracturing Fluids, 3rd Ed. Dallas, TX: American Petroleum Institute. Gidley, John L., Stephen A. Holditch, Dale E. Nierode, and Ralph W. Veatch, eds. 1989. “Chapter 9.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 177–209. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Appendix C.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 388–393. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Appendix D.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 394–396. Richardson, TX: Society of Petroleum Engineers.

References Gidley, John L., Stephen A. Holditch, Dale E. Nierode, and Ralph W. Veatch, eds. 1989. “Figure 1.18,” “Figure 9.4.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 7, 184. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.45.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 18. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.46.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 19. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.47.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 19. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.48.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 20. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.53.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 22. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Table 9.1.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 178. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.4.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 184. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Equation 9.17.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 185. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.8.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 186. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.13,” “Figure 12.10.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 188, 254. Richardson, TX: Society of Petroleum Engineers. 378

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Fracturing Fluid System Rheology and Proppant Transport

———. 1989. “Equation 9.30.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 190. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.16.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 190. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.17.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 190. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.34 and Figure 9.35.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 199. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 9.38.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 201. Richardson, TX: Society of Petroleum Engineers. Halliburton Co. 1986. “Figure 2.11 and Figure 2.12.” In The Fracbook II: Design/Data Manual for Hydraulic Fracturing, 5. Duncan, OK: Halliburton Services. ———,0. “Figure 2.71.” In The Fracbook II: Design/Data Manual for Hydraulic Fracturing, 5. Duncan, OK: Halliburton Services. ———. 1986. “Figure 2.72.” In The Fracbook II: Design/Data Manual for Hydraulic Fracturing, 5. Duncan, OK: Halliburton Services. ———. 1986. “Figure 3.4.” In The Fracbook II: Design/Data Manual for Hydraulic Fracturing, 5. Duncan, OK: Halliburton Services. Harris, P. C., R. G. Morgan, and S. J. Heath. 2005. “SPE Paper 95287: Measurement of Proppant Transport of Frac Fluids.” Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, October 9–12. Subhash N. Shah, Mahmoud Asadi, and David L. Lord. 2001. “Proppant Transport Characterization of Hydraulic-Fracturing Fluids Using a High-Pressure Simulator Integrated With a Fiber-Optic/Light-Emitting-Diode (LED) Vision System.” SPE Journal paper 69210-PA. 42–49. Richardson, TX: Society of Petroleum Engineers.

379

7 Proppants and Fracture Conductivity Proppants (fracture propping agents) are strong, rounded particles of various size ranges and materials. They are injected into a fracture via fracturing fluid system slurries during treatment to hold the fracture faces apart after the treatment is completed. Their residence in the fracture creates and maintains a flow conductivity that serves as a highway for reservoir fluids to flow from the fracture extremities to the wellbore. Using proppant-laden slurries is the underlying basis for the original hydraulic fracturing patent. Previous discussion and examples in chapter 2 focus on methods for calculating production increase from fracture conductivity, which in turn dictates revenue increase. There is now a plethora of proppant types, strengths and sizes available to the industry. These span a wide variety of applications for the many different formations and in situ conditions associated with fracturing treatments. Proper design involves selecting which proppant to use and determining the proppant concentrations of the injected slurry, such that the residual proppant pack in a closed fracture provides the desired long-term fracture conductivity. To provide design engineers assistance in this endeavor, this chapter presents • Proppant types and materials • Proppant specifications, quality, and testing • Examples of estimating proppant effectiveness inherent to post-fracture conductivity and production increase There is an abundance of proppants to select from, both in materials and mesh sizes. Primarily, four basic proppant types are commonly available: sand, manufactured ceramics, and their counterparts, resin- or polymer-coated sand or ceramic. Additional types continue emerging; however, sand, ceramics, and resin-coated proppants constitute the dominant menu. Fracture conductivity plays a major role in post-fracturing production performance. Proppants play a major role in effecting fracture conductivity. Hence, the axiom “When one buys hydraulic fracturing, one is in essence buying fracture conductivity” emphasizes the importance of proppant selection and placement in fracture treatment design. 381

Essentials of Hydraulic Fracturing

Proppants Figure 7–1 depicts the evolving menu of proppants that have emerged and re-emerged since the advent of hydraulic fracturing. Proppant history is interesting. River sand was the first proppant material used. Mined and processed industrial silica sand quickly replaced it. Then other materials emerged. Some have remained prominent (e.g., northern white sand, brown sand, sintered bauxite, intermediate and lightweight ceramics, and resin-coated sand and ceramics).

Fig. 7–1. The evolution of proppants used for hydraulic fracturing Some proppant types rise in popularity temporarily, then fade, then rise again (e.g., nut shells, zirconium, marginal fit-for-purpose sand, and even a no-proppant theory). To date the no-proppant theory is on its third cycle, with varying degrees of success. Other proppant types rise in popularity temporarily, then fade forever (e.g., aluminum pellets, Teflon beads, glass beads). Galvanic action between aluminum pellets and steel pipe caused undesirable corrosive effects. Teflon proppants did not display long-term performance. Solid glass beads, being perfect spheres, yielded excellent conductivity at low closure stress, but failed catastrophically at higher stress, crushing to a fine powder, which resulted in unacceptably low fracture conductivity.

Proppant development history Since the first use of riverbed sand in the late 1940s, and the creation of the first fracturing sand plant to produce API fracturing sand outside of the United States (CSS Ltd., Chelford, England, 1986), the production of fracturing sand has expanded greatly worldwide. Sand used as proppant and as a substrate for resin coating traditionally accounts for most of the proppants used for fracturing treatments. Ceramic proppants were introduced by Exxon Research Production Company in the mid1970s with the advent of high-strength sintered bauxite, a high-density (3.6 g/cc) proppant. (Cooke, Hedden, and Chard, 1978, “Hydraulic Fracturing Method Using Sintered Bauxite 382

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Propping Agent,” US Patent 4,068,719). Subsequently, many versions of ceramic proppants have emerged that include lower density and intermediate strengths (between sand and sintered bauxite). The costs for ceramic proppants is many times that of sand. However, the potential production returns in wells with high in situ stresses can yield high economic returns. Consequently, ceramic proppants have become prominent throughout the industry. Resin-coated proppants are not new to fracturing. The concept was introduced to the industry by Gulf Research & Development in the late 1960s (“Propping Agent for a Fracturing Process,” US Patent 3,026,938, filed September 2, 1958, and patented March 27, 1962. Assigned to Gulf Research and Development in Pittsburgh, PA) However, the use of resin-coated sand did not begin in earnest until the mid-1970s, after another patent was issued to Exxon Research Production Company in 1975. (US Patent 3,929,191, assigned to Exxon Research Production Company on December 30, 1975), Even though resin-coated proppants were commercialized by the mid-1970s, their acceptance and widespread use did not occur until the early 1990s.

Proppant future supply and demand The industry’s attempt to develop lighter, stronger, and cheaper materials has resulted and will continue to result in new proppant technologies, ranging from recycled waste materials to nanobased, high-strength, and ultra-lightweight proppants. At the time of this writing, there are more than 60 mines supplying fracturing sand in North America and more than 115 sand plants worldwide. Fracturing sand production requires more than just digging sand. It involves significant mining, washing, drying, and screening. Thus, fracturing sand production plants are costly investments. A new, dedicated sand-proppant plant today with a production capacity of over 2 million tons per year may cost upward of $50 to $100 million. There are more than 90 plants supplying ceramics and more than 18 plants supplying resincoated proppants. These can require even larger investments. Marketing research indicates that over the past decade, proppant demand increased on the order of 1,400%. Thus, money spent on proppants is now in the mid-billions of dollars. Current projections, for whatever they are worth, imply a 200%+ increase over the next decade.

Primary proppant materials Even though many types of proppants and proppant materials have been introduced over the years, the primary basic proppant materials used today consist of well-rounded, nearly spherical, and tightly size-graded (a) naturally occurring sand, (b) manufactured ceramic products, and (c) sand and ceramic proppants that are encapsulated with a resin-coating material to enhance their fracture conductivity performance. Consequently, discussion in this chapter focuses on the primarily used proppants: • Natural sand (hereafter called sand) • Manufactured ceramics (hereafter called ceramics or ceramic) • Resin-coated sand and ceramics

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Essentials of Hydraulic Fracturing

Proppant typical sizes of the past Traditionally, proppants are identified by a range of sieve mesh sizes consistent with standard sieving terminology, Mesh size applies to all proppants, be they sand, ceramic, or resin-coated. It is presumed that the reader is familiar enough with particle sieving processes to forego further discussion on them. Instead, this discussion addresses the specific mesh sizes pertinent to fracture treatment design. Table 7–1 shows fracturing sand mesh size designations from the past ranging from 6/12 (largest diameter: 1,700 µm, 0.0669 in.) to 70/140 (smallest diameter: 106 µm, 0.00417 in.). As is discussed later, these API designations have been expanded to include developments in ceramic and resin-coated proppant manufacturing. Table 7–1. API fracturing sand sizes

Source: “Table 1.2,” Gidley et al. 1989, 10.

Sand proppants Sand proppant quality Sand proppants are currently classified by three categories of quality: • Premium quality (Tier 1) sands • Good quality (Tier 2) sands • Fit-for-purpose (Tier 3) sands. The classifications are based on proppant performance under laboratory test conditions. However, sand properties that dictate performance are particular to each sand deposit. These properties vary from deposit to deposit. Premium (Tier 1) sand deposits predominantly reside in the northeastern United States and primarily comprise white- or near-white-colored sand.

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Good (Tier 2) deposits lie mostly in the southwestern United States, where the sand contains impurities that give them a brown-tinged color. Hence, in the fracturing community it is common to imply quality in terms of geographic location, sand deposit name, or color.

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Fit-for-purpose (Tier 3) deposits, which were rarely used in the past, have become popular for wells that do not require high fracture conductivities. Premium quality (Tier 1) sands—northern white. All northern white fracturing sands are of premium quality. They are renowned for their high silica content, monocrystalline grain structure, particle strength (crush resistance), and shape. The majority of premium quality sand substrate is produced from ancient sandstone formations located in Illinois, Iowa, Minnesota, and Wisconsin. These are mined from Galesburg, Ironton, Jordan, Ottawa, Mt. Simon, St. Peters and Wonewoc sand deposits. They are typically white in color because of their high quartz content. St. Peter and Jordan deposits are the predominant sources for Tier 1 sand. These are not glacial deposits, as often erroneously described, but rather cratonic sheet sandstones formed as a result of ancient, transgressional seas that eroded and deposited quartz-rich sand in shorelines and offshore bars by means of extensive wind, wave, and tidal action. St. Peter sandstone is an Ordovician formation that is over 400 million years old. It is geographically large, with mineable outcrops in the upper Midwest and specific southern states. However, the most notable sources are from near-surface outcrops near Ottawa, Illinois, southwest of Chicago. The Jordan, Wonewoc, and Mt. Simon formations are older Cambrian formations with mineable resources largely isolated to southeastern Minnesota and western Wisconsin. Although these sands are not typically as white as the St. Peter sandstone, they are renowned for having higher percentages of sand larger than 40 mesh, as well as providing Tier 1 performance. Good quality (Tier 2) sands—Brady-type, Hickory, or brown sand. These come primarily from southwest US mines in the Hickory sand deposits, near Brady or Voca, Texas. Their impurities (which cause the brown color) degenerate proppant performance somewhat. These sands are neither as well-rounded, nor chemically or mineralogical1y pure, nor texturally mature as northern white sands. They also contain more polycrystalline quartz grains and other minerals that add color. However, they have proved to be good quality by both laboratory tests and postfracture production performance. Additionally, they are located close to major oil producing regions in the United States, which reduces transportation costs. Other good quality sand sources with Tier 2 qualities have been developed in both other US locations as well as international locations. A few Bidahochi and Colorado Aeolian (dune deposit) mines do exhibit Tier 2 qualities. However, Aeolian dune sands quality varies significantly from one deposit to another. Some are Tier 2, but many fall in the Tier 3 category. Thus, proppants from Aeolian mines should be tested before being considered for use in a treatment. Fit-for-purpose (Tier 3) sands. “Fit-for-purpose” (replacing “marginal” or “substandard”) is a recent term popularized by an independent testing lab. These proppants emerged from the increased use of nontraditional sands in unconventional horizontal wellbore completions. Tier 3 sand sources, often regionally located near various shale plays in the United States and abroad, often do not meet one or more of the current specifications for proppants and generally do not perform nearly as well in standard long-term conductivity testing. They can, however, be used in areas where (1) producing formation permeability is very low and (2) supply, logistics, and costs negate economic use of higher quality sands, ceramics, or resin-coated proppants. 385

Essentials of Hydraulic Fracturing

Comparative tier quality proppant images. Figures 7–2 through 7–5 show images of Tier 1 (premium, excellent), Tier 2 (good), and Tier 3, (fit-for-purpose, marginal, substandard) fracturing sands, respectively. Here, the comparison of roundness between the three tiers is evident. It degrades as quality decreases.

Fig. 7–2. Sand images by type Source: PropTester, Inc., and Kelrik, LLC 2014.

Fig. 7–3. Sand images: excellent quality fracturing sands, Northeast US mines Source: Western Petroleum 1984.

386

Fig. 7–4. Sand images: good quality fracturing sands, Southwest US mines Source: Western Petroleum 1984.

Fig. 7–5. Sand images: Tier 3, “fit-for-purpose” fracturing sands Source: Western Petroleum 1984.

Essentials of Hydraulic Fracturing

Tier 1 quality sand images. Tier 1 quality sands (figure 7–2, left, and figure 7–3). Here, figure 7–3 shows examples of shape variations that prevail in Tier 1 fracturing sands. Though often called white sands, Tier 1 proppants sometimes contain color variations. However, those that do also exhibit essentially the same performance as their counterpart noncolored quartz proppants. Thus, color alone is not a quality criterion for northern white fracturing sands. Tier 2 quality sand images. Both the Brady (figure 7–2, middle) and the Hickory (figure 7–4) sands are less rounded and more oblate than the Tier 1 sands. Also, notice the effects of stress loading on both Tier 1 and Tier 2 quality sands that are shown in figures 7–3 and 7–4, i.e., (a) the whole grain, not-loaded images and (b) the proppants loaded at 3,000 and 4,000 psi. With no stress load, the particle shapes between Tier 1 and Tier 2 particles are significantly different. However, under stress load, especially above 4,000 psi, the differences between the two tiers in both particle size and particle shape somewhat disappears. Obviously, increasing stress loading increases particle fragmentation and compaction. If stress loads are increased significantly, some point is reached where there is minimal difference in fracture conductivity performance between Tier 1 and Tier 2 sands. This has been corroborate by many laboratory tests. Tier 3 quality sand images. The fit-for-purpose sands shown in figure 7–2 and figure 7–5 are from many different locals and deposits: Georgia and Carolina Tuscaloosa deposits; Arkansas, Oklahoma, and Missouri Saint Peter mines; Colorado Aeolian dune mines; the Missouri River; Ohio River Valley Sharon conglomerate mines; East and South Texas Carrizo sand deposits; and central Colorado Sawatch quartzite mines. As can be seen, they exhibit a much wider range of particle size and shape differences than do Tier 2 sands. However, Tier 3 sands have recently found a place in the fracturing industry. Their low cost is sometimes economically attractive even though their conductivity performance declines rapidly at stress loads above 2,000 psi.

Generalized sand information Table 7–2 shows a basic summary of select physical properties with respect to tier quality. It lists basic fracturing sand designations, characteristics, source formations, Krumbein-Sloss roundness-shape values (per figure 7–2), and crush values for various mesh sizes. Shape (roundness and sphericity) and crush resistance (K value) are from multiple public and private sources using ISO 13503-2: 2006 and API RP 19C procedures (PropTester, Inc., and KELRIK, LLC 2014). There are additional important, industry-standard physical property and performance measurements presented later in this chapter.

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Table 7–2. Basic fracturing sand types

Chart adapted from the Kelrik Basic Sand Classification Chart, 2012, p. 16. Accessible at http://www. frac-sand-logistics-canada-2014.com/media/downloads/51-jason-renkes-proptester-chris-gall-calfrac. pdf, p. 16.

Ceramic proppants Ceramic proppants are essentially a high-strength artificial proppant made by sintering materials with high alumina contents, such as bauxite or bauxitic-kaolin clay. After the raw material is mined, ore is ground into an ultra-fine powder and formed into beads using either a wet or dry process. The dry process utilizes blenders such as an Eirich mixer to build the beads, whereas the wet process uses a fluidized spray approach. Once formed, the beads are then carefully sintered at very high temperatures, cooled, and screened to ensure correct mesh sizes. Ceramic proppants have several potential benefits over fracturing sand, notably improved shape, strength, and heat-resistant properties, all of which aid proppant-pack permeability. The industry generally classifies ceramic proppant quality in terms of strength, density, or both, as opposed to the tier classification used for sand. The initially developed proppants in the mid-1970s adhered closely to specifications. Many still do. However, like sand, ceramic proppants vary in quality from one supplier to another. Some of ceramic proppants available today exhibit significant quality diversity. Thus quality testing is essential. Sintered bauxite, the original high-strength and high-density proppant, is still in use today. With an alumina content of approximately 80%, it is heavy (bulk density ~2.00 g/cc and >127 lb/ft3) and therefore, abrasive. Lighter weight options are popular alternatives. Lightweight proppants are manufactured to have bulk densities similar to sand (~1.60 g/cc), but significantly higher strength. Modern ceramic proppants range anywhere from ultra-high-density, high-strength proppants to ultralight-density proppants that are nearly self-suspending in water. Figure 7–6 and figure 7–7 show magnified images of manufactured ceramic proppants with various bulk densities. 389

Essentials of Hydraulic Fracturing

The particles in each image are much more round and uniform in size than is sand. Also, per figure 7–7, after stress loading, the particle fragmentation is not as pronounced as sand exhibits. Additionally, the lightweight proppant on the right is even lower than sand, which has a bulk density on the order of 115 lb/ft3.

Fig. 7–6. Ceramic proppant images (photo courtesy of 2013 Proppant Market Report, PropTester, Inc.). Figure 7–7 shows crushed samples after closure stress is applied.

Fig. 7–7. Crushed ceramic grains (photo courtesy of PropTester, Inc.) Table 7–3 summarizes basic ceramic proppant properties for the proppants shown in figure 7–6.

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Table 7–3. Basic ceramic proppant types Type/ Properties

Ultra-high Density UHD

Density Bulk Density* Strength Solubility Primary Feed Examples

~2.3 g/cc >145 lb/ft3 Highest

>> >> >> >> >> >> @ 1,340

30% 29% 29% 28% 28% 27% 26% 26% 25%

Job Average Max Job Average Pumping Concentrations for 2.65 Specific Gravity Proppant Fluid Fraction Particle Fraction Maximum Job Average % % ppgS ppgL 75% 25% 5.4 7.2 76% 24% 5.3 7.0 76% 24% 5.2 6.9 77% 23% 5.2 6.7 77% 23% 5.1 6.6 77% 23% 5.0 6.4 78% 22% 4.9 6.3 78% 22% 4.8 6.1 4.7 6.0 79% 21%

Treatment injection rate input data In light of the fact that 90 BPM injection rates are commonly used by other operators in the field, it was considered for the design. However, 120 BPM was thought worth investigating. This shows how the design injection rate depends on comparative injection rate scenario study results.

Fluid system search criteria: in-fracture viscosity required to achieve target fracture width Table 10–7 shows results for 90 and 120 BPM. The fluid system search focuses on maximum required viscosity. This occurs at Xƒ = 1,340 feet. In-fracture viscosity is shear rate–dependent. At Xƒ = 1,340 feet, 90 and 120 BPM injection rates yield in-fracture shear rates of 3.2 and 4.2 sec–1 respectively for the average fracture width. The model-calculated in-fracture slurry viscosities (µ S) and neat fluid viscosities (µN) required to achieve the target fracturing friction pressure and widths are listed in table 10–5 at Xƒ = 1,340 ft, fracturing friction pressure ΔPƒMAX = 410 psi, WƒP = 1.273 and WƒPA = 1.018 in. (average fracture width, pumping). No laboratory viscosity data are available on fracturing fluid proppant-laden slurries. It is measured only on neat fluid systems. Hence, the fluid search focuses on neat fluid system viscosity. The relation between proppant-laden slurry and neat fluid viscosity is dependent on 567

Essentials of Hydraulic Fracturing

particle fraction. This is per the discussion in chapter 6, section “Fluid System Apparent Viscosity Increase due to Proppant Concentration.” The SPG model maximizes proppant concentration at 52% particle fraction, as determined by proppant specific gravity. Here, viscosity ratio, µS/µN = 5.018. Table 10–7 reflects this slurry-to-neat-fluid viscosity adjustment. Table 10–7. Apparent in-fracture fluid system slurry and neat fluid viscosities required to develop fracture width at fracture penetration Cooresponding Maximun Fracture Allowable Fracture Fracture Widths Penetration Friction Height @Wellbore @Average

Xƒ

for Hƒ

ft 150 300 450 600 740 890 1,040 1,190 1,340

PƒMAX psi 208 247 280 309 334 359 382 398 410

Hƒ

ft 950 978 1,001 1,022 1,040 1,058 1,075 1,091 1,106

WƒP in 0.554 0.678 0.786 0.886 0.974 1.064 1.152 1.218 1.273

WƒPA in 0.443 0.543 0.629 0.709 0.779 0.851 0.921 0.974 1.018

In-Fracture @ 90 BPM Shear Rate Target Viscosities @ for Fp = 52%, S/ N = 5.02

WƒPA

Slurry S

Neat Fluid N

1/sec cp cp 123 953 190 41 2,077 414 20 3,662 730 12 5,777 1,151 8.1 8,290 1,652 5.6 11,627 2,317 4.1 15,701 3,129 3.5 17,739 3,535 3.2 18,778 3,742 Slurry, S - With Proppant Neat Fluid, N - No Proppant

In-Fracture @ 120 BPM Shear Rate Target Viscosities @ for Fp = 52%, S/ N = 5.02

WƒPA

Slurry

Neat Fluid

S N 1/sec cp cp 175 626 125 56 1,457 290 27 2,681 534 16 4,363 870 11 6,408 1,277 7.3 9,174 1,828 5.5 11,338 2,260 4.7 12,808 2,553 4.2 13,632 2,717 Slurry, S - With Proppant Neat Fluid, N - No Proppant

From hereon, the design focuses on a search for fracturing fluid system targeting the maximum fracture width contained in table 10–5, at Xƒ = 1,340 feet. Hence, the search targets neat fluid systems that exhibit the viscosity at in-fracture shear rates to yield the required ΔPƒ, and thus fracture widths.

Prospective fluid systems The fluid system data considered for the design are contained Halliburton’s fracbook II publication. Use of Halliburton materials does not constitute preferential endorsement. Other pumping service companies offer systems with comparable capabilities. Halliburton has granted publication permission. The book fracbook II has been widely distributed throughout the industry for many years. Thus design engineers who wish to compare their computations against this example have ready access to the data. The prospective fluid systems that are capable of exhibiting the required viscosity are made of 60 ppts of Halliburton WG-19 guar, cross-linked with titanate containing the following temperature stabilizing agents: • Prospective system (1): 10 parts/Mgal Halliburton Gel-Sta • Prospective system (2): 5 parts/Mgal methanol (MeOH) • Prospective system (3): 5 parts/Mgal MeOH and 10 parts/Mgal Halliburton Gel-Sta

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Processing prospective fluid systems laboratory test data for model input The SPG model uses only a single set of n´ and K´ rheology parameters, adjusted to in-fracture shear rate, at an average constant fracture width. It does not contain features that automatically adjust them to in-fracture conditions of time, temperature (and possibly fluid loss), and in-fracture location shear rate, as do some other fracture design models. Only laboratory data tested over a 200°F–250°F temperature range was published. Thus, processing is required to comply with the SPG model input requirements for the example case in situ conditions (180°F). Rheology parameters were obtained from a variety of different sets (for each fluid) of laboratory data published in the Fracbook II. This required compiling the data into sets suitable for processing to arrive at values applicable for 180°F. What follows is a discussion on the processing. Tables 10–8 through 10–10 and corresponding figures 10–5 through 10–7 show the results of the compiled and processed laboratory test n´ and K´ data for the prospective fluid systems: • Prospective system (1): table 10–8 and figure 10–5 • Prospective system (2): table 10–9 and figure 10–6 • Prospective system (3): table 10–10 and figure 10–7 The compiled original data in the above tables span temperatures of 200°F–250°F over a sixhour time period. Application for the 180°F formation temperature and fluid system duration in the fracture of 4–6 hours required curve-fit processing as discussed in chapter 6, section “Developing Equations for Fracturing Fluid Systems Rheology Behavior,” to arrive at n´ and K´ parameters applicable to this design. The compiled original data shown in the tables emanates from numerous tests that may not have been conducted by the same individuals or with the same viscometers. Also, curve-fitting data for extrapolation to conditions outside the testing spans is subject to issues discussed in chapter 6 in the section Resources for Fluid System Apparent Viscosity and Rheology Data. Thus, there is a question about the reliability of rheology performance predictions at 180°F. However, it is the only resort available, outside of requesting additional laboratory tests specific to this example. At this design stage, that option was not chosen. Examination of figures 10–5 through 10–7 showed that all fluid prospects appear well behaved at 180°F. K´ is relatively stable, even at 6 hours exposure time. The decreasing n´ value in the 2to 4-hour range for Prospects (1) and (2) appears somewhat contrary to what was expected. Typically, n´ is expected to increase somewhat with time exposure at a given temperature. However, in the 4- to 6-hour range, they level out somewhat, except for the Prospect (3) system where, as expected, n´ exhibits an increase over time. Even with the questionable Prospect (1) and Prospect (2) n´ performance, the respective n´ and K´ values at 180°F at 4 hours were considered for design.

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Essentials of Hydraulic Fracturing

Processed rheology parameters Prospect (1) My-T-Gel HT: 60 parts WG-19 titanate XL, 10 parts Gel-Sta At 180°F and 4 hours fracture residence time, Prospect (1) parameters: n´ = 0.5951, K´ = 0.1072 Table 10–8. Prospect (1) My-T-Gel HT: 60 parts WG-19 titanate XL, 10 parts Gel-Sta Compiled Original Laboratory Data Temp. °F

Time hours

200 200 200 225 225 225 250 250 250

0 3 6 0 3 6 0 3 6

180 180 180

2 4 6

Lab 0.610 0.615 0.620 0.620 0.640 0.660 0.620 0.665 0.710

n' Values Calc’d Err Lab 0.610 0.00% 0.1150 0.615 0.00% 0.1017 0.620 0.00% 0.0900 0.620 0.00% 0.1010 0.640 0.00% 0.0711 0.660 0.00% 0.0500 0.620 0.00% 0.1050 0.665 0.00% 0.0397 0.710 0.00% 0.0150 Curve-Fit Calculated Data

K' Values Calc’d 0.1150 0.1017 0.0900 0.1010 0.0711 0.0500 0.1050 0.0397 0.0150

0.613 0.595 0.595

Err 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

0.1060 0.1072 0.0924

n–Prime & K–Prime Behavior: Prospect ( 1 ) n' vs Time @ 180 ºF

0.615

K' vs Time @ 180 ºF

1.00

0.610

K'

n'

0.605 0.600

0.10

0.595 0.590

2

3

4 5 Time ( hrs )

6

0.01

2

3

4 Time ( hrs )

Fig. 10–5. Prospect (1) My-T-Gel HT: 60 parts WG-19 titanate XL, 10 parts Gel-Sta

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Prospect (2) My-T-Gel HT: 60 parts WG-19 titanate XL, 5 parts MeOH At 180°F and 4 hours fracture residence time, Prospect (2) parameters: n´ = 0.5821, K´ = 0.1048. Table 10–9. Prospect (2) My-T-Gel HT: 60 parts WG-19 titanate XL, 5 parts MeOH Prospect (2) MY-T-GEL HT: 60 parts WG-19, TitanateXL, 5 parts MEOH Compiled Original Laboratory Data Temp. °F

Time hours

200 200 200 225 225 225 250 250 250

0 3 6 0 3 6 0 3 6

180 180 180

2 4 6

n' Values Calc’d Err Lab 0.610 0.00% 0.1150 0.630 0.00% 0.0643 0.650 0.00% 0.0360 0.620 0.00% 0.1010 0.680 0.00% 0.0270 0.740 0.00% 0.0072 0.620 0.00% 0.1050 0.720 0.00% 0.0102 0.820 0.00% 0.0010 Curve-Fit Calculated Data

Lab 0.610 0.630 0.650 0.620 0.680 0.740 0.620 0.720 0.820

K' Values Calc’d 0.1150 0.0643 0.0360 0.1010 0.0270 0.0072 0.1050 0.0102 0.0010

0.623 0.582 0.576

Err 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

0.0781 0.1048 0.0894

n–Prime & K–Prime Behavior: Prospect ( 2 ) n' vs Time @ 180 ºF

0.630

K' vs Time @ 180 ºF

1.00

0.620

0.600

K'

n'

0.610 0.10

0.590 0.580 0.570

2

3

4 Time ( hrs )

5

6

0.01

2

3

4

5

6

Time ( hrs )

Fig. 10–6. Prospect (2) My-T-Gel HT: 60 parts WG-19 titanate XL, 5 parts MeOH

571

Essentials of Hydraulic Fracturing

Prospect (3) My-T-Gel HT: 60 parts WG-19 titanate XL, 10 parts Gel-Sta, 5 parts MeOH At 180°F and 4 hours fracture residence time, Prospect (3) parameters: n´ = 0.6303, K´ = 0.1145 Table 10–10. Prospect (3) My-T-Gel HT: 60 parts WG-19 titanate XL, 10 parts Gel-Sta, 5 parts MeOH Prospect (3) MY-T-GEL HT: 60 parts WG-19, TitanateXL, 10 parts Gel-Sta, 5 parts MEOH Compiled Original Laboratory Data Temp. °F

Time hours

200 200 200 225 225 225 250 250 250

0 3 6 0 3 6 0 3 6

180 180 180

2 4 6

Lab 0.610 0.615 0.620 0.620 0.625 0.630 0.620 0.655 0.690

n' Values Calc’d Err Lab 0.610 0.00% 0.1150 0.615 0.00% 0.1072 0.620 0.00% 0.1000 0.620 0.00% 0.1010 0.625 0.00% 0.0829 0.630 0.00% 0.0680 0.620 0.00% 0.1050 0.655 0.00% 0.0571 0.690 0.00% 0.0310 Curve-Fit Calculated Data

K' Values Calc’d 0.1150 0.1072 0.1000 0.1010 0.0829 0.0680 0.1050 0.0571 0.0310

0.613 0.630 0.648

Err 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

0.1098 0.1145 0.1021

n–Prime & K–Prime Behavior: Prospect ( 3 ) n' vs Time @ 180 ºF

0.650

K' vs Time @ 180 ºF

1.00

0.630

K'

n'

0.640 0.10

0.620 0.610

2

3

4 5 Time ( hrs )

6

0.01

2

3

4 5 Time ( hrs )

Fig. 10–7. Prospect (3) My-T-Gel HT: 60 parts WG-19 titanate XL, 10 parts Gel-Sta, 5-parts MeOH

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Laboratory test rheology parameters for model input Table 10–11 lists input design data used for the three prospective systems. The n´ and K´ values at 180°F and 4 hours exposure represent what is considered an average for the entire fracture, over the expected life (4 hours until fluid-loss consumption) of the injected fluid in the fracture. Table 10–11. Prospective fluid systems: performance at 180°F, 4 hours PROSPECTIVE FLUID SYSTEMS Rheology Values Fluid System Description n' (1) My-T-Gel HT: 60 parts WG-19, titanate XL, 10 parts Gel-Sta (2) My-T-Gel HT: 60 parts WG-19, titanate XL, 5 parts MEOH (3) My-T-Gel HT: 60 parts WG-19, titanate XL, 10 parts Gel-Sat, 5 parts MEOH

K'

Viscosity Target Lab Viscosity 90 BPM ý 3.2 120 BPM ý @ý 3,742 cp 4.2 2,717 cp 170 In-Frac @ ý sec–1 cp cp cp

0.5951 0.1072

642

3,205

2,871

0.5821 0.1048

587

3,086

2,755

0.6303 0.1145

821

3,566

3,225

Rheology values n´ and K´ yield power-law viscosities at the respective shear rates shown in the table. As can be seen, all prospective systems come close to satisfying the in situ viscosity requirements given in table 10–7, at in-fracture temperature and time. The 120-BPM injection rate yields lower in-fracture viscosities per the shear rate than does a 90-BPM rate. Final injection rate selection depends on comparative fracture conductivity and FOI calculations.

Prospective proppant input data Table 10–12 lists the prospective proppants for the design. Input data pertinent to description performance was determined using published information, adjusted to in situ conditions of 5,400 psi confining stress (on fracture closure) and 180°F formation temperature. Typically, published data are stated for standard API test temperature and load conditions. Thus, adjustments are necessary. Table 10–12. Prospective proppants BASE-LINE PROPPANT PERFORMANCE TEST DATA

IN SITU EFFECTIVE

Pack Conditions: 5,400 psi, 180°F Est. Perm. Cond. Prop. Prop. Proppant Description: Width Pack Results Conc. Conc. Mesh Size and Type Wƒ (in.) Time Temp. Kƒ KƒWƒ Dam’g Kƒ KƒWƒ 2 2 lb/ft lb/ft @Conc. hours °F Darcy’s md-ft % Darcy’s md-ft 20/40 API Sand-Ottawa, US Silica 16/30 Bauxite-HyperProp G2 Curable Resin Ctd 12/18 Ceramic-CarboLITE 16/30 Bauxite-Carbo-HSP

2.56

2

0.234

50

180

58

993 98%

1.3

3.58

2

0.173

50

180

619

9,118 95%

32.6

2.71 3.56

2 2

0.229 0.174

50 50

180 180

880 15,630 90% 1,911 28,248 85%

103 311

22.4 486 1,855 4,650 573

Essentials of Hydraulic Fracturing

As with the fluid systems, use of the prospective proppants in this example does not constitute product trade name endorsement. Data for them was obtained from publicly available tradeshow sources. They are, however, what is market available at the time of this writing, and exhibit properties that are considered applicable for example purposes. The comparative specific gravities between HyperProp G2 Curable Resin-coated (3.58 sp. gr.) 16/30 bauxite and CarboHSP (3.56 sp. gr.) 16/30 bauxite posed the issue of suspect data. Typically, for the same material (bauxite), resin-coated proppants exhibit lower specific gravity. Revisiting the source data confirmed the table values as shown. Hence, they were taken as published. Note: Sintered bauxite specific gravity can be as high as 3.6, depending on composition and manufacturing; thus, it is possible that the concern is ill founded. In view of the 10 md formation permeability, proppants exhibiting high permeability and conductivity (except for sand) were chosen for the design. This proppant set offered maximum performance available in their proppant category. The prices (dollars per pound) stated are general, and are subject to market supply and demand. As seen they vary significantly: sand, $0.10; resin-coated bauxite, $0.45; CarboLITE, $0.65; and bauxite, $0.90. The dollar return from well production per dollar proppant cost is a critical design aspect. Sand was included as a matter of comparative interest, with no expectation that it would be a factor in the final design proppant selection. The SPG model bases in situ effective conductivity values (right columns, table 10–12) on closed fracture width. Design results for the collective four-proppant set in table 10–12 are inherent to the SPG model output. Table 10–13 lists proppant pack damage for each prospective proppant. The input estimates were made based on past experience with previous treatment designs. They are, among other things, fluid-system-dependent. Hence, fluid system design changes require corresponding changes to damage data. Table 10–13. Estimated proppant pack damage for fluid system prospects FLUID SYSTEM AND PROPPANT

DAMAGE

Prospect (1) MY-T-GEL HT: 60 parts WG-19, titanate XL, 10 parts Gel-Sta 20/40  API Sand-Ottawa, US Silica 16/30  Bauxite-HyperProp G2 Curable Resin Ctd 12/18 Ceramic-CarboLITE 16/30 Bauxite-Carbo-HSP Prospect (2) MY-T-GEL HT: 60 parts WG-19, titanate XL, 5 parts MEOH 20/40  API Sand-Ottawa, US Silica 16/30  Bauxite-HyperProp G2 Curable Resin Ctd 12/18 Ceramic-CarboLITE 16/30 Bauxite-Carbo-HSP

98% 95% 90% 85% 98% 95% 90% 85%

Prospect (3) MY-T-GEL HT: 60 parts WG-19, 10 parts Gel-Sat, 5 parts MEOH 20/40  API Sand-Ottawa, US Silica 16/30  Bauxite-HyperProp G2 Curable Resin Ctd 12/18 Ceramic-CarboLITE 16/30 Bauxite-Carbo-HSP 574

99% 97% 95% 90%

Chapter 10

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Pre-Fracture Treatment: Model Design Examples

The table 10–12 pack damage values apply to both fluid system Prospects (1) and (2). Estimated higher damage for fluid system Prospect (3) is suspect because it contains more temperature-stabilizing additives. Access to industry consortiums that address these issues provides better insight. Such was not available for this design.

Estimated effectively propped Xƒ and total production recovery input data Table 10–14 shows two aspects of how the SPG model addresses fracture treatment effectiveness for • Propping the lateral extent of the created fracture • Impacting total reservoir recovery increase These are user-specified, based on past experience, intuition, etc. It may be presumptuous to expect that proppant is effective all the way to the fracture extremity. Also, for a 10 md formation, little is expected regarding an increase in total reservoir recovery. Table 10–14. Estimated effectively propped xƒ and total reservoir recovery increase relative to fracture propagation Effectively Propped Fracture, Xƒp

Created Fracture Xƒ ft 150 300 450 600 740 890 1,040 1,190 1,340

@ 150 ft >> >> >> >> >> >> >> @ 1,340 ft

%

ft

98% 96% 95% 93% 92% 90% 88% 87% 85%

147 289 426 559 678 800 918 1,031 1,139

Estimated Total Recovery Increase @ 150 ft >> >> >> >> >> >> >> @ 1,340 ft

%

MBSTO

0% 0.6% 1.3% 1.9% 2.5% 3.1% 3.7% 4.4% 5%

8,853 8,909 8,965 9,021 9,073 9,129 9,184 9,240 9,296

With the SPG model, both effectively propped fracture length and reserve increase (if applicable), are specified for the shortest and longest Xƒ fracture penetrations in the design set. Values for each interim Xƒ point are proportioned logarithmically. No data entry implies that there is no effect. In this example, estimated values are shown at Xƒ = 150 feet and 1,340 feet respectively. Based on intuition, it was estimated that more of the fracture would be effectively propped at Xƒ = 150 feet than at 1,340 feet. As previously stated, there was little expectation of increasing total reservoir recovery, especially for the shortest fracture penetration. However, as fracture penetration increases, the chance for increased total recovery also increases somewhat. Though in this case, expectations are small. Whereas, in very tight formations, experience has shown that values of 1,000% to 2,000% increase are justified for the fractured versus non-fractured cases.

575

Essentials of Hydraulic Fracturing

Considerations for selecting fluid system for design Table 10–15 shows results of preliminary model calculations for the three prospective fluids at Xƒ = 1,340 feet. The SPG model employs three fracture widths for each Xƒ: • Wƒp: At the wellbore during injection, per PKN theory • WƒpA: Average injection width, i.e., the width at a point in the fracture equal to 60% Xƒ (for friction pressure, ΔPƒ, during injection) • WƒCA: Average width for settled proppant after fracture closure (for fracture conductivity) Table 10–15. Preliminary model results—maximum achieved values Prospect (3) 10 parts Gel-Sta & 5 parts MEOH

Comparitive Fluid System Performance

Prospect (2) 5 parts MEOH Prospect (1), i.e., 10 parts Gel-Sta Achieved

Immediately Prior to Pumping Shut-Down In-Fracture Net Pressure, psi Fracture Widths (Wellbore, Injection), Wƒp, in Vertical Fracture Heights, ft -1 In-Fracture Shear Rate, sec In-Fracture Viscosity, cp

Target 446 1.333 1,136 @ 3.17 3,742

Achieved

Achieved

90 BPM 120 BPM 90 BPM 120 BPM 90 BPM 120 BPM 352 386 384 343 405 487 1.090 1.162 1.147 1.061 1.194 1.390 1,091 1,141 1,136 1,090 1,125 1,156 3.17 3.58 3.69 3.20 2.99 3.75 3,206 3,057 2,906 3,087 3,654 3,348

After Fracture Closure on Proppant Average Closed Fracture Flow Width, WƒCA, in 2

In-Fracture Proppant Concentrations, lb/ft Proppant Pack Damage, % Effective Fracture Conductivity, md-ft Production Folds of Increase, FOI

0.436 5.166 85% 10,440 4.07

0.464 5.516 85% 11,128 4.18

0.458 5.447 85% 10,992 4.16

0.424 5.025 85% 10,165 4.03

0.477 5.678 90% 7,628 3.61

0.555 6.645 90% 8,880 3.82

Fracture closed width (WƒC) is determined for a 37.5% particle fraction settled proppant pack, volumetrically adjusted for proppant specific gravity. It is then used to calculate fracture conductivity per proppant pack permeability and conductivity at closed pack stress load. Calculations are per discussion and figures in chapter 7 in the section on closed fracture width versus proppant concentration. Prospect (1) appears to be the better system for the design. It exhibits higher viscosity than Prospect (2). Even though Prospect (1) exhibits lower viscosity than Prospect (3), the results suggest a higher FOI potential by virtue of lower proppant pack damage. Hence, Prospect (1) My-T-Gel HT, 60 parts WG-19 titanate XL, 10 parts Gel-Sta is the system of choice. Further discussion focuses on its performance.

Achieved versus target fracture geometry—fluid prospect (1) Table 10–16 shows a comparison between the target design and the achieved results at each Xƒ in the design set. Note that the “target” values for viscosity and width in table 10–16 are a bit different from those listed in table 10–7. This difference results from the interactive effects of fracture geometry and shear rate.

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Pre-Fracture Treatment: Model Design Examples

Table 10–16. Target versus achieved: model-calculated in-fracture viscosity and fracture geometry for Prospect (1) at a 90-BPM injection rate Fracture Penetration Neat Fluid System Viscosity In-Fracture Pumping Widths & Vertical Height In-Fracture @ Friction Pressures Wƒps @ Wellbore Target Calc'd Target Achieved Target Achieved Target Achieved Xƒ Hƒ Hƒ Viscosity Viscosity Friction Friction Wƒp Wƒp ft ft ft cp cp psi psi in. in. 130 218 195 0.537 0.486 150 950 958 190 321 262 237 0.669 0.614 300 978 991 414 450 1,001 1,019 730 612 299 273 0.784 0.727 1,022 332 304 0.891 0.832 600 1,022 1,043 1,151 1,531 360 331 0.986 0.925 740 1,040 1,064 1,652 890 1,058 1,085 2,317 1,995 389 349 1.083 0.994 2,473 404 363 1.147 1.054 1,040 1,075 1,104 3,129 1,190 1,091 1,123 3,535 2,863 418 375 1.206 1.109 1,340 1,106 1,141 3,742 0.817 3,057 431 386 1.262 1.162 Viscosity: -Target / -Achievd Ratio = 0.817

At Xƒ = 1,340 feet, the Prospect (1) fluid system, injected at 120 BPM, achieved an in-fracture viscosity of 3,057 cp, which was 86% (0.861) target viscosity. This imposed an in-fracture friction pressure, or net fracturing pressure, of 386 psi versus the target 431 psi (calculated), 410 psi (arbitrary). This resulted in a pumping fracture width of 1.162 inches at Xƒ = 1,340 feet versus the target 1.262 inches. Thus the prospective fluid fell short of achieving the target. However, there was no better fluid system available for the design. Accordingly, fracture widths at penetrations from Xƒ = 150 feet to 1,190 feet are viscosity proportioned to target widths by the computed µ-Target/µ-Achieved ratio of 0.817 for fracture volumetric, fracture width, and proppant pounds/square foot concentration calculations. Per discussion in the chapter 6 section “Apparent Viscosity Behavior in Different Shear Rate Environments,” the in-fracture shear rates for Xƒ > 600 feet (table 10–7) may result in lower-thancalculated viscosities. However, this may be offset by higher-than-calculated viscosities due to • Fluid loss increasing fluid system gel concentration • Lower in-fracture temperatures in 50% of Xƒ nearest the wellbore (per discussion in chapter 6, “example 6–4, In-Fracture Viscosity Performance at Time, Temperature and Shear”). Thus, the message is that one should always be cautious of taking model results at face value, especially to the third decimal place.

Projected fracture conductivity, FOI, post-fracture production, and present value Table 10–17 shows the entire set of resulting SPG model calculations at each fracture penetration for each prospective proppant. Present value of the resulting production (right column) excludes fracturing treatment costs. Fracture closed widths, conductivities, and FOIs are calculated per discussion in chapter 7, section “Closed Fracture Width versus Proppant Concentration in the Fracture,” and chapter 2 pertinent to semi-steady state flow. 577

Essentials of Hydraulic Fracturing

Table 10–17. Post-frac proppant conductivities, FOIs, production, and production present value Widths Wellbore Wellbore In End of After fracure Created Propped Pumping Closure Flow Xƒ Xƒp Wƒwp Wƒwc Wƒavg ft ft in in in Penetration

Proppant Performance Pack In Situ Conc. KƒWƒ FOI #/ft

md-ft

Post-Fracturing Results Prod'n Prod'n Present Rate Life Value q ta PVƒ BOPD mos M$'s

20/40 API Sand—Ottawa—US Silica: 2.65 sp.gr.

150 300 450 600 740 890 1,040 1,190 1,340

147 289 426 559 678 800 918 1,031 1,139

0.486 0.614 0.727 0.832 0.925 0.994 1.053 1.109 1.162

150 300 450 600 740 890 1,040 1,190 1,340

147 289 426 559 678 800 918 1,031 1,139

0.486 0.614 0.727 0.832 0.925 0.994 1.053 1.109 1.162

150 300 450 600 740 890 1,040 1,190 1,340

147 289 426 559 678 800 918 1,031 1,139

0.486 0.614 0.727 0.832 0.925 0.994 1.053 1.109 1.162

150 300 450 600 740 890 1,040 1,190 1,340

147 289 426 559 678 800 918 1,031 1,139

0.486 0.614 0.727 0.832 0.925 0.994 1.053 1.109 1.162

0.236 0.298 0.353 0.404 0.449 0.482 0.511 0.538 0.563

0.194 0.245 0.291 0.332 0.370 0.397 0.421 0.443 0.464

1.65 2.10 2.50 2.88 3.21 3.46 3.67 3.87 4.06

18.8 23.8 28.2 32.2 35.8 38.5 40.8 43.0 45.0

1.04 1.11 1.16 1.20 1.23 1.26 1.29 1.31 1.33

2,069 2,209 2,310 2,391 2,455 2,511 2,560 2,605 2,644

949 903 875 855 841 829 821 814 808

$6,855 $17,215 $24,670 $30,651 $35,404 $39,747 $43,631 $47,174 $50,442

16/30 Bauxite—HyperProp G2 Resin Curable—Santrol: 3.58 sp.gr. 0.236 0.298 0.353 0.404 0.449 0.482 0.511 0.538 0.563

0.194 0.245 0.291 0.332 0.370 0.397 0.421 0.443 0.464

2.25 2.87 3.42 3.93 4.38 4.72 5.01 5.29 5.55

502 634 751 860 956 1,027 1,089 1,147 1,202

1.64 1.74 1.81 1.87 1.91 1.95 1.98 2.00 2.03

3,271 3,460 3,600 3,718 3,814 3,881 3,938 3,989 4,036

12/18 Ceramic—LITE—Carbo: 2.71 sp.gr. 0.236 0.298 0.353 0.404 0.449 0.482 0.511 0.538 0.563

0.194 0.245 0.291 0.332 0.370 0.397 0.421 0.443 0.464

1.69 2.15 2.56 2.94 3.28 3.54 3.76 3.96 4.16

1,426 1,804 2,136 2,445 2,719 2,921 3,098 3,262 3,416

2.02 2.19 2.31 2.42 2.50 2.57 2.62 2.67 2.72

4,016 4,364 4,606 4,813 4,985 5,114 5,224 5,323 5,414

641 615 597 585 575 570 567 564 561

$73,076 $82,280 $89,207 $95,083 $99,945 $103,785 $107,232 $110,477 $113,558

537 503 483 468 456 449 443 439 435

$101,495 $114,125 $122,789 $130,149 $136,278 $141,250 $145,693 $149,847 $153,773

464 404 370 345 327 313 302 293 285

$123,721 $143,227 $155,065 $163,790 $170,363 $175,494 $179,703 $183,318 $186,375

16/30 Bauxite—HSP—Carbo: 3.56 sp.gr.

578

0.236 0.298 0.353 0.404 0.449 0.482 0.511 0.538 0.563

0.194 0.245 0.291 0.332 0.370 0.397 0.421 0.443 0.464

2.24 2.85 3.40 3.90 4.36 4.69 4.99 5.26 5.52

4,645 5,876 6,958 7,964 8,858 9,515 10,090 10,626 11,128

2.39 2.80 3.10 3.35 3.56 3.74 3.90 4.05 4.18

4,756 5,570 6,165 6,668 7,091 7,451 7,769 8,060 8,321

Obviously, a fracture penetration of 1,340 feet propped with CarboHSP 16/30 bauxite (the most expensive proppant) yields the highest present value return. Treatment costs pertinent to each proppant type and fracture penetration, and corresponding net present values for each Xƒ remain to be determined.

Chapter 10

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Pre-Fracture Treatment: Model Design Examples

Comparative post-fracture production streams versus fracture penetration Figure 10–8 shows post-fracture production rates versus time for facture penetrations of 300, 600, 890, and 1,340 feet, propped with CarboHSP 16/30 bauxite. The figure curves imply a rather significant Xƒ impact on the production streams. This is somewhat surprising for a 10 md permeability formation. Conventional rules of thumb suggest that fracture penetration plays a lesser role than fracture conductivity on post-fracture production as permeability increases. However, 16/30 bauxite proppant yields a very high conductivity in this example. Here fracture penetration obviously plays an important role. Production streams (rate versus time) for each of the 36 cases listed in table 10–17 determine their post-fracture present value ($PVƒ).

Oil Production Rate (BOPD)

9,000 for: Xƒ = 1,340 ft for: Xƒ = 890 ft for: Xƒ = 600 ft for: Xƒ = 300 ft Pre-Fracture

8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0

0

2

4

6

8

10

Time (Years) Fig. 10–8. Pre- and post-fracture production rates versus time for various fracture penetrations propped with CarboHSP 16/30 bauxite

Treatment pumping considerations and costs Here, the design progresses to treatment pumping considerations and costs. This entails collaboration with company field-operating staff and pumping service companies.

Service company pumping and blending equipment limitations In this example, particle fraction limitations and slurry proppant concentrations as listed in table 10–6 do not pose potential equipment pumping or blending problems. They are easily handled by any pumping service company. Here, prospective service company equipment operates satisfactorily at particle concentrations up to 54%. Thus, no pumping or blending problems are anticipated. Table 10–18 shows 579

Essentials of Hydraulic Fracturing

the equipment particle fractions and corresponding proppant concentration limitations for each example 10–1 proppant. These are well above treatment design particle fractions and concentrations shown in table 10–6. Note: For low permeability formations, where fluid system fluid-loss efficiencies are much higher, injection proppant concentrations may become an issue, causing pump head destruction or blender screen-out. Hence, in any treatment design it is wise to check with the service company. Table 10–18. Equipment check: service company pumping and blending slurry concentration limitations Proppant Size/Type

Specific Min Fluid Max Prop Slurry Liquid Gravity % % ppgS ppgL

20/40 API Sand—Ottawa, US Silica 16/30 Bauxite—HyperProp G2 Resin Curable—Santrol 12/18 Ceramic—LITE—Carbo 16/30 Bauxite—HSP—Carbo

2.65 3.58 2.71 3.56

46% 46% 46% 46%

54% 54% 54% 54%

12.1 16.3 12.3 16.2

26.2 35.4 26.8 35.2

Tubular pipe friction Pipe friction during injection pertains to hydraulic horsepower pumping requirements, and pipe and wellhead pressure limitations. Sufficient data input is required to investigate options for injecting down tubing, casing, annulus, or manifold tubing–casing annulus configurations. Here, 4.000-inch OD, 19.00 lb/ft, 3.000-inch ID tubing was designated as a possible tubing frac string. Table 10–19 and figure 10–9 contain pumping service company tubular flow friction data pertinent to the example. Table 10–19. Pipe flow: friction versus injection rate CHART Pipe Flow Rates & Corresponding Friction Losses Example 10–1 Pipe Data

Pipe Data

Points

Rate @ Point

dP/dL @ Point

O.D. (in.) Wt (lb/ft) I.D. (in.)

Tubing: 4.000 19.00 3.000

in. lb/ft in.

4.5 11.6 4

in O.D. lb/ft in I.D.

Tubing: @ Min Rate 1 @ Bend/Mid Point 13 @ Max Rate 100

BPM BPM BPM

1.2 3.4 52

psi/100' psi/100' psi/100'

O.D. (in.) Wt (lb/ft) I.D. (in.)

Casing: 9.625 53.50 8.535

in. lb/ft in.

7 23 6.366

in O.D. lb/ft in I.D.

Casing: @ Min Rate 6.8 @ Bend/Mid Point 28 @ Max Rate 100

BPM BPM BPM

1 1.8 10.5

psi/100' psi/100' psi/100'

2.875

in O.D.

6.355

in I.D.

Annulus: @ Min Rate 1.1 @ Bend/Mid Point 26 @ Max Rate 100

BPM BPM BPM

1 3.5 23

psi/100' psi/100' psi/100'

Annulus: Tbg O.D. (in.) 4.000 in. Annulus Hyd. Dia, DH = 3.480 in. Csg I.D. (in.) 8.535 in.

580

Prospect (1) MY-T-GEL HT: 60 parts WG-19, titanate XL, 10 parts Gel-Sta

Chapter 10

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Pre-Fracture Treatment: Model Design Examples

Pipe Friction (psi/1,000 ft)

100 Tubing Annulus Casing

10

1

1

10 Flow Rate (BPM)

100

Fig. 10–9. Friction versus injection rate—prospect (1) My-T-Gel HT Note that the input data CHART pipe data dimensions come from data published by service companies. They differ from the example 10–1 design pipe configuration sizes. No service company data was available in this regard. However, for friction loss calculations, the SPG model calculates input rate dP/dL values on the basis of relative hydraulic diameters to address the example 10–1 pipe design (chapter 6, section “Tubular Friction Loss During Injection”). Hence, the pumping service company data that are closest to the design pipe data are satisfactory for design.

Wellbore fracturing configuration All treatment designs on wells, especially for new developments, require a wellbore schematic of some type. This is to ensure against encountering unpleasant surprises during treatment, like packers left in the hole after completion, etc. Hence, corroboration with completion staff is essential. Table 10–20 is a very simplified rendering for injection down casing for this example. A plethora of sophisticated wellbore design software is available commercially in this regard. Displacement times and volumes to the perforations are particularly important. It gives the person monitoring the treatment a reference to closely watch surface injection pressures when changes in proppant size or concentration reach the perforations. It is also necessary if ball sealers are part of the design. Fortunately, in this example the casing program provided to the design engineer posed no pressure limitations for the wellhead equipment, or at any critical point in the pipe. Injection down casing at 120 BPM required 6,615 hydraulic horsepower, and 2,250 surface injection pressure. Alternative calculations for injection down 8,000 feet of 4.500-inch tubing, injection down the annulus, and tubing–annulus manifold injection exhibited higher horsepower and surface injection pressure. They offered no benefit to the treatment, and thus were rejected for this design. 581

Essentials of Hydraulic Fracturing

Table 10–20. Fracturing treatment wellbore configuration, displacement volumes, times and pressure at depth

Displacement Pressure Well Csg Volume Time @ Intrv'l Schematic Top Bottom ID to Bottom to Bottom Top Depth @120 BPM Wellhead ft ft in. bbls min-sec psi Max psi 0 8.535 2,250 12,000 5,000 8.535 353.8 2m-57s 5,000 8.535 3,960 T Cmt 8,600 8.535 608.5 5m-4s 8,600 8,800 8.535 622.7 5m-11s 5,200 Perfs 8,800 9,200 Rat Hole Rat Hole 9,200 9,600 Plugback Interval Plugback Interval

Depth Interval

Injection Rate 120 BPM Csg Limit 10,900 psi

Treatment cost: service and materials Table 10–21 constitutes input data requirements for calculating fracturing treatment costs. It comprises typical service company charges, and is essentially adequate for conventional fracturing treatments. The border-outlined values designate required input values. Values not border-outlined are calculated from input data. The template is relatively self-explanatory. Note that maximum pumping time (20 hours) pertains to the maximum fracture penetration and lowest density proppant (which constitutes the largest volume per pound). Thus, excess pumping time charge input data is required for the calculations. Such charges are invoked in the SPG model if applicable. Also, note the input data for standby equipment. Every job should include at least one standby pump and blender. In view of the expected duration for the deeper fracture penetrations, two standby units are specified. Regardless of whether or not they are used, they constitute service company charges, and thus are included in the design cost. Material unit costs (fluid and proppant) reflect current market prices, which vary constantly depending on availability and supply and demand issues. It is essential that costs and charges (including hauling) be well established with the prospective pumping service company prior to considering selection for a design. Total material costs (fluid and proppant) are determined per quantity requirements for each Xƒ in the design set. In this design, an additional 5% fluid volume (above calculated volume requirements) is included for well-site requirements to account for prospective tank bottom waste. No excess well-site proppant volume requirements are designated. This is because all proppant not injected is to be returned to the vendor and costs refunded to the operator. Issues such as these also require up-front understandings.

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Pre-Fracture Treatment: Model Design Examples

Table 10–21. Treatment cost: service and materials input data template

Pumping/Blending Requirements

Maximum Pumping Time Pumping Rate Surface Injection Pressure HHP Required

20.3 120 2,250 6,615

hrs BPM psi HHP

Wellsite Pumping & Blending Services Costs Pumping Services—In Service & Standby In Service

$/HHP $6.00 $39,690 4 hrs $2.00 $13,230 HHP/Pmp Req'rd HHP per Pump 2,250 3

Cost Summary

HHP Extra Charges Kick In Time Extra Time Charges > 4 hrs

Standby

$52,920 Standby 2

Blender Services—Required & Standby In Service

Standby Requirements Other Related Costs

$79,920

$/Blender Blending Equipment $18,000 BPM/Blender Rate per Blender 100 Rental Equipment Other Equipment Other Services Other Sub Total

$14,000 $31,500

Distance Unit Rate Tonnage Rate

50 $0.80 $40.00

Wellsite Material Unit Costs Hauling Services

$27,000

Fracturing Fluid System

MY-T-GEL HT: 60 parts WG-19, XL, 10 parts Gel-Sta

Proppants

20/40 API Sand—Ottawa—US Silica 16/30 Bauxite—HyperProp G2 Resin Curable—Santrol 12/18 Ceramic—LITE—Carbo 16/30 Bauxite—HSP—Carbo

Req'rd 2

Standby 2

$72,000

$17,500

Pumping & Blending Recap Pumps $79,920 Blenders $72,000 Other $31,500 Total Pumping & Blending $183,420 Miles /ton-mile /ton

Price, $/gal Haul, $/gal Total, $/gal $0.600 $0.167 $0.767 SpGr Price, $/lb Blnd'g, $/lb Haul'g, $/lb 2.65 $0.10 $0.00 $0.02 3.58 $0.65 $0.00 $0.02 2.71 $0.45 $0.00 $0.02 3.56 $0.90 $0.00 $0.02

Total $/lb $0.120 $0.670 $0.470 $0.920

Preliminary model design results Table 10–22 lists the model-computed design for each fracture penetration including: pumping times, fracture geometry, treatment material quantities and costs, plus net financial returns ($NPVƒ and discounted return on investment). Figure 10–10 graphically depicts fracturing treatment costs (left) and net present value (NPVƒ) returns (right) versus Xƒ. Several aspects are apparent from the figures and the table 10–22 data: • CarboHSP 16/30 bauxite proppant, though the highest cost, yields the highest NPVƒ returns of all proppants in the design set. • The other proppants are not sufficiently financially competitive for consideration. • The economic optimum with 16/30 bauxite is for Xƒ = 1,340 feet. However, for Xƒ penetrations of 1,040 and 1,190 feet, NPVƒ returns are close to the optimum.

583

Table 10–22. Treatment design results: achieved geometry, required material volumes, costs, and economic returns

TreatmentDesignResults Fracture Geometry

Pumping hrs. @ 120 BPM

Xƒ

Hƒ

Wƒp

ft

ft

in

0.7 1.8 3.4 5.4 7.7 10.3 13.3 16.6 20.3

150 300 450 600 740 890 1,040 1,190 1,340

958 991 1,019 1,043 1,064 1,085 1,104 1,123 1,141

0.486 0.614 0.727 0.832 0.925 0.994 1.053 1.109 1.162

Treatment Quantities Proppant Fluid Conc'n Amount M-Gal ppg M-Lbs

20/40 API Sand 120 323 608 977 1,405 1,904 2,472 3,118 3,845

6.6 6.0 5.5 5.1 4.8 4.6 4.3 4.0 3.8

Fracturing Costs ( M$ ) Fluid

Ottawa 752 1,850 3,206 4,781 6,424 8,293 10,075 11,903 13,762

Prop Pmp/Srv Total

150 300 450 600 740 890 1,040 1,190 1,340

958 991 1,019 1,043 1,064 1,085 1,104 1,123 1,141

0.486 0.614 0.727 0.832 0.925 0.994 1.053 1.109 1.162

120 323 608 977 1,405 1,904 2,472 3,118 3,845

0.7 1.8 3.4 5.4 7.7 10.3 13.3 16.6 20.3

150 300 450 600 740 890 1,040 1,190 1,340

958 991 1,019 1,043 1,064 1,085 1,104 1,123 1,141

0.486 0.614 0.727 0.832 0.925 0.994 1.053 1.109 1.162

120 323 608 977 1,405 1,904 2,472 3,118 3,845

8.9 8.1 7.5 6.9 6.5 6.2 5.8 5.4 5.1

1,016 2,499 4,331 6,459 8,679 11,204 13,610 16,080 18,592

$92 $248 $466 $749 $1,077 $1,460 $1,895 $2,390 $2,948

12/18 Ceramic LITE 6.8 6.1 5.7 5.3 4.9 4.7 4.4 4.1 3.8

769 1,892 3,278 4,889 6,570 8,481 10,303 12,172 14,073

NPVƒ

DROI

$6,503 $16,575 $23,649 $29,145 $33,373 $37,109 $40,344 $43,172 $45,660

18.5 25.9 23.2 19.4 16.4 14.1 12.3 10.8 9.5

US Silica

$92 $90 $248 $222 $466 $385 $749 $574 $1,077 $771 $1,460 $995 $1,895 $1,209 $2,390 $1,428 $2,948 $1,651

16/30 Bauxite HyperProp G2 ResinCurable 0.7 1.8 3.4 5.4 7.7 10.3 13.3 16.6 20.3

Net Returns ( M$ )

$681 $1,674 $2,902 $4,328 $5,815 $7,507 $9,119 $10,774 $12,457

$170 $170 $170 $183 $183 $183 $183 $183 $183

$352 $640 $1,021 $1,506 $2,031 $2,638 $3,287 $4,002 $4,782

Santrol $170 $170 $170 $183 $183 $183 $183 $183 $183

$943 $2,092 $3,538 $5,260 $7,075 $9,149 $11,197 $13,347 $15,587

$72,133 $80,188 $85,669 $89,824 $92,870 $94,636 $96,035 $97,130 $97,971

76.5 38.3 24.2 17.1 13.1 10.3 8.6 7.3 6.3

$170 $170 $170 $183 $183 $183 $183 $183 $183

$623 $1,307 $2,177 $3,230 $4,348 $5,629 $6,921 $8,294 $9,745

$100,871 $112,818 $120,612 $126,919 $131,930 $135,621 $138,773 $141,553 $144,028

161.8 86.3 55.4 39.3 30.3 24.1 20.1 17.1 14.8

$170 $170 $170 $183 $183 $183 $183 $183 $183

$1,192 $2,704 $4,598 $6,841 $9,200 $11,892 $14,529 $17,284 $20,140

$122,529 $140,523 $150,466 $156,948 $161,163 $163,601 $165,174 $166,034 $166,235

102.8 52.0 32.7 22.9 17.5 13.8 11.4 9.6 8.3

Carbo

$92 $248 $466 $749 $1,077 $1,460 $1,895 $2,390 $2,948

$361 $889 $1,541 $2,298 $3,088 $3,986 $4,842 $5,721 $6,614

16/30 Bauxite HSP Carbo 0.7 1.8 3.4 5.4 7.7 10.3 13.3 16.6 20.3

150 300 450 600 740 890 1,040 1,190 1,340

958 991 1,019 1,043 1,064 1,085 1,104 1,123 1,141

0.486 0.614 0.727 0.832 0.925 0.994 1.053 1.109 1.162

120 323 608 977 1,405 1,904 2,472 3,118 3,845

8.9 8.1 7.4 6.9 6.5 6.1 5.7 5.4 5.0

1,011 2,485 4,307 6,423 8,630 11,141 13,534 15,990 18,488

$92 $248 $466 $749 $1,077 $1,460 $1,895 $2,390 $2,948

$930 $2,286 $3,962 $5,909 $7,940 $10,250 $12,451 $14,711 $17,009

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Fracturing Costs & Net Present Value Increase from Fracturing Fracture Penetration Xƒ (ft)

Fracture Penetration Xƒ (ft) 150 350 550 750 950 1,150 1,350

$180,000

$18,000

$160,000

$16,000

$140,000

NPVƒ Increase ($Ms)

Fracturing Costs (M $s)

$20,000

$14,000 $12,000 $10,000 $8,000 $6,000 $4,000

150 350 550 750 950 1,150 1,350

$120,000 $100,000 $80,000 $60,000 $40,000

$2,000

$20,000

$0

$0 16/30 Bauxite HSP Carbo 16/30 Bauxite HyperProp G2 Resin Curable Santrol 12/18 Ceramic LITE Carbo 20/40 API Sand Ottawa US Silica

Fig. 10–10. Fracturing treatment costs and NPVƒ increase in returns versus fracture penetration An additional observation, not pertinent to proppant selection for this case, is the importance of fracture conductivity, especially for the 10 md formation permeability versus costs to achieve that conductivity. This is evidenced by comparison of NPVƒ returns between the lower-cost CarboLITE 12/18 ceramic and higher-cost HyperProp G2 curable resin-coated 16/30 bauxite from Santrol. The CarboLITE yielded higher NPVƒ returns. As previously stated, proppant costs change constantly, due to availability. These can result in wide variations in cost/KƒWƒ, and thus NPVƒ. Hence, guaranteed proppant prices prior to selecting the economic optimum treatment is an essential aspect in design. At this stage, the preliminary optimum economic design range indicates • 2.5 to 3.8 million gallons of My-T-Gel HT, 60 parts WG-19 XL, 10 parts Gel-Sta • 14 to 19 million pounds of CarboHSP 16/30 bauxite proppant • Pumped down casing at 120 BPM • Expected fracturing cost $15 to $20 million • NPVƒ returns on the order of $165+ million • Discounted return of investment (DROI) of 8 to 11 Note: The previously mentioned data verity concern (a published 3.58 sp. gr. for the HyperProp G2 16/30 Bauxite) is now a nonissue. It is not a proppant of choice for this design. If it were NPVƒ-competitive, confirmation directly with the manufacturer, or a proppant testing service is a definite must.

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Essentials of Hydraulic Fracturing

Investigation: prospective benefits of piling proppant above the pay top Typically, treatments are intentionally designed to • Perforate only the gross pay interval • Inject only sufficient proppant quantities to cover the gross pay (as listed in table 10–22) Under certain conditions, additional revenue may be achieved by propping outside the pay: • Perforating the entire fracture confinement interval • Injecting additional proppant quantities to pile proppant above the gross pay top This practice has potential to increase total fracture flow capacity into the wellbore. It enlarges available flow area throughout the fracture and at the wellbore. This reduces the flow resistance imposed by limiting flow primarily to gross pay interval confines.

The concept—propping outside the pay The two charts in figure 10–11 showing fracture half-width profile, pay, perforated intervals, and proppant portray the concept. The left chart depicts a typical design: perforated only in the pay, with proppant at the pay top. The right chart shows perforations over the majority of the fracture confining interval, and proppant piled 400 feet above the pay top. The practice of connecting the entire fracture confining interval to the wellbore, prior to initiating the treatment, increases total fracture flow capacity from the pay formation to the wellbore. In essence, it enhances effective fracture conductivity. As can be seen, for this example, there is enough additional flow capacity available both above and below the pay to warrant investigation. Propping Outside the Pay, Proppant: @ Pay Top & Above the Pay 0

Fracture Half-Width (in.) 0.6 8,000

8,200

8,200

8,400

8,400

8,600

Fluid SlurryPay Sand

8,800 9,000 9,200

Proppant-laden Slurry Fracture Edge Proppant @ Pay Top Perforations

Depth (ft)

Depth (ft)

8,000

Fracture Half-Width (in.) 0.2 0.4

8,600

0

0.2

0.4

0.6

Proppant laden Slurry

Sand Pay

8,800 9,000 9,200 Fracture Edge Proppant 400 ft above Pay Perforations

Fig. 10–11. Propping to pay top (left) and propping outside the pay concept (right): fracture half-width cross section 586

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Obviously, the practice entails additional proppant and perforating costs. Proppant costs constitute the greatest consideration by far. Typically, perforating, pumping service, and fluid costs are relatively minor compared to proppant costs. Computation involves addressing every Xƒ and each proppant in the design set for a sufficient set of prescribed proppant heights above the pay top to arrive at an economic perspective.

Economic return versus proppant height above the pay top Figure 10–12 depicts the maximum NPVƒ returns versus proppant height above the pay top, and the corresponding fracture penetration associated with that maximum. It appears that NPVƒ returns can be increased from $1.65 to $1.80+ million by perforating the entire in situ stress-confining interval, and designing the treatment to pile proppant from between 100 and 200 feet above the pay top.

Proppant Top—Above Pay (ft) $200,000

0

100

200

300

400

$180,000

NPVƒ ($M)

$160,000 $140,000 $120,000 $100,000 $80,000 $60,000 $40,000

Xƒ = 1,340 ft Xƒ = 1,340 ft Xƒ = 1,340 ft Xƒ = 1,340 ft

16/30 Bauxite HSP Carbo 12/18 Ceramic LITE Carbo 16/30 Bauxite HyperProp G2 Resin 20/40 API Sand Ottawa US Silica

Santrol

Fig. 10–12. NPVƒ versus propped height above the pay top where Xƒ = 1,340 ft

587

Essentials of Hydraulic Fracturing

What-if scenario studies It has been repeatedly emphasized throughout previous chapters that prudent fracture treatment designs require scenario study investigations pertinent to the following questions: • What if input data for the design do not reflect in-fracture performance? • What is the economic impact if they do not? • How should issues be addressed where they do not? Scenario studies can vary significantly in nature. For example, they can address any or all of the following formation or fracturing material parameters used for design: • A few obviously pertinent design parameters or those including comprehensive parameter sets • A few variations for a given parameter or a wide span of multiple values for given parameters • Individual parameters or parameter combinations The options are essentially unlimited. Scenario study sets are at the design engineer’s discretion. Their individual effect(s) on the final treatment design can also vary widely. Some may show potential negative economic or job execution effects. Some may highlight possible options for increased revenue that may be considered risk-worthy. Others may indicate parameters that, even though they vary widely, have minimal effect on economic returns or job execution. Scenario studies: • Are unique to fields or formations in a given field • Are possibly unique to individual wells • Pose risks if results from one study are projected to different candidate formations, and possibly other wells • Provide awareness on how to improve economic returns, material selection, or job execution • Are beneficial to expediting fracturing treatment designs that maximize economic returns throughout a field development • Are useful when focused on parameter values subject to uncertainty What follows is a series of scenario studies considered, for the most part, pertinent to this example. Admittedly, they are more comprehensive than might be necessary to arrive at an economic optimum fracture treatment design. This is intentional to demonstrate where input data precision is critical, and where precision uncertainty may have minimal impact.

Base case scenario Table 10–23 displays the example 10–1 optimum economic treatment design. These data serve as the comparative reference for the scenario study results. Note: The base case does not include the propping outside the pay scenario.

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Table 10–23. Optimum NPVƒ fracturing treatment for the base case scenario Xƒ = 1,340 ft, with 16/30 Bauxite—HSP—Carbo Proppant Fluid System: MY-T-GEL HT: 60 parts WG-19, XL, 10 parts Gel-Sta.  Injection Rate: 120 BPM. Down Casing. DESIGN RESULTS Pumping Created Fracture Fluid Prop- PropFracturing Costs hours Vol. pant pant Penetr’n Height Width Fluid Proppant Pumping Total @ 90 Conc. Quantity Xƒ Hƒ Wƒp Service BPM M-Gal ppg M-Lbs ft ft in (M$) (M$) (M$) (M$) 20.3

1,340

1,141

1.162 3,845

5.0

18,488 $2,948 $17,009

$183

Net Returns NPVƒ

DROI

(M$)

$20,140 $166,235 8.3

Worst-case and best-case scenarios In each study, only one parameter is changed per scenario. The other parameters remain at base case values. The results reflect differences in NPVƒ returns, compared to the table 10–24 optimum NPVƒ value for both downside- and upside-case scenarios. Downside-case results reflect negative changes to NPVƒ. Upside-case results reflect positive NPVƒ changes. The study addresses the following parameters: • Spacing and formation data ˡˡ Net pay, h ˡˡ Permeability, k ˡˡ Porosity, φ ˡˡ Oil saturation, So ˡˡ Voumetric cumulative recoverfy factor, Vƒ • Reservoir oil viscosity and formation volume factor ˡˡ Viscosity and formation volume factor combined • Financial parameters ˡˡ Oil price and production taxes ˡˡ Future value discount rate • Fracturing treatment input data parameters ˡˡ Fracturing fluid rheology: n´ and K´ combined ˡˡ Fracturing fluid system efficiency: for Xƒ = 150 ft and Xƒ = 1,340 ft ˡˡ % kƒWƒ proppant pack damage Table 10–24 contains a summary of scenario results. Changes to base case parameters are listed in the table. Their difference magnitudes are considered to be within reason, as they are either (1) by factors of 10% to 20%, or percentage values or (2) from 80% to 70% or 80% to 90%. Most changes are relatively small. 589

Essentials of Hydraulic Fracturing

The NPVƒ scenario results and differences are references to the base case optimum NPVƒ design at Xƒ = 1,340 feet. Hence, they reflect results of using the same base case fluid system and proppant quantities. However, for each scenario case, a different Xƒ optimum may result. If so, different material quantities are required. This aspect is discussed in more depth later. Table 10–24. Worst-case and best-case effects of individual design parameter input data on NPVƒ

Scenario commentary Formation and reservoir parameters The data in table 10–24 emphasize the need for formation and reservoir data that accurately reflects in situ values, reservoir performance, and fluid behavior. If such data are erroneous, either of the following can occur from using the calculated design for the job: • Serious reduction in NPVƒ returns, from a minimum of $20 million to possibly much more for compounded parameter differences • Significantly higher-than-expected NPVƒ returns of $20 million and possibly more than five times that for combined parameter errors

590

A check with all sources for the formation and reservoir input data confirmed that they are the best currently available. There are constraints for this example. Management advised that, unless the studies indicate a significant increase in dollar returns, additional testing is not considered a viable option. Management was made aware of the scenario results and elected to proceed with the design as is.

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Financial parameters As shown in table 10–25, changes in oil price and taxes significantly impact economic returns. Future discount rate effects are also significant. Again, as with formation and reservoir data, the values used in the preliminary design are confirmed as the best available. Also there is no latitude here. Prices, taxes, and discount rates are beyond the design engineer’s control, except to ensure they are the best data available. Here, there is no basis for changing the treatment design in regard to financials.

Fracture treatment parameters The fracture treatment parameter scenarios suggested no justifiable changes to fluid system or proppant quantity requirements. Fluid rheology parameters showed minimal impact. However, fluid system changes were not an option. There were no alternative available fluid systems that satisfied the ΔPƒ friction pressure requirements. Fluid loss, which is a major design factor in proppant transport, does not play a significant economic role for this case. With the high average proppant concentrations (ppgS ≈ 10), fluid system volume is relatively low, thus the impact of fluid loss on cost is low. The relative fluid and proppant costs ($0.60/gal fluid versus $0.90/pound) resulted in a small fluid-loss effect on NPVƒ. Fracture conductivity damage seriously impacted the scenario NPVƒ returns. However, again, no alternative, less-damaging fluids are available. Also, the CarboHSP 16/30 bauxite proppant exhibited the least damage of any appropriate prospects available. Additionally, no proppant pack damage reduction additives were on the horizon for the fluid system. Consequently, the treatment pumping and blending requirements, and the material quantities as shown in tables 10–26 and 10–23 for Xƒ = 1,340 feet and CarboHSP 16/30 bauxite proppant constitute the optimum NPVƒ treatment design.

Final treatment design The final design calls for the following treatment: • Three 2,250 HHP in-service pumps, plus two additional 2,250 HHP standby pumps • Two 100 BPM in-service blenders, plus two additional 100 BPM standby blenders • 3.8 million gallons of My-T-Gel HT, 60 parts WG-19 titanate XL, 10 parts Gel-Sta • 18.5 million pounds of CarboHSP 16/30 bauxite proppant • Pumped down casing, at 120 BPM • Expected fracturing cost of $20 million • NPVƒ returns on the order of $166 million • DROI of 8.3 Pumping pressure, horsepower and equipment requirements are shown in table 10–25.

591

Essentials of Hydraulic Fracturing

Table 10–25. Treatment Pumping Summary at 120-BPM Injection Rate TREATMENT PUMPING SUMMARY @ 120 BPM Estimated Max Perforation Pumping Friction: 2 psi, @ 120 BPM & 16.3 ppgS—3.6 Sp.Gr Proppant Estimated Max Tbg/Csg Pumping Friction: 780 psi Estimated Total Pumping Friction: 780 psi Less Hydrostatic Head: 3,770 psi Total Fracture Extension Pressure: 4,800 psi Surface Pumping Pressure: 2,250 psi, Max Wellhead Limit: 8,000 psi WELLSITE EQUIPMENT REQUIREMENTS Hydraulic Horsepower: Pumps In Service: Standby: Blenders In Service: Standby:

6615 HHP @ 2,250 psi & 120 BPM 3 2 2 2

The resulting fracture geometry, treatment costs and net returns are summarized in table 10–25 for Xƒ fracture penetrations that are in the economic optimal range. Table 10–26. Fracture treatment design economic options

The phrase “economically optimal design range” requires further consideration. As can be seen in table 10–26, NPVƒ returns do not differ significantly for fracture penetrations from Xƒ = 1,040 feet to 1,340 feet. The decision about which treatment to implement again rests with management before the AFE is approved and operations commence.

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In view of the relatively close NPVƒ returns between Xƒ = 1,040 feet and Xƒ = 1,340 feet, the final design decision often depends on prevailing economic focus, and the conservative or aggressive nature of those in charge when it comes to risk-taking. Regarding this, the following options are available: 1. Realize a DROI increase from 8.3 to 11.4 for Xƒ = 1,040 feet by spending $5.6 million less on the treatment and sacrificing a potential $1 million in NPVƒ. 2. Realize a DROI increase from 8.3 to 9.6 for Xƒ = 1,190 feet by spending $2.9 million less on the treatment and sacrificing a potential $200,000 in NPVƒ. 3. Choose the calculated maximum NPVƒ optimum. 4. Realize an NPVƒ increase of $15 million by spending an additional $4.9 million for propping outside the pay.

Future treatment designs—preplanning The previous scenario results and discussion pertained to how input data that differ from what actually exists or occurs apply to only this case. The design engineer can do little to change the design, as pursuing more accurate data that may imply a significantly different design is not viable at this stage. However, the scenarios provide guidance for future designs. What follows discusses parameter differences that suggest a better optimized economic design, ones that call for more or less fluid or proppant, etc. Impact studies of parametric differences on the economic results are useful for determining the focus of testing for future treatment designs.

In situ stress profiles As mentioned in chapter 3, example 3–11, acoustic wave train logs are the typical resource for generating in situ stress profiles. Such profiles are derived from compressional and shear travel time log values. The chapter 3 discussion points out that ±10% shear wave travel time accuracy constitutes relatively good data (Some experienced acoustic log engineers claim ±10% is an extremely good log). These are inherent to Poisson’s ratio and elastic modulus calculations. Calculated values determine in situ stress (per Poisson’s ratio) and fracture width (per elastic modulus). Figure 10–13 shows in situ stress profiles and SPG model-calculated target fracture halfwidths for four scenarios: • Measured ΔtS values • Minus 10% measured ΔtS values • Plus measured 10% values ΔtS • Confinement boundaries, upper and lower

593

Essentials of Hydraulic Fracturing

Within the confinement boundaries, the following in situ stress differences are found between the measured, and minus and plus 10% ΔtS cases: • Minus 10% ΔtS: The in situ stress difference between the confining upper boundary and the lowest confining interval stress is approximately 30 psi lower than for the measured stress profile. This resulted in a wider target fracture width. • Plus 10% ΔtS: The in situ stress difference across the upper confining boundary is about 170 psi lower than for the measured case. This resulted in less confinement, and thus higher vertical fracture growth. In Situ Stress (psi) 3,500 7,600

4,500

SPG Fracture Half-Width (ft)

5,500

6,500

7,600

9,000 9,200

8,200 Depth (ft)

Depth (ft)

Upward Growth Confinement

8,400

8,800

1

1.5

8,000

8,000

8,600

0.5

7,800

7,800

8,200

0

Sand Pay Downward Growth Confinement Stress @ Measured ∆ts Stress @ Minus 10% ∆ts Error Stress @ Plus 10% ∆ts Error Confinment

Upward Growth Confinement

8,400 8,600 8,800

Sand Pay

9,000 9,200

Downward Growth Confinement Width @ Measured ∆ts Width @ Minus 10% ∆ts Error Width @ Plus 10% ∆ts Error Confinment

Fig. 10–13. In situ stress profile versus depth and SPG model fracture half-widths for ΔtS: measured and minus 10% and plus 10% ΔtS error Figure 10–14 shows the SPG model-calculated effects of the different shear wave travel times on NPVƒ versus fracture penetration Xƒ where the differences affected both the magnitudes and the optimum points. Table 10–27 compares results for the optimum NPVƒ designs. The difference magnitudes in NPVƒ returns from designs where acoustic wave train log accuracies, (i.e., errors of ± 10% which are considered “good logs”) justifies in situ stress profile studies on future wells. Such studies are discussed in chapter 3 pertinent to tables 3–13 and 3–14. This suggests comparing point-by-point microfrac stress test measurements with acoustic log data, and developing corresponding correlations. These can be conducted in concert with openhole logging programs prior to completion. Tests on a few wells are usually sufficient to determine whether a correlation exists, and if so, what the relationship is. Hence, such tests should be considered for only a few wells in the field, and the results incorporated in future treatment designs. 594

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Fracture Penetration Xƒ (ft) 150

300

450

600

740

890

1,040

1,190

1,340

$180,000

NPVƒ Increase (M$s)

$160,000

$140,000

$120,000

$100,000

$80,000

@ Measured ∆ts

@ Plus 10% ∆ts Error

@ Minus 10% ∆ts Error

Fig. 10–14. NPVƒ versus fracture penetration per acoustic wave train log stress profiles: measured ΔtS, minus 10%, and plus 10% ΔtS travel time errors Table 10–27. Optimum NPVƒ treatment design comparison per acoustic wave train log stress profiles: measured, minus 10%, and plus 10% ΔiS travel times

Formation and reservoir parameters Table 10–28 shows results for optimum NPVƒ treatment designs pertinent to formation and reservoir parameters: • Formation permeability • Porosity • Oil satuation • Oil properties: viscosity and formation volume factor

595

Essentials of Hydraulic Fracturing

Table 10–28. Future wells: impact of input data on optimum NPVƒ treatment designs

Here, as with in situ stress, the difference magnitudes for worst-case and best-case differences suggest that it is essential to confirm formation and reservoir data. Again, NPVƒ returns for either case show potential gains or losses that far outweigh testing costs. Thus, comprehensive efforts to obtain the most reliable data possible are warranted. The SPG model showed that the fluid system and proppant selected for design were the best available to maximize fracture conductivity, which was the target for example 10–1. Additionally, it provided guidance pertinent to data precision for future wells that could potentially improve economics. Thus, a lower end model such as SPG, or any P–3D model, has the potential to provide some beneficial guidance relatively quickly with minimal effort. The SPG model performed as expected. Although the scenario studies did not change the example design, they provided guidance for future design data acquisition on future wells. Thus, the results should be made available to others who may be designing treatments for the same formation in that field.

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GOHFER Model Treatment Design Example 10–1 provided in-depth discussion of the many aspects involved in arriving at a prospective fracturing treatment design for the example target formation. In example 10–1, decisions for treatment size, fluid systems, and proppants were based on results obtained with the SPG model. The discussion presented here shows how, for the example 10–1 final design, models such as GOHFER, with high-end fracture design capabilities, can enhance one’s perspectives of fracture propagation, fracturing fluid rheology, and fluid-loss behavior, as well as the resulting fracture conductivity effectiveness.

Comparing treatment designs—GOHFER versus SPG Chapters 8 and 9 discuss the models and data aspects pertinent to comparing different fracturing treatment design using different models for a specific formation. Figure 10–15 (a composite of figures 8–6 and 8–36) shows the differences between the two model’s capabilities. The left image depicts the SPG model general construction; however its width profile is not restricted to the elliptical configuration. It can address only layered intervals with varying in situ stresses. The right image portrays a very complex fracture behavior that GOHFER can address if given adequate information. They are very different models. In the comparative design example that follows, both models respected identical data as best possible; including formation description, lithology, layering, reservoir description (size, permeability, porosity), reservoir conditions (pressure, temperature), hydrocarbon content, wellbore construction, rock mechanics, and in situ stress. Preferably, the fluid system rheology (apparent viscosity), fluid loss, and proppant performance at time, temperature, shear rate, etc., are comparable. However, for the two examples, this is not the case. GOHFER employs a different rheology approach than does the SPG model, as discussed in what follows.

Fig. 10–15. Comparative model capabilities—SPG predicted geometry (left), actual fracture behavior (middle), and GOHFER pressure match (right). 597

Essentials of Hydraulic Fracturing

The SPG model uses single, average values for rheology parameters, and fluid efficiency at specified in-fracture conditions (time, temperature, shear rate). Fracture conductivity is an average value for the entire propped fracture length. This is determined from in-fracture proppant concentration, lb/ft2 for total proppant injected and propped fracture area. Conductivity is based on published data for proppant type and size, adjusted for temperature, and estimated damage pertinent to fluid system, pack stress load, etc. GOHFER determines material performance internally, using material property values contained in its resident database and pertinent algorithms for performance behavior (fluid system rheology, fluid loss, and fracture conductivity). The algorithms automatically calculate performance at in-fracture conditions. Fluid system rheology and fluid-loss performance are determined at each grid per time, while temperature shear rate and pressure differential are determined at each point. Fracture conductivity is in accord with Predict-K software for proppant size and type, stress due to fracture closure, temperature, time, and conductivity damage. It is essentially orders of magnitude, technologically and computationally, above what is offered by SPG. GOHFER provides the opportunity to examine fracture geometry, rheology, fluid loss, and fracture conductivity at numerous spatial and time points throughout the fracture.

Example 10–1 Description and Design Considerations Barree & Associates provided two designs that replicated different aspects of the example 10–1 results: 1. A treatment targeting a propped fracture penetration Xƒp ≈ 1,200 ft, using sand for the proppant 2. Injecting 18.4 million pounds of sintered bauxite, as indicated by example 10–1 to maximizing fracture conductivity for the 10 md formation permeability These two designs produced very different results. Discussion of the design approach focuses primarily on the second design. A synopsis of the results is presented in what follows.

In situ stress versus depth Figure 10–16 depicts the GOHFER in situ stress versus depth profile used for the Example 10–1 profile. The legend on the left designates lithology distribution versus depth. The right legend specifies color-correlative in situ stress magnitude (e.g., solid black represents the lowest; stippled black the highest). In the middle portion, perforations span the entire 200 ft gross pay. In situ stress magnitude (per the right legend) is depicted versus both depth and distance from the wellbore. Here, only a small distance is included. This corresponds with figure 10–3, where in situ stress is only depth-dependent, and remains constant away from the wellbore.

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Gohfer Model In Situ Stress Data Formation In Situ Stress 7,600

Perfs Sand Limestone Dolomite Shale

7,770

5,026

7,940

5,253

8,110

5,480

8,280

5,706

8,450

5,933

PSI

Depth (feet)

Lithology Distribution

In Situ Stress Magnitude Code 4,800

8,620

6,160

8,790

6,386

8,960

6,613

9,130

6,840

9,300

7,069

Fig. 10–16. GOHFER model lithology and in situ stress profiles versus depth The example case here could hardly be simpler. The fracturing vertical interval is 4.5 times gross pay thickness. Minimum in situ stress, which occurs in the 200-ft-thick gross pay, is nearly 1,500 psi below maximum stresses in formations that overlie and underlie the fracturing interval. Two 100-ft-thick formations, each with stress approximately 500 psi above minimum stress, immediately overlie and underlie the gross pay. It is not a complex in situ stress profile. The fracture initiates in the gross pay. Stress intervals immediately above and below the gross pay pinch fracture width somewhat. Vertical growth breaks out of these pinch-points and progresses upward and downward in various stages until encountering layers at 8,200 ft and 9,200 ft depths where high in situ stress layers strongly inhibit further growth.

In-fracture fluid system rheology, apparent viscosity, and specific gravity Figure 10–17 shows a chart of in-fracture rheology parameter values: n´, K´, an apparent viscosity at in-fracture shear rate and temperature, as well Newtonian behavior from the Carreau model (the fluid model type used in GOHFER). The three numbered vertical lines, marked 1, 2, and 3, designate reference measurement times of 15, 30, and 60 minutes.

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Essentials of Hydraulic Fracturing

Fig. 10–17. GOHFER model in-fracture rheology parameters versus time

Rheology Parameters n´ and K´ Initially, flow behavior index (n´) values start at about 0.6 and gradually increase to about 1 over time. The initial value is close to that used in example 10–1 (0.595) for the SPG model that makes no adjustment for time. Consistency index (K´) values in the GOHFER software start at about 0.1, which is fairly close to the example 10–1 value (0.107) that also is not adjusted for time in the SPG model. However, the GOHFER calculated K´ values quickly start declining after about 10 minutes. The chart does not show values beyond 15 minutes, and appear to be decreasing somewhat rapidly, which significantly affects apparent viscosity.

Newtonian The Newtonian curve depicts GOHFER-calculated values for Carreau model fluid behavior. Carreau fluids are types of generalized Newtonian fluids where effective viscosity µEFF(γ) is used for apparent viscosity µAPP(γ), which depends upon the shear rate γ, as shown in equation 10–1. µEFF(γ) = µINF + (µ0: µINF) × [1 + (tR × γ)2][(n´: 1)/2] where

600

µEFF(γ)

Effective viscosity (Pa-sec)

µINF

Viscosity at zero shear rate (Pa-sec)

µ0

Viscosity at infinite shear rate (Pa-sec)

tR

Relaxation time (sec)



n’

Fluid system flow behavior (power law) index



γ

Shear rate (sec–1)

Equation 10–1

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At low shear rate (γ > 1/t) as a power-law fluid. Note: Equation 10–1 is expressed in cgs units, i.e., Pascal-seconds. Thus, viscosity values that are expressed in centipoise must be converted accordingly: 1.0 cp = 0.001 Pa-sec, for use in Equation 10–1. Also, The Carreau equation is discussed in chapter 6, pertinent to figure 6–20.

Apparent viscosity Notice in figure 10–17 as both temperature and shear have a dramatic effect on apparent viscosity. Within 30 minutes it declined from 2,000 cp to 200 cp. After 100 minutes in the fracture at temperature, apparent viscosity declined to 4 cp. In regard to the effects of various parameters on apparent viscosity, GOHFER also accounts for viscosity increase by virtue of filtrate fluid-loss dehydration causing increased polymer concentration.

GOHFER calculations and design results Fracturing treatment data Figure 10–18 replicates model calculations of what a typical treating chart should look like for this example. The horizontal axis: time (0–1,300 min, or 21⅔ hr). The left three vertical axes (left to right): (1) the widest fracture width anywhere in the fracture, which is usually at the wellbore, (2) fracture width (axis range: 0–6 in.), proppant concentration (axis range: 0–6.0 lb/gal slurry), and (3) injection rate (axis range: 0–150 bbl/min). The right axis is pressure (axis range: 0–10,000 psi). In this example injection rate is constant throughout the entire treatment at 120 bbl/min.

Fig. 10–18. GOHFER model fracturing treatment data versus time 601

Essentials of Hydraulic Fracturing

Fracture width As can be seen, during pad injection, fracture width rapidly opens to 0.4 inches. This is more than sufficient (8½ times the requirement) for accepting 16/30 mesh proppant (max OD 0.0469). As in-fracture fracture pressure increases, fracture width gradually increases to a maximum 0.7 inches at the end of the treatment. Notice that after shut-in, at about 1,210 minutes, fracture width does not quickly decrease. (Fracture width had not decreased much below 0.7 inches 20 minutes after shut-in, and does not quickly decrease even 1,210 minutes after shut-in.) In regard to this, also notice that pressure at the wellbore, though it has declined approximately 1,000 psi in that same time, in-fracture pressure downhole is still at about 7,000 psi. Thus, a large amount of stored pressure remains near the wellbore. Since fluid system friction is essentially out of the picture, the wellbore pressure is transferring toward the fracture extremity. It is high enough to effect further fracture extension, and will continue to do so for a while. This implies that segments of the near-wellbore proppant-laden slurry are also moving away from the wellbore, and will continue to do so until the proppant bridges somewhere in the fracture. Hence, proppant concentration will also redistribute after shut-in. This, in turn, will affect fracture conductivity distribution in certain portions throughout the fracture.

Proppant injection stages The design for this treatment calls for 12,000 gal pad. Then proppant injection is commenced, starting at 1 lb/gal slurry, followed by four incremental ramps of 1 lb/gal slurry increments, to a maximum of 5 lb/gal slurry, where it remains constant at that concentration throughout the remainder of the treatment.

Treating pressure Note that as injection time progresses, both bottomhole and surface pressure trends exhibit several changes. It is obvious that GOHFER possesses relatively sophisticated capabilities. However, for this example, net fracturing pressure calculations pertinent to Nolte–Smith analysis are not displayed. Such data is graphically displayed in a different chart than that shown in figure 10–18. The reason it is not included is because the authors were very grateful for what Barree & Associates did provide, and were hesitant to burden them with work that is not necessary for this example. This would not be the case if the data were other than gratis. It is essential to a fracturing treatment design. Regardless, additional information that is available in the figure’s treating pressure record warrants discussion.

Surface injection pressure Surface injection pressure reached approximately 6,800 psi by the end of injection. At 120 bbl/min, this equates to approximately 20,000 HHP, which requires at least 10 in-service fracture pumps for injection. The extensive 21-hour injection duration warrants possibly three to four standby pumps. 602

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Notice the time correlations between surface injection pressure and where increased proppant concentration stages are introduced. This is due in part to slurry proppant concentration (particle fraction), which increases pipe friction as concentration increases. Apparently, the increased hydrostatic column pressure associated with slurry density increase is not sufficient to reduce the combined bottomhole pressure increase and pipe flow friction resistance pressure. However, notice that the bottomhole and surface injection pressure differential decreases as the proppant stage concentration increases.

Bottomhole pressure and vertical fracture growth behavior This is discussed in chapter 3, pertinent to figure 3–20. For design engineers that have access to high-end models (whether in-house, via the service company, or from a consulting firm), prefracture model-calculated Nolte–Smith data are extremely valuable. If real-time, accurate, measured bottomhole pressure data is a part of the treatment diagnostics, then pre-fracture model calculations should certainly be included in the fracturing service company’s software for display and monitoring during treatment. Thus, expected vertical fracture growth behavior can be compared to actual behavior as injection progresses. This provides a perspective of both fracturing propagation behavior as well as perspectives about input data verity for the design. This progression is not as obvious from the bottomhole pressure data shown in figure 10–18 as it would be in a Nolte–Smith analysis. As a matter of interest, it is possible to infer from the in situ stress profile how vertical fracture growth would behave during injection. Vertical fracture growth would progress as shown in the sequence below, if the in situ stress profile shown in figure 10–19 represents the true in situ stress profile of the formation layers. If it does not, the in situ stress profile used for design should be investigated. Note: Figure 10–19 is equivalent to figure 10–3 for the SPG model in example 10–1. Sequence  1  2  3  4  5  6  7  8  9 10

Fracture Vertical Growth Behavior

Depths to Top and Bottom

Relatively confined with tops and bots between Upward growth to Very rapid upward growth to Downward growth to Very rapid downward growth to Relatively confined with tops and bots between Upward growth to Downward growth for a short period Relative confined with tops and bots between Downward growth for a short period Upward growth to the end of injection

8,600 ft and 8,800 ft 8,500 ft (top)–8,800 ft (bot) 8,400 ft (top)–8,800 ft (bot) 8,400 ft (top)–8,900 ft (bot) 8,400 ft (top)–9,000 ft (bot) 8,400 ft and 9,000 ft 8,200 ft (top)–9,000 ft (bot) 8,200 ft (top)–9,100 ft (bot) 8,200 ft and 9,000 ft 8,200 ft (top)–9,200 ft (bot) 8,050 ft (top)–9,200 ft (bot)

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Essentials of Hydraulic Fracturing

In Situ Stress (psi) 4,500 7,600

5,000

5,500

6,000

6,500

7,000

7,800 8,000

Depth (ft)

8,200

Upward Growth Confinement

8,400 8,600 8,800

Sand Pay

9,000 9,200

Downward Growth Confinement

9,400 9,600

Fig. 10–19. In situ stress profile versus depth, and upper and lower fracture vertical growth confining bounds

Design (1)—SPG approximate target—1,200 ft of fracture penetration Figure 10–20 shows the proppant concentration profile for the initial design, where the focus is to achieve a propped fracture penetration of approximately 1,200 feet. This is achieved with 180,000 gallons of fluid and 300,000 pounds of 20/40 mesh sand injected at a 40 bbl/min rate. However, observe that sand concentrations on the order 4–5 lb/ft2 extend out only 150–250 feet away from the wellbore. With sand effecting less than 10%–20% of the reservoir drainage radius, expectations of production increase are lower than desired. However, there is another aspect depicted in the design that warrants discussion. Notice the three-fingered profile in the right portion of the display. Although the configuration at the fracture extremity may not be as pronounced, the inference is that the fracture width configuration is somewhat proportional to the finger extents. This coincides somewhat with the SPG model fracture width profile shown in figure 10–19. This reflects the fracture width pinch-points imposed by the higher stress layers above and below the gross pay. In a fracture mechanics sense, this is consistent with the figure 10–19 in situ stress profile.

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GOHFER Model — 40 bbl/min, 20/40 Sand In-Fracture Proppant Concentration (lb/ft2) versus Propped Fracture Penetration

180,000 gal, 300,000 lb

7,940 8,110

8,460 8,620

0.793 1.596

P E R F S

2.399 3.193 3.995

lb/ft2

Depth (ft)

8,280

Proppant Concentration Legend 0.000

4.796

8,790

5.592

8,960

6.394 9,130 0

300

600 900 Propped Fracture Penetration (ft)

1,200

7.197 8.000

Fig. 10–20. GOHFER model in-fracture proppant concentration (SPPG, slurry) versus penetration— proppant: 20/40 sintered bauxite, injection rate: 40 bbls/min

Design (2)—SPG approximate target—injecting 18.4 MMlb of sintered bauxite Figure 10–21 shows the proppant concentration for the initial design where the focus is to injected a total of 18.4 MM lbs of 16/30 sintered bauxite into the fracture at a 120 bbl/min injection rate. This required 5,225,000 gallons of fluid injection. There are several aspects displayed in the proppant concentration profile that require consideration: • Extensive resulting fracture penetration ˡ Encroachment on offset operators ˡ Reservoir drainage interference • Potential for enhanced economics by propping outside the pay • Resulting fracture conductivity

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Essentials of Hydraulic Fracturing

GOHFER Model—120 bbl/min, 16/30 Sintered Bauxite In-Fracture Proppant Concentration (lb/ft2) versus Propped Fracture Penetration 7,600

5,225,000 gal,

7,700

18,400,000 lb

0.793

7,940

1.596

8,460 8,620

2.399 P E R F S

350 620 230 430 750

1 2 3 4 5

8,790

3.193

6

1,490

3.995

lb/ft2

Depth (ft)

8,110 8,280

Proppant Concentration Legend 0.000

4.796 5.592

8,960

6.394

9,130 0

640

1,280

1,920

Propped Fracture Penetration (ft)

2,560

3,200

7.197 8.000

Fig. 10–21. GOHFER model in-fracture proppant concentration (SPPG, slurry) versus penetration— proppant: 16/30 sintered bauxite; injection rate: 120 bbls/min

In-fracture proppant distribution As previously stated, Barree & Associates provided a preliminary example design to replicate the example 10–1 propped penetration (Xƒp ≈ 1,200 feet). This was achieved with 180,000 gallons of fluid, and 300,000 pounds of 20/40 mesh sand proppant injected at 40 bbl/min. However, the initial preliminary design displays some interesting aspects that are not shown in the preceding discussion. Design (1) was for an injection rate of 40 bbl/min, with 20/40 mesh sand as the proppant, instead of Design (2): 120 bbl/min with 18.4 MM lb, 16/30 sintered bauxite proppant. The remaining design data were identical to that of example 10–1. Figure 10–20 and figure 10–21 designate lb/ft2 proppant concentration per the legend on the right, which reflects the proppant concentration in the fracture at the end of a 15-minute shut-in period after injection has stopped. This indicates that segments of the near-wellbore proppant-laden slurry have moved away from the wellbore and bridged. This accounts for the lower concentrations near the wellbore and higher lb/ft2 concentrations 300–400 feet in the fracture across the gross pay, as is suggested in figure 10–21. Although a correlative fracture conductivity profile is not displayed, the ability to create one is available in the model software. Barree & Associates advises that GOHFER incorporates the conductivity damage mechanisms that are present in the Predict-K software. It generally gives a pessimistic but realistic production profile. Additionally, there is no easy way to dissect those damage mechanisms that are incorporated in the code itself. In view of this, the authors present an approach for inferring a fracture conductivity value to use for folds-of-increase calculations. This is presented later in the chapter. GOHFER uses an internally set value of 0.1 lb/ft2 as a cutoff for effective fracture conductivity. 606

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Resulting fracture conductivity—18 MM lb sintered bauxite proppant To obtain an inference of fracture conductivity, the gross pay vertical interval in figure 10–21 is parsed into six segments from the wellbore to the reservoir drainage boundary. The parse sizes are such that, as best determined, an estimated uniform proppant concentration resides in each, per the figure legend. These are designated by the left to right numbers one through six. Data for the parsed segments are listed in table 10–29, along with values pertinent to fracture conductivity in each parse. The calculated resulting average fracture conductivity from the propped fracture extremity to the wellbore (4,379 md-ft) is shown in the far right column. Table 10–29. Parsed fracture conductivity segments from figure 10–21

Determining KƒWƒ = 4,379 md-ft from the values for each parse requires using (a) the discussion contained in chapter 7, and (b) the established concentric circle radial flow averaging approach. The process is as follows: • Radial distances rI and ro specify inside and outside radial distances from the wellbore • Proppant concentration (CPROP) and in situ stress (σPACK) yield average closed fracture width (WƒC) per equation 10–2 and table 10–30 (see chapter 7, equation 7–17 and table 7–14) • Sintered bauxite permeability, Kƒ = 311 darcys (σPACK = 5,400 psi, T = 182°F, 85% damage), per example 10–1, table 10–12 • The above products yields Kƒ WƒC • ∑1…N KƒWƒC × ln(rO/rI) = 0.00182688 • ln(re/rw) = 7.997 • Total fracture KƒWƒ = ln(re/rw) / [∑1…N KƒWƒC × ln(rO/rI)] = 4,379 md-ft Table 10–30. Equation 10–1 coefficients: fracture proppant concentration ► fracture closed width Proppant Type Sintered Bauxite

Equation 7–14 Coefficients AC►W –1.089

BC►W 1.0512

CC►W 14000

DC►W –1.1807

EC►W 1.126

FC►W –1.089

GC►W 1.0512

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Essentials of Hydraulic Fracturing

WƒC = 10^[AC►W + BC►W log(CPROP)] + [(σPACK: 1,000)/WC►W] × {10^[DC►W + FC►W log(CPROP)]: 10^[FC►W + GC►W log(CPROP)]}

Equation 10–2

where WƒC

Closed/healed fracture width (in.)

CPROP

Proppant pack concentration (lb/ft2)

σPACK

Stress on the closed proppant pack (psi)

AC►W–GC►W

Equation 10–3 coefficients per table 7–1

Resulting FOI for 18 MM lb sintered bauxite proppant In accord with Prats’s approach, as discussed in chapter 2, the following calculation determines the resulting FOI for the 18 MM lb sintered bauxite proppant treatment:

Formation permeability, k = 10 md



Propped fracture penetration, Xƒp = 1,490 ft



Fracture conductivity, KƒWƒ = 4,379 md-ft

Thus, dimensionless fracture conductivity (FCD) = KƒWƒp/(kXƒp) = 0.2939. Pseudo-wellbore radius (r´w) is determined by equation 10–3:

r´w = Xƒp × 10[A + B Log10 (FCD) + C Log10 (FCD)2] = 100 ft

Equation 10–3

where for the 0.1 < FCD < 1 range, equation 10–2 coefficients A, B, and C (per table 2–1 in chapter 2) are:

A

=

–0.73053



B

=   0.74033



C

=

–0.17378

For the reservoir drainage boundary radius (re) = 1,490 ft, which is also equivalent to the propped fracture penetration (Xƒp), FOI is determined by equation 10–4:

FOI = [log(re/rw)/log(re/r´w)] = 2.96

Equation 10–4

Encroachment on offset operators—per figure 10–21 Well spacing for the example is 160 acre/well. This equates to 1,340 ft from a lease boundary to a centered well. The fracture has a calculated maximum propped length of 2,920 ft. Undoubtedly, the created fracture extends farther. The SPG model calculated a maximum total fracture penetration of 1,340 ft, which did not suggest encroachment. GOHFER calculated a much deeper fracture penetration. This is an example of where some P–3D models may not provide accurate fracturing behavior. Potential fracture encroachment is a matter of very serious concern. An issue such as this must be brought to management’s attention. If the well directly offsets another operator’s, or anyone’s, 608

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property line, it poses possible legal action against the offender. Such knowledge contained on record subjects the offender to more seriously consequential legal action. Even without knowledge from a design model, a created fracture that encroaches on another’s property can result in legal consequences. It is inexcusable to ignore the issue.

Reservoir drainage interference, per figure 10–21 Even if encroaching on others’ property is not an issue, reservoir drainage interference is. The reservoir drainage boundary, 1,490 ft from the wellbore is shown on figure 10–21. Also, arrows show the reservoir fluid flow directions for the fracture candidate and that for offsetting wells, if they exist. If they don’t exist, they eventually will. This possibility must also be brought to management’s attention. Not doing so can pose even more serious consequences than fracture encroachment on another’s property. It may affect a design engineer’s employment.

Potential for Enhanced Economics by Propping Outside the Pay Figure 10–21 reveals a significant amount of potentially available fracture flow capacity created by the fracturing treatment. The fracture extends over the entire 1,100 ft vertical fractured interval in both the GOHFER figure 10–21 design and the SPG figure 10–22 design. There is significant in-fracture proppant concentration over the entire 1,100 ft fractured interval. Thus, there is a lot of fracture flow capacity that is available from resident propping above and below the pay. Fracture Half-Width (in.) 8,000

Depth (ft)

8,200

0

0.2

0.4

0.6

Proppant–laden Slurry

8,400 8,600

Sand Pay

8,800 9,000 9,200

Fracture Edge Proppant 400 ft Above Pay Perforations

Fig. 10–22. Propped fracture half-width cross section from example 10–1

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Essentials of Hydraulic Fracturing

Connecting the entire vertical fracture to the wellbore takes advantage of this large area of proppant concentration. Merely perforating the gross pay does not. Admittedly, conformance flow will occur in the fracture near the top and bottom of the pay from the propped extremity to the wellbore, but it is not expected to significantly increase total production. However, above and below the pay there is an opportunity to increase total flow capacity for the entire propped system. Obviously the design is out of the question because of the two previous situations mentioned, i.e., encroachment or interference. However, the final treatment is pending a design with different fluid and proppant volumes, and possibly injection rates and stage schedules. The pending design should investigate the economic potential for propping outside the pay. The extent and nature of the in situ stress profile in this example is well-suited to the process. Detailed discussion for propping outside the pay is contained in the chapter 7 section “Total Fracture Flow Capacity—Propping Outside the Pay to Increase FOI.” It is also addressed pertinent to a different stress profile in the chapter 12 section “Post-fracture Wellbore In-Flow Production Profiling.” Hence, discussion here is limited to the following bullet points essential to the process: • Prior to pre-fracture breakdown or injection, perforate the entire expected vertical fracture interval. • Employ a sufficient perforation density (shots per foot) to ensure that the fracture is connected to the wellbore over that entire interval. • Inject a sufficient quantity, type, and size of proppant to economically optimize the treatment.

Summary of Results for Examples 10–1 and 10–2, and Ideas for Redesign Table 10–31 contains a summary of the SPG and GOHFER model results for the examples. Significant differences are apparent in the table data. The term “NA” implies data that is not available or that was not further addressed. The fracture width differences between SPG and GOHFER are partly attributed to different rheology parameters (n´ and K´). The SPG constant average values yielded much higher apparent viscosity than the GOHFER calculated values, where apparent viscosity degraded due to time exposure at temperature and shear rate. This resulted in the SPG calculation being a much wider and shorter fracture than GOHFER calculated. Such behavior is concordant with the precepts presented throughout this book. As a matter of interest (and somewhat contrary to prior comments about tweaking input data to yield desired results), the authors investigated the effect of using higher n´ and lower K´ values in the SPG. As expected, narrower widths resulted. Also, as expected, it shortened the economically optimal fracture penetration, and thus the required treatment volumes.

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Table 10–31. Summary of the results for example 10–1 and example 10–2 SUMMARY–FRACTURING TREATMENT DESIGNS Example 10–1, SPG (P3-D) & Example 10–2 GOHFER (G3-D) Fluid System: MY-T-GEL HT: 60-ppt WG-19, XL, 10-ppt Gel-Sta Model

SPG

GOHFER

FRACTURING TREATMENT Injection Rate: Down Casing Fluid Volume, M-Gal Proppant Type Proppant Size Proppant Quantity, M-Lb Max. Proppant Concentration, SPPG Avg. Proppant Concentration, SPPG

120 3,845 Bauxite 16/30 18,488 6.0 4.18

Design (2)

Design (1)

120 5,225 Bauxite 16/30 18,400 5.0 3.52

40 180 Sand 20/40 300 4.0 1.67

NA 1,150 2,920 0.7 NA

NA 1,150 1,200 0.4 NA

640 4,379

Est 250 NA

FRACTURE GEOMETRY Fluid System Efficiency Max. Fracture Height Hƒ, ft Max. Fracture Penetration Xƒ, ft Fracture Width Wƒ, in:  Wellbore Average

25% 1,141 1,340 1.16 0.464 PROPPED CLOSED FRACTURE

Max. Effectively Propped Penetration Xƒ, ft Fracture Conductivity KƒWƒ, md-ft

1,139 11,128

POST-PRODUCTION (Pre-Frac Q = 1,900 BOPD) Production Folds-of-Increase, FOI Initial Post-Frac Production, BOPD

4.18 8,320

2.96 5,890

NA NA

The calculated fracture penetration differences are especially important. The SPG model did not indicate any potential for encroaching on another’s property or offsetting well drainage area interference. Thus, there was no awareness of the issue. It was discovered with the GOHFER model results. Had a fracture design engineer used only a P–3D model design for the treatment, serious consequences could have ensued. The results definitely call for redesigning the treatment using a high end model.

Considerations for Treatment Redesign One primary consideration for the design is to maintain fracture penetration inside the reservoir boundary drainage radius and also maximize revenue. Another is that 10 md formation permeability calls for maximizing fracture conductivity. This implies large fracture widths and high in situ proppant pack permeability. A fluid system that would yield wider fractures than the example fluid is not currently market available. Sintered bauxite yields the maximum fracture permeability of any available proppant. Hence, the design must include those materials. As has 611

Essentials of Hydraulic Fracturing

been demonstrated, a G3-D or FE-3D type model is required for the design. With these in mind, many approaches remain possible. The redesign may require several iterations. A few of the possible approaches are cited below for consideration: • Reduce the pad volume stage, increase the maximum slurry concentration, and design the stage ramping to achieve that maximum as quickly as possible. • Design the injection staging schedules to effect a hard tip screen-out when fracture penetration reaches 1,000–1,200 ft, then increase slurry proppant concentration to the injection pump maximum limit, so as to cram as much proppant as possible into the fracture. Note: With a tip screen-out, continued injection widens the fracture. • Investigate the propping-outside-the-pay procedure for either of the above.

Commentary on Pre-Fracture Treatment Designs with Models Progression through the SPG treatment design and using a different fracture design model and comparing results from the GOHFER model showed the following: • Reliably accurate and representative design input data is essential to the design. • Computerized models facilitate investigating numerous options for design. • Scenario studies are essential for arriving at better economic designs. • Different models, using identical fracturing materials, can yield significantly different designs for the same formation. • Higher-end models provide significantly more and better insight about fracture propagation behavior. The way different models handle input design data is important. For example, the SPG model employs constant rheology from wellbore to fracture tip. It does not account for non-powerlaw behavior at low in-fracture shear rates, nor viscosity increases due to fluid loss. GOHFER accounts for these aspects. Factors such as these will undoubtedly affect fracturing predictions. However, in this particular example, the probability of selection fluid or proppant types different than those used here is relatively low because no viable alternatives are available. The more sophisticated models that address time, temperature, shear rate, and fluid-loss effects on rheology are strongly recommended for design. The above issues emphasize how important it is that the design engineer be aware of model limitations and capabilities. Many design engineers may be faced with the situation, where they are limited to using lower end models. However, reservations about model inadequacy warrant efforts to advise upper management of the potential economic downside so as to correct the situation. Whatever model is used for design provides opportunities to investigate relative performance resulting from a variety of materials, as well as the relative impact of other pertinent parameters, including ranges in parameter values.

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Scenario studies It is obvious that scenario studies benefit economic returns. Capabilities for such studies are embedded in some models and not others. However, the output from most models can be readily exported to spreadsheet format. Thus, specific templates can be developed to facilitate importing spreadsheet data pertinent to parameters that are of interest to the design engineer. The capabilities of models available today facilitate and expedite doing many scenario studies. As previously stated, scenario construction is left to the discretion of the design engineer. Scenarios can be concise or comprehensive in regard to parameter designations. They can comprise a limited or large range of parameter values. Regardless, they are a significant part of fracture treatment design.

Model credibility Model output credibility, as discussed in chapter 8, is re-emphasized here. Cautions are reiterated about taking results quantitatively at face value, and not calculating a sufficient number of cases to thoroughly investigate results. Sufficient design engineer intuition and knowledge to recognize potentially unrealistic results are also important. Again, the model tells design engineers what design engineers tell it to tell them. Hence, accurate, representative input data is requisite for all model designs, regardless of model sophistication. Design models remain the best tools available for pre-fracture design and post-fracture analysis. While degrees of sophistication vary, regardless of which model is used, it offers potential insight for investigating relative performance pertinent to fluid systems and proppants, as well as quantity requirements, injection practices, and relative economic returns.

Commentary on higher-end fracturing design models Example 10–2 displayed only a minimal perspective of the capabilities available from higherend model types. It is beyond the scope of this book to cover the gamut of additional capabilities that they offer. GOHFER demonstrates only the tip of the iceberg of the menu of their features. Therefore, the authors reiterate statements from chapter 8 and those mentioned in this chapter, encouraging design engineers to access these higher-end models to explore the entirety of their benefits. Additionally, the developers of such models are continually upgrading their model capabilities and augmented features to accommodate user needs. These improvements serve to further enhance the benefits of using the most sophisticated applicable model available. This applies to even relatively simple target formations that exhibit minimal design complexities, such as the formation used for the example in this chapter.

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Exercises Exercise 10–1 A gas well was fractured. Fracture and formation properties include the following:

T = 250°F

pi = 4,030 psi k = 0.1 md

µ = 0.0244 cp



Φ = 0.13

cT = 9.68 × 10–5 psi–1

A = 120 acre (square)

rw = 0.328 ft

h = 58 ft (net pay and propped fracture height)

Lf = 345 ft wkf = 2,300 md-ft 1. Use the McGuire and Sikora graph to determine the productivity-index (PI) ratio. 2. Repeat the computation, except the fracture length is now 414 ft. 3. Repeat the computation, except the fracture conductivity is now 2,760 ft (keep fracture length of 345 ft). 4. Briefly discuss the effects of fracture length and the fracture conductivity on the values of productivity-index ratio for this reservoir.

Exercise 10–2 How many (reservoir) barrels of fluid can fit into an 80-acre, 100 ft, 30% porosity reservoir?

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Nomenclature Symbol

Units/Value

Description

English eƒ

fraction

Fracturing fluid efficiency

µAPP(γ)

Pa-sec

Apparent (effective) viscosity

µINF

Pa-sec

Viscosity at zero shear rate

µ0

Pa-sec

Viscosity at infinite shear rate

t

sec

Relaxation time

n´

dim.

Fluid system flow behavior (power law) index

γ

sec–1

Shear rate

Reference Warpinski, N. R., Z. A. Moschovidis, C. D. Parker, and I. S. Abou-Sayed. 1994. “Comparison Study of Hydraulic Fracturing Models—Test Case: GRI Staged Field Experiment No. 3 (includes associated paper 28158).” SPE Production and Facilities 9:7–160.

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11 Fracturing Horizontal Wellbores

Introduction Horizontal wells have an 80-year history, but the most interesting developments have occurred in the past 25 years as horizontal well technology found a home in the development of shales and other low-permeability reservoirs. The first horizontals were drilled from the 1930s through the 1950s, but economic success in terms of increased production was elusive. By the mid-1970s, the first breakthrough came when the horizontal well, now 40 years old but still in its infancy, was united with the proven technology of hydraulic fracturing. This marriage of techniques, patented in 1974, evolved the horizontal well into a platform for multiple hydraulic fractures in low-permeability carbonate, sandstone, conglomerate, and shale wells (Strubhar and Glenn 1973; Austin, Rose, and Schuh 1988; Norris et al. 1996). The combination of horizontal well and fracturing technologies has kick-started the unlocking of large oil and gas reserves in both source rocks and conventional reservoirs thought to be unrecoverable just a few decades ago. However, as with many breakthroughs, optimizing the process and maximizing the efficient recovery of hydrocarbons from these low-permeability formations requires breaking habits gained from operating in the conventional reservoirs and generating new approaches that go beyond the comfort zone of traditional recovery to access fluids that have non-traditional ways of moving through low-permeability rocks. Thousands of horizontal wells had been drilled worldwide by the mid-1990s, and multi-fractured horizontal wells were common in soft and hard fractured chalks, marginally consolidated sands, tight sands, moderate viscosity oil reservoirs, and even water source wells (US EIA 1993; Dees, Freet, and Hollabaugh 1990; Chambers, Mueller, and Grossman 1995; Andersen et al. 1990; Overby, Yost, and Wilkins 1988;). Multi-fractured horizontal wells were a standard approach by the early 1990s although many factors of well design such as well orientation, well spacing, fracture spacing, and stress effects from the multiple fracturing process were still evolving. The lure of contacting more reservoir was enhanced by the addition of fractures, which increased the volume of contacted reservoir far beyond what was possible even with the longest possible lateral. The information required to optimize horizontal wells and fracture treatments that enable production begins with geology and reservoir knowledge and encompasses significant information from geophysics,

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petrophysics, stimulation mechanics, and production engineering. The difference in increased production and economics for well and stimulation designs that rely on scientific approaches will likely be higher than for a manufacturing design that is not optimized before the well and fracture designs are locked in. Formation characteristics are major influences on the design of both the horizontal well and the hydraulic fracture. There are wide variances in characteristics within most formations that require design flexibility to optimize production. There may also be several formation members in repeating layers that reflect depositional history, some of which are production enablers (like higher permeability sand bodies), while others (like ductile shales and laminates) may be barriers to flow and fracture stimulations. As wells were turned toward the horizontal plane, the advantage of fracturing became clear, even for the increased area contact offered by horizontal wells. In thick or highly layered or laminated pays, the vertical permeability (frequently only a tenth to one-hundredth of the average horizontal permeability) is a definite limit on inflow from above and below the plane of the wellbore. While this vertical-flow-limiting behavior is an advantage in controlling gas coning from above or water coning from below, it creates a problem in flow from a thick or layered formation where coning control is not needed. Overcoming this vertical permeability limit in non-naturally fractured wellbores requires hydraulic fracturing. The fracturing concept, first field-tested in 1947 (Montgomery and Smith 2010; Clark 1949) and commercialized in 1950, is a basic technology in concept but complicated in application as any idea or process becomes when the application is made on a structure deposited in many small layers with building materials washed from changing sources over millions of years and modified by natural forces and events over several more million years. As with any symbiotic relationship of joined technologies like horizontal wells and hydraulic fracturing, there will always be economic and technical reasons to optimize the process for the specific applications created by the changing depositional environment. Lateral length in horizontals increased to over 8,000 ft in the most successful developments as confidence in the drilling phase grew (DeMong, Hands, and Affleck 2010). Longer lateral lengths usually deliver lower development costs if frac stages are increased to effectively break up the formation exposed by the extended wellbore reach, although the increase in rate is not exactly proportional to increased lateral length. The interplay from multiple fractures along a wellbore is complicated by variances in the rock as well as the individually created fractures. The difficulty in predicting or even understanding these flow variances are part of the continuing puzzles that must be explored for each new formation that is tackled by horizontal wells. Wells are fractured either to increase formation stability in soft sand formations or to accelerate or enable production from moderate to very low permeability reservoirs ( Rawlings 1958; Norman 2004;). Just two years after hydraulic fracturing was commercialized, multiple fracturing applications in a single well found a home in offshore wells, quickly becoming common both in on-shore and off-shore wells where the geologic basins contained stacked pay zones (Clark and Fast 1952). Beginning with these first multi-fractured vertical wells in 1952 and the first multifractured deviated wells in 1974, the wellbore, be it vertical, deviated, or horizontal, has been increasingly viewed as a platform for fracture delivery (Clark and Fast 1952; Strubhar and Glenn, 1973; King 2014a). Currently, approximately 60% to 80% or more of all new US wells will be fractured and nearly half of these wells will be horizontals (www.FracFocus.org). The percentage of low-permeability unconventional reservoir wells or shale wells that require fracturing is nearly 100% and fracturing will account for 75% of US gas supplies in the future (API, 2013). 618

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Hydraulic fracturing technology has made a number of unconventional formations into producers with a very large impact on the supply of energy on a world-wide scale. Tight gas, marginally consolidated formations, highly naturally fractured formations, coal bed methane recovery, North Slope wells, soft chalks, and now gas- and hydrocarbon-liquid-rich shales have been developed into stable supply sources by implementing multi-fracturing in horizontal wells. The same fracturing process that is widely used in the oil and gas industry has also found utility in fresh water supply wells and mining. The environmental safety of hydraulic fracturing has been recently questioned, but industry and non-aligned academic risk-evaluation studies of the fracturing process and well construction integrity have identified only minor risks in the transport and isolation integrity as valid concerns (Kell 2011; King 2012; King and King 2013) and virtually no risk in fracturing itself (King 2012). In horizontal well developments, decreasing well penetrations through the water table and grouping wells onto concentrated pads also sharply reduces both environmental footprint and risk of groundwater contamination by drilling or gas migration (Kell 2011; King and King 2013). Horizontal well design that optimizes the well as a platform for fracture application links the well with a host of geological factors and some mechanical factors that were generally ignored in vertical wells (Vincent and Pearson 1995). Fracturing a horizontal well introduces layers of complexity such as in situ stress development and diverging radial flow into the overall fracture design and necessitates a more detailed look at both the stimulation design and geoscience inputs that influence well path, including orientation, azimuth, and stress variation before the details of fracturing topics can be addressed. Even in the case of a near-perfect fracture treatment from the horizontal well, the basics of production flow must also be considered to take advantage of the enhanced area of contact delivered by the combination of horizontal well and fracture stimulation.

Fracturing Technology Although fractured horizontal wells have been used primarily in shales for the last few years, many of the original targets were conventional reservoirs. In both unconventional and conventional applications, many technically based actions and activities have coalesced into modern well development. Hydraulic fracturing is the cornerstone that enables these low-permeability formations to produce at economic rates. Inventions, innovations, and adaptations have incrementally but steadily changed the landscape of gas and oil production in North America and will eventually change today’s unconventional producers into tomorrow’s conventional energy supply. Technology in shale and tight formation development has driven recovery of original gas in place (OGIP) from a starting point of around 1% for shale developments in the 1990s to between 10% and 30% or more today, depending on the specific shale (fig. 11–1). The dates of the first use of a technology and the general acceptance of that technology, such as multi-fractured horizontals (MFH), are indicative of variation in the technical abilities of producers as well as regional resources to apply the technology.

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Fig. 11–1. Percent recovery of initial gas in place versus year of the development Not every production technology has worked in every shale, but every shale will likely yield its resources to a specific adaptation of a stimulation that will likely include hydraulic fracturing technology. Whether a low-permeability formation can be made profitable or not is a pointin-time decision and depends on the cost of the necessary technology and the price obtained for the produced fluids. There are also limits placed on the type of stimulation or the type of fluids that flow from a specific formation that may preclude development for practical purposes. These problems may include lack of flow enhancing characteristics like natural fractures or fluid compositions such as high CO2 or H2S levels that increase costs of recovery. Early field-based research into fracturing from horizontal wells was largely trial and error, often practiced in secret to maintain competitive advantage as large areas of shale were leased and evaluated through the drill bit and frac pump. Advances in horizontal wells and fracturing often appear as sudden breakthroughs, while the trial-and-error path that lead to the success is rarely seen. Multiple fracturing in horizontal wells provides an efficient way to access resources held in low-permeability formations while reducing the number of vertical wells necessary to access those same reserves (Vincent 2011). The goal of fracturing in horizontal wells is to access as much area as possible within the hydrocarbon-bearing formation from a single wellbore. Techniques to keep the fracture in the pay zone have been received with great interest, since fracturing out of zone is both unproductive and unprofitable. Fractures, whether placed from a vertical or a horizontal well, are limited in growth by one or more physical controls, including leakoff of fluids from the fracture into the rock, natural rock barriers of sufficiently different Young’s modulus or Poisson’s ratio that they may resist fracturing, and earth stresses, either natural or induced by previous fractures that prevent or alter fracture growth. Multiple fracturing of horizontal wells has made production possible from very low-permeability formations by increasing contact area by six or more orders of magnitude (fig. 11–2). The number of fractures along a wellbore that can be economically supported is a question of comparing stimulation cost to current value of produced fluids. The number of fractures can be easily modeled but the results are frequently questioned if the formation is not sufficiently homogeneous to predict steady flow delivery to the wellbore. 620

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Fig. 11–2. Completion designs and formation character impacts on economic limits (modified from Vincent 2011) Oil and gas flow through a low-permeability formation preferentially follow pathways of large pores and natural fissures and are slowed by the restricted pore passages and very narrow natural fractures. In sandstones, there is a typical permeability variation of two to three orders of magnitude between high- and low-permeability areas of the formation, dictated by pore throat size, pore connection, fissures, and natural fractures. In shales, the primary flow paths are via microfissures and occasional natural fractures with a typical permeability of 0.1 to 0.001 mD, while the matrices of most of the productive shales are often less than 0.0001 mD horizontal permeability (Bustin, Bustin and Cui, Ross and Pathi 2008; Sakhaee-Pour and Brant 2011; Letham 2011). The effect of even the smallest microcracks and natural fractures on the total permeability for a very low-permeability formation is striking. As shown by Barree and colleagues (2014), increased presence and density of 0.001-inch-wide natural fractures can have a significant impact on system permeability, especially at very low matrix permeabilities (fig. 11–3). Matrix permeabilities of tight sandstones are generally higher than shales and natural fractures occur much less frequently than in shales, thus the tight sands have been most commonly completed with vertical wells stimulated with long bi-wing planar fractures, although horizontal wells are gaining popularity for tight gas developments, particularly where pad locations are required for wells (Schuler and Santos 1996; Abou-Sayed et al. 1995; Baumgartner et al. 1993). In wells deeper than about 1,000 feet true vertical depth (TVD), hydraulic fractures are commonly vertical or near-vertical and, in an undisturbed formation stress environment with a consistent horizontal stress pattern, form perpendicular to the plane of least principle horizontal stress (ohmin). In some instances, wellbore orientation relative to the minimum and maximum in situ horizontal stresses will influence how the fracture intersects the wellbore (Zoback 2014). Figure 11–4 shows three basic intersections of a wellbore and an ideal planar fracture. Vertical fractures are common for stress environments where the vertical stress is the dominant stress. Fracture initiation and fracture development may be influenced by near- and far-field stresses as well as both vertical and horizontal stresses. 621

Folds of Increase in System Permeability

100000

10000

Matrix Permeability 0.0001 md 0.001 md 0.01 md 0.1 md 1 md

0.0001 md

0.001 md

1000 0.01 md 100 0.1 md 10 1 md 1 e-09

e-08

e-07

e-06

e-05

Ratio of Fracture Area to Total Area

Fig. 11–3. Folds of permeability increase created by presence and density of natural fractures (modified from Barree et al. 2014)

σv b

a

σhmin σhmax c

Fig. 11–4. Ideal well and frac plane orientations for (a) vertical fracture in a vertical well, (b) longitudinal or axial fracture in a horizontal well, and (c) transverse fracture in a horizontal well

e-04

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At very shallow depths and in a few other instances where the horizontal stresses exceed the vertical stresses, a horizontal fracture may be developed (fig. 11–5). Horizontal fractures are very detrimental to fracture development and may screen out very quickly. Their occurrence in the oil and gas industry is most often noted in highly stressed areas near mountains and other uplifts, although local stress variations and natural fractures may also be influences.

σhmin > σv σhmax > σv

σv σhmax

σhmin

Fig. 11–5. Horizontal fractures may develop where either or both σhmin and σhmax stresses are greater than the vertical stress (σv) Although creating horizontal fractures from vertical wells was envisioned in the 1950s as a way of developing thin zones or placing a pancake of cement to inhibit water coning, the reality is that creating a horizontal fracture is a function of in situ stresses and is not feasible as a planned engineering practice in the majority of wells. In the 1960s, downhole TV cameras confirmed vertical fractures to be the most common fracture type and the theory of fracture mechanics and design has progressed based on vertical fractures (Prats 1961; Smith, Rosenberg, and Bowen 1982; Veatch 1973, 1983a, 1983b; Nolte and Smith 1981).σ When the wellbore is not perfectly perpendicular to the fracture plane, the fracture in the near-wellbore area may exhibit a growth pattern that reflects the changing stress environment as it grows away from the near-well effects influenced by stress relief from the free face of the borehole toward the far-field effects dominated by more undisturbed in situ formation stresses and characteristics. The growth in this near-wellbore area may be influenced by stored or released stresses from drilling, perforating charge penetration, formation layers of different composition, natural in situ stresses, or other factors (Wallace, Kabir, and Cipolla 2014). Any disturbance to fracture growth in the near-well may produce tortuosity, or resistance to fluid flow due to complexity of the flow path, applying a backpressure on the flowing fluid. This restrictive condition is proportional to the complexity and the rate of flow and may be especially pronounced at high production flow rates.

Fracture Orientation In open-hole completions with transverse fracturing, initiating true transverse fracs would ideally result in a sharp departure of the frac from the wellbore with minimum wellbore contact. Radioactive tracer profiles of this occurrence are known, but other tests show that some 623

Essentials of Hydraulic Fracturing

transverse fracs initiate as short longitudinal fracs before building up sufficient in situ stresses and re-emerging from the perf cluster as a transverse frac (Behrmann and Eibel 1991; Behrmann and Nolte 1999). Tracking fracture growth that is shaped by in situ forces has been mapped by microseismic and tiltmeters (Siebrits et al. 2000; Wolhart 2002). Fractures will increase reservoir communication potential with the wellbore, but the total effect of tortuosity on production rates is an important factor (Powell et al. 2007). The reason for the longitudinal fracture initiation is related to the effects of the hoop stress, which can be a dominating force and far exceed the maximum and minimum horizontal stresses. As fractures are placed, fracture direction may vary due to both in situ stress before the first fracture was placed, and the additional stresses produced by each preceding fracture. One result of multiple fractures along the wellbore is that the preferred fracture direction may be shifted a few degrees along the length of the lateral by increasing local stresses as more fractures are added to the wellbore. The volume of fracturing fluid and proppant that enters each fracture may create different levels of stress. The concept of the in situ stress forcing fracture growth upward or downward in the formation has also been advanced. Limited longitudinal fracture development along the wellbore is likely in open holes and perhaps some cased and cemented holes, even when the wellbore is perpendicular to maximum horizontal stress and transverse fractures are desired (fig. 11–6). This is most likely when the minimum and maximum horizontal stresses are very similar and the orientation of the wellbore is parallel to one of the fracture directions dictated by stresses and/or presence of natural fracture directions.

(a)

(b)

Fig. 11–6. Axial starter fracture (a) and final transverse fracture (b) as predicted by stressed block fracture tests and tracer profiling

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Stresses are removed from the face of the wellbore by drilling the hole. The removal of rock offers an unsupported free face and creates a difference between the near-wellbore (near-field stress) and undisturbed far-field stresses. The drilling alteration lowers a component of stress along the wellbore, reducing the formation’s resistance to fracture initiation and allowing a fracture to grow longitudinally along the low-stress wellbore for a distance. This type of development will likely produce a rapid change in injection pressure measured at the wellbore and might force a screen-out if insufficient fracture width is generated to allow entry and transport of proppant at the design loading of the fracture stimulation. The distance that a fracture may grow along the wellbore is likely affected by the local stresses and whether the natural fracture joint sets are parallel with the wellbore. Fracture initiation is expected in high tension points around the wellbore, with the most likely fracture initiation sites near 0° (straight up) and 180° (straight down) positions. The vertical stress becomes more locally dominant after the wellbore is drilled, creating a hoop stress around the wellbore (fig. 11–7). The resulting compression zone at the sides (90° and 270°) of an openhole horizontal wellbore are sites of compressive failure and the tension areas at the top and bottom focus the fracture initiation to the 0° and 180° positions. Local composition variances, perforating, and other factors may also influence the initiation point.

σv

σv

area of tension

σt σh σt

σh σt

σh

σh

area of compression

Fig. 11–7. Local forces around a horizontal wellbore. Areas of tension are the most likely point of fracture initiation, but fracture reorientation may occur as the developing fracture extension leaves the wellbore and is affected by far-field forces. The effects of stresses around the horizontal hole will diminish with increasing distance from the free face of the wellbore. This return to the natural in situ stress condition will affect the position of the realignment of the fracture and may be the location of tortuosity in flow through the fracture (Kogsboll, Pitts, and Owens 1993; Samuel and Liu 2009). This behavior may create a fracture re-orientation from the primary frac direction to a secondary fracture direction as was documented in the Barnett shale (Siebrits et al. 1998; Wolhart 2002). Other impacts, including stress changes from production, are also important for long-term fracture conductivity stability as well as consideration of the well as a refracturing candidate (Weng and Siebrits 2007). The flow pattern in a vertical fracture placed from a horizontal well is also altered by settling of proppant carried by the fracturing fluid into the bottom of the fracture and potential for loss of flow area and conductivity if the upper fracture area closes due to lack of proppant (fig. 11–8).

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Essentials of Hydraulic Fracturing

Marginal Sand, Low Conductivity Conventional Slick Water Frac

Settled sand, conductivity dependent on sand size, cleanup and stresses

Fig. 11–8. Vertical transverse fracture from a horizontal well. Proppant settles quickly where there is little support from the frac fluid and low-permeability results in slow fracture closure. The injected fluid velocity in the fracture varies widely as the fracture grows, with fluid velocity dropping rapidly just a short distance from the casing exit point. With this loss of velocity, the proppant support of a water frac or other low viscosity fluid will likely be insufficient to carry proppant into the upper part of the fracture or into the far reaches of a long fracture. Therefore, most proppant in slickwater fracturing will likely drop out quickly in the fracture, forming dunes and creating a proppant bank in the lower half of the fracture. Fracture-to-wellbore connection and the resultant production flow patterns vary sharply between vertical wells and horizontal wells (fig. 11–9). The restrictions imposed by the flow patterns described in these two figures illustrate the challenges in fracture flow dynamics that exist in a horizontal well. The severity of the pressure drop in the inward or convergent radial flow experienced in transverse fractures (fig. 11–9b) has been estimated to be in the range of 15 psi/ft in areas away from the wellbore and as much as 100 psi/ft in the fracture within a few feet of the wellbore (Shor and Sharma 2014). In formations with slow fracture closure times, production flow may carry proppant out of the critical near-well area and conductivity in this area can be severely decreased. Depending on the formation and the local stresses, operators have reported shut-ins of two to four days as being necessary to minimize proppant backflow and preserve the near wellbore flow capacity. The formation area and flow paths near-wellbore, although important in any fracture development, are critical in a transverse fracture from a highly inclined or horizontal well. Large proppant is a major benefit in this near-wellbore area, especially where higher viscosity fluids (usually oils) are the primary production. High-rate gas flow may be similarly affected. Each formation may have different properties and responses to fracturing. Since many formation properties are interconnected, hard rules about minimums and maximums for specific values of all but the most independent characteristics are difficult to make. For optimum completions, the flow dynamics within the reservoir must be understood, even before well orientation or fracture initiation points are selected. 626

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b

Fig. 11–9. Flow patterns through a vertical fracture in a simplistic view of (a) fracture from a vertical well showing a mixture of flow patterns vs. (b) flow from a vertical fracture into a horizontal well showing inward convergent radial flow with increasing interference

Complex and Planar Fractures Deciding factors of whether fracturing will be planar or complex depends on the presence of natural fractures within the reservoir, differences in the horizontal stresses ohmax and ohmin, the type of fracturing fluid, and how injection rate is ramped up to design rate. As previously described, initial reservoir stresses—vertical (ov), maximum horizontal (ohmax), and minimum horizontal (ohmin)—define whether the fractures are vertical or horizontal. Horizontal stresses dictate the orientation of the fracture, while differences between ohmax and ohmin, and the presence or absence of natural fractures determine the possibility of creating a planar fracture or a complex fracture. Variations in stresses along a single wellbore may be caused by deposition content variation and post-depositional forces such as uplift, faulting, karsts, and basement features. These stresses may be generally similar across a section of a play, but areas with local variations are known. Variations of the stresses along the same wellbore can cause the occurrence of both predominantly planar and predominantly complex fracturing (Rich and Ammerman 2010). Planar fractures and complex fractures (also called network fractures or discrete fracture networks) are radically different outcomes from similar but not identical methods. Planar fractures are visualized as bi-wing, with approximately equal-length planes thought to extend from each side of the wellbore, with fracture direction perpendicular to the plane of minimum horizontal stress (ohmin). Complex fracturing may involve an initial planar fracture that is altered by the leakoff of frac fluid into the natural fracture system and subsequent enlargement of the natural fracture system, often at 90° to the initial fracture direction (fig. 11–10). Regular patterns of primary and secondary fractures, when present, increase the possibility that complex fracturing will produce significant formation contact area. If natural fractures are present, then in situ stresses control whether natural fractures will open and which set of fractures will open if multiple natural fracture sets are present (fig. 11–11). 627

Fig. 11–10. Planar fracture (left) and complex fractures (right). Planar fractures are most common in low- to moderate-permeability formations and complex fractures are common in very low-permeability natural fractures where horizontal stresses are similar.

Secondary Fracturing

Primary Fracturing

σhmin

σhmax

Fig. 11–11. Vertical fracture departure from horizontal well. A planar frac may initiate from a horizontal well, but if natural fractures are present and horizontal stresses are similar, the fracture may grow by opening the primary and the secondary natural fractures.

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Opening the natural fractures as a way of altering the fracture path or increasing flow area was recognized early and efforts to enhance the effect by initial design or fracture pumping changes were widely discussed and practiced in sandstones during the 1970s (Kiel 1970, 1977) and shales in the late 1980s (Overbey, Yost, and Wilkins 1988; King et al. 2008). As more shales with a high rate of natural fractures were fracture-stimulated, it was recognized that the fractures, whether closed or even filled with calcite, could be re-opened at a fraction of the pressure required to fracture the non-naturally fractured rock (Gale, Reed, and Holder 2007; Gale and Holder 2008;). The bonding strength of the calcite fill in natural fractures is very low because the calcite grows over non-carbonate grains without chemical bond, so there is little structural resistance to keep the fracture from re-opening. Closed and mineralized fracture breakdown pressures have been measured by some researchers at about 60% of the initial breakdown of non-naturally fractured rock (Gale and Holder 2008). Natural fractures are present in nearly all gas-productive shales but are only productive in a small way until opened and connected with a hydraulic fracture treatment. Whether the fractures are simply closed or mineralized and plugged, they offer a plane of weakness in the rock. Lab work places the width of these fractures in the range of about 0.002 inches (Sondergeld et al. 2010). Natural fracture density may vary from a few cracks over a large area to densities of millimeters separation of microcracks and natural fractures. Primary, secondary, and tertiary natural fracture sets have been photographed in outcrops (Engelder and Lash 2008; Lash 2008). Shear fracture event patterns (characteristic of opening multiple orthogonal natural fractures) are seen on microseismic records of hydraulic fracture treatments in many gas shales (Cipolla 2009; Cipolla, Warpinksi, and Mayerhofer 2008; Cipolla, Maxwell, and Mack 2012). The carbonate fill of most natural systems does not bond to the high silica content of shales and may be both a flow path (even in the closed and cemented state) and a weak point that opens quickly to fracturing pressures (fig. 11–12).

Fig. 11–12. Non-bonded carbonate fill layer from a fracture in a silica-based shale (Gale and Laubach 2009)

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The ability to re-open natural fractures was confirmed repeatedly in the Barnett shale, where microseismic imaging and mapping of hydraulic fractures show the fractures intersecting and traveling along primary, secondary, and sometimes tertiary natural fracture networks (Maxwell et al. 2002). When extensive natural fracturing in brittle shale (high Young’s modulus and low Poisson’s ratio) produces both horizontal and vertical fractured sections (“gas chimneys”), the potential for unstimulated gas flow increases (fig. 11–13). If open natural fractures are encountered from a horizontal well, changes in drilling and completions are often necessary to prevent severe damage to the flow capacity of the naturally fractured flow system from drilling or cementing.

Fig. 11–13. Outcrop with upward joints or fractures (Engelder and Lash 2008) Preferential opening of the natural fracture systems during hydraulic fracturing have been described by several authors (Overbey, Yost, and Wilkins 1988; Gale, Reed, and Holder 2007). Overbey (1988) observed that increasing the rate in small steps would often preferentially open the natural fracture system, while quicker application of surface injection rate would form more planar hydraulic fractures through the shale. Application of this technique has seen successful application in the Barnett and other shales (King et al. 2008). This fracture-opening behavior by incremental increases in the surface injection rate can also be enhanced by using a low viscosity fluid such as slick water (fresh or salt water with 0.025 to ~1.0 gallons per thousand gallons of a polyacrylamide slurry for friction reduction). The ability to develop fracture complexity depends on presence of natural fracture systems and similar levels of minimum and maximum horizontal in situ stress. The development and growth of a hydraulic fracture through the natural fracture systems of shale is more complex than can be described here, but may be somewhat predictable if the fracture system and the development of stresses (and how fracturing affects in situ stresses) can be explained. Fracture mapping with microseismic monitoring and tiltmeters indicate that many areas of a naturally fractured shale may be stimulated at once. The result is that the pressuredependent leakoff produces enlargement of the natural fractures, often without significant loss of fluid into the pores of the shale. This inflation of the natural fracture system sharply increases in situ stresses in most shales. 630

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Activation of natural fractures (enlarging the natural fracture volume) in relatively large volumes of rock at some distance away from what would normally be considered a planar fracture, and transfer of fracturing fluid laterally through the shale to other shale wells (sometimes a thousand feet or more apart) indicate multiple permeable pathways are established during fracture stimulation in formations with complex fracturing potential. Complex fracturing may occur in naturally fractured formations with one or more natural fracture system orientations. When formations contain in situ stress, there is usually a small difference between the minimum and maximum horizontal stresses. If a fracture is created or a natural fracture is opened, the stresses will try to unload or shift the rock very slightly—this is “shear fracturing.” The movement of the rock faces, relative to each other, is a tiny distance that may on the order of a fraction of the thickness of a human hair, releasing energy in the form of a small sound—this is a microseism. As fracturing pressures are applied in naturally fractured shales, a progression of microseismic events may be detectable that relate to injection of water or proppant. The energy of these events, usually in the range of about –2.5 moment magnitude (mm), is about 1 billionth of the energy in a 6.0 mm quake. These microseismic events, when positioned accurately, then ranked by magnitude and sequenced in time, may describe the direction and vertical growth of shear fracturing occurrence. Figure 11–14 shows a sequence of these events during a fracture stimulation in the Barnett shale (King et al. 2008).

Fig. 11–14. Microseismic events in a single stage fracture in the Barnett shale. The first events indicate a planar development, followed by widening of the microseismic cloud with events defining complex fracturing. Although some authors believe that the widely spaced microseismic information could be all from a planar frac, other information, including horizontal leakoff of fracture fluid to adjacent wells and the gradual closure of those leak paths, indicates fluid entry into the unpropped natural fractures. This finding is also supported by the salinity differences and ion ratios that are seen in chemical analysis of flowback. An example of this lateral leakoff and an overlay of microseismic events are shown in figure 11–15 (Fisher et al. 2002; Fisher et al. 2004). These leakoff channels often are only open during the fracture treatment and frequently close as fracturing pressure is released and in situ stress is changed by fluid production that removes gas or liquids that have been a load-supporting (and fracture-filling) element in the formation.

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Fig. 11–15. Vertical well example of five adjacent wells hit or loaded with fluid by the fracture of one well (modified from Fisher et al. 2004) The pattern of microseismic events also indicates some amount of shear fracturing adjustment of the rock volume near the injection sites, and a cloud of microseismic events often localizes along the preferred fracture direction. As fracture growth progresses, it is not uncommon for a secondary frac to begin. Reflection on this complex fracturing behavior suggests a number of technology gaps for reservoir description, proppant transport, fluid selection, and methods of monitoring fracture growth. Although initial or induced stress differential has been identified by many authors as a control in both planar and complex fracture direction, the stresses created during hydraulic fracturing may produce variances in local stress fields that eclipse all but the highest-order pre-frac in situ stresses (Sneddon 1946; Pearson et al. 1991; Ramakrishnan et al. 2009; Roundtree, Eberhard, and Barree 2009; Warpinski and Branagan 1989). An example of well-to-well communication behavior following fracturing and the decrease in that communication over time (fig. 11–16) is provided by Litchfield and Lehman (2013). The communication that was very apparent immediately after the fracture treatments shows very sharp reduction with time. Fracture closure occurs in almost every fracture job, usually within minutes to hours in higher permeability conventional reservoirs where fracturing fluid leakoff into the formation matrix quickly reduces the hydraulic pressure that holds the fractures open. Fracture closure in unconventional reservoirs is often much slower since leakoff is limited and fluids must generally be produced to reduce the hydraulic pressure and allow the fractures to close.

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Start-up Connections

Mid-Time Connections

Muskaw C Otter Park A

Evie

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Persistent Connections

Muskaw C Otter Park A

Evie

Muskaw C Otter Park A

Evie

Fig. 11–16. Well-to-well connections after fracturing followed by connection changes during production time. Well-to-well connections were maintained in the Muskaw and Otter Park formations where planar fractures are prevalent but were mostly closed in the Evie where complex fracturing was common (Litchfield and Lehman 2013)

Well Spacing and Orientation Spacing of horizontal wells in shale gas developments can be influenced and even dominated by how fractures are initiated and propagated (Ketter et al. 2008; Dunek, Walser, and Astakhov 2009). The best completions for maximizing recovery take characteristics of the shale being developed into account. The impact of preferential frac direction and the resulting optimum wellbore direction often define the well configuration and, when combined with stress information and natural fracture extent, may set well spacing and influence fracture initiation points (Dahaghi and Mohaghegh 2009; Samuel and Liu 2009). Natural fracture behavior during the fracturing treatment is a deciding factor on wellbore direction. In reservoirs with orthogonal fracture sets where the difference is small between minimum and maximum horizontal stresses, the stresses created during fracturing can change the fracture growth direction from primary to secondary natural fracture sets during the job. A wellbore that is laid out 90° to the primary fracture direction in a shale with a secondary fracture set at 90° to the primary fracture may create a longitudinal fracture along the wellbore and ruin fracture isolation and initiation opportunities in multi-fracture completions (King et al. 2008). Sufficient rock mechanics knowledge is required to effectively break down perforation clusters and develop dominant fracs and maximum frac complexity (King et al. 2008; Le Calvez et al. 2007; Cipolla, Warpinski, and Mayerhofer 2008). Knowledge of maximum practical fracture-tofracture interference, both from the same wellbore and from adjacent wellbores will help set well spacing and fracture initiation points. Findings from Barnett shale wells show that in the best part of the field where frac barriers are present, orientation of the wellbore may be important but not be critical to economic success. In other areas, particularly around geological hazards and the fringes of the field, wellbore orientation and even consideration of the secondary frac direction to the well orientation can make a significant difference in production. Primary natural fracture orientation and hydraulic fracture growth directions across a field may be similar, although local stress variances may create exceptions. Well spacing in fractured horizontal well development is different than spacing in a vertical well and is impacted by the expected fracture length and boundaries set by either regulations or nature. When fractures are expected to be planar, the frac length is often the determinant for spacing, but planar fracture spacing along the wellbore can be adjusted to prevent communication even when planar fractures overlap adjacent wellbores (fig. 11–17).

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Essentials of Hydraulic Fracturing

Perf Cluster

Well 1

Well 2

Fig. 11–17. Offsetting perforated fracture clusters (or frac sleeve positions) along two parallel wellbores to reduce chances of fracture communication with an offset wellbore This type of spacing can be used on either initial completions or on refracs when more is known about the formation and the expected fracture type. When natural fractures are present, the complex frac length may be shorter than that of a planar fracture, generally encouraging closer well spacing in naturally fractured areas to maximize recovery.

Placement of Fractures Selecting the optimum fracture initiation point depends on whether the fracturing target is a conventional reservoir, a naturally fractured reservoir, or a low-permeability non-naturally fractured reservoir. For multi-fractured horizontal wells, some common decision points include: initial in situ stresses, variation of in situ stresses, stress shadowing, how the fluids move in the reservoir, and the overall ability to economically recover fluids from the reservoir. A mud log with a gas show analyzer can be used during drilling to locate zones capable of flowing at higher rates than would be possible for matrix flow, especially from low-permeability formations. This type of measurement in tight formations is possible for oil and very practical for gas, especially where natural fractures contribute substantially to the total possible flow from the formation. Some gas will be released from the shale as it is drilled; this is background gas. However, spikes of gas above the volume of gas stored in a drilled volume may indicate greater porosity and higher organic content gas flow from natural fractures or higher density of natural fractures. Shows of gas and oil while drilling, combined with mud log and conventional electric logging, may offer clues as to formation fabric and incidence of natural fractures in conventionally drilled wells. The basic information provided on an oil or gas show recording may confirm whether the drilled rock contains hydrocarbon, represented by the measured gas and oil and the cuttings circulated to the surface. Sections of many source and reservoir rocks, although part of large hydrocarbon generation or storage accumulations, may not contain hydrocarbons. A plot of hydrocarbon volume measured at surface and plotted against depth can identify where peak shows exist and whether these flows likely originated from hydrocarbons trapped in the matrix or the fractures. Recovered hydrocarbon volumes are important, but the ratio of components must also be considered. Establishing a background level for the rock as it is drilled sets a baseline as 634

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described by Cherif and colleagues (2009). Volumes above this line must originate from rock with a higher porosity, higher organic content, or from natural fractures where large amounts of gas or oil can be held even in the small amount (1%–2%) that commonly describes the porous volumes of natural fractures (fig. 11–18).

Productivity Index of Correlation

Flow from Fractures

Matrix Production

Increasing Depth

Little or no Production

Matrix Production

Productivity observed from drilling shows Estimate of matrix permeability contribution

Fig. 11–18. Trend of productivity calculated from hydrocarbon shows against increasing depth. The near-steady increasing trend of matrix production is likely due to pressure increases as true vertical depth is increased simply because of more gas in free storage at higher pressures correlating to increasing depth. The technique in figure 11–18 could also be used in horizontals by using a matrix contribution line with a zero slope. The gas and oil shows at the surface often do not correlate well with the rock that surfaces at the same time as hydrocarbons. Surface arrival time of the heavier cuttings must be corrected for the lag created by the faster rise of lower density gas and oils. In low-permeability rocks where 95% of the pore throat size may be in the size range of a methane molecule, the ability to move significant quantities of gas through the matrix is sharply diminished. It is possible to gain more knowledge about both the flowing fluids and the formation fabric by analyzing the composition of the gas and oil captured in the cuttings. A technique of using the ratio of C1 (methane) to the sum of C1 through C4+ (methane + ethane + propane + butane) is useful in indicating changes in the fabric of the formation, the presence of compartments, and changes in the preferential flow paths through the rock. Although the composition of gas in a source rock can vary widely, the changes are usually incremental along the relatively short area of a wellbore unless some modification in the rock allows segregation of individual components of the hydrocarbon liquids. One such flow-impacting modification is the presence of natural fractures in a lowpermeability rock. Dry methane with a molecule width and length of 0.4 × 0.4 nanometers 635

Essentials of Hydraulic Fracturing

flows much easier through very low-permeability rock than wetter gases like butane which has a molecule width and length of 0.42 × 0.82 nm. In black oil reservoirs, the molecule size is in the 1–2+ nanometer range, easily exceeding the size of the pore throats in much of the matrix (Bruner and Smosna 2011). Compared to methane gas, wetter gases and oils have larger molecules, higher interfacial and surface tensions, and higher viscosity, all of which can contribute to sharply increased capillary threshold pressures, especially in low-permeability formations, as can be seen in figure 11–19.

Pcap Threshold Pressure (psi)

10,000

? 1,000

100

10

1 0.0001

0.001 0.01 0.1 Permeability (md)

1

Fig. 11–19. Capillary blocking pressure vs. permeability (modified from Penny, Pursley, and Holcomb 2005) When above-the-baseline shows of wet gases (e.g., ethane, propane, butane and pentane— C2–C5) and oils are recovered with drill cuttings, the cause may be a hot shale, where more organic carbon has undergone thermogenic conversion to oils. Longer chain molecules (i.e., the wet gases and oils) are less likely than gases to flow far from their creation site (thermogenically altered organic carbon) unless there is a higher permeability flow path. If wet gas and oils are recovered with the cuttings, a hot shale or a high permeability flow path such as a natural fracture are indicated in the fabric of the rock that is associated with the cuttings. The key to deciphering the gas log is to examine the gamma-ray log readings, porosity logs, and the ratio of gases that are recovered. The gamma-ray log picks up higher isotope activity when organic content increases. The gas ratios, however, may be a much better clue. Figure 11–20 illustrates how the hydrocarbon chain ratios change during drilling in a section of a lateral.

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In this case, methane dominates the gas flow in the first and second gas show with a relatively constant ratio of methane to ethane, propane, and butane, but the gas composition changes in the third gas show, indicating a change in either organic carbon content (on which heavier gases can

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Fracturing Horizontal Wellbores

1000000 PPM C4

40000

1000000 PPM C3

Gas Shows While Drilling

PPM

1000000 PPM C2

Gas

Units C1

Mudlog

10000

adsorb), or a higher permeability streak. Differentiating the two possibilities requires a gammaray log, which will show that the increase in heavier gas fractions is probably due to proximity to a hotter shale.

Measured Depth (MD)

Gamma Ray

Fig. 11–20. Comparing gas composition gathered from shows while drilling for locating hot shales and areas of higher total formation permeability Gas show composition analysis has been advanced by several authors as a way to correlate the top and bottom of the formation, and identify leaking cap-rock seals, coning, and higher permeability pathways such as natural fractures (Pixler 1969; dePazzis et al. 1989; Garcia-Hernandez et al. 2007; Kandel et al. 2001). Knowledge of the location of potentially more liquid-rich fractions can be very helpful in planning fracture stimulation points. If the target is gas, the wetter (less thermogenically mature) areas and the areas that can flow liquids can be avoided and relative permeability problems minimized. If the target is oil, then the completion design changes to allow more liquid flow with minimum relative permeability problems. This approach allows for more targeted fracturing by minimizing the frac treatments pumped into potentially unproductive sections of a horizontal wellbore. Reservoir engineers often disagree with this approach because there are sometimes natural fractures nearby that do not intersect the wellbore, but that might be contacted through hydraulic fracturing. While this argument is reasonably valid, the absence of gas in a section of a shale should, at minimum, be taken as a warning about either extremely low permeability or low 637

Essentials of Hydraulic Fracturing

organic content. Concentrating the fracturing investment in areas that show the greatest potential for flow may prove to be the most economic action. Other considerations for fracture initiation points include brittleness and ductility calculations based on logging. Sonic logging may also be useful for identifying modulus variation. Other logging methods for identifying and locating natural fractures in shale gas wells have been described (Kubik and Lowry 1993); and information on how to preferentially propagate at least starter fracs through the natural fracture systems are encompassed in the work of Gale and Holder (2008). Carbon isotopes of methane gas in shale and linkage to flow routes may also be useful. Increasing water saturation (Sw) in the shales is viewed as a detriment but a moderate amount of Sw is commonly present in all known gas shales. Water molecules are slightly smaller that methane molecules, and can possibly create blockages in smaller pores. In formations with high Sw, effective matrix perms might be nonexistent and fracturing may not be productive. Minerals (specifically silica, calcium, dolomite, and clays) are keys to brittleness and increased calcite presence, as streaks in cuttings may be an indicator of fracture fill (Britt and Shoeffler 2009. In general, prospective shales have limited clay constituents that are usually less than 40%, static Young’s modulus in excess of 3.5 × 106 psi, dynamic-to-static Young’s preferred modulus ranges for prospective formations that are consistent with clastic reservoirs (not ductile or high clay content shales), and have sufficient brittleness to flow gas at effective confining conditions through an un-propped crack at reservoir stresses.

Stress Factors Affecting Fracturing from Horizontal Wells The influence of stress shadowing is an inhibitive influence from the stresses created by a developed fracture on the initiation or growth of a nearby fracture (Sneddon 1946). As a fracture is developed, the widening of a vertical fracture exerts lateral or side forces into the formation, creating an area around the fracture that has higher stress than other areas along the wellbore at a distance from the developed fracture. The magnitude of this stress diminishes with distance from the fracture so that the inhibition of fracture initiation and growth is a factor of separation distance. Figure 11–21 is an estimation of this stress as a function of distance (Waters et al. 2009). As seen in the figure, formations with a lower elastic modulus (ductile rocks), such as soft chalks and high clay content shales, offer minimum stress interference with closely spaced fractures, while higher modulus formations such as harder sandstones (5,000,000+ psi) have significant interference from stresses produced by existing fractures and their effect on other fractures nearby. Although there is some level of stress interference out to twice the thickness of the materials, the realistic effect on fracture initiation in rocks diminishes by at least 90% at 5- to 15-foot fracture spacing for ductile rocks, and at 20- to 30-foot fracture spacing for more brittle rocks. This value will vary with the created width of the fracture (and height) and the ability of the formation to transmit stresses. Ductile formations and brittle formations react in different ways and formations with natural fractures may also react in their own manner to the transmission of stresses and the effects of stress on fracture initiation and growth. 638

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Stress Change (psi)

100,000

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Fracturing Horizontal Wellbores

Modulus = 1,000,000 Modulus = 3,000,000 Modulus = 5,000,000

10,000 1,000 100 10

0

10

20

30 40 50 60 70 Hydraulic Fracture Spacing (ft)

80

90

100

Fig. 11–21. Fracture-created stress interference with fracture initiation and growth of an added fracture (modified from Waters et al. 2009) Naturally fractured formations may be very individualized, both in the initial opening of the often closed fractures, and in the ability of the natural fracture to remain open following release of the fracturing pressure. Breakdown and initiation tests in the first few wells in an area will be a factor in establishing the initial fracture spacing design. Production from the reservoir will remove some of the load-bearing fluids, which will change resistance to overburden and confining stresses, closing natural fractures and possibly even changing porosity and matrix permeability. When stimulation designs are considered, the most important questions are: how much of the formation can contribute fluids in the expected life of the well; what is the optimum number of fractures needed to access these areas of the formation (establishing the target drainage area); and what is the cost of this stimulation versus the return on investment. This last item requires both effective modeling and economic projections at possible pricing scenarios. Fluid flow in a conventional reservoir with permeability sufficient to flow formation fluids in an economic time frame can be treated with conventional reservoir engineering principles with reserve content established by total porosity, saturation, and a quasi-standard recovery factor, hopefully analogous to the formation in question. In shales and very tight formations; however; flow occurs in a very different manner with the predominant flow path being the natural fractures, fissures, and microcracks. In this type of formation, the effective flow paths must be found by investigation and connected to the wellbore through either direct access or induced coupling by hydraulic fracturing. Determining the location of these flow paths and their impact on both regional and local flow is critical to development of the resource. First, the impact of regional fractures must be assessed since the regional fractures are essential to effective and economic development. As a quick comparison, if the initial production (second month or maximum 30-day production preferred) for all the wells has a flat trend (fig. 11–22a), the effect of significant regional fractures is expected to be minimal. A trend of reduced production with newer wells is usually an indication of a regional fracture that can make early wells much higher producers than later wells, because the early wells are able to capture significantly more production, provided by mobile fluids existing in the high permeability natural fractures (fig. 11–22b). The differences in these fields require separate approaches in both economic development and stimulation design. 639

Max Month Rate/Ft. BOPM

Essentials of Hydraulic Fracturing

16

Maximum Monthly Oil Per Ft: Sanish Field 2,000–7,000 feet 7,000–14,500 feet

14 12 10 8 6 4 2 0 1/2007

1/2008

Max Month Rate/Ft. BOPM

(a)

(b)

16

1/2009 1/2010 Date

1/2011

1/2012

Maximum Monthly Oil Per Ft: Parshall Field 2,000–7,000 feet 7,000–14,500 feet

14 12 10 8 6 4 2 0 1/2007

1/2008

1/2009 1/2010 Date

1/2011

1/2012

Fig. 22 a & b. Maximum month production normalized per foot of lateral length. (a) Roughly equivalent first month production indicating contained, generally equivalent drainage conditions. (b) Declining first month production for newer wells, perhaps indicating regionally or otherwise connected higher permeability drainage paths (modified from LaFollette, Holcomb, and Aragon 2012) In low-permeability formations with matrix permeabilities of less than about ten millidarcys for oil and less than 0.1 millidarcys for gas, presence of natural fractures dominates the system permeability. The presence of natural fractures and knowledge of how they are connected is of primary importance in designing well spacing, fracture spacing, initial stimulation design, refracturing opportunities, and production controls such as backpressures held on the flow to optimize recovery. Even closed and sealed natural fractures have a higher permeability than the matrix of most low-permeability formations. When these fractures reach across a broad area, either as a widely branched natural fracture cluster or as a communicating fault, the effect overwhelmingly shapes the flow of the free gas and oil stored in the fractures and increases the ability for early wells in the development to produce at much higher initial rates and reach higher cumulative production than will be possible for later wells in the development. Opportunities in this type of interconnected, but low matrix permeability reservoirs may require gas injection to maintain pressure. 640

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Mapping natural fracture systems can be approached by various means including seismic methods (Parney, Jenner, and Williams 2004), tiltmeter, microseismic recording (Estrada et al. 2009), and production data comparisons (Gaskari and Mohaghegh 2006; Evans, Holzhausen, and Wood 1982). Based on this type of analysis, well and fracture spacing and well orientation in an area for connected natural fractures will vary widely from a well design for a well with only local natural fracture influence.

Completion Design Completion design for a horizontal well can take many forms, from openhole to fully cemented, casing the entire length of the lateral. The primary requirements are access to the formation along the lateral for the number of fractures designed for the well and enough isolation between fractures to allow each fracture to be initiated and developed to the design intent. The primary types of isolation are cemented with plug and perforated clusters, ball-actuated packer sleeves and coiled tubing or ball-actuated cemented sleeves. The operator will generally pick a completion type that offers the best economic and productivity potential for the development. Completion selection involves the number of stages desired, drilled-hole quality, ability to reduce fracturing down-time, fracturing rate limits, time from start of frac to production sales, isolation ability, cost and other factors. Completion isolation along the wellbore depends on drilled-hole condition and cement or packer seal integrity. Perforations or ports opened in sleeves can transmit sufficient pressure to allow a fracture to be initiated. Containment of the fracture after the fluid leaves the formation depends on the formation and the stresses and barriers in the immediate area of the fracture. The number of locations where a fracture could be formed defines the number of stages, which may number from one to ten perforation clusters or ports per fracture stage. The number of these clusters is further defined or limited by the available perforating rate and the specific rock type. The most common completion system varies between operators, even within a single field. From an engineering point of view, the initial rate and the total amount of fluids recovered are dictated less by completion type and probably more by operations over many years after the fracture stimulation. A common mistake is to use a smaller stimulation based on a short production time evaluation. This effect has been noted in early tight gas fracture stimulations in the southeast Oklahoma Red Oak and western Oklahoma Morrow formations where small hydraulic fracture volume stimulations behaved similarly to larger volume stimulations for 6 months before a 10%+ decline per year was noted for the smaller volume jobs compared to a steady 6% decline for the larger jobs. Whether this behavior applies to shales is a matter of discussion, although most operators are leaning toward larger jobs.

Microseismic and Other Monitoring Methods Field measurements that enable understanding of hydraulic frac behavior and water recovery include microseismic monitoring while fracturing, radioactive tracers to mark frac entry points, chemical tracers that allow tracing of fluid return efficiency for different stages, quantitative records of water volumes, salinity, solids, gas rates and pressures, and finally, tools that can qualitatively differentiate the type of fluid entering the well on backflow, the relative rates of return, and the entry points.

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Chemical and radioactive isotope tracers are useful in both gas shale stimulation and tracing fluid flowback (Munoz et al. 2009; Woodroof et al. 2003; Sullivan et al. 2004). Chemical tracers are used throughout the treatment and return as the load water is recovered. By combining the timing of the volumes of marked load recovery, a picture begins to emerge of stage-by-stage load fluid backflow and water input from other formation-fed sources of water. Tracing the timing, volume, and contamination of the frac fluid return in a stage-by-stage manner can assist in differentiating the performance of the frac and the ability of a section of the formation to return fluids. In addition, monitoring the dilution of the tracer in a mass balance model can improve understanding of fracture fluid breakout, confirm the effect of frac barriers, and directly measure the flowback efficiency of each frac stage. Variability in the rate of fluid return may be caused by gel damage, relative perm effects, the complexity of the fracture system, frac behaviors that strand fluids (fracture closure), and other factors (Crafton and Gunderson 2007). Gamma-ray tracers (tagged proppants) are used to mark frac points and diagnose shallow fracture and cement isolation problems, and can be useful in determining a vertical well’s frac height (Silber et al. 2003).

Perforating Horizontal Wells for Fracturing Perforating is necessary to set up each stage of a cased and cemented well used in a plugand-perf completion. Since the objective is to place fracture initiation points to gain maximum access to the formation, the principles of hydraulic diversion and fracture stress effects must be considered. The actual layout of a perforated cluster arrangement may use a simple division of frac length, brittleness variations, formation stress effect, or gas shows for selecting frac placement. The clusters are usually short, generally about 2 feet in length, and contain about 6­–10 perforations. The number of perforations used will depend on the fracture rate and is explained in the next sections. Figure 11–23 illustrates the principles of a perforation cluster arrangement for a four cluster-per-frac stage design with ranges of separation distances.

Fig. 11–23. Perforation cluster layout in a horizontal well using four clusters and assuming 120–200 ft fracture stage with 30–50 ft cluster spacing and 2 ft cluster length. The expected injection rate would be between 80 and 100 bpm. 642

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Fracturing Although many fracture treatments are run by pump- and blender-controlled computers using output from a fracture modeling program, this section will focus on pumping a fracture stimulation with only the pressure, flow rate, and proppant loading information as measured by the well’s response to the injection of fracture fluid and proppant. A very large disadvantage of the multi-fracturing application in horizontal wells is that the pressure used for this realtime analysis is surface injection pressure and not the more accurate bottomhole pressure. The difficulty with collecting bottomhole pressure data (either real-time or recorded) to compare to fracture performance is that the only current bottomhole pressure measurement capability is with capillaries or fiber optics cemented on the outside of the casing reading out at the surface, or with recording instruments hung below the fracture zone. Design of the multi-fractured horizontal makes recording of fracturing pressure impractical at best unless coiled tubing is present. The most practical approach is using an incompressible fluid with relatively consistent friction reducer to provide reasonable accuracy. This practice is never exact. If the physics of fracturing are understood and the formation is reasonably described, most, if not all, of the responses from rate, pressure, and proppant loading can be translated into signals that at least indicate fracture behavior. Fracturing is a dynamic reaction between injected fluid properties and the related reaction of the rock. Accepting any variable as a constant during fracturing introduces uncertainty. For that reason, fracturing models may be acceptable for planar fractures but may not be accurate enough for complex fracturing without measuring and using ranges of real values for formation characteristics in the model. Recognizing the signals from the standard output is a necessity for effective fracture design, over and above what most fracture models can predict. There is a significant difference between pumping the job away and establishing a long-lived conductive pathway between the productive parts of the reservoir and the wellbore. The first is the desire of a manufacturing approach while the second is a recognition of the impact of formation variability on the stimulation design. Fracturing can be separated into four sections: fracture initiation or breakdown and early fracture growth, fracture extension (routine pumping), late stage fracture behavior, and post-fracture behaviors. At each of these steps, there are caution flags that, if properly acted upon, can prevent a problem either in pumping the fracture job or producing through the fracture later.

Fracture Initiation and Early Fracture Growth Fracture initiation involves overcoming the formation tensile strength at an exposed area and forcing the formation past the point of tensile failure, so that a crack develops and grows proportionate to the rate of fluid injection and inversely proportionate to the leakoff losses. Formation stresses are a major control on fracture initiation and growth. Further complications are added by completion actions, particularly as the expected radial growth of a planar fracture continually opens more area in the outward radial pattern away from the small area of fracture contact with the horizontal wellbore. Fracturing may occur when the injection rate of any fluid exceeds the ability of the matrix permeability to accept all the fluid injected. When this point is passed, 643

Essentials of Hydraulic Fracturing

hydraulic pressure increases rapidly until the tensile forces in the rock are exceeded and the rock breaks. Transition from high fracture breakdown pressures to diminishing pressure during early growth may occur more rapidly in a horizontal well as compared to a vertical well, due to the point source application of pressure and transverse fracture growth; however; the fracture size-limiting effect of leakoff in the outward radial pattern increases exponentially as the fracture grows, and surface injection pressure may decrease rapidly for a short time. The early phase of the fracturing includes the initial breakdown and early growth of the fracture. There are several contingencies to consider when developing an effective fracture. The initial frac, shown schematically in figure 11–24, tracks the pressure response with increases in surface injection rate.

Breakdowns

6000

Rate Pressure Proppant

70 60

Proppant Loading (lb/gal)

Pressure (psi)

7000

80

Rate (BPM)

100,000

5000

50

4000

40

3000

30

2000

20

2

1000

10

1

0

5 4 3

Time from Start of Frac (minutes)

Fig. 11–24. Fracture initiation with multiple breakdowns The decision to step up surface injection rate in segments or to quickly bring injection rate up to the design level depends on knowledge of the formation. Stepping up the rate gradually helps open the natural fracture systems in shales while helping to keep the fracture in zone. Bringing the rate up quickly is common in areas with planar fracs and no potential (or perhaps desire) for complex fracturing. Bringing the injection rate up too quickly in a shale with no physical fracture barriers has been associated with quickly fracturing out of zone (King et al. 2008). Breakdowns of additional zones, or reorientation of the fracture is not uncommon in the startup period. If the fracture design uses more than a single short perforating cluster or a single opening sleeve, hydraulic diversion or ball sealers will be necessary to create fractures at each cluster location. Hydraulic diversion is an effective method of breaking down multiple perforation clusters in the same frac stage, but care must be taken to establish enough pressure differential in this limited entry concept to raise the pressure high enough to break down other zones. Hydraulic diversion depends on perforation friction and the back pressure it generates. Although perforation friction is first seen at rates as small as 0.5 barrel per minute per perforation, friction pressures sufficient to increase back pressures and create breakdown in other zones generally do not occur until the rate of current pumping reaches about 2.0 to 2.5 bpm/perm, assuming a 0.5-inch perforation (Crump and Conway 1988). The difficulty during this early time 644

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period is that this rate per perforation may not be reached until full target rate is nearly achieved. The formation variation, the stress differences, and the number and location of the openings provided by perforation clusters or ports at injection sleeves will also play an important role in creating starter fractures during the first part of the fracturing stage. It is not unusual to see sharp surface injection pressure losses in the fracturing treatment record as new zones are opened often just as rate is stepped up, or later, as proppant is added. Adding proppant, which typically has a density in the range of silica (i.e., 2.65 gram per cc), increases the total density of the injected fluid, increasing the pressure at the pay zone. Proppant in the fracturing fluid also acts as a bridging agent in the formation, reducing the injectivity or flow capacity of the formation. Both of these actions act to increase bottomhole pressure, increasing the likelihood of reaching the breakdown pressure of another treating interval. In a few cases, microseismic monitoring has indicated fracture reorientation as pressure is stepped up or when proppant hits the formation. The decision of when to begin adding proppant to the fracturing fluid depends on experience with fracture width development of the formation in a specific area. The need to inject proppant through the created fracture (or natural fracture) without bridging of the proppant particles in the fracture or perforation, requires sufficient fracture width to avoid the known, but simplistic bridging range in which solid particle diameters of roughly 1/3 to 1/7 of an opening size will tend to form semi-rigid blockages. The bridging theory is much more complicated than a simple diameter range. Fracture width, shape, length, plus particle shape and concentration in the flowing fluid are all interconnected variables in the bridging consideration (Tran, Civan, and Robb 2010). To minimize the potential for near-wellbore proppant screen-outs, industry accepts that the width of the fracture should be about seven times wider than the diameter of the largest proppant. For the common 100 mesh (–70/+140 mesh), the minimum frac width to avoid nearwellbore screen-outs (based on the 0.0083 inch or 0.210 mm size of the 70 mesh particles) would be about 0.06 inches, but for larger proppants, such as 20/40 mesh, the fracture would need to be almost 0.25 inches wide. Achieving a necessary fracture width is an objective of the fracture design and, arguably, the main two variables available for width generation are injection rate and fracturing fluid viscosity. One of the most striking differences in fracturing from a horizontal well instead of a vertical well is the area of the formation accessible from the wellbore—the transition from the casing to the formation. In a vertical well, this transition may extend over the length of the perforated section with the fracture growing mostly upward along the plane of the well; but in a horizontal well, the access from the wellbore will be a matter of inches, where often only a single digit percent of this formation access area is available in the horizontal well. Pressure responses may be sharper and occur much quicker in the early stages of a fracture treatment. Because of the need for width generation and the striking differences in fracture development in some shales, where complex fracturing may be possible, versus sandstones, where planar fracturing is probable, the point in the fracturing treatment execution when proppant can be added to the injected fluid is dictated by the local experience on the extent of fracture width development. Although equations and estimates are available, the variability of the formation is the final factor. How the proppant is added is also a challenge in some formations and fracture systems. Traditional practice has been to add proppant in small steps, increasing in increments ranging from 0.1 to 0.25 ppga, but field experience, especially when fracturing in horizontal wells, often 645

Essentials of Hydraulic Fracturing

indicates that a step-wise proppant slurry suddenly reaching the small entry area of the fracture that was at equilibrium with the previous proppant slurry may cause a sudden pressure fluctuation at the wellbore. While this may assist in raising bottomhole pressure, it can also lead to sudden screen-outs if the fracture width cannot be increased fast enough. Newer proppant methods have centered on steadily but slowly raising the proppant concentration through the ramp-up section. The progression from fracture initiation to fracture growth is marked by frac height and length development as the formation seeks to relieve the applied stress of fluid injection by creating a crack that grows radially outward until limited by barriers, fluid loss rate to the formation or initial or created stresses. Fractures initiated from a horizontal well may require higher initiation pressures than fractures initiated from a vertical well due to several factors, including limited contact area, local laminations in the formation, and high stress environments. As the fracture progresses, the fracture growth difference between vertical and horizontal wells may widen due to the restricted formation entry point in the formation (fig. 11–25).

a

b

Fig. 11–25. Near-well fracture growth and fluid flow from a vertical well (left) and a transverse fracture in a horizontal well (right) Initially, fracture growth is opposed by formation stresses in the near- and far-field areas. During the transition from early-stage fracture growth to late-stage fracture growth, the factors that limit fracture growth are dominated by the increasing area open to fracturing fluid leakoff. Fracture fluid injection rate must overcome leakoff in order to generate enough pressure to continue fracture growth. When the area of the fracture and the permeability of the formation are sufficient to accept all the fluids being injected, the fracture will stop growing. In late growth fracturing, leakoff is the dominant factor in fracture growth control. Figure 11–26 shows an example of the leakoff effect for a balanced growth planar fracture (100 ft total height and 600 ft half-length) with an injection rate of 100 barrels per minute. If the leakoff rate were constant, the injection rate of 100 bpm would be taken up completely by a leakoff rate of about 0.015 ounces per in2 or 0.07 cc per cm2 of formation contact area of contact area. The leakoff rate is rarely constant, but the example demonstrates the power of leakoff as a growth barrier. The examples used in this text are of an ideal nature, assuming a homogeneous formation and a constant permeability. In reality, formations vary widely and reflect depositional and 646

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post-depositional changes from oceans to dry land over a time period of millions of years that often produced heterogeneous rocks, widely differing within a layer. Even thin formations can show varied structures complete with permeable and impermeable streaks (fig. 11–27). However, the repeating layers created by transgressive and regressive shore lines (and water depths) may actually be similar over large intervals.

Frac Width = 0.3”

Injection Rate = 100 bpm 100’

600’

600’

Leakoff of 0.015 ounces per minute per sq. in. (0.07 cc/min/cm2) exceeds fracture injection rate of 100 bpm and stops fracture growth. Fig. 11–26. Leakoff control of fracture growth in a vertically contained fracture

Fig. 11–27. Outcrop showing layering in Woodford shale. Photo from Halliburton (Vincent 2011)

647

Essentials of Hydraulic Fracturing

Propped fracture development in a laminated or layered formation is recognized as a challenge, regardless of the wellbore orientation, but since horizontal wells are exposed to less of the formation thickness, the difficulties are amplified. Fracturing in highly laminated formations is usually associated with a higher proportion of screen-outs. Layered reservoirs prove the value of multiple hydraulic fractures in both vertical and horizontal wells through modeling and in actual production comparisons, which can be seen in Figure 11–28 (LaFollette, Holcomb, and Aragon 2012).

Max Month Gas Production, mcf

Barnett Shale, 15379 Samples for 16970 Wells Predominantly Horizontal Wells

Small Energized Fracs 300000 200000

Cross Link MHF Predominantly Vertical Wells SWF

100000 0 1981

1991

2001

2011

Fig. 11–28. Barnett shale learning timeline of maximum monthly gas production in first year (modified from LaFollette, Holcomb, and Aragon, 2012).

Rate In the most general terms, the fracture injection rate produces the pressure to drive the type of fractures needed in a completion; however; to fracture from multiple initiation points requires some thought about how to both initiate and extend a fracture. If only a single fracture was created, the design would be much simpler. However, multiple initiation points require carefully spaced cluster perforating, and sufficient rate to initiate and extend fractures. In ductile formations, 20 bpm per perforation cluster is used as a minimum, but as the fracture grows and leakoff increases, any injection rate will reach a point where the injected fluid is completely lost in leakoff and the fracture no longer grows. In more brittle formations, a figure of about 10 bpm per perforation cluster has been accepted in specific areas such as the Barnett shale. Total surface injection rates of less than about 25 bpm with slickwater have not been successful in some applications for creating a successful shale gas well if several perforation clusters are open at once (King 2010). Examining shale fracturing records shows that a surface injection rate range of 60–100 bpm became common for slickwater fracture stimulations in cased and perforated completions with multiple open perforation clusters in the Barnett shale (Palmer, Moschovidis, and Cameron 2007). Other shales will present different formation characteristics and the completion and fracture designs will be different, but many other horizontal shale well stimulations have fallen into this range, especially with slickwater fracturing fluids. 648

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Fracture Extension and Later Stage Fracturing Behavior Net pressure rise during fracturing has been linked to increased fracture complexity in some shales, and pressure changes during the job are used by some appliers as an indicator of frac quality (King et al. 2008; Wiley et al. 2004; Cramer 1992). The effect of net pressure rise is not agreed upon over the whole spectrum of frac theory, but those who use the indicator argue a net pressure rise of about 700–1,000 psi net (corrected for fracture fluid column density and friction) is an acceptable indicator of a fracture that is building complexity. A number of tests have arrived at general conclusions that increasing frac pressure and complexity may be related. In fracture stimulation experience in the Barnett shale, a modest uncorrected surface pressure rise of 1–5 psi per minute has been correlated with an increase in complex fracture development and with fractures staying in zone in areas without a lower frac barrier. Some operators tie it in to production increases compared to offset wells (King et al. 2008). A more rapid net pressure rise of 8–15 psi per minute has been linked to what appears to be increasing potential for a screenout within the fracture. Since the pressure rise at the end of a fracture treatment is rapid but not sudden, the restriction is probably developing somewhere in the fracture but away from the wellbore. A composite sketch of a complete slickwater frac in a gas shale where pressure trends are well-proven is shown in figure 11–29.

6,000 5,000

d

a c

4,000

f

e

70

gh

60 50

Pressure

j

40 30

3,000 2,000 1,000

n b

l

Proppant

o

m

0

k

Proppant Loading (lb/gal)

Pressure (psi)

7,000

80

i

Rate (BPM)

Rate

5 4 3

20

2

10

1

Time from Start of Frac (minutes) a b c d e f g h i j k l m n o

injection rate raised in small steps and held for a few moments pressure response—several early perf cluster breakdowns pressure response controlled by hydraulic diversion early frac extension, leakoff and slight pressure decline surface pressure flat but net pressure gradually increasing frac reorientation possible—net pressure increasing more rapidly slope change—press increase nearly double previous press trend. Screenout approaching? unit slope pressure rise as proppant feed is stopped pumps are shut down after post flush—this job not overflushed immediate pressure drop—friction pressure during injection expanded grid—pressure “hammer”—frac-to-wellbore connection OK instantaneous shut in pressure (ISPI)—hold to get frac closure pressure proppant started at minimum rate that proppant can be transported in wellbore proppant held constant (single proppant size shown in this frac) proppant injection stops at surface as blender is cleared

Fig. 11–29. Elements of a gas shale fracture recording of pressure, rate, and proppant loading

649

Essentials of Hydraulic Fracturing

90 Day Cumulative Gas Production (MMSCF)

Palmer, Moschovidis, and Cameron (2007) describe complexity events as shear failures on planes of weakness outside the path of the main fracture plane (the events are marked by microseisms). The complexity is created by shear and/or tensile fractures and describes a failed reservoir volume (FRV) that implies a higher potential gas rate. In low matrix permeability formations such as shale, the developing shear (and tensile) failures typically produce a pore pressure increase that is transmitted through the natural fracture system. This pressure transmission, along with the increasing difficulty (surface pressure trend changes) of generating more fracture volume in these complex fractures leads to increasing net pressure during the frac. A weak linkage of this net pressure increase to productivity was shown by Coulter, Benton, and Thomson (2004) in figure 11–30. 90 Day Cumulative Production vs. Frac Pressure Increase

180 160 140 120 100 80 60 40 20 0

0

100

200

300

400 500 600 700 Frac Pressure Increase, psi

800

900 1,000

Fig. 11–30. Calculated net pressure increase vs. 90-day cumulative production (modified from Coulter, Benton, and Thomson 2004) Linkage of net pressure rise to staying in zone was presented by King and colleagues (2008). This discussion of net pressures in shale fracs uses calculated net pressures, thus a potential source of error is introduced in the absence of bottomhole pressure measurements. Non-shale areas have mixed reviews on the importance of net pressure to fracture effectiveness. Olsen, Bratton, and Thiercelin (2009) produced a plot of closure pressure rise in a shale frac that shows the relationship of closure pressure to the stresses added during fracturing by injection of fluid (fig. 11–31). Surface injection pressure may change during a job for many reasons, including: opening up a new area of the rock, initiating a new fracture from the wellbore, encountering a plane of weakness (laminations or fault), frac plug or ball failure, or fracturing out of zone. Surface pressure records are often the only data available on a frac, so experience with pressure trends is important. Although measured bottomhole pressures are much preferred over calculated bottomhole pressure values, equipment capable of reliably obtaining bottomhole pressures during multistage fracturing in a horizontal well is not typically included in a routine completion. 650

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Closure Pressure (psi)

Fracture Closure Pressure vs. Volume Injected 7,600 7,400 7,200 7,000 6,800

0

500

1,000 1,500 2,000 Fracture Fluid Volume Injected, bbls

2,500

Fig. 11–31. Closure pressure (in a contained zone) increases with total fluid pumped (modified from Olsen 2009)

Simultaneous and Sequential Fracturing Simultaneous or sequential fracturing of multiple, relatively closely spaced parallel wells uses stresses created by fracturing one stage to divert another frac stage direction and even increase complexity development in subsequent fracturing stages. The effect was reported by Warpinski and Branagan (1989) as altered stress fracturing, where a frac direction was modified by a previous frac in the area. Simultaneous fracturing has been successfully used in a number of shale developments (Mutalik and Gibson 2008; Waters et al. 2009). Two to five parallel wells have been fractured at once by one frac unit (blender and pumps) for each well. Perhaps the most famous Barnett shale simultaneous fracs are the EOG Fowler fracs in the Barnett shale in northeast Johnson County. Five wells were fractured with five frac equipment sets. The total initial production rate for these five wells at 375 ft (114 m) well-to-well spacing was nearly 34 mmscf/d (962 × 103 m3/day). Estimated ultimate recovery was projected as 31.6 billion cubic feet (bcf ) (894 × 106 m3) and EOG estimated ultimate recovery of the gas in place was 54%—more than double the normal GIP recovery expectation for the area of the field. Candidate requirements for simultaneous or sequential fracture operations are not welldefined. Most companies that have used the processes in the shales have indicated good production responses; however, the distances between most of the paired wells have been on the order of 1,000 ft (300 m) or less with extreme cases of 1,500 ft (450 m) separation. The maximum distance will probably depend on the time between the fracs, the specific formation, initial stresses, and the fracture-induced stresses that may be linked to fluid volume, pump rates, and diverting methods. Simultaneous fracturing requires exceptional coordination between the frac crews and equipment. Large pads, and often multiple pads, are a necessity. The increase in production produced by simultaneous or sequential fracturing in Barnett wells over single well stimulations averages about 20% to 30% for a 2-well simultaneous frac and 30%+ for a 3-well simultaneous frac. The success of the simultaneous frac will likely depend on how the stresses in the rock are modified by the frac, which in turn depends on individual shale characteristics and local stresses existing before the frac (Mutalik and Gibson 2008; Waters et al. 2009). Brittleness of the shale also likely has some control over the success of simultaneous fracturing. 651

Essentials of Hydraulic Fracturing

In a zipper or sequential frac, there is only one fracture pumping spread, with the frac job alternated between closely spaced parallel wells. In theory, up to three wells could be sequentially fractured although no documentation could be found of more than two sequential fracs at a time. Holding full shut-in pressure on the wellbore of one well while the other is being fractured does not appear to be a necessity, but backflow should be limited. In the fracs described by King and colleagues (2008) for example, the well not being fractured was concurrently being perforated by pump-down perforating guns at somewhat less than final shut-in (post-frac) pressure while the offset well was being fractured. Results on this approach were within the bounds of increase described for simultaneous fracturing.

Refracturing Refracs of some early shale wells have been spectacularly successful when compared to refracs in conventional reservoirs. There are many reasons for these successes (Vincent 2010; King 2014b; French, Rogerson, and Feik 2014): • Enlarged fracture geometry and reservoir contact • Improved pay coverage—increased frac height in vertical wells • More thorough coverage in laterals (more fracs) • Increased fracture conductivity • Restoration of fracture conductivity (various) • Propping previously unpropped fractures • Improved production profile • More suitable fracture fluids • Re-energizing or inflating natural fissures • Reorientation of fracs—field stress alternations—new rock contacted • Over-flushed frac jobs—may repair by straddle frac and large, high quality proppant • Wells negatively impacted by frac hits Failures are more difficult to assess since little data is often collected, but tend to occur in wells with the following characteristics: • Fracturing low-pressure, depleted wells • Low press or fault isolated wells—limited reserves • Wells in which diagnostics already indicate effective fractures and drainage to boundaries • Wells with undesirable existing perfs or uncertain mechanical integrity of tubulars or cement • Wells that don’t allow access to better parts of wellbore • Where off-set wells have recovered more than their share of reserves The analysis required to select a good refrac candidate requires a considerable amount of completion and production data from both the well in question as well as offset wells. The 652

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heterogeneity of the formation may also play a role in well performance, particularly in shales. A set of non-shale-specific criteria was advanced by Hopkins, Jochen, and Fink (1993) to separate poor completions from poor geology before progressing towards a restimulation. The timing of a refrac is more important than it may seem, though perhaps more from an economic optimization standpoint than from an eventual reserve recovery view. The initial considerations are fairly obvious—with age, many of the wells, especially shale wells, have declined rapidly, usually associated with flush production from fractures. However, two key points must be considered: first, is the flow composition changing, and second, how good was the initial completion. These are not independent variables. If the liquids are declining and the gas is increasing, then, assuming there is no gas cap, the passages wide enough to allow liquid flow are closing while the lower viscosity gas is still capable of reaching the wellbore. If the initial completion was perfect, then fractures will have adequate proppant. If not, unpropped fractures will respond to the increasing stress from the removal of fluids by closing. The timing of a refrac is based on cost vs. benefit: Is the value of the lost production worth the cost and risk to refrac? After any frac, the oil production should increase while the gas–oil ratio (GOR) may be steady or fall. Oil rate may then begin a decline as the GOR increases. Fracturing or refracturing opened the fractures, re-establishing the flow path, but unpropped fractures will narrow with time. This lesson is relearned repeatedly with refracs, but the industry has yet to find, or perhaps to use, a proppant that will confirm whether this recovery by refrac must be re-established regularly or whether a design change can start the transition of the unconventional shales into conventional pay zones. Most reported refracs where production numbers are available have been restimulations of wells that were initially fractured with gelled fluids or foam fluids (Wolhart 2002; Lantz et al. 2007; Potapenko et al. 2009; Phillips et al. 2007; Siebrits et al. 2000). Slickwater refracs of wells that are initially fractured with polymer gels most likely capitalize on three things: removing or bypassing the polymer damage from gels; opening the small fractures and microcracks that gelled fluids could not invade; and extending the frac system due to the larger volume of a slickwater fracturing treatment.

Fracture Hits A fracture hit is well-to-well horizontal communication in the pay zones by hydraulic fracture or natural fracture intersections. It is particularly common in closely spaced multi-fractured horizontal wells and has occurred whether the fractures are planar or complex. The first widely reported incidences were in areas of the Barnett Shale with relatively common communication between wells 500–1,000 feet apart, decreasing with increasing well separation distance, but rare occurrences in wells 2,500–4,000 feet apart were also reported. There also may be a connection between high frac pump rates, and quick application of injection rate and pressures that tend to produce long-reaching planar fractures. There are both physical and economic problems associated with the frac hits. Prediction and prevention actions can help resolve many of the problems. The typical response after a frac hit is a sharp decline in gas and oil rates, followed by a slow recovery (fig. 11–32). Water production after a frac hit increases sharply and then slowly declines. In areas where a brine formation underlies the pay zone, a fracture stimulation that communicates with the brine zone may increase brine production in both wells. The economic impact of 653

Essentials of Hydraulic Fracturing

these hits is dependent on the characteristics of the formation including how quickly the opened fractures close. The effects are seen in temporary relative permeability changes, short-term pressure depletion, and potential fluid incompatibilities. In general, the impact of frac hits on liquid-rich reservoir well performance is detrimental. In gas shales such as the Barnett, the effect was often split fairly evenly between helping and hurting production in the well that was intersected by a fracture from an offset well (Woodroof et al. 2003; King and Leonard 2011). Frac Hit

Production

Gas Oil Water

Time

Fig. 11–32. Production response in a well after a frac hit from a fracture being pumped in a nearby well Production responses vary from positive to negative Reducing the incidence of frac hits requires better knowledge of fracture type (planar or complex), locations of easily-opened subsurface flow paths such as natural fractures, and better control of how much fracturing fluid enters each segment of the fracture through either the sleeves or the perforation clusters along the wellbore. Reducing abnormally large fracture halflengths by balancing the volume injected into each perforation cluster will not only reduce the occurrence of hits, but will also likely improve overall hydrocarbon recovery. If two or more fractures are hydraulically connected beyond the wellbore, or if the fluid is not from a point source (multiple sources possible), then controlling the flow is very difficult. Physical damage to the upper well completion might be controlled by pressurizing the wellbore, allowing the well to build up pressure, or by incorporating pressure controlling devices in the well completion. Increasing the distance between wells or using offset perforations to minimize fracture pressure communication also have been successful. Drilling all the wells at the same time and using variations of simultaneous fracturing will reduce damage potential and may significantly increase production (King 2010).

Fracture Flowback

654

The amount of fracture fluid recovery in a fractured formation varies with the formation character, the frac design, and the type of fluid (Sullivan et al. 2004; Soliman and Hunt 1985; Crafton and Gunderson 2007;). Planar fractures that are more conventional, with long reach and minimum complexity, often flow back quickly and the percentage of frac fluid recovered is high. In shale fracs where extensive complexity is developed or the shale is mildly reactive, the amount of fluid recovered may be 10% to 50% of the total injected fluid and the time for fluid

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recovery may stretch over several weeks. Fracture fluids returned from complex fracturing may have different ion-pair composition and differences in TDS levels. This relationship also depends on system energy and closure stresses. Controlling back pressure to use available formation gas energy to most efficiently remove the load water from the frac may have significant benefits in reducing returns of fluids and proppant. Smaller natural fractures that are the source of fracture complexity may be the main cause of delays in water recovery. Relative permeability effects in the narrow fractures, related wetting phenomena, and the tortuous path from the far reaches of the frac fluid penetration are the main causes of these delays. The flowback techniques and results discussed here deal mainly with slickwater fracs. Gelled fracs have an entirely different dependency on cleanup as shown by Willberg and colleagues (1998). Capillary pressure increases sharply in smaller pores and fractures. This may have less effect on fractures than on pores, but capillary forces will still be a factor limiting water displacement from a highly fractured flow system. Lowering surface tension with surfactants or other chemicals is only effective if the materials are not lost by preferential adsorption in the formation. The method by which fracturing fluids are flowed back after a fracture treatment can have a significant impact on both well productivity and total estimated ultimate recovery in some formations. Analysis of the returning fluid can • Provide an indication of whether the frac is planar or complex • Provide an indication of whether the predominant salt addition is by mixing or leaching • Demonstrate whether shut-in or slow-flow operations can hinder or help fluid recovery • Identify what drawdown control is optimum for an area Produced fluid rates and volumes after a frac will generally peak within 5 to 15 days and decline sharply (fig. 11–33). Fracturing base fluids are the first fluids recovered from a well, followed by a mixture of frac fluid and connate water at ever decreasing volumes and rates, and then by potentially several years of low-rate flow comprised of connate water moved by producing hydrocarbons and water condensing from the produced gas. The identity of minerals within the water, specific ion ratios, and total salinity are the data that suggest reactions that occurred in the formation during the frac. The returning fluid composition may have waters from one of more formations, stable and unstable compounds, isotopes that may range from benign backgrounds to very low-strength radioactive isotopes from shales, as well as a very small amount of chemicals from the frac treatment. The concentration of these materials varies widely, but trends established over time may be useful for understanding fracture parameters. Compositions of water recovered immediately after fracs are shown in table 11–1. These numbers vary widely and are shown here for generalized comparison. The amount of fluids returning is dependent on length of shut-in time in some formations. Nearly all surface active chemicals are adsorbed in the formation.

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Essentials of Hydraulic Fracturing

Fig. 11–33. About 40% of the produced water from a well a well after fracturing comes back as rapid flow recovery in the first one to two weeks of production (0.1%–0.5% of total well life). From Gay et al. 2012. Table 11–1. Volumes Ranges of Water and Additives Used in One Well Basin or Area Cumulative Volume % of Total of All Fracs in One Water Well (Gallons) SWF Recovered

Total Volume of Chemicals as a % of Water Volume

% of Added Chemicals in Early Produced Fluid

Barnett (TX) Devonian (PA) Eagle Ford (TX)

4 to 5 million gal 4 to 5 million gal 4 to 5 million gal

30% to 50% 40% to 50% 5% to 15%

0.2% 0.2% 0.3% to 0.4% (hybrid)

Fayetteville (AR) Haynesville (LA)

3 to 4 million gal 4 to 6 million gal

30% to 60% 5% to 15%

0.2% 0.3%

Woodford (OK)

4 to 5 million gal

30% to 50%

0.2%

0.01% to 0.05% 0.05% to 0.1% ~0.2% polymer dominated 0.05% to 0.1% ~0.2% polymer dominated 0.01% to 0.05%

The composition of water returning depends both on the formation fluids and the composition of the fluid being injected as fracturing base fluid. The volumes of fluid returned will vary considerably but several characteristics of flowback have been proven useful as indicators of fracture type, amount of leaching and mixing, and for optimizing fracture volumes, additive type, and additive volumes, and whether the fracture treatment reopened natural fractures or created new fractures. Changes in the chemistry of the water reflect the architecture of the producing stimulated area of the formation (Bearinger 2013). The dissolved solids, specific solubilized minerals, and ratios of ions in returns are specific to a set of conditions described by area-to-volume ratios, leaching events, temperature, pressure, pH, dissolved gasses, and other factors within the reacted area of the rock. 656

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References Abou-Sayed, I. S., S. Schueler, E. Ehrl, and W. Hendricks. 1995. “Multiple Hydraulic Fracture Stimulation in a Deep Horizontal Tight Gas Well.” Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, October 22–25. Andersen, S. A., J. M. Conlin, K. Fjeldgaard, and S. A. Hansen. 1990. “Exploiting Reservoirs with Horizontal Wells: the Maersk Experience.” Oilfield Review 2:11–21. API (American Petroleum Institute). 2013. Shale Energy: 10 Points Everyone Should Know. http://www.api.org/~/media/Files/Policy/Hydraulic_Fracturing/Hydraulic-Fracturing-10points.pdf. Austin, C. E., R. E. Rose, and F. J. Schuh. 1988. “Simultaneous Multiple Entry Hydraulic Fracture Treatment in Horizontally Drilled Wells.” Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, October 2–5. Barree, R. D., S. A. Cox, J. L. Miskimins, J. V. Gilbert, and M. W. Conway. 2014. “Economic Optimization of Horizontal Well Completions in Unconventional Reservoirs.” Paper presented at the SPE Hydraulic Fracturing Technology Conference, Houston, TX, February 4–6. Baumgartner, W., J. Shlyapobersky, I. Abou-Sayed, and R. Jacquier. 1993. “Fracture Stimulation of a Horizontal Well in a Deep, Tight Gas Reservoir: A Case History from Offshore the Netherlands.” Paper presented at the Offshore European Conference, Aberdeen, Scotland, September 7–10. Bearinger, D. 2013. “Message in a Bottle.” Presented at the SPE Unconventional Resources Conference, August, 12–14. Behrmann, L. A., and J. L. Eibel. 1991. “Effect of Perforations on Fracture Initiation.” Journal of Petroleum Technology 43:608–615. Behrmann, L. A., and K. G. Nolte. 1999. “Perforating Requirements for Fracture Stimulations.” SPE Drilling and Completions 14:228–234. Britt, L. K., and J. Schoeffler. 2009. “The Geomechanics of a Shale Play: What Makes a Shale Prospective.” Paper presented at the SPE Eastern Regional Meeting, Charleston, West Virginia, September 23–25. Bruner, K. R., and R. Smosna. 2011. “A Comparative Study of the Mississippian Barnett Shale, Fort Worth, and Devonian Marcellus Shale, Appalachian Basin.” NETL (National Energy Technology Laboratory) Report, Department of Energy, US Federal Government. Bustin, R. M., A. M. M. Bustin, X. Cui, D. J. K. Ross, and V. S. M. Pathi. 2008. “Impact of Shale Properties on Pore Structure and Storage Characteristics.” Paper presented at the SPE Shale Gas Production Conference, Ft. Worth, Texas, November 16–18. Chambers, M. R., M. W. Mueller, and A. Grossman. 1995. “Well Completion Design and Operations for a Deep Horizontal Well with Multiple Fractures.” Paper presented at the SPE Offshore Europe, Aberdeen, Scotland, September 5–8. Cherif, M. M., H. H. Quotob, K. Kartobi, and N. Barakat. 2009. “Identification and Characterization of Producing Fractures in Naturally Fractured Reservoirs Using PIWD.” Paper presented at the SPE Middle East Oil and Gas Show and Conference, Bahrain, Bahrain, March 15–18.

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Cipolla, C. L. 2009. “Modeling Production and Evaluating Fracture Performance in Unconventional Reservoirs.” Distinguished Author Series. Journal of Petroleum Technology 61:84–90. Cipolla, C. L., N. R. Warpinski, and M. J. Mayerhofer. 2008. “Hydraulic Fracture Complexity: Diagnosis, Remediation, and Exploitation.” Paper presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Perth, Australia, October 20–22. Cipolla, C. L., S. Maxwell, and M. Mack. 2012. “Engineering Guide to the Application of Microseismic Interpretations.” Paper presented at the SPE Hydraulic Fracturing Conference, The Woodlands, Texas, February 6–8. Clark, J. B. 1949. “A Hydraulic Process for Increasing the Productivity of Wells.” American Institute of Mining Engineers, Petroleum Transactions 186:1–8. Clark, J. B., and C. R. Fast. 1952. “A Multiple-fracturing Process for Increasing the Productivity of Wells.” API Conference Paper. Drilling and Production Practice, 52–104. Coulter, G. R., E. G. Benton, and C. L. Thomson. 2004. “Water Fracs and Sand Quality: A Barnett Shale Example.” Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, September 26–29. Crafton, J. W., and D. Gunderson. 2007. “Stimulation Flowback Management: Keeping a Good Completion Good.” Paper presented at the SPE Annual Technical Meeting and Exhibition, Anaheim, California, November 11–14. Crafton, J. W., G. Penny, and D. M. Borowski. 2009. “Micro-Emulsion Effectiveness for TwentyFour wells, Eastern Green River, Wyoming.” Paper presented at the SPE Rocky Mountain Technology Conference, Denver, Colorado, April 14–16. Cramer, D. D. 1992. “Treating-Pressure Analysis in the Bakken Formation.” Journal of Petroleum Technology 44:20–27. Crump, J. B., and M. W. Conway. 1988. “Effects of Perforation Entry Friction on Bottomhole Treating Analysis.” Journal of Petroleum Technology 40:1,041–1,048. Dahaghi, A. K., and S. D. Mohaghegh. 2009. “Economic Impact of Reservoir Properties and Horizontal Well Length and Orientation on Production from Shale Formations: Application to New Albany Shale.” Paper presented at the SPE Regional Meeting, Charleston, West Virginia, September 23–25. Dees, J. M., T. G. Freet, and G. S. Hollabaugh. 1990. “Horizontal Well Stimulation Results in the Austin Chalk Formation, Pearsall Field, Texas.” Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, September 23–26. DeMong, K. L., R. Hands, and B. Affleck. 2011. “Advancements in Efficiency in Horn River Shale Stimulation.” Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, January 24–26. dePazzis, L. L., T. R. Delahaye, L. J. Besson, and J. P. Lombez. 1989. “New Gas Logging System Improves Gas Shows Analysis and Interpretation.” Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, October 8–11. Dunek, K. L., D. W. Walser, and D. M. Astakhov. 2009. “Far-Field Volumetric Distribution of Fracturing Fluids Away from an Uncemented Horizontal Liner in the Bakken Formation.” 658

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Paper presented at the SPE Rocky Mountain Petroleum Technology Conference, Denver, Colorado, April 14–16. Engelder, T., and G. G. Lash. 2008. “Marcellus Shale Play’s Vast Resource Potential Creating Stir in Appalachia.” American Oil and Gas Reporter, May 2008. Estrada, E., N. R. Roberts, L. Wejers, T. G. Riebel, and S. D. Logan. 2009. “Fracture Mapping in the San Juan Basin.” Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, October 4–7. Evans, K., G. Holzhausen, and D. M. Wood. 1982. “The Geometry of a Large-Scale Nitrogen Gas Hydraulic Fracture Formed in Devonian Shale: An Example of Fracture Mapping with Tiltmeters.” Society of Petroleum Engineers Journal 22:755–763. Fisher, M. K., B. M. Davidson, A. K. Goodwin, E. O. Fielder, W. S. Buckler, and N. P. Steinsberger. 2002. “Integrating Fracture Mapping Technologies to Optimize Stimulations in the Barnett Shale.” Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, September 29–October 3. Fisher, M. K., J. R. Heinze, C. D. Harris, B. M. McDavidson, C. A. Wright, and K. P. Dunn. 2004. “Optimizing Horizontal Completion Techniques in the Barnett Shale Using Microseismic Fracture Mapping.” Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, September 26–29. FracFocus. 2014. "Hydraulic Fracturing: The Process." Accessed April 28, 2014. http://fracfocus. org/hydraulic-fracturing-how-it-works/hydraulic-fracturing-process. French, S., J. Rogerson, and C. Feik. 2014. “Re-fracturing Horizontal Shale Wells: Case History of a Woodford Shale Pilot Project.” Paper presented at the SPE Hydraulic Fracturing Technology Conference, Houston, Texas, February 4–6. Gale, J. F. W., and J. Holder. 2008. “Natural Fractures in Shales and Their Importance for Gas Production.” Paper presented at the Tectonics Studies Group Annual Meeting, La Roche-enArdenne, Belgium, January 8–10. Gale, J. F. W., R. M. Reed, and J. Holder. 2007. “Natural fractures in the Barnett Shale and their importance for hydraulic fracture treatments.” AAPG Bulletin 91:603–622. Gale, J. F. W., S. E. Laubach and L.J Fidler. 2010. “Natural Fractures in the New Albany Shale and Their Importance for Shale-gas Production.” Poster presented at AAPG Annual Technical Conference and Exhibition, New Orleans, Louisiana, April 11–14. Garcia-Hernandez, A., S. Z. Miska, M. Yu, N. E. Takach, and C. Zettner. 2007. “Determination of Cuttings Lag in Horizontal and Deviated Wells.” Paper presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, November 11–14. Gaskari, R., and S. D. Mohaghegh. 2006. “Estimating Major and Minor Natural Fracture Pattern in Gas Shales Using Production Data.” Paper presented at the SPE Eastern Regional Meeting, Canton, Ohio, October 11–13. Gay, M. O., S. Fletcher, N. Meyer, and S. Gross. 2012. “Water Management in Tight Plays.” IHS Energy White Paper, published online, August, http://connect.ihs.com/StaticDocuments/ LandingPage/WaterManagement.pdf. Grigg, Murray. 2008. Conversation on simultaneous fractured shale wells and production uplift. 659

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Holditch, S. A. 1999. “Factors Affecting Water Blocking and Gas Flow from a Hydraulic Fractured Gas Well.” Journal of Petroleum Technology 31:1515–1524. Hopkins, C. W., J. E. Jochen, and K. J. Fink. 1993. “A Comparison of Two Devonian Shale Wells: Why Is One Well Better Than the Other?” Paper presented at the SPE Eastern Regional Conference and Exhibition, Pittsburgh, Pennsylvania, November 2–4. Kandel, D., R. Quagliaroli, G. Segalini, and B. Barraud. 2001. “Improved Integrated Reservoir Interpretation Using Gas While Drilling Data.” SPE Reservoir Evaluation and Engineering 4:489–501. Kiel, O. M. 1970. “A New Hydraulic Fracturing Process." Journal of Petroleum Technology 22:89–96. ———. 1977. “The Kiel Process Reservoir Stimulation by Dendritic Fracturing.” SPE 6984 (unpublished, in SPE eLibrary). King, R. F. 1993. Drilling Sideways—A Review of Horizontal Well Technology and Its Domestic Application. US Energy Information Administration, Office of Oil and Gas, DOE/EIA-TR0565, Distribution Category UC-950. Kell, S. 2011. “State Oil and Gas Agency Groundwater Investigations and their Role in Advancing Regulatory Reform.” Prepared for the Ground Water Protection Council. http://fracfocus.org/ sites/default/files/publications/state_oil__gas_agency_groundwater_investigations_optimized. pdf. Ketter, A. A., J. R. Heinze, J. L. Daniels, and G. Waters. 2008. “A Field Study in Optimizing Completion Strategies for Fracture Initiation in Barnett Shale Horizontal Wells.” SPE Production and Operations 23:373–378. King, G. E. 2010. “Thirty Years of Shale Gas Fracturing: What Have We Learned?” Paper presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, September 19–22. ———. 2012. “Hydraulic Fracturing 101: What Every Representative, Environmentalist, Regulator, Reporter, Investor, University Professor, Neighbor and Engineer Should Know About Estimating Frac Risk and Improving Frac Performance in Unconventional Gas and Oil Wells.” Paper presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, February 6–8. ———. 2014a. “60 Years of Multi-Well Fractured Vertical, Deviated, and Horizontal Wells: What Have We Learned.” Paper presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands, October 27–29. ———. 2014b. “Refracturing Timing, Prerequisites Diversion and Application,” SPE Webinar, June 17, 2014. King, G. E., and D. E. King. 2013. “Environmental Risk Arising From Well-Construction Failure— Differences between Barrier and Well Failure, and Estimates of Failure Frequency across Common Well Types, Locations, and Well Age.” SPE Production and Operations 28:323–344. King, G. E., L. Haile, J. Shuss, and T. A. Dobkins. 2008. “Increasing Fracture Path Complexity and Controlling Downward Fracture Growth in the Barnett Shale.” Paper presented at the SPE Shale Gas Production Conference, Fort Worth, Texas, November 16–18. 660

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King, G. E., and R. S. Leonard. 2011. “Deciphering Chemical Tracer Results in Multi-Fractured Well Backflow in Shales: A Framework for Optimizing Fracture Design and Application.” Paper presented at the SPE Hydraulic Fracturing Conference, The Woodlands, Texas, January 24–26. Kogsboll, H., M. Pitts, and K. Owens. 1993. “Effects of Tortuosity in Stimulation of Horizontal Wells—A Case Study of the Dan Field.” Paper presented at the Offshore European Conference, Aberdeen, Scotland, September 7–10. Kubik, W., and P. Lowry. 1993. “Fracture Identification and Characterization Using Cores, FMS, CAST and Borehole Camera: Devonian Shale, Pike County, Kentucky.” Paper presented at the SPE Low-Permeability Reservoirs Symposium, Denver, Colorado, April 26–28. LaFollette, R. F., W. D. Holcomb, and J. Aragon. 2012. “Impact of Completion System, Staging, and Hydraulic Fracturing Trends in the Bakken Formation of the Eastern Williston Basin.” Paper presented at the SPE Hydraulic Fracturing Conference, The Woodlands, Texas, February 6–8. Lantz, T., D. Greene, M. Eberhard, S. Norrid, and R. Pershall. 2007. “Refracture Treatments Proving Successful in Horizontal Bakken Wells: Richland County, Montana.” Paper presented at the SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, April 16–18. Lash, G. G. 2006. "The Upper Devonian Rhinestreet Shale: An Unconventional Fractured Reservoir in Western New York State." Presentation at the AAPG Annual Convention, Houston, Texas, April 9–12. Le Calvez, J. H., R. C. Klem, L. Bennett, A. Erwemi, M. Craven, and J. C. Palacio. 2007. “Real-Time Microseismic Monitoring of Hydraulic Fracture Treatment: A Tool to Improve Completion and Reservoir Management.” Paper presented at the SPE Hydraulic Fracturing Technology Conference, College Station, Texas, January 29–31. Letham, E. A. 2011. “Matrix Permeability Measurement of Gas Shales: Gas Slippage and Adsorption as Sources of Systematic Error.” Bachelor’s thesis, University of British Colombia. Litchfield, T., and J. Lehman. 2013. “Interwell Interference During Stimulation, Flowback, and Production History.” SPE slide presentation, SPE Workshop on Hydraulic Fracture Flowback, San Antonio, Texas, November 6­–7. Maxwell, S. C., T. J. Urbancic, N. Steinsberger, and R. Zinno. 2002. “Microseismic Imaging of Hydraulic Fracture Complexity in the Barnett Shale.” Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, September 29–October 2. Montgomery, C. T., and M. B. Smith. 2010. “Hydraulic Fracturing: History of an Enduring Technology.” Journal of Petroleum Technology 62:26–32. Munoz, A. V., M. Asadi, R. A. Woodroof, and R. Morales. 2009. “Long-Term Post-Frac Performance Analysis Using Chemical Frac-Tracers.” Paper presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Cartagena, Colombia, May–June 3. Mutalik, P. N., and B. Gibson. 2008. “Case History of Sequential and Simultaneous Fracturing of the Barnett Shale in Parker County.” Paper presented at the Annual Technical Conference and Exhibition, Denver, Colorado, September 21–24. 661

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Nolte, K. G., and M. B. Smith. 1981. “Interpretation of Fracturing Pressures.” Journal of Petroleum Technology 33:1767–1775. Norman, D. 2004. “The Frac-Pack Completion: Why Has It Become the Standard Strategy for Sand Control?” SPE-101511. SPE Distinguished Lecture presentation, slides. Norris, M. R., B. A. Bernsten, P. Myre, and W. Winters. 1996. “Multiple Proppant Fracturing of a Horizontal Wellbore: An Integration of Two Technologies.” Paper presented at the European Petroleum Conference, Milan, Italy, October 22–24. Olsen, T. N., T. R. Bratton, and M. J. Thiercelin. 2009. “Quantifying Proppant Transport for Complex Fractures in Unconventional Formations.” Paper presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, January 19–21. Overbey, W. K., A. B. Yost II, and D. A. Wilkins. 1988. “Inducing Multiple Hydraulic Fractures From a Horizontal Wellbore.” Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, October 2–5. Palmer, I., Z. Moschovidis, and J. Cameron. 2007. “Modeling Shear Failure and Stimulation of the Barnett Shale after Hydraulic Fracturing.” Paper presented at the SPE Hydraulic Fracturing Conference, College Station, Texas, January 29­–31. Parney, R., E. Jenner, and M. Williams. 2004. “Mapping Reservoir Fabric, Pressure Compartments and Natural Fracture Patterns Using Azimuthal Seismic Velocity.” Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, September 26–29. Pearson, C., A. Bond, M. Eck, and J. Schmidt. 1991. “Results of Stress-Oriented and Aligned Perforating in Fracturing Deviated Wells.” Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, October 6–9. Penny, G., J. T. Pursley, and D. Holcomb. 2005. “The Application of Micro-emulsions in Drilling and Stimulation Results in Enhanced Gas Production.” Paper presented at the SPE Production and Operations Symposium, Oklahoma City, Oklahoma, April 17–19. Phillips, Z. D., R. J. Halverson, S. R. Strauss, J. M. Layman, and T. W. Green. 2007. “A Case Study in the Bakken Formation: Changes to Hydraulic Fracture Stimulation Treatments Result in Improved Oil Production and Reduced Treatment Costs.” Paper presented at the SPE Rocky Mountain Oil and Gas Technology Symposium, Denver, Colorado, April 16–18. Pixler, B. O. 1969. “Formation Evaluation by Analysis of Hydrocarbon Ratios.” Journal of Petroleum Technology 21:665–670. Potapenko, D. I., S. K. Tinkham, B. Lecerf, C. N. Fredd, M. R. Samuelson, M. R. Gillard, J. H. Le Calvez, and J. L. Daniels. 2009. “Barnett Shale Refracture Stimulations Using a Novel Diversion Technique,” Paper presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, January 19–21. Powell, A., O. Bustos, T. Kordzeil, T. Olsen, D. Sobernheim, and T. Vizurraga. 2007. “FiberLaden Fracturing Fluid Improves Production in the Bakken Shale Multi-Lateral Play.” Paper presented at the SPE Rocky Mountain Petroleum Technology Conference, Denver, Colorado, April 16–18. Prats, M. 1961. “Effect of Vertical Fractures on Reservoir Behavior-Incompressible Fluid Case.” SPE Journal 1:105–118. 662

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Ramakrishnan, H., G. Waters, E. Boratko, A. Latifzai, D. Bentley, and J. Kelley. 2009. “Application of Downhole Injection Stress Testing in Barnett Shale Formation.” Paper presented at the SPE Annual Technical Meeting, New Orleans, Louisiana, October 4–7. Rawlings, H. E. 1958. “Use of Hydraulic Fracturing Equipment for Formation Sand Control.” Journal of Petroleum Technology 10:29–32. Rich, J., and M. Ammerman. 2010. “Unconventional Geophysics for Unconventional Plays.” Paper presented at the SPE Unconventional Gas Conference, Pittsburgh, Pennsylvania, February 23–26. Roundtree, R., M. Eberhard, and R. Barree. 2009. “Horizontal, Near-Wellbore Stress Effects on Fracture Initiation.” Paper presented at the SPE Rocky Mountain Petroleum Technology Conference, Denver, Colorado, April 14–16. Sakhaee-Pour, A., and S. L. Brant. 2011. “Gas Permeability of Shale.” Paper presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 30–November 2. Samuel, R., and X. Liu. 2009. “Wellbore Tortuosity, Torsion, Drilling Indices and Energy: What Do They Have to Do with Well Path Design.” Paper presented at the SPE Annual Technical Meeting, New Orleans, Louisiana, October 4–7. Schuler, S., and R. Santos. 1996. “Fraced Horizontal Well Shows Potential of Deep Tight Gas.” Oil and Gas Journal 94:46–53. Shor, R. J., and M. M. Sharma. 2014. “Reducing Proppant Flowback from Fractures: Factors Affecting the Maximum Flowback Rate.” Paper presented at the SPE Hydraulic Fracturing Technology Conference, Houston, Texas, February 4–6. Siebrits, E., J. L. Elbel, E. Detournay, C. Detournay-Piette, M. Christianson, B. M. Robinson, and I. R. Diyashev. 1998. “Parameters Affecting Azimuth and Length of a Secondary Fracture during a Refracture Treatment.” Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, September 27–30. Siebrits, E., J. L. Elbel, R. S. Hoover, I. R. Diyashev, L. G. Griffin, S. L. Demetrius, C. A. Wright, B. M. Davidson, N. P. Steinsberger, and D. G. Hill. 2000. “Refracture Reorientation Enhances Gas Production in Barnett Shale Tight Gas Wells.” Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, October 1–4. Silber, R., J. Martin, S. Willis, and G. Kozera. 2003. “Comparing Fracture Simulation Design to Radioactive Tracer Field Results: A Case History.” Paper presented at the SPE Regional/AAPG Eastern Section Joint Meeting, Pittsburgh, Pennsylvania, September 6–10. Smith, M. B., R. J. Rosenberg, and J. F. Bowen. 1982. “Fracture Width: Design vs. Measurement.” Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, September 26–29. Sneddon, I. N. 1946. “The Distribution of Stress in the Neighbourhood of a Crack in an Elastic Solid.” Proceedings of the Royal Society A 187: 229–260. Soliman, M. Y., and J. L. Hunt. 1985. “Effect of Fracturing Fluid and Its Cleanup on Well Performance.” Paper presented at the SPE Eastern Regional Meeting, Morgantown, Pennsylvania, November 6–8.

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Sondergeld, C. H., K. E. Newsham, J. T. Comisky, M. C. Rice, and C. S. Rai. 2010. “Petrophysical Considerations in Evaluating and Producing Shale Gas Resources.” Paper presented at the SPE Unconventional Gas Conference, Pittsburgh, Pennsylvania, February 23–25. Strubhar, M. K., and E. E. Glenn. 1973. Method of Creating a Plurality of Features from a Deviated Well. US Patent 3,835,928, filed Aug. 20, 1973, and issued September 17, 1974. Sullivan, R., R. Woodroof, A. Steinberger-Glaser, R. Fielder, and M. Asadi. 2004. “Optimizing Fracture Fluid Cleanup in the Bossier Sand Using Chemical Tracers and Aggressive Gel Breaker Deployment.” Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, September 26–29. Tran, T. V., Civan, F., and Robb, I. D. 2010. “Correlating Flowing Time and Condition for Plugging of Rectangular Openings, Natural Fractures, and Slotted Liners by Suspended Particles.” Paper presented at the SPE International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, February 10–12. Veatch, R. W. 1983a. “Overview of Current Hydraulic Fracturing Design and Treatment Technology—Part 1.” Journal of Petroleum Technology 35:677–687. ———. 1983b. “Overview of Current Hydraulic Fracturing Design and Treatment Technology— Part 2.” Journal of Petroleum Technology 35:853–864. Vincent, M. C. 2010. “Refracs—Why Do They Work, and Why Do They Fail in 100 Published Field Studies?” Paper presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, September 19–22. ———. 2011. “Optimizing Transverse Fractures in Liquid-Rich Formations.” Paper presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 30– November 2. Vincent, M. C., and C. Pearson. 1995. “The Relationship between Fractured Well Performance and Well Performance and Hole Deviation.” Paper presented at the Rocky Mountain Regional/ Low-Permeability Reservoirs Symposium, Denver, Colorado, March 20–22. Wallace, J., C. S. Kabir, and C. Cipolla. 2014. “Multiphysics Investigation of Diagnostic Fracture Injection Tests in Unconventional Reservoirs.” Paper presented at the SPE Hydraulic Fracturing Technology Conference, Houston, Texas, February 4–6. Warpinski, N. R., and P. T. Branagan. 1989. “Altered Stress Fracturing.” Journal of Petroleum Technology 41:990–997. Waters, G., B. Dean, R. Downie, K. Kerrihard, L. Austbo, and B. McPherson. 2009. “Simultaneous Hydraulic Fracturing of Adjacent Horizontal Wells in the Woodford Shale.” Paper presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, January 19–21. Weng, X., and E. Siebrits. 2007. “Effect of Production Induced Stress Field on Refracture Propagation and Pressure Response.” Paper presented at the SPE Hydraulic Fracturing Conference, College Station, Texas, January 29–31. Wiley, C., B. Barree, M. Eberhard, and T. Lantz. “Improved Horizontal Well Stimulations in the Bakken Formation, Williston Basin, Montana.” Paper presented at the SPE Annual Technical Meeting and Exhibition, Houston, Texas, September 26–29.

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Willberg, D. M., N. Steinsberger, R. Hoover, R. J. Card, and J. Queen. 1998. “Optimization of Fracture Cleanup Using Flowback Analysis.” Paper presented at the SPE Rocky Mountain Regional/Low-{ermeability Reservoirs Symposium and Exposition, Denver, Colorado, April 5–8. Wolhart, S. 2002. “Hydraulic Fracture Restimulation.” SPE 101458. SPE Distinguished Lecture presentation. Woodroof, R. A., M. Asadi, R. S. Leonard, and M. Rainbolt. 2003. “Monitoring Fracturing Fluid Flowback and Optimizing Fracturing Fluids Cleanup in the Bossier Sand Using Chemical Frac Tracers.” Paper presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 5–8. Zoback, M. D. 2014. Reservoir Geomechanics. 10th ed. Cambridge, UK: Cambridge University Press.

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12 Fracturing Diagnostics With all the research, developed technology, and experience since the advent of hydraulic fracturing, the precision level for predicting propagation behavior still remains relatively low. However, technologies have emerged and continue to emerge that increase precision. Regardless, current state-of-the-art capabilities have yet to attain the necessary degree of precision to guarantee that model predictions will be dependably close to fracturing results. The primary reason lies with the natural variations in the distribution of the in situ properties that govern fracture propagation, and the industry’s inability to definitively ascertain those properties over the entire region that influences the fracture propagation systems. In regard to precision, a tongue-in-cheek observation still prevails: “Industry now knows about everything there is to know about fractures except certainties of: • The number of fractures created • The nature of the fracture system • Which directions, and how far in those directions, they went • How deeply they penetrated horizontally • How far they grew vertically, upward, or downward • What their perimeter configurations and cross-sections look like • Where, how and in what quantities proppant is distributed within the fracture • The prevailing in situ conditions that caused them to behave as they did.” Even though quandaries remain, technologies developed over the years provide significant insight about many important aspects of fracturing. Some technologies that were research projects a decade ago have developed into commonly used, commercially available services. To evaluate the credibility of a treatment design, it is essential to reconcile results from diagnostics with input design data and fracture design model computations. Otherwise, without full evaluation of comparable information, the following can occur: (1) diagnostic expenditures are wasted, and (2) the potential benefits of economically optimizing future treatments are not 667

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realized. Hence, inferences that are diagnostically attainable, and cause–effect follow-up analyses are important for • Vertical fracture growth extent (upward, downward) • Horizontal fracture penetration extent and symmetry • Fracture system azimuthal (compass) direction components • Fracture system propagation nature (planar, curved, zigzag, dendritic, mixed, etc.) • Near-wellbore proppant pack residence (location, quantity, type) • Borehole production fluid entry profile Inferences of the above are derived from a combination of (1) pre-frac tests, (2) real-time measurements during injection, and (3) post-frac surveys. These range in complexity and cost from simple and relatively inexpensive, to somewhat more difficult at nominal costs, to sophisticated and comprehensive at relatively high costs. Obviously their application depends on relative fracturing costs and prospective revenue. Accordingly, it is suggested that diagnostics be conducted until the benefit/cost ratio declines to an unacceptable value. Over the history of fracturing, experience has demonstrated that overall it is rare for the cost of knowledge to exceed the cost of ignorance. Discussion here is, by necessity, basic in nature. Requirements, technologies, intricacies, complexities, nuances, procedures, costs, etc., for addressing the different aspects listed above vary widely. Additionally, many are performed by diagnostic service companies, rather than pumping services. Test procedures and analyses pertinent to each aspect are specific to each company. Thus, in-depth details about them are beyond the scope of this book. Hence, what is presented here focuses on diagnostic types pertinent to each aspect. It minimally addresses procedures, but does expand on certain credibility issues and cautions relative to them. Certain reminders and cautions are reiterated from chapter 9. It is presumed that commonly run logs for lithology, porosity, and saturation profiling are standard scripts for the well’s formation evaluation logging suite. Hence, discussion pertinent to them is not included here.

Fracturing Diagnostic Methods The term “fracturing diagnostics” covers the entire spectrum of information pertinent to fracture treatment design, behavior, performance and evaluation. The tests and surveys listed below provide a menu of resources for diagnostic information. Diagnostics that are covered in detail in other chapters are not addressed here, even though they are included (as reminders) in the list below. Specifically these apply to in situ stress profiling, fluid loss, and the Nolte–Smith net fracturing pressure versus injection time charts. In-depth pre- versus post-fracture production performance is presented in chapter 2. The term “fracturing diagnostics” also implies requirements for (1) well-site and field data acquisition and (2) laboratory or data processing and possibly outside consulting and analyses services. These are readily accessible via oil field directories, websites, or existing company networks. 668

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The lists below show tests that have proven insightful for fracturing diagnostics. Subsequent discussion addresses pertinence to deriving inferences to vertical and horizontal propagation behavior, as well as fracture conductivity resulting from a treatment.

Pre-fracture methods • Conventional core samples • Oriented core samples ˡˡ Microscopic crack observations ˡˡ Grain fabric observation ˡˡ Fracture point load failure studies ˡˡ Differential strain relaxation tests ˡˡ Triaxial sonic velocity tests • Downhole log surveys ˡˡ Electrical and induction ˡˡ Conventional gamma and neutron ˡˡ Acoustic wave train ˡˡ Borehole proximity ˡˡ Baseline temperature profiles ˡˡ Baseline radioactive and chemical component temperature profiles ˡˡ Wellbore triaxial seismic ˡˡ Oriented wellbore caliper logs (borehole elongation orientation) ˡˡ Fiber optic casing strain • Openhole impression packers • Downhole point-by-point, micro-frac formation breakdown pressure closure tests

Real-time measurements • Fracture interval wellbore injection pressure (Nolte–Smith net fracturing pressure versus injection time behavior) • Observation wells ˡˡ Microseismic arrays ˡˡ Fiber optic casing strain ˡˡ Surface and downhole tiltmeter arrays

Post-treatment fracture surveys, tests • Wireline borehole surveys ˡˡ Temperature–time profiles ˡˡ Radioactive profiles ˡˡ Chemical component profiles ˡˡ Cement bond profiles ˡˡ Acoustic, microseismic

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ˡˡ Sonic televiewer surveys ˡˡ Downhole television ˡˡ Multiple or single interval flow profiling • Physical observations ˡˡ Investigative drilling or coring to intersect the fracture ˡˡ Mine-back digouts away from the wellbore

Near-Wellbore Vertical Fracture Extent Post-fracture cement bond logs Comparisons between post- and pre-fracture cement bond logs (CBLs) can provide an inference of existing fractures alongside the casing. During injection, casing annulus cement integrity is essentially destroyed along the trace of the fracture contiguous to the borehole. As injection continues, fracture width enlarges at the wellbore. Thus, either the cement pulls away from the casing, the formation pulls away from the cement, or both the cement and the bore-hole wall disaggregate. Detectable changes between pre- and post-fracture profiles indicate the presence of integrity disturbance. If sufficiently definitive, the inference from CBLs is that the changes resulted from fracturing. However, the term “definitive” poses several issues. One is that casing expansion caused by increased pressure during treatment, though slight, can potentially affect cement integrity. This may be difficult to differentiate from formation movement associated with fracture width effects. Another is that during fracture closure, the disaggregated cement that pulled apart from the casing or formation may only partially reconstruct, which makes it difficult to discern cement integrity loss using the CBL. Other post-frac issues can make CBL signals difficult to interpret (noise from continuing fracture closure, reservoir fluid movement, etc.). Experiences with CBLs range from poor to excellent; however, logging costs are relatively low, so the information benefits may exceed them.

Temperature, radioactive, and chemical profiling Figure 12–1 depicts the concept for inferring vertical fracture extent from post-fracture temperature, radioactive, or chemical logs. Inferences from temperature surveys are based on comparing baseline pre-fracture against post-fracture profiles, looking at deviations from undisturbed conditions prior to injection.

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Fig. 12–1. Post-fracture profiling concept with temperature, radioactive, and chemical logs

Temperature–time profiling Figure 12–2 depicts an example of fluid system in-fracture temperature versus dimensionless penetration, at various injection times. As can be seen, in the near-wellbore region (dimensionless length = 0.0–0.01), fracture temperature is close to that of wellbore injection temperature (which is often close to surface injection temperature). During injection, over time, this cools the formation adjacent to the fracture and area around the wellbore. After shut-in, formation and fracture temperature gradually return to in situ static pre-fracture levels.

Fig. 12–2. In-fracture fluid system temperature versus dimensionless fracture penetration, injection times: 5 to 60 minutes Repetitive temperature profiles reflect the reheating phenomenon and thus provide an inference of created vertical fracture upper and lower bounds near the wellbore. The method requires that profiling commence as soon as possible after shut-in. Thus, the temperature tool must be 671

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ready to drop to the bottom as soon as the initial shut-in pressure (ISIP) has been established. Also, fluid backflow compromises the profile, and must be prevented. Recording includes both downward and upward traverses that sufficiently span the fracture interval depths. The run-torun time lapse captures formation reheating rate. The runs are continued until the fractured interval is sufficiently determined. Interpretation is enhanced by baseline pre-fracture profiles that are not influenced by the existence of a created fracture. They are conducted pre-fracture by circulating fluid in the annulus with tubing in the hole. The circulation period must be commensurate with expected injection time. Circulation is followed by repeated temperature buildup profiles until subsequent runs exhibit minimal analysis benefit. Pre-fracture profiles have proven to be extremely valuable in cases where interpretations of post-fracture surveys are questionable. Interpretation of vertical fracture top versus fracture bottom. With post-fracture temperature profiling, determining fracture tops is commonly more definitive than determining fracture bottoms. This is because of proppant settling during injection. Minimal fluid flow in settled proppant packs inhibits heat transfer. This accelerates temperature increase in the pack portions. Thus adjacent wellbore diminished temperature differentials in those intervals mask interpretation.

Radioactive and chemical profiling Radioactive and/or chemical tracer logs imply vertical fracture extent from residual nearwellbore tagged proppants and fluids. Common radioactive tracers are isotopes with different half-lives: • Antimony • Iridium • Scandium Porous ceramic proppants impregnated with designated detectable non-radioactive chemicals are also emerging as tracing agents. During certain pre-determined injection stages, tracer-tagged proppants and fluids are introduced into the injection stream. These then are the focus of detection during post-fracture surveys. Tagging material for either may differ. That is, one fluid or proppant stage may contain tag A, another tag B, another tag C, etc. A variety of fluid and proppant chemical markers are also available for these methods. Requirements that radioactive and chemical tracer logging runs be commenced immediately after treatment shut-in are typically not important. In fact, with currently available tagging materials it is possible to conduct surveys after the wellbore has been cleaned up, or even put on production. Figure 12–3 shows an example of a post-treatment radioactive profile on a well with five nonisolated wellbore fluid entry intervals during treatment. Interpretation of this particular profile leads to inferences of relative injection fluid entry preference in the various intervals during treatment, and the resulting associated width profile throughout the entire fracture.

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0 GRT1 [GAPI 0 150 0 GRT2 [GAPI 0 150 0 GR CH 0 90 0 ProTechnics

Shale Prop. Width Sand Conc. Scandium Iridium SBRD PW [IN] 25 -0.3 0.3 Antimony IRRD SCON Antimony [IN] 25 0 6 3000 0 SCRD PW Iridium [IN] 25 0.3 -0.3 3000 0 CASI CCL1 SCF 25 -400 100 3000 0 Width Shale

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Fig. 12–3. Post-fracture radioactive tracer profile (complements of ProTechnics)

Essentials of Hydraulic Fracturing

Typically, tagged fluids provide the better indication of fracture tops. Tagged proppants are better for identifying downward growth. Upper fracture portions usually contain higher fluid concentrations, whereas proppants segregate lower in the fracture. One critical aspect for proppants is whether the fluid system exhibits equilibrium banking, partial settling, or near perfect transport. With equilibrium banking fluid systems, early stage injected proppants reside nearer the wellbore. With near perfect transport fluids, late-stage proppants tend to reside near the fracture extremity. Critical aspects involve prescribing tagged material staging, i.e., when, what quantity, and what type of tagged material to inject at what stage. This is determined by the diagnostic service company, as well as all issues related to hazardous material safety. The previously discussed cement integrity aspects pertinent to CBLs also apply, especially for issues of residual proppant pack concentration profiling. Relatively large masses of proppant can lodge or settle in the borehole annulus where cement integrity is poor and voids possibly exist. This can confound interpretations focused on propped fracture width profiling.

Interpretation quandaries and proppant bed-height inferences Figure 12–4 shows a post-fracture temperature profile that poses interpretation quandaries about vertical fracture extent. The horizontal axis depicts temperature (°F and °C). Definitions of the curves and lines within the chart are written left to right, along the upper border of the figure: • Far left—depth, feet • Electric log spontaneous potential • Wellbore perforated intervals (two, separated, shaded) • Pre-fracture temperature model-simulated wellbore temperature profile after cooldown circulation • Pre-fracture measured wellbore temperature profile after cooldown circulation • Post-fracture measured wellbore temperature profile, at shut-in time consistent with pre-fracture profiling • Far right—depth, meters Interpretation involves comparing post- and pre-fracture temperature profiles. The prefracture profile delineates the wellbore exposed to the same heat transfer phenomena during fracturing, but without the effects of a fractured formation. The quandaries relate to inferred vertical fracture height, plus the unusually high temperatures in upper portions above the perforations, called the “warm nose” (a term introduced in the late 1970s per post-fracture temperature surveys). The pertinent questions in regard to figure 12–4 are: • Is the fracture top at 9,800 ft or 9,650 ft, and • Why are warm nose temperatures higher than pre-fracture profile values? The most plausible height interpretation for figure 12–4 is 9,650 ft. Such interpretations on similar profiles have been subsequently supported by communication flow tests between wellbore-isolated upper and lower perforation intervals.

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Fig. 12–4. Post-fracture temperature profile with warm-nose behavior Source: “Figure 1.57,” Gidley et al. 1989, 25. The figure 12–4 example is definitely not unique to a few specific wells. Similar behaviors have been observed in numerous wells, throughout many fields, in differing states (geographically speaking). The commonality is that they are more definitive for massive hydraulic fracturing (MHF) treatments that require large volumes and long injection times, where net fracturing pressures are relatively large, e.g., 500 to 1,800+ psi.

Warm-nose temperature behavior The warm nose is attributed to asymmetric fracture propagation during injection, along with fluid system redistribution in the fracture after shut-in. During injection, by virtue of fluid system flow friction, in-fracture pressure at the wellbore is well above formation in situ stress levels. At shut-in, with no fluid friction, wellbore pressure is transmitted to the fracture extremities. This results in post-shut-in fracture extension, more at one extremity than at the other. Thus, the fluid system redistributes in the fracture accordingly. Heated fluid segments cross-flow in the fracture toward, possibly past, the wellbore point. This increases wellbore temperature.

Settling proppant-packs—bed height Figure 12–4 shows another inference, i.e., proppant pack bed height. During the period between shut-in and early temperature profiling stages, proppant is settling as the fracture closes and fluid redistribution is occurring. Settling proppant or settled proppant packs inhibit in-fracture cross-flow. Here, fluid movement, and thus heat transfer, at the wellbore is less than 675

Essentials of Hydraulic Fracturing

that in the overriding fluid segments. Here, the inferred proppant bed top is at about 9,800 ft depth, i.e. below the cross-flow segment. Profiles much flatter than that shown in the figure have been observed. These have been interpreted as proppant top indications. However, this has yet to be irrefutably substantiated. Methods for definitively measuring in-fracture proppant pack tops in areas remote to the wellbore are yet to come..

Factors affecting total fracture vertical extent diagnostics Several phenomena present difficulties in using downhole tools for determining total vertical fracture extent, viz, • Proppant in the rat hole, below injection fluid entry points • Wellborehole deviation Regardless, they are not insurmountable, and should not be the basis for discarding profiling considerations. Suitable other methods for circumventing both are available. Also, even though difficulties occur, wellbore profiles provide supplemental fracture top information.

Proppant in the rat hole, below perforations If the injection interval bottom is near plug-back depth it is commonly difficult to run tools much deeper than that. Even if the interval bottom is several hundred, or a thousand feet above plug-back depth, for severe cases, it may not be possible to log deeper than 20 to 30 feet below the lowest injection point. Downward momentum during injection carries proppant past the lowest injection point. Turbulence, as the slurry redirects to enter the fracture, inhibits proppant settling at the immediate lowest fluid entry point. Proppant settling after displacement and shut-in adds to residual fracture-string proppant top. Thus, residual proppant tops in the rat hole stops the tool from going deeper. This affects temperature profiling depths, but not radioactive or chemical tracer, which can be run after wellbore cleanup. The benefit of near-wellbore measurements is that they provide a more definitive fracture top near the wellbore than do remote microseismic mapping or tiltmeter surveys.

Wellbore hole deviation Rock mechanics theory, supported by laboratory experiments, indicates that internal wellbore pressure during fracture initiation aligns the fracture with the wellbore until it progresses into the region where formation in situ stresses dominate. Thus, created fractures remain contiguous to the wellbore over the initiation interval span. During subsequent further propagation they “bat-wing” to conform to prevailing in situ stress fields. Hence, along the wellbore the fracture angle coincides with bore-hole inclination angle. Away from the wellbore, vertical and horizontal fracture propagation realign to the formation in situ stress field. In regard to this, wellbore survey tools have a limited radial investigation depth, i.e., 18 to 24 inches. Figure 12–5 depicts the concept for detection limitations. It shows a vertical fracture created from a non-vertical wellbore. Detection limits are shown by the arrows. A fracture beyond them goes undetected. Assuming vertical fracture orientation and a deviated wellbore, vertical fracture growth may be much greater than indicated by log surveys. 676

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Fig. 12–5. Detection from logs—non-vertical wellbore, vertical fracture extent inference less than actual Source: “Figure 2.7,” Gidley et al. 1989, 44. Small wellbore deviations, within those typically acceptable for drilling operations, can yield misleadingly low total fracture height values. For example, consider a treatment through a 100-foot perforated interval, in a slightly deviated wellbore that resulted in a 500-foot vertically extensive fracture near the wellbore. Here, the radial detection limit for post-fracture surveys is 24 inches from wellbore center. Simple comparative trigonometry calculations for three wellbore deviation cases, i.e., Case A—0.28°, Case B—1.0°, and Case B—3.0°, yield the following total fracture heights (Hƒ):

Case A (0.28°) ≈ 250 ft beyond the perforated interval: Hƒ ≈ 500 ft



Case B (1.00°) ≈ 60 ft beyond the perforated interval: Hƒ ≈ 220 ft



Case C (3.00°) ≈ 20 ft beyond the perforated interval: Hƒ ≈ 140 ft

Even the relatively small 1° wellbore deviation showed diminutive Hƒ results from post-fracture surveys. For this example, a wellbore with 0.28° deviation is required to yield the created fracture height. Hence, drilling personnel should be advised that hole deviation can yield poor diagnostics. However, at the least with credible wellbore surveys, the existence of a vertical fracture can be ascertained.

Corroboration with other resources Real-time microseismic mapping surveys and tiltmeter surveys also provide inferences of both near-wellbore and far-field vertical height extent. Thus, corroboration between post-fracture borehole surveys and real-time microseismic mapping data with fracture design model height calculations is an important part of treatment evaluation. Figure 12–6 depicts both an aerial and depth microseismic analysis for two horizontal wellbores with multiple fracturing treatments conducted from one pad. The figure integrates analyses for multiple toe-to-heel, separately fractured intervals. The focus here is the depth microseisms. The data suggests upper and lower vertically confined propagation in the target formation. 677

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Microseismic mapping (such as shown here) and tiltmeter surveys have proven to be reliable technologies for inferring vertical fracture growth confinement, as well as azimuthal propagation preference. Typically, such services are not employed on a regular basis in vertical wellbore fracturing. Regardless, they serve as resources to greatly improve post-fracture vertical growth diagnostics in all wellbores, be they perfectly vertical, slightly deviated, highly inclined, or essentially horizontal. This relates to more economically optimized treatment designs.

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Fig. 12–6. Microseismic events, two horizontal wellbores, multiple isolated fracture intervals, Marcellus shale Source: Mayerhofer et al. 2011 678

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In areas where concerns relate to the invasion of potable water sources, microseismic mapping is essential until the degree of concern diminishes to a non-threatening level. Figure 12–7 shows a composite of microseismic mapped fracture heights for 22 Marcellus shale fracturing sites across the United States. These data are also contained in figure 1–11 in chapter 1. However, here potable water source depth is definitively shown, as are inferences of natural faults that may, if connected to a hydraulically created fracture, over time be a potential path for reservoir fluids to percolate into potable water sources. However, in these data, none are detected. 0

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Fig. 12–7. Composite microseismic, 22 Marcellus Shale treatments, vertical fracture extent (complements of Pinnacle Technologies, Inc.)

Post-Fracture Wellbore In-Flow Production Profiling Wellbore production profiling provides inferences about relative producing contributions of various portions of the target fracturing interval. It applies to both single and multiple separated intervals. Multiple intervals are those fractured by the various techniques presented in chapter 1, i.e., limited entry, mechanically isolated, ball sealers, etc. The various methods employed for profiling include downhole flow sensors, densitometers, high-resolution temperature differential surveys, etc. Coinciding radioactive tracer surveys enhance diagnostics for fracturing treatment evaluation. Such investigations yield a comparative perspective of effective fracturing treatment and proppant placement uniformity. These are also especially useful for identifying intervals that were not effectively stimulated, propped, or effectively perforated. This provides guidance for remedial work, such as reperforating, water and gas shutoff, annulus cement repair, etc., and for design and implementation changes on future fracturing treatments. 679

Essentials of Hydraulic Fracturing

Figure 12–8 depicts a composite post-fracture production profile and radioactive tracer survey. The example is for a gas-water producing reservoir in a well with 10 separate perforated intervals. The figure shows seven columnar, partitioned data sets, identified by the boxes at each column top. Left to right, they are • Depth and perforated intervals (far left) • Gas or water holdup (ratio), fraction, range: 0–1 • Wellbore flowing gas rate, MCFPD, range: 0–2,500 • Wellbore flowing water rate, BFPD, range: 0–300 • Radioactive tracer strength: scandium (SCFM), iridium (IRFM), antimony (IBFM). • Composite temperature and velocity ˡˡ Temperature, °F, range: 236–256 ·· Flowing ·· Geothermal ˡˡ Velocity, ft/min, range: 0–400 ·· Measured ·· Theoretical • Composite pressure and density (far right) ˡˡ Wellbore pressure, psi, range: 1,800–2.100 ˡˡ Fluid density, g/cc, range: 0–1.3 Obviously, the major gas production comes from one half of the intervals. Contributions from the others are comparatively small. Water entry appears to be rather uniform. Here, the design engineer has several options for enhancing fracturing performance. Two viable suggestions (among several possibilities) are offered: • Reperforate the entire interval from top to bottom. Use a small frac-pack treatment with high proppant concentrations to enhance near-wellbore connection to the fracture (if possible). • On future treatments: Determine in situ stress bounding interval spans with acoustic wave train surveys, then ˡˡ If there are strongly bounded multiple intervals, fracture each separately using mechanical wellbore isolation (otherwise fracture all intervals concurrently); ˡˡ Perforate the entirety of each span (or all intervals) prior to fracturing; ˡˡ Near the end of injection, increase slurry concentration significantly; and ˡˡ As the displacement fluid approaches the perforated interval, decrease injection rate somewhat to place high proppant concentrations in the fracture near the wellbore. In regard to the four comments above, consider the following: • Perforating the entire span prior to fracturing increases the probability of fracture connection to the wellbore. In the example case, separated initiation intervals may lead to echelon vertical fractures that do not vertically connect during the treatment (as discussed in chapter 3). 680

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• Total vertical fracture height depends only on upper and lower confinement. It is independent of perforation intervals, such as those shown in figure 12–8. Regardless of perforation spans, fracture height spans the entirety between upper and lower fracture bounding formations. • Width profiles are greater for a single vertical fracture than for unconnected, multiple echelon fractures, thus fracture conductivity is greater. Twf [DegF] 256 Vap [FPM] 400 SCFM 0 QWater Pwf SCRD SBFM 0 [FPM] OpWater 400 1800 [psi] 2100 IRFM Geothermal Temperature QWater RhoFluid [BFPD] 300 Perfs 236 256 0 [DegF] [g/cc] 1.2 C:\CP_Brochure\cp.pttrk.ptprs ProTechnics 50 236

Water Oil Gas Holdu Perfs 0 1 0 ProTechnics 50

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Fig. 12–8. Wellbore production flow, radioactive tracer, temperature profile results (compliments of ProTechnics, Core Laboratories, SpectraScan) 681

Essentials of Hydraulic Fracturing

A perennial quandary with in-flow profiling With wellbore flow profile surveys, it often seems that the whole is not equal to the sum of the parts. When each interval is tested separately, and test data from all separate intervals are combined, the flow for all intervals flowing together seldom adds up to the separate totals. This even happens in sophisticated reservoir model simulations. Regardless, proportioned in-flow surveys, such as are shown here, are useful post-fracture evaluation tools.

Fracture Propagation Azimuth and Propagation Geometry Many methods and techniques have been employed in efforts to either predict or determine fracture propagation azimuth. Some have proven themselves; several remain in the shadows; others have fallen by the wayside. Discussion here focuses mostly on the proven, with mention of several that remain in the shadows. Knowing the preferential fracture azimuth of propagating fractures is important for • Tight formations (both oil and gas) where fracture penetration is deep enough to interfere with drainage patterns on offset wells, or future well locations • Enhanced recovery injection projects where the existence of hydraulically created fractures influences sweep and conformance efficiency, and thus recovery performance.

Azimuth and drainage patterns Figure 12–9 shows two examples for the same well pattern: • On the left (Case A), the north–south azimuth of the fractures do not invade offset well-drainage patterns. Also, total reservoir drainage is fairly well covered by individual drainage from each well. ˡˡ Note that more complete drainage is possible by shifting one row (for example, the upper row) of wells in the east–west direction by one half the well-to-well spacing distance, and moving the two rows a bit closer together. Doing this is possible with credible diagnostics and improved fracture treatment designs. It has the potential to increase total recovery, and thus revenue, throughout the play development. • On the right is Case B, with the same drilling pattern. If instead of a north–south azimuth, fractures were to follow an ENE–WSW azimuth, much of the reservoir remains un-drained. If fractures were to follow an east–west azimuth, the situation is worse. Hence, it is important that both design and reservoir engineers be involved and work together during early field development stages, or infill drilling plans. It is also important that they make strong, united cases to company management, who may have strong opinions about deviating from conventional “governmental spacing” practices. 682

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Fig. 12–9. Reservoir drainage versus fracture azimuth Source: “Figure 16.1,” Gidley et al. 1989, 342.

Azimuth and enhanced recovery injection projects Figure 12–10 shows the impact that fracture azimuth can have on enhanced recovery injection projects. This applies to practically all projects where the fracture penetration is more than one-fourth of the well-to-well spacing distance. On the left (Case A) there is an east–west preferential fracture azimuth. Conformance and sweep can possibly be improved by hydraulically fracturing designated injection wells. Results may be further improved by also fracturing producing wells. On the right (Case B), with the preferential fracture azimuth shown, disaster would be the result of fracturing either the indicated injectors or producers. Enhanced recovery displacement fluids would quickly break through to the producers, leaving the reservoir un-swept. Once fractures are created, the only remediation possible is to change the azimuth-aligned injectors to producers, and vice versa. Again, as with development, it is important that both the design and the reservoir engineer be involved from the start if hydraulic fracturing is being considered for enhanced recovery injection projects.

Fig. 12–10. Reservoir enhanced recovery sweep versus fracture azimuth Source: “Figure 16.2,” Gidley et al. 1989, 342.

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In situ stress effects on fracture azimuth and orientation Figure 12–11 coincides with in situ stress and fracture azimuthal preferences discussed in chapter 3. Here in situ stress (σ) subscripts V, H1, and H2 designate in situ stress directional components: • V—Vertical • H1—Horizontal • H2—Horizontal, orthogonal to H1 In regard to the figure, the directions and magnitudes of in situ stress components have a significant impact on fracture azimuth and orientation: • Case A (upper left): σH1 ≈ σH2 > σV → Horizontal fracture • Case B (upper right): σV > σH1 > σH2 → Vertical fracture, H1 direction • Case C (lower left): σV1 ≈ σH1 ≈ σH2 → Horizontal fracture, dipping angle • Case D (lower right): σV > σH1 ≈ σH2 → Dendritic vertical fractures

Fig. 12–11. In situ stress orthogonal magnitude effects on fracture propagation preference Source: “Figure 16.3,” Gidley et al. 1989, 343.

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Hence, diagnostics that yield both in situ stress magnitudes and directional components are essential to arriving at fracture propagation directional and inclination preferences. Also note that, with Case D, where σV > σH1 ≈ σH2, propagation preferences become dependent on other factors, such as • Rock tensile strengths • Grain orientation and structure • Fissures and joints that cause branching and blunting as fracturing fluids invade them and exert in-fracture pressures in various directions.

Near-wellbore versus far-field data Fortunately, methods for a priori predictions in the near-wellbore region are available for all cases. Unfortunately, away from the wellbore, in the far-field region, there is currently a paucity of information available for a priori predictions. The industry currently relies on hindsight from real-time mapping. Data from high-cost methods such as physical observations (post-fracture investigative cores that intersect the fracture, mine-back digouts, etc.) are, understandably, extremely limited. With horizontal wellbores, full-scale diagnostics (cores, logs, mapping, etc.) have a high potential to provide significant resource data for far-field a priori predictions. However, this approach is somewhat costly. Credibly addressing this requires • Correlation diagnostics throughout the entire pay, top to bottom, in vertical boreholes at pad surface locations • Diagnostics (full-hole cores, log suites, etc.) in a sufficient number of horizontal boreholes to characterize the expected fracturing areas It also requires in depth post-fracture evaluations and correlations using appropriate, credible diagnostics, and computer fracture propagation models. Hence, increasing the database for horizontal wellbore costly diagnostics depends on cost of ignorance versus cost of knowledge issues. To date, the cost of ignorance seems to be relatively high in regard to unrealized production revenue versus potential revenue improvements made possible by additional diagnostic data.

Fracture azimuth inferences from oriented core samples This discussion addresses several common methods for obtaining azimuth preference implications from oriented cores in target fracturing intervals. More reliable data is obtained with pressurized core barrels. Here, tests pertinent to azimuth relate to rock expansion at ambient conditions relative to that at in situ confinement: • Microscopic crack observations • Point load failure studies • Differential strain curve tests • Triaxial acoustic measurements Additionally, concurrent data is also available during core acquisition (porosity, permeability, fluid saturations, acoustic velocity, elastic modulus, Poisson’s ratio, fracture toughness, etc.). 685

Essentials of Hydraulic Fracturing

Microscopic crack observations Figure 12–12 depicts the concept of microscopic crack observations. When removed from the in situ stress and temperature burial environment over geologic time, cores contain residual stresses that relax and gradually expand to surface ambient conditions. It is somewhat akin to a rubber ball being compressed for a very long period, and then allowed to expand. During rock expansion, microscopic cracks develop. These are observable under a microscope for a wellpolished flat core surface (sometimes with the naked eye). Crack alignment indicates directional component. Typically, a majority align more or less parallel to the in situ minimum horizontal stress.

Fig. 12–12. Fracture azimuth inference from core relaxation microcracks (more in the maximum stress direction than in the minimum stress direction) Source: “Figure 16.21,” Gidley et al. 1989, 351.

Point load failure tests Figure 12–13 shows another method for studying cracks created by rock expansion. Such a sample may not have relaxed sufficiently for visible cracks to appear. However, it may have weakness planes. These are detected by imposing a point load stress in the center of a core wafer until it cracks. The tests require several relatively thin (¼-inch) wafer samples from each depth over a sufficient number of depths to be representative of the fracturing interval. A point load test machine is shown on the upper left. The point load application on a core wafer is shown on the upper right. Various possible results of a test on one wafer are shown on the lower left. It depicts the point load (left), a single plane failure (middle), and bifurcated (secondary plane) failures. A composite of tests on multiple wafer sets is shown on the lower right. Overall results are typically consistent with microcrack observations, if they are visible. A predominate number of cracks in the same direction, as shown in the upper pictures on the lower right, implies subsurface in situ stress direction. Randomness, or bifurcation, suggests that there is not a large differential between maximum and minimum principle stress magnitudes in the formation. The lower right picture compares point load bifurcations (upper) with rosettes of elongated grain orientation (shown below point load data).

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In formations where point load tests have been compared against subsequent real-time mapping data, results were relatively consistent in the near-wellbore region.

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Point Load Test

LOADING PATTERN NORMAL FAILURE SECONDARY FAILURE PLANE

Fig. 12–13. Point load tests for fracture azimuth inferences Source: “Figure 16.22,” Gidley et al. 1989, 352.

Different strain curve tests Strain curve relaxation tests also measure the same phenomena as described above. However, they often provide better resolution to azimuthal preference than either microcrack or point-load studies. Here, they provide implications of relative magnitudes between maximum and minimum principle stresses at in situ conditions. These tests use high-resolution strain gauges to measure relaxation. If pressurized core barrels are not employed, cores must be caught at the well site, immediately after exiting the core barrel. Upon capture, they must also immediately be fitted with strain gauges, positioned so as to measure strains in x, y, and z directions.

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Figure 12–14 shows the x, y, and z direction strains over time. Here cores were cut with a standard (unpressurized) core barrel. Thus, expansion occurred while tripping (retrieval to surface) the core barrel. The starting time on the time axis is 6 hours. This is because the pipe trip time off the bottom with the core barrel was 6 hours. The upper portion of the chart shows the amount of strain relaxation. The lower portion shows the maximum principle strain directional calculations. These results and calculations imply that a fracture will propagate parallel to the maximum horizontal strain direction (N70E).

Fig. 12–14. Fracture azimuth inference from core strain curve relaxation Source: “Figure 16.20,” Gidley et al. 1989, 351.

Triaxial acoustic measurements Here triaxial (x, y, z) acoustic velocities provide azimuth perspectives. Microcracks attenuate wave travel times. Hence, differential x, y, and z velocities across the core sample, over several time periods, yield an inference of azimuth preference, much like the above strain curve relaxation tests.

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Triaxial acoustic tests often accompany conventional laboratory mechanical stress–strain tests for elastic modulus and Poisson’s ratio. Proper mechanical tests are conducted at in situ confinement pressure and temperature. Hence, the core samples are somewhat restored to their initial in situ state. Cores taken with pressurized core barrels are less subject to trip-out retrieval expansion. Here, with accelerated pre-test core plug processing time, the expansion microcrack issue is somewhat mitigated (but not totally).

Commentary on core orientation accuracy and deeply penetrating fractures Even with technology advances, core orientation accuracy remains subject to question. Accuracies have improved over the decades. Claims suggest that accuracies on the order of 12° to 18° have been improved to 6° to 12°, or better. Methods and techniques for confirming accuracy have also improved. However, there are still three potential errors: misalignment of the core barrel, misalignment of the survey tool, and survey tool accuracy. Error in each compounds total error. Additionally, downhole cores comprise a miniscule representation of the formation penetrated by a propagating fracture. Deeper penetrations are subject to higher endpoint error. The fluctuations of nature often cause changes in direction as propagation progresses. This further compounds the issue for deeply penetrating fractures. Hence, azimuth precision, if pertinent to economic treatment optimization, should be included in treatment design scenarios.

Downhole methods used previously Several methods previously used to infer fracture azimuth have essentially been supplanted by microseismic mapping. These previous methods include • Oriented borehole caliper logs (borehole elongation orientation) • Openhole impression packers Interpretation and operational issues with both, along with other advances in technology, have essentially removed them from the current azimuth diagnostic menu. The reason for their inclusion in the book is to discourage further consideration of these methods for use in inferring fracture azimuth. This is done because the authors understand the well-established adage that “History often repeats itself.”

Oriented borehole caliper logs In previous decades, openhole, oriented borehole caliper logs (borehole elongation orientation) were sometimes a part of pre-fracture azimuth data acquisition. The basis lay in the understanding that borehole washout during drilling provided an implication of in situ stress component direction. In some formations it does. In situ stresses can oblate a borehole during drilling. Cracks that form at the tips of an oblong hole disaggregate the formation. Drilling mud circulation further enlarges the washout at such points. These are discernable with oriented borehole calipers. However, many other factors also masked interpretation, such as drilling pipe tripping and rotational erosion, natural fissures and fractures, lack of formation consolidation, etc. 689

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Openhole impression packers This was a method used in early azimuth studies. Impression packer tests are conducted in the target fracturing openhole interval prior to setting the casing. Internal pressure sufficient to create a fracture is applied to the packer external element. The element is sufficiently soft to squeeze into and make an impression of the created fracture, and yet firm enough to retain the deformation upon release. Several issues with this method (outside of rig time and test costs) involve orientation, borehole ID versus packer element OD, uniform element impression, borehole elongation, element destruction when tripping out, pressure requirements to obtain an impression, overpressure setting effects. If all these issues can be adequately addressed, the information is useful for both near-wellbore azimuth and borehole vertical fracture configuration; however, addressing all these issues tends to be very costly and inefficient as compared to other approaches that have evolved.

Fracture azimuth and propagation behavior from microseismic measurements Real-time microseismic methods have become commonly used for mapping fracture propagation behavior. They have proven to yield very credible indications of behaviors and dynamic extents during injection: • Horizontally • Vertically • Configuration ˡˡ Planar, dendritic ˡˡ Orientation ˡˡ Direction When fractures are created, they impart shear stresses within, around, and ahead of the injected fluid system. Shear failure during formation fracturing exhibits significantly more pronounced energy, compared to tension (parting) failure. Thus, shear wave measurements are the crux of microseismic fracture mapping surveys. Shear wave magnitudes, being stronger than compressional waves can be detected at relatively long distances. With microseismic mapping, shear events occurring both beyond and within the fracture boundaries are recognized. Thus, mapping results may not precisely determine the fracture geometry.

Microseismic mapping configurations Figure 12–15 depicts a typical mapping configuration. It is comprised of vertically spaced arrays of multiple triaxial (three-dimensional) seismic receivers in one or more vertical observation wells. These are remote to the fracturing candidate. Shear wave arrival time differentials between each receiver provide the basis for computing fracture shear energy release locations. Prior to fracturing, directional sensing is calibrated, either while perforating, or with string shot detonations in the fracturing candidate well. Supplemental calibration is possible with detonations at other known locations and depths remote to observation wells. 690

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Obviously, interpretation accuracy depends on the location and number of observation wells, the number of receivers, receiver array spacing, and relative depths of the receivers and arrays compared to the fracturing interval. The mapping service designates those requirements pertinent to specific fracturing treatment expectations. In the chart, the left observation well provides better information about the fracture system horizontal extent and configuration, while the right observation well yields better information about the vertical fracture extent. Better vertical growth definition happens in places where these arrays span depths above, within, and below the target fracturing interval.

Fig. 12–15. Microseismic mapping: observation wells and receiver arrays

Early microseismic experiments Figure 12–16 shows results of a microseismic mapping project conducted in the 1980s by Sandia National Laboratory in Albuquerque, New Mexico. This was in concert with numerous other fracturing-related tests that made up the comprehensive DOE, Multi-well Experiment (MWX), south of Rifle, Colorado. The figure is a composite of aerial and side view projections of events recorded during injection in the MWX-1 well. A series of triaxial receivers were located at different depths in well MWX-3. Three fracturing procedures were conducted: two minifrac treatment, and a step rate injection and flowback test. Chart symbols identify the 7,000+ ft depth fracturing seismic event data: Minifrac #1, Minifrac #2, step rate injection and flowback.

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Fig. 12–16. Microseismic mapped fracturing shear events, DOE MWX-1, Colorado Source: “Figure 1.65” and “Figure 1.66,” Gidley et al. 1989, 29. The upper chart implies azimuthal progression and fracture penetration. The lower chart depicts fracture vertical growth progression. The receiver well (MWX-3), being left of the injection well (MWX-1), was unable to detect any definitive weaker signals for events that may have occurred remotely right of the injection point. Hence, perspectives of fracture symmetry are not available. The fracturing industry benefitted greatly from the demonstration that microseismic mapping can be an extremely valuable addition to hydraulic fracturing diagnostics. With the expanding development of shale formations, microseismic technologies have expanded accordingly.

Wellbore triaxial borehole seismic

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Triaxial microseismic surveys have essentially been supplanted by advances in remoteobservation well-mapping methods. Here the wireline receiver arrays are run in the target fracturing wellbore, as opposed to an observation well. The arrays are similar to those used in

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observation wells. They must be directionally oriented (x, y, and z). With this configuration, they provide definitive perspectives of near-wellbore fracturing behavior. Tests can be conducted in cased or open holes. Surveys are conducted prior to the fracturing treatment. The target fracturing interval is then perforated. Small-volume, neat-fluid systems are injected to create the fracture system, much like minifrac shut-in pressure decline tests for closure pressure and fluid-loss data collection. Such surveys offer applicability to investigating fracturing interval isolation integrity in horizontal wellbores. After wellbore isolation intervals have been established, either with external borehole packers or cement, the well is ready for wellbore triaxial testing. With relatively small volume pre-fracture tests, these surveys can yield inferences of whether the fractures are being contained by or are bypassing the isolation points. However, they are subject to noise that is not fracture-related (cross-flow, etc.). Experience has shown that interpretation difficulties can be overcome using methods with lower logistical complications.

Fiber optic strain measurements—horizontal wellbores Fiber-optic methods have essentially preempted triaxial methods for investigating fracturing interval isolation integrity in horizontal wellbores. Measurement relies on differential laser light wave separation transmitted through fiber optics that provide high-resolution micro-order fiber strain. Thus, relatively long fiber-optic strands, adhered to casing, are used to detect casing strain or deflection. With this method, the data on fracture activity that affects minute casing behavior can serve as the interpretation basis for fractures that bypass isolation points.

Massive shale planar fracture propagation—horizontal wellbores Figure 12–17 is a composite of aerial real-time microseismic mapping results from 11 separate fracturing treatments in a single horizontal wellbore. Shades differentiate seismic events during each treatment. The solid line, trending NW–SE, represents the wellbore with perforation points and isolation packers. The surface injection point is at the lower right. The arrow identifies the microseismic observation well. Rectangular figures denote wellbore isolation packers for the various treatments. Diamond-shaped figures represent perforation intervals. As can be seen, all of the fracturing treatments exhibited essentially planar propagation behavior. Azimuthal preference showed a relatively consistent SW–NE directional component. However, each fracturing treatment demonstrated a somewhat different penetration extent, and different symmetry about the injection point. Also note (e.g., for the perforated interval at the upper left well extremity) that the fracturing fluid bypassed the packers. It initiated and extended in the second fracturing stage interval. Packer bypass occurred in several stages. This is common in horizontal wellbore treatments. Diagnostics such as microseismic mapping and fiber optic strain measurements are necessary to detect such occurrences.

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Perforations Packers Observation Well

Treatment Well Fig. 12–17. Microseismic mapped fracturing shear events Source: Shaffner et al. 2011.

Massive shale planar and dendritic fracture propagation—horizontal wellbores Figure 12–18 shows an aerial view composite, on 200-foot grid spacing, of both planar and non-planar propagation in a Barnett Shale formation where four separate fracturing treatments were conducted in the same wellbore. Shades denote seismic events for each of the four treatments. The solid line, trending WNW–ESE, represents the wellbore. Surface injection point is at the lower right. The lone circle on the left, below the wellbore, identifies the microseismic observation well. Circle-shaped figures along the wellbore denote interval isolation points for the treatments. The figure reveals that both planar and dendritic propagation occurs in relatively small pockets of the same formation. The extent, azimuth, and symmetry are relatively consistent for the planar fractures on the left. However, moving to the right, dendritic behavior becomes apparent. The far right indicates prominent dendritic propagation over a specific area, with additional dendritic extension beyond the right of the pad location well.

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Observation Well Treatment Well

1000 ft

Fig. 12–18. Aerial perspective—fracture propagation behavior from real-time microseismic measurements Source: Daniels et al. 2007.

Commentary on microseismic automatic signal recognition Methods have emerged to accelerate microseismic analysis for real-time on-site analysis during a treatment. These employ automatic shear wave signature recognition technologies. Processing and analysis rely on a series of predefined acoustic shear wave patterns. These are the focus for automatic shear event recognition during injection. Thus, incoming shear waves that do not conform to predefined patterns are ignored. This leads to an incomplete diagnosis of shear events. These technologies are mostly in the embryo stage at this writing. Comparative post-fracture scrutiny of some of the results has revealed deviations from the real-time on-site results. Thus, design engineers are cautioned about taking real-time well-site analyses at face value. Hence, until technology advances to the degree necessary, all real-time mapping data should be exposed to detailed post-fracture scrutiny. Taking this into account, however, real-time, on-site, automatic analyses still provide significant information about dynamic fracture propagation behavior.

Fracture azimuth and propagation behavior from tiltmeter measurements This method involves implanting a number of high-resolution (nanoradian) tiltmeters in patterns designed to sense formation displacement patterns caused by fracture width enlargement during treatment injection. When in situ fractures bow outward during injection, this horizontal fracture width enlargement is reflected elsewhere. This horizontal width displacement translates to vertical displacement at the surface. However, the vertical magnitudes are significantly attenuated, as compared to fracture width. In between, the displacement trend is angular, depending on depth. 695

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Early tiltmeter fracture azimuth mapping Initially, tiltmeters were located in near surface, shallow wells. With proper near- and subsurface formation conditions, nanoradian tiltmeters yielded credible, verified results for fractures created at 8,000- to 10,000-foot depths. Figure 12–19 depicts a typical tiltmeter near-surface array pattern for early mapping work. It required circular patterns with radii extending somewhat beyond the expected fracture penetration length.

Fig. 12–19. Typical surface tiltmeter array Source: “Figure 16.5,” Gidley et al. 1989, 345. Figure 12–20 contains a composite of processed results for two different fracture orientations (horizontal and vertical). The upper chart shows the tilt pattern for the horizontally oriented propagation. The lower chart depicts a surface tilt pattern for the vertically oriented propagating fracture shown below. Notice the different configurations between the two orientations. Surface response to the horizontal fracture is as intuitively expected: a single bulge. For vertically oriented fractures, fracture width expansion (horizontally) translates to upward surface bowing on both sides of the fracture. The trough aligns with the fracture as it propagates. This yields an inference of fracture azimuth.

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Fig. 12–20. Tiltmeter surface vertical displacement—horizontally and vertically oriented fractures Source: “Figure 16.4” and “Figure 16.5,” Gidley et al. 1989, 344, 345. In this example, maximum displacements are extremely small for both cases. For the horizontal fracture, vertical displacement is 0.01 inch vertically per 100 linear feet. With the vertical fracture, vertical displacement is 0.002 inches per 1,000 linear feet.

Tiltmeter array density—effect on resolution Figure 12–21 shows a comparison of azimuth results for two tiltmeter array density patterns. Fracture horizontal penetration is at about 10,000 ft depth. The left portion (Case A) has only eight tiltmeter sites in the pattern. The right portion has 18 sites. The higher density obviously yields more definitive results. Notice the offshoot indications marked 2, 3, and 4 on the 18-site chart. These are transverse fractures initiating near the wellbore resulting from high in-fracture pressures in the wellbore vicinity. These greatly exceed formation in situ stress, where net fracturing pressures became 697

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excessive due to friction pressures via fracturing fluid system rheology. This is an example of the additional information available with tiltmeters. 8 - Sites

Azimuth Resolutions — 8 versus 18 Tiltmeter Sites

18 - Sites

2 3

4

A

1

B

Fig. 12–21. Relative tiltmeter fracture resolution—8 tiltmeter sites versus 18 sites Source: “Figure 1.67,” Gidley et al. 1989, 29.

Azimuthal diagnostic comparison—tiltmeter mapping and triaxial wellbore Microseismic Figure 12–22 shows a comparison between tiltmeter and triaxial microseismic results for the same fracture treatment. The left chart (Case A), which shows the results from tiltmeter seismic measurements, displays the same results as shown in the right chart (Case B), which shows the results from triaxial borehole seismic measurements. The numbers on both charts indicate identical segments of the fracture. Here, the number 1 designates the main fracture. Numbers 2, 3, and 4 represent the transverse offshoot fractures previously mentioned. As can be seen, results of the two methods corroborated well.

2 4

A

2

1

1

3 4

B

Fig. 12–22. Comparative tiltmeter versus triaxial borehole fracturing behavior Source: “Figure 1.67” and “Figure 1.68,” Gidley et al. 1989, 29, 30.

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Tiltmeter mapping technology advances In addition to near-surface tiltmeter placement, subsequent advances in technology also include the use of downhole tiltmeter arrays over various spans of depth in one or more observation wells. Thus, tiltmeters now provide a much broader perspective of fracture propagation behavior. When tiltmeters are used in concert with microseismic data, the frame of reference is even larger. Current technology now addresses fracture configuration. Analyses for advanced technology remain based on the basic theory of the past. Current tiltmeter methods provide a threedimensional perception of fracturing behavior. Figure 12–23 depicts both tiltmeter downhole array configuration and formation displacement resulting from fracture width growth during injection. In this figure, tiltmeters are shown in both the fracturing treatment well and the off-set observation well. Note that this is not typically the case during fracturing treatments, where tiltmeters are only placed in observation wells. The treatment well data is obtained concurrently using pre-frac, neat-fluid injection tests (e.g., minifrac shut-in pressure decline tests for fluid-loss data). The figure displays angular deviations from the vertical in both wells. Contoured grids throughout the formation depict angular displacement trends. The fracture lies near the center and maintains a constant height throughout. Arrows along the top represent surface dip angle response to fracture width horizontal expansion. The fracture-induced surface trough aligns with the vertical fracture.

Fig. 12–23. Tiltmeter horizontal and vertical displacement from a fracture (Tech Update 01 TM, compliments of Pinnacle Technologies, Inc.)

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Figure 12–24 shows a variety of current tiltmeter diagnostic capabilities. The six pictures pertain to fracturing in both vertical and horizontal wellbores, fracturing single and multiple formation layers, and fracturing single and multiple isolated intervals. The left portion of each chart implies what is desired from the fracture treatment. The right portion represents only one of the many possibilities for what actually occurred during a treatment. Diagnostics such as these are important to calibrate treatment designs and design data against fracturing behavior.

Pay zone coverage

Multizone coverage Pay zone Pay zone

or

Pay zone

Pay zone

What we want

What we get?

Fracture length

What we want

Horizontal well trajectory Horizontal well

800 ft

Horizontal well

300 ft Pay zone

Pay zone

What we want

What we get?

What we get?

What we want

Fracture growth versus time

What we get?

Perforation strategy

or Pay zone

What we want

What we get?

What we want

What we get?

Fig. 12–24. Fracture propagation behavior implications from tiltmeter applications (Tech Update 01 TM, complements of Pinnacle Technologies)

Commentary on Fracturing Diagnostics The discussion and figures presented in this chapter merely introduce a menu of available diagnostic resources. However, they provide comparisons between types of diagnostics pertinent to types of fracturing behaviors. All of the aforementioned tests, methods, etc., have been performed extensively, and are recognized as credible sources of specific information. They have proven to enhance understanding of propagation behavior and to improve revenue from fracturing treatments. Hence, what is presented here serves as a springboard for pursuing answers to specific aspects of fracture treatment design. 700

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A long-standing, humorous oilfield saying goes as follows: “Never run more than one type of diagnostic to determine the same fracturing parameter. Running more than one type gives more than one answer. Then you’ve got a problem: Which one is right?” Such humor, however, does not extend to the fracturing economic community. Unfortunately, the implication “one diagnostic—one perception, three diagnostics—three perceptions” is commonly more the rule than the exception. However, multiple diagnostics for specific parameters can define fracturing behavior bounds. This is best addressed with full-cycle economic fracture design scenarios that span those bounds. Currently, the average per-well fracturing treatment cost is on the order of $4 million. This comprises from 40% to 80% of total well costs. Assuming a minimum payout requirement of 5.0 for any oil or gas development investment, this results in a $25 million to $50 million net revenue return. Thus, a minimal 5% revenue increase by virtue of fracturing treatment designs enhanced using diagnostics could mean revenues improved by $1.25 million to $2.5 million per fracturestimulated well. Again, the cost of ignorance versus the cost of knowledge must be considered. As the industry continues delving into the lower portion of the resource triangle, per-well fracturing costs will rise accordingly (as they have over the past four decades). Experience has shown that high technology diagnostic programs, though sometimes costly have a high potential to increase revenue. This was the case for massive hydraulic fracturing (MHF) in vertical wellbore tight formations. The massive shale fracturing learning curve appears to be similar to that exhibited during MHF development. Here again, accelerated diagnostic programs pose a similar potential. Hence, design engineers are faced with the question of what information is required for their specific formations in order to improve fracture treatment designs. Additionally, and more importantly, is the question of how to use that information to maximize fracturing revenue from the formations. Answers to these questions must be brought to management’s awareness, with the understanding that full-sweep diagnostics may result in bumpy endeavors that eventually smoothen to higher revenue.

References Daniels, John L., George A. Waters, Joel Herve Le Calvez, Doug Bentley, and John T. Lassek. 2007. “Contacting More of the Barnett Shale through an Integration of Real-Time Microseismic Monitoring, Petrophysics, and Hydraulic Fracture Design.” Paper presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, November 11–14. Gidley, John L., Stephen A. Holditch, Dale E. Nierode, and Ralph W. Veatch, eds. 1989. “Figure 1.57.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 25. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.65” and “Figure 1.66.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 29. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 1.67.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 29. Richardson, TX: Society of Petroleum Engineers.

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———. 1989. “Figure 1.67” and “Figure 1.68.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 29, 30. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 2.7.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 44. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 16.1.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 342. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 16.2.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 342. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 16.3.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 343. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 16.4” and “Figure 16.5.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 344, 345. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 16.5.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 345. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 16.20.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 351. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 16.21.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 351. Richardson, TX: Society of Petroleum Engineers. ———. 1989. “Figure 16.22.” In Recent Advances in Hydraulic Fracturing (SPE Monograph V. 12), 352. Richardson, TX: Society of Petroleum Engineers. Mayerhofer, Michael J., Neil A. Stegent, James O. Barth, and Kevin M. Ryan. 2011. “Integrating Fracture Diagnostics and Engineering Data in the Marcellus Shale.” Paper presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 30–November 2. Shaffner, Jonathan T., Alick Cheng, S. Simms, E. Keyser, and M. Yu. 2011. “The Advantage of Incorporating Microseismic Data into Fracture Models.” Paper presented at the Canadian Unconventional Resources Conference, Alberta, Canada, November 15–17.

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Appendix A Fracture Vertical Height Calculations Chapter 3 introduced a method that facilitates and expedites calculating fracture height related to in situ stress, stress intensity factor, and in-fracture pressure. What is presented here describes the approach used to develop that method. This includes equations, algorithms, and tables pertinent to applying the method. Chapter 3 contains several results obtained using the method. Appendix B contains details that can be used to incorporate this method into a threeinterval rock mechanics spreadsheet model. Figure A–1 replicates chapter 3, figure 3–22. Figure A–2–1 contains plots of regressioncalculated data shown in figure A–1. The data in these figures were extended to an hS/h range of 0 to 15. Figure A–2–2 depicts regression-calculated values for the extended hS/h data range.

Fig. A–1. Generic height growth curves through barriers: left, symmetric case; right, nonsymmetric case 703

3

Interval

hs3/h versus ƒ( ,Pƒ)

1.5

Interval

hs2/h versus ƒ( ,Pƒ)

1.5

h3

R=1

h2

R=1

h3

R = 0.75

h2

R = 0.75

h3

R = 0.5

h2

R = 0.5

h3

R = 0.25

h2

R = 0.25

1.0

hs3/h

hs2/h

1.0

2

0.5

0.0

0.5

0.0

0.2

0.4 0.6 ƒ( ,Pƒ)

0.8

0.0

1.0

0.0

0.2

0.4 0.6 ƒ( ,Pƒ)

0.8

1.0

Fig. A–2–1. Regression-calculated relative fracture height versus stress-pressure function for symmetric and nonsymmetric cases: left, upper σ3 interval; right, lower σ2 interval

3 Interval

hs3/h versus ƒ( ,Pƒ)

2 Interval

15.0

3.0

12.0

h3

R=1

h3

R = 0.75

h3

R = 0.5

h3

R = 0.25

2.5 2.0

hs2/h

hs3/h

9.0 6.0

h2 h2 h2 h2

R=1 R = 0.75 R = 0.5 R = 0.25

0.6

0.8

1.5 1.0

3.0 0.0

hs2/h versus ƒ( ,Pƒ)

0.5

0.0

0.5

ƒ( ,Pƒ)

1.0

0.0

0.0

0.2

0.4

1.0

ƒ( ,Pƒ)

Fig. A–2–2. Extended data range regression-calculated relative fracture height versus stress-pressure function for symmetric and nonsymmetric cases: left, upper σ3 interval; right, lower σ2 interval

Appendix A

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Fracture Vertical Height Calculations

Descriptions and Comparisons of Figures A–1, A–2–1, and A–2–2 The separate charts in figure A–1 differentiate symmetric from nonsymmetric fracture vertical growth, as is indicated in the chart legends. Figure A–1 (left) applies to symmetric vertical growth, and shows the effects of various in situ stress differentials between the middle (Interval 1) and bounding intervals (which have equal in situ stresses) where stress intensity factors KIC = 1,000. Figure A–1 (right) applies to nonsymmetric growth effected by unequal in situ stress differentials between (a) Interval 1 and overlying Interval 3, and (b) Interval 1 and underlying Interval 2 where KIC = 0.

Nomenclature and pertinent equations Interval designations Designations of the upper, middle, and lower intervals (3, 1, and 2, respectively) are consistent with those in chapter 3. Fracture growth hS/h nomenclature adheres to interval numbers for Intervals 3 and 2 (i.e., h3/h occurs in Interval 3, and h2/h in Interval 2). Nomenclature for Interval 1 thickness, h, is consistent with figure A–1. In what follows, nomenclature for interval rock properties, in situ stresses, and pore pressure designations are consistent (e.g., σ3 and KIC3 imply Interval 3 in situ stress and stress intensity factor). Also, in-fracture pressure, P, in figure A–1 is equivalent to Pƒ in figures A–2–1 and A–2–2.

Horizontal axes The horizontal axes in figure A–1 are replaced by equation A–1 in figures A–2–1 and A–2–2.

ƒ(σ,Pƒ) = [ (σ3 + σ2)/2 – Pƒ]/(σ2 – σ1) + Δƒ(σ,Pƒ)SHIFT

Equation A–1

where Δƒ(σ,Pƒ)SHIFT = 10^[–3.053021 + 0.5Log(KIC ) + 3.776238E – 13Log(KIC )2] Equation A–2 and KIC denotes stress intensity factor. This accounts for the absence of KIC in figures A–2–1 and A–2–2.

In situ stress difference ratios In figure A–1 (right), curves are identified by ratios of in situ stress differences. These are defined by equation A–3:

ΔσR = (σ3 – σ1)/(σ2 – σ1)

Equation A–3

The legends in figures A–2–1 and A–2–2 identify interval and curve specificity. For example, h3 ΔσR = 1 implies applicability to the curve for Interval 3 where (σ3 – σ1)/(σ2 – σ1) = 1. 705

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Curve equivalence When σ3 = σ2, then ΔσR = 1. This implies equal upward and downward growth. Hence, the following designated curves are equivalent: • Figure A–1–left curve, KIC = 0 and all σ2 – σ1 • Figure A–1–right curve, (σ3 – σ1)/(σ2 – σ1) = 1 • Figure A–2–left curve, h3 ΔσR = 1 • Figure A–2–right curve, h2 ΔσR = 1

Regression-calculated data Figures A–2–1 and A–2–2 derive from second order regression of extended figure A–1 data. The extension, by inference, allows application to a much higher vertical growth range than is shown in figure A–1, where hS/h ranges from 0 to 1.5. Also, unlike figure A–1, the left and right charts in figures A–2–1 and A–2–2 are interval specific. The curves in figure A–2–1 (left) and A–2–2 (left) apply to Interval 3 calculations. The right chart curves in the figures are specific to Interval 2. Figures A–2–1 and A–2–1 are applicable to both symmetric and nonsymmetric vertical growth and obviously contain identical data. Figure A–2–1 is presented, however, for visual comparison with the figure A–1. Figure A–2–2 shows regression-calculated data points over the entire extended data range (i.e., hS/h from 0 to 15). The extended range is considered (by the authors) to be sufficient for treatment design. Stress intensity factor, KIC , does not appear in the figure. It is integral to the horizontal axes per equations A–1 and A–2.

Fracture initiation interval Fracture initiation occurs in Interval 1, and grows into Intervals 3 and 2, which are infinitively thicker than Interval 1. In-fracture pressure, Pƒ, is depth independent throughout all intervals. Rock properties, and in situ stress (σ) are depth independent within their respective intervals. In situ stresses σ2 ≥ σ3 > σ1. Upward and downward vertical growth occurs in the bounding intervals in accord with Pƒ magnitude, and the relative σ and KIC magnitudes between the intervals.

hS/h limits and ƒ(σ,Pƒ) ranges for different ∆σR values Note that in both figures A–2–1 (right) and A–2–2 (right), the Interval 2 curves truncate at different points on the horizontal axis value. These points identify axes values that differentiate confined from unconfined Interval 3 vertical growth. Table A–1 identifies the ƒ(σ,Pƒ) range limits used for calculations. These are unique to each ΔσR set. When ƒ(σ,Pƒ) values fall below the table minimum values, h3/h increases so rapidly that it constitutes unconfined growth. This is considered by the authors to be the ƒ(σ,Pƒ) point where h3/h > 15. Unconfined growth occurs first in Interval 3 because σ3 < σ2. At that point, calculations for Interval 2 are meaningless.

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Also note the different points on the horizontal axis where essentially no interval height growth occurs (i.e., h3/h and h2/h ≈ 0). For ƒ(σ,Pƒ) values greater than the maximum, where hS/h ≈ 0, a value of hS/h = 0.001 is used. For example, consider the table A–1 set, where ΔσR = 0.25. For all ƒ(σ,Pƒ) values < 0.334, hS/h is set to 15. For all ƒ(σ,Pƒ) values > 0.629, hS/h is set to 0.001 Table A–1. Range limits for ƒ(σ,Pƒ) values, based on limiting hS/h to a maximum of 15, and a minimum of 0.001 Figures A–2–1 and A–2–2 hS/h vs ƒ(σ,Pƒ) Curves hS ∆σR = 1 hS ∆σR = 0.75 hS ∆σR = 0.5 hS ∆σR = 0.25

ƒ(σ,Pƒ) Range Limits Minimum ƒ(σ,Pƒ) where hS/h = 15 0.0184 0.924 0.201 0.334

Maximum ƒ(σ,Pƒ) where hS/h = 0.001 0.99 0.89 0.772 0.629

Utility of the Height Growth Curves Figure A–2–2 provides extremely important information for calculating vertical fracture growth. The basic technology pertinent to the figures constitutes a basis for rock mechanics and in situ stress effects in many hydraulic fracturing models. Equations used to generate the curve data allow design engineers to calculate fracture height on a spreadsheet platform. They also serve as a springboard to address many aspects of fracture design beyond that, including: fracture width, fracture volume, fluid and proppant selection, and fracture conductivity. Equations and algorithms can also be used to construct a simple fracture design model for use in predesign that yields perspectives on the effects that different parameters such as Poisson’s ratio, in situ stress, elastic modulus, stress intensity factor, fluid rheology, and fluid loss can have on fracture length, height, and width geometry.

Regression of the Height Growth Curve Data Equations developed from the figure A–1 extended curve data greatly facilitate and expand the applicability of the curves. For example, application of the original figure A–1 data is limited to the following: hS/h