Applied Well Cementing Engineering 0128219564, 9780128219560

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APPLIED WELL CEMENTING ENGINEERING

APPLIED WELL CEMENTING ENGINEERING

Edited by

GEFEI LIU Pegasus Vertex, Inc., Houston, TX, United States

Gulf Professional Publishing is an imprint of Elsevier 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, United Kingdom Copyright © 2021 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-821956-0 For information on all Gulf Professional publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Joe Hayton Senior Acquisitions Editor: Katie Hammon Editorial Project Manager: Ruby Gammell Production Project Manager: Nirmala Arumugam Cover Designer: Mark Rogers Typeset by SPi Global, India

Contributors Hu Dai Pegasus Vertex, Inc., Houston, TX, United States Gunnar DeBruijn Progressive Talent Solutions Inc., Calgary, AB, Canada Boyun Guo University of Louisiana at Lafayette, Lafayette, LA, United States Kirk Harris ThoroughBond LLC, Lafayette, LA, United States Gefei Liu Pegasus Vertex, Inc., Houston, TX, United States John E. McCormick Pegasus Vertex, Inc., Houston, TX, United States David Allan Poole Cementing Consultant, Jay, FL, United States Alfredo Sanchez P.E. MorphPackers, The Woodlands, TX, United States Joseph M. Shine, Jr. Houston, TX, United States Sarah Misser Whitton Schlumberger Canada Limited, Calgary, AB, Canada Jiang Wu Retired from Chevron, Houston, TX, United States

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Foreword Cementing is arguably the single most critical step in the construction of a well. When drilling a well, formations that originally provided seals between permeable zones are penetrated, opening the possibility for formation fluids with different pore pressures to migrate from one permeable zone to another or even back to surface. A combination of casing and cement are used to form hydraulic barriers that restore these seals, isolate permeable zones, and prevent the occurrence of fluid migration. The cement must maintain its barrier status throughout the life of the well from drilling through production and on into permanent abandonment. Failure of cement to provide a proper hydraulic seal can result in lost production, fluid cross-flows, contamination of aquifers, sustained casing pressure or loss of well control. Wells have been cemented since the turn of the 20th century. Although the basic method of placing cement in a well has remained relatively unchanged since the pump and plug method was first introduced by A.A. Perkins in 1910, cementing technology has evolved significantly over the years and continues to do so today. These advances have been driven by the need to meet the ever increasing challenges and requirements presented by cementing HTHP, deepwater and horizontal extended reach wells. Advances have been made in many areas, including cementing equipment, cementing additives, cement placement physics, cement sheath integrity, and cement sheath evaluation. Today’s cementing equipment is capable of automated mixing of cement with very precise density control. Additives have been developed that allow cement to be placed in today’s most challenging environments across broad temperature extremes ranging from deepwater wells with mudline temperatures lesser than 40°F to HTHP wells with temperatures greater than 500°F. Ultralow density cements and stage cementing tools are available for cementing long columns across zones susceptible to losses. The physical process of mud removal during cementing is now much better understood and modeled. Numerous technologies for inhibiting gas migration through hydrating cement have been developed. Models to predict mechanical failure of a cement sheath resulting from imposed wellbore stresses are now available and cements that are resistant to stress failure have been developed. Methods have been developed to aid in the evaluation of the quality of a cement sheath including job signature pressure matching and sonic and ultrasonic logging tools.

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Foreword

In this book the reader will find invaluable information on a broad range of topics related to cementing beginning with casing design and ending with well abandonment. This information will aid the user in designing and executing well cementing operations to meet the required job objectives for the life of the well in a safe, effective, and efficient manner. David Stiles ExxonMobil Upstream Integrated Solutions Company, Spring, TX, United States

Acknowledgments The editor and contributors wish to thank Jenny Ng from PVI for her multiple illustrations, including the book cover. We also thank Leisly Choz, Cissy Zhao, and Jeannette Hu from PVI for proofreading and text formatting.

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CHAPTER ONE

Introduction to cementing engineering Gefei Liu Pegasus Vertex, Inc., Houston, TX, United States

1.1 What is well cementing? Millions of years ago, algae, plants, and bacteria lived, died, and sank to the seafloor. Over millions of years under high pressure and high temperature, the buried organic substance had slowly broken down and transformed into oil and gas. Well drilling is the only way to extract oil and gas from the earth. Before we discuss about the modern drilling process, let us take a look at a drilling scene 2000 years ago in China, where the Chinese in the Sichuan province originated deep drilling. The primary motive for deep drilling in China was the search for salt. The ancient percussive cable drilling system involves a derrick with a height of 33 ft and all parts of the rig made from wood (mainly bamboo). A large wooden drum of 16 ft diameter was used to perform round trips. The rocking movement of the balancing beam created the percussive impulses on the bit, which sometimes weighed over 300 lbs. By alternately lifting the bit and letting it fall, they achieved rates of penetration from 1 in. to 3 ft per day. By the beginning of the 3rd century CE, wells were being drilled up to 500 ft deep. Fig. 1.1 shows a typical bamboo rig. The boreholes were lined with bamboo and connected by watertight male-female joints. The bamboo casing prevented water seepage during drilling. They also used straw mixed with Tung oil and lime to make primitive cement and keep the bamboo casing in position. This way, when the brine was reached, the brine would not be diluted by seeping freshwater from shallow zones. This is arguably the earliest record of the casing and cementing. Deep drilling for brine yielded natural gas (primarily methane) from time to time. The boreholes producing methane were known to the Chinese as “fire wells.” Drilling for natural gas followed and was developed at the same time. Natural gas was then used to heat evaporation pans of brine to make salt: killing two birds with one stone. Applied Well Cementing Engineering https://doi.org/10.1016/B978-0-12-821956-0.00004-3

Copyright © 2021 Elsevier Inc. All rights reserved.

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Fig. 1.1 Ancient Chinese drilling rig. (Credit: Tiangongkaiwu, 1637 AC).

The first successful cementing job was performed in an oil well (Hill no. 4 Spudded September 26, 1905, and completed April 30, 1906) in which a water shutoff was attained by pumping cement through the tubing and behind the casing-forerunner of the modern cementing technique. The well, drilled by the Union Oil Company of California to a total depth of 2507 ft of 10 in. casing and 2237 ft of 8 in. casing, was so securely cemented off that the well subsequently produced for over 45 years. By 1917, oil well cement became commonly available. And by 1948, API code 32 was adopted for oil well cements. In the modern era, oil and gas wells are drilled using a rotary drilling rig with thousands of feet of drill pipe and a drill bit at the bottom. By rotating the drill pipe from the surface or downhole motor, the drill bit is turned rapidly to cut the formation and create a section of the open wellbore. A well is drilled and completed in stages. As the well is drilled deeper, formation pressure changes. It is necessary to line the bottomhole with a steel pipe (casing) to keep the wellbore from caving in. Other important reasons for casing and cementing are explained in the next section of this chapter.

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After a casing is run into a wellbore, it needs to be secured inside the wellbore, concentrically if possible. The material used to achieve this purpose is cement. Unlike the cements used in construction concrete, well cements do not contain coarse sand or gravel. Finely grounded cement is mixed with water and other chemicals (additives) to make pumpable cement slurry, which has predictable rheological, thickening, and final strength properties. To hold the casing in position, cement slurry is pumped down the casing and flowed back to the annulus between the casing and borehole. An adequate length of cement column, when set, can firmly bond casing to the borehole. This process of placing liquid cement slurry in the annulus is called primary cementing. A cement slurry starts its solidification process as soon as it is pumped into casing. Within hours of placement (typically 12–24 h), the cement slurry sets or hardens and forms a solid seal between the casing and borehole. After the cementing job, drilling activity continues to the next depth, and a new and smaller casing is run and cemented. This process repeats until the target is reached. Well cementing is like a series of bridges that link the drilling phase to the production phase. Today, it is possible to drill through more than 6 miles of rock to reach an oil and gas reservoir. Casing and cementing provide a stepby-step foundation to make deep drilling possible. The development of oil well cementing was one of the most significant events in the history of petroleum technology. It has increased the productive life of thousands of oil wells and has thereby made available millions of barrels of oil that might otherwise have remained buried. In conjunction with increasing oil and natural gas production, concerns have also mounted in regard to the environmental impacts of these well developments on groundwater quality, public health, and climate due to subsurface gas and fluid migration. Well cementing provides structural barriers consisting of cement and casing strings, to prevent the problems ranging from gas leaks to well blowouts.

1.2 Why do we cement wells? Even during ancient drilling in China 2000 years ago, water seepage from formation was a serious problem. During brine production, dilution by

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seeping freshwater from shallow zones was a concern. Bamboo casing and primitive cement that consisted of Tung oil and lime were used to create a seal between the casing and formation. This primitive casing cementing enabled the ancient drilling for salt and gas. Casing and cementing have become very sophisticated and play many key roles in completing a well nowadays. From a well construction perspective, the roles of casing and cementing are as follows: • Casing prevents the collapse of a wellbore A well is normally drilled in stages. At the end of each stage, a casing is run into the end of the drilled section and cemented. Each subsequent casing is smaller than the previous one. The first and widest casing is called the conductor, which prevents the collapse of loose soil near the surface. The next size in the casing string is the surface casing, followed by an intermediate casing. The last type of casing, the smallest in diameter, is the production casing that is run directly into the oil and gas reservoir. Together, those casing strings serve as a major structural component of a wellbore and prevent the rock from caving into the wellbore. • Cement supports casing The annual space between casing and rock needs to be filled with cement, which secures casing after the cement sets. Once the cement has set, the sheer strength of the cement column can hold a casing string of several thousand feet in length. This is especially important for the surface casing: the cement supports the surface casing, which supports the blowout preventers (BOPs) for subsequent drilling operations. • Cemented casing provides a foundation for subsequent drilling Cementing casing provides a flow passage for drilling fluid and production fluids. It also provides a smooth borehole for deeper drilling. The friction factor between the casing interior and drill pipe is usually lower than that of the open hole and drill pipe. Therefore, the torque-and-drag issues tend to be less severe for cased hole sections. Drilling is a destructive process of rock cutting and the resulting drill string vibrations and shocks cause unavoidable damage to the drill pipe and downhole tool. Among these, bottomhole assembly (BHA) whirl is the eccentric rotation of the BHA (around a point other than its geometric center). It generates lateral displacements, shocks, and increased friction against the wellbore. The cement provides support to the casing and protects casing from shock loads. Cemented casing serves as a solid foundation for subsequent drilling.

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The ultimate goal of the casing and cementing is to provide a hydraulic seal (cement sheath) between the casing, cement, and formation, which prevents fluid communication between the zones. This objective is called zonal isolation. From a zonal isolation point of view, casing and cementing provide the following functions. 1. Water Protection Federal, state, and local governments each regulate various aspects of oil and gas operations. Drilling permits protect groundwater by mandating a casing and cementing program for each well. Hardened cementing seals off the annulus to prevent the vertical migration of formation fluids from one layer along the wellbore and polluting the fluids in another layer. Normally, surface casing and its cementing provide the primary barrier against the vertical migration of fluids into freshwater formation. 2. Circulation Loss Prevention Wells, especially deep ones, often encounter abnormally pressured formations, troublesome lost circulation zones, and incompetent shale formations. Casings, often intermediate casings, are required to drill these zones troublefree. 3. Casing Corrosion Protection Oxygenated waters, acidic waters, chemical salts, and other highly corrosive subsurface fluids can corrode the casings’ steel surface. Elevated casing temperatures accelerate the corrosion rate. The consequences of corrosion in casing include the reduction of wall thickness, overall strength, and ductility, which could eventually lead to casing failure. Cementing will effectively protect the casing from any corrosive formation fluids contacting the casings’ steel surface. 4. Blowout Prevention Zonal isolation prevents oil and gas at high pressure from escaping the formation and traveling up the wellbore. The uncontrolled release of crude oil and/or gas, called blowout, can lead to a catastrophic fire and oil spill. Cementing problems are associated with many well blowouts. Although modern wells have BOPs designed to cut through and seal the drill pipe, casing cementing is the frontline defender to prevent blowouts. In addition to providing the seal, the cement supports the casing which supports the BOPs which provide a last line of defense against blowouts. Fig. 1.2 illustrates the reasons why we cement wells.

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Fig. 1.2 Why do we cement wells? (Credit: Pegasus Vertex, Inc.).

1.3 How do we cement wells? Cementing is one of the most critical steps in the drilling and completion of an oil and gas well. With successful cementing jobs, subsequent drilling operations and well production are likely to be successful. Because cement remediation is costly, difficult, and not always successful, cementing is usually a one-shot deal. Cementing jobs in a well can either make or break the financial goals of the well. This fact makes the time spent on designing and executing a cementing job a good investment. The German philosopher Friedrich Nietzche once said: “He who has a why to live can bear almost any how.” People realized the importance of a cementing

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job and in turn, they developed a series of steps to standardize the cementing procedure. Here is how cementing engineers perform their jobs in steps. 1. Run casing into a well At predefined depths, the drill pipe is removed, and the casing is run into the wellbore. Compared to a drill pipe, a casing is a relatively thin-walled steel pipe that comes around 40 ft (13 m) long with a threaded connection at each end. Centralizers and scratchers are often installed on the outside of the casing to keep it centered and to clean the wall. A guide shoe, made of steel and concrete, is installed on the bottom joint of the casing to protect the lower edge of the casing. The tapered or bullet-nosed shape helps guide the casing through narrow, deviated hole sections. A float collar is installed near the bottom of the casing. The check-valve assembly, fixed within the float collar, prevents drilling mud or cement slurry from entering the casing when pumping is halted. It also serves as a receptacle for cement plugs. Running a casing into a wellbore is accompanied by a displacement of mud in the hole, leading to surge pressure. The accurate prediction of surge pressure is of great importance in wells, where the pressure must be maintained within narrow limits to ensure trouble-free drilling and completion operations. Another concern associated with casing running is the torque and drag loaded on the casing string. The upward frictional drag on the casing may cause casing buckling. And the torque, if the casing is rotated especially in an extended well, may twist the string or damage the liner top. 2. Condition the mud by circulating After casing running, the condition of mud clears the way for a good cementing job. It is normally recommended to circulate two-hole volumes of the drilling fluid. This conditioning cleans out cuttings or other debris, breaks up mud gels, and reduces the bottom hole temperature. 3. Pump spacer To separate drilling fluid from cement slurry and to avoid cement contamination, a spacer fluid is pumped ahead of cement slurry to wet the borehole and make the mud displacement more complete. 4. Pump cement slurry The cement and additives are mixed with water to form a cement slurry and pumped down through the casing and up in the annulus to create a desired cement column. The cement slurry is followed by the drilling or completion fluid pumped after the cement to push the cement to its planned location.

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To further prevent the drilling fluid from contaminating the cement, a 2-plug system is used. The one released ahead of cement slurry is called the bottom plug. It stops at the float collar, and pump pressure ruptures the diaphragm so that the cementing slurry can pass through it. A top plug, similar to the bottom plug but without the diaphragm, isolates the displacement fluid and cement slurry. The top plug stops on the bottom plug, and an increased pump pressure signals the completion of mud displacement. 5. Wait on cement This period, ranging from a few hours to several days, is for liquid cement slurries to solidify and develop sufficient compressive strength. Meanwhile, pipe-cement and formation-cement bonds begin to develop, ensuring the ultimate goal of zonal isolation. 6. Evaluate cement job After the cement is set, we want to confirm that the cement is in place to provide the desired performance. The first indication that the cement is in place is when cement job measurements including fluid volumes, cement density, surface pressure, and returns all match pre-job expectations. If there are any concerns with the top of cement (TOC), cement quality, or if it is required, a temperature survey or cement evaluation log should be run. A temperature survey, run several hours after cement placement, takes advantage of the heat generated by the cement column in the annulus. It is very useful to determine the location of TOC. Cement bond log (CBL) is obtained using acoustic waves sent by a transmitter and received by a receiver. The variation of the acoustic wave amplitude represents the quality of the cement bond. Variable-density log (VDL) is another method to evaluate the quality of a cement job, which presents the amplitude of acoustic waves in various shades of a greyscale to identify the cement bond quality. One of the purposes of the casing and cementing is to provide a solid foundation for subsequent drilling operations. To ensure the quality of a cementing job, it is common to pressurize inside the newly cemented casing until the pressure at the shoe reaches the maximum anticipated pressure at that depth during the next drilling operation. If the pressure declines significantly or if there are other indications of leakage, the casing should be recemented using squeeze cementing operation. Fig. 1.3 shows major casing accessories and the displacement of drilling fluid in a cement job.

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Fig. 1.3 How do we cement wells? (Credit: Pegasus Vertex, Inc.).

1.4 Avoid common cementing problems The effectiveness of zonal isolation achieved through the casing and cementing depends on the casing integrity, the quality of cement, the casing-cement bond, and the formation-cement bond. Even if the displacement process of a cementing job is a success, it does not guarantee a healthy well life. Cement sheath may fail due to vibration, temperature and pressure changes, and shock loads induced by subsequent drilling, stimulation, and production operations. Fig. 1.4 shows some common leakage pathways found around the cemented casing, together with some causes.

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Fig. 1.4 Common cementing problems. (Credit: Pegasus Vertex, Inc.).

Failure of set cement is usually attributed to contamination, either from the mixing water or drilling fluid during pumping. Water is used to wet the cement solids and create a pumpable cement slurry. Contaminants may accelerate or delay the setting of cement. Thus, the water used to mix cement should be kept as pure as possible. Besides water contamination, poor mud removal is a major factor of cement quality. When drilling fluid is displaced by another fluid, such as cement slurry inside a pipe or in an annulus, the displacing fluid sometimes flows in a channel on certain sides of the casing or wide side of the eccentric annulus and fails to rise uniformly in the annulus. This cement and mud

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channeling weakens the bond of cement to the formation and the cement to the casing. It also creates a weak cement sheath. To minimize cement channeling, a spacer or chemical wash is pumped before the cement slurry to leave the casing and formation water-wet (free of oil), preparing the wellbore for a good bond. Centralizers are strategically installed on the casing at optimal intervals to maintain a good casing standoff profile. The eccentric annulus is one of the most detrimental factors in limiting the efficiency of displacement. Without centralizers, sections of the casings in a directional well may touch the wellbore. The fluid will flow through the least resistant path on the wide annular side, leaving a mud channel on the narrow annular side. Fluids are specially designed with rheological properties. Pumping rates are carefully selected to control the bottomhole pressure and to achieve a high displacement efficiency. Often, special chemicals, called additives, are blended with dry cement or measured into the mixing water properties. Pumping to optimize properties of cement slurry such as the thickening time, density, or viscosity. Applying a rotation or reciprocation to the casing during cementing is an effective way to improve job quality. Casing movement breaks up areas of stagnant mud, which can cause cement channeling. As soon as slurry is mixed, it starts thickening. Thickening time, the duration that the cement slurry remains pumpable, is affected by downhole temperature and pressure. Of the two, the temperature has the most significant influence. As the downhole temperature increases, the cement slurry sets faster. The pumping time needs to be adjusted accordingly. Therefore, it is desired to predict the dynamic temperature profile along the wellbore during cementing by calculating the transient heat transfer between wellbore fluids and formation. Cementing is the last step in drilling operations and the first step in completion. Throughout the life of the well, the cement sheath not only supports subsequent drilling operations but also withstands the temperature and pressure changes induced by well testing, simulation, and production operations. Although we may have a good cement placement, the severe downhole condition in the late stage of completion and production may lead to cement sheath failure as shown in Fig. 1.4. It is desirable to predict cement sheath integrity using a computer model, considering various temperature and pressure changes.

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1.5 Overview of the contents The cementing operation for the production casing is a closure of drilling operations and a beginning of the production of a well for the next few decades. Therefore, cementing quality is closely related to the longevity and productivity of a well. Since the first use of cement slurry in a Union Oil Co. well in California in 1903, well cementing technology has matured and evolved, ensuring greater production and environmental protection. At the same time, well cementing has become one of the most interesting areas of research because it requires an interdisciplinary approach. Talents are desired from scientific and engineering disciplines, including chemistry, mechanical, physics, petroleum, rheology, geology, electrical engineering, and computer science. It is a team effort. Cementing engineers need to interact with different disciplines to perform jobs. Looking ahead, we see an array of new and potential technology advances, including new tools to run casing, innovative chemicals to make cement for high-temperature and high-pressure wells, fine-tuned best practices to place cement, and artificial intelligence to predict the success rates, etc. Over the past 30 years, it has been my privilege to be involved in the fascinating well cementing engineering. I had the pleasure of working with many seasoned experts, including Dr. William C. Maurer (Maurer Engineering), the late Larry Moran (ex-ConocoPhillips), Lawrence Weber (ex-Chevron), Craig Gardner (ex-Chevron), Tongyou Wang (COSL), Donald Jagpath (Tucker Energy Services), Jason Schneider (Sanjel Energy Services), and many other people who have encouraged me and showed me the ropes. My main areas of research and development include mechanical engineering and computer simulation in cementing engineering. Nevertheless, I do not claim that I am an overall cementing expert. That is why we have a team of 11 contributing authors who are experts of their fields. Collectively, these authors bring together knowledge from over 250 years of experience in cementing and condense their knowledge into this book. The purpose of this book is to provide a practical guide for both new and seasoned cementing engineering professionals. It focuses on the fundamental and applied engineering aspects of cementing operations, with some of the industry’s best practices. The structure of this book starts from casing string design to plug and abandonment. However, you can select any chapter and study it. The fact that the individual authors write different chapters makes each topic relatively independent. Readers will be able to quickly access the specific subjects.

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The introductory chapter is an overview of cementing engineering. Chapter 2 (Casing String and Design) covers casing string and casing design, which is an important part of well construction and well barrier. It covers casing types, their functions, and casing design basics. Casing equipment is a fundamental technology for successful cementing operations. Chapter 3 (Casing Equipment) focuses on the importance of casing accessories, which is often ignored or misunderstood. In reality, improper selection and utilization of casing equipment can lead to unfavorable financial, environmental, and safety consequences. This chapter provides a detailed description of the most common types of casing equipment and casing centralizers. Cementing job starts with running a casing into a hole. The challenges associated with running casing include torque and drag (e.g., buckling, casing connection damage) and surge and swab (e.g., loss of circulation, hole integrity). Chapter 4 (Casing Running) discusses these issues, methods, and tools to reduce the undesirable impacts of these challenges. Chapter 5 (Fluids) discusses how to design cementing fluids and their target properties to achieve the cementing and zonal isolation objectives. Once drilling is completed and the hole is ready to be cased and cemented, the fluid in the hole has the objective to keep well control, as a primary barrier, maintain hole stability, and finally, to have minimum properties to be removed from the wellbore and be thoroughly displaced by cementing fluids. Preflushes and spacers provide a barrier to prevent fluid contamination inside the casing and in the annular space. This chapter describes the connection between the selection of fluid properties, laboratory, and field execution to the success of the cementing operation. The success of placement of cement in the designed annular space requires fundamental knowledge and understanding of cement slurry hydraulics. Among several issues in cementing is the frictional pressure that can cause cementing job failure due to equipment rupture and loss of circulation in the wellbore. Chapter 6 (Hydraulics) provides basic knowledge of hydraulics of cement slurry which is critical to designing for safety and the success of cementing operations. Applications of the fluid rheology models are demonstrated through illustrative examples and output of computer programs. Computer-assisted design of primary cementing is the main tool for the cementing engineer to ensure the success of the zonal isolation objectives. Chapter 7 (Job Simulation and Design) shows how the design engineer can literally play various scenarios and forecast the potential outcome through software simulation. Today’s software simulation has the power to visualize

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fluid behavior behind the casing, including their intermixing and other placement consequences such as channeling and immovable mud. In this chapter, an explanation of these elements that jeopardize the validity of the model and the predicted outcome, the strategy, and methods to overcome or mitigate the effect of these elements, along with the importance of the leading role of the cementing engineer, is presented. The main parameters that affect slurry design and performance are downhole temperature and pressure, which increase with the depth of the well. As soon as we mix cement with water, the slurry starts thickening. The increased down-hole temperature reduces the thickening time of cement. Chapter 8 (Temperature Prediction) highlights the physical explanation and modeling approach of the wellbore transient heat exchange during cementing. Displacement efficiency determines cement bonding quality. Unfortunately, it is an inadequately studied area involving complicated physics. Chapter 9 (Displacement Efficiency) focuses on using and interpreting computer simulations to optimize the displacement efficiency of cementing jobs. Factors with significant influence on the job performance are examined, such as fluid rheology, density, pumping rate, casing standoff, well inclination, casing movement, and so on. Understanding these factors will help engineers design better jobs through many aspects such as selecting proper fluids, pumping schedule, centralizers, and utilizing cement equipment or tools and other strategies. Chapter 10 (Job Execution) discusses three main components to each job’s success: job preparation, wellsite execution, and post-job reporting. Each of the topics discussed in previous chapters is integrated with job execution. Job execution requires a holistic view of the service delivery. This chapter closes the link between design and execution, highlighting the significance of job preparation, planning, and on-site QA/QC to the success of the cementing operation. Chapter 11 (Job Evaluation) introduces many ways of evaluating the qualities of cementing jobs, beginning with the cement job operation itself. Job data is analyzed as the first step in determining success. After that, the well is observed to determine any obvious problems, such as annular flow. Throughout the life of the well, monitoring of the wellbore pressures will continue to evaluate zonal isolation in the wellbore. Acoustic logging is another popular way to evaluate the quality of the cement job. The purpose of the cement job evaluation is to determine if the operation successfully achieves its goal of placing cement across a given interval and achieving zonal isolation.

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Chapter 12 (Plug and Abandonment) provides basic design and equipment knowledge to the cement and drilling engineer to assist in successful zonal isolation during temporary and permanent abandonment (TA/PA) as well as remedial cementing. Legend has it that Chinese philosopher Confucius once stated 2500 years ago “I hear and I forget. I see and I remember. I do and I understand.” The aim of this book is not just about the knowledge it contains, but the understanding and application of it to the next cementing job. We sincerely hope that this book builds a pathway for those who enter the field and bridges the gap between knowledge acquisition and field application.

CHAPTER TWO

Casing string and design Jiang Wua a

Retired from Chevron, Houston, TX, United States

2.1 Casing string and design Casing string is typically hollow steel tube set and cemented in an oil and gas well to ensure safe drilling, completion, and production of the well. This chapter provides the fundamental knowledge of casing string and design to help drilling and completion engineers on the planning and operation of oil and gas well construction. The following aspects of casing string and design are discussed in this chapter: • Casing types (conductor, surface, intermediate, and production) and functions, • Casing grades (American Petroleum Institute (API) and non-API grades) and performance properties, • Casing design (casing design principle, casing strength, casing triaxial stress analysis, casing load, and casing design factor), • Casing connection (connection types, performance, evaluation, and qualification), and • Cementing quality and planning consideration in casing design (casing external pressure, top of cement (TOC) in deepwater well).

2.2 Casing types and functions 2.2.1 Casing types and functions Casing string is used in oil and gas well to ensure safe drilling, completing, and production operations, by protecting shallow fresh water zone, isolating high- or low-formation pressure, and preventing wellbore collapse, etc. Several casing strings of different sizes are set to different well depths in oil and gas well by their various functions. Fig. 2.1 shows an example of well construction with four casing strings (conductor casing, surface casing, intermediate casing, and production casing) in an oil and gas well. Conductor casing, surface casing, intermediate casing, and production casing are generally the four casing types used in an oil and gas well, with Applied Well Cementing Engineering https://doi.org/10.1016/B978-0-12-821956-0.00007-9

Copyright © 2021 Elsevier Inc. All rights reserved.

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Fig. 2.1 Example of well construction with four casing strings.

the following running sequence, application functions, and cement planning, respectively: • Conductor casing is the first casing, normally in size of 1600  2600 – Normally drive-in for on-land well or jet-in for subsea well – Used to prevent the top formation washout in deeper drilling operation – Cement to surface if the conductor would be set in a drilled hole (not drive-in, not jet-in) • Surface casing is the second casing, normally in size of 13 3/800  18 5/800 – Used to protect shallow fresh water zone from contamination by drilling mud – Also used to support wellhead and subsequent casing/tubing string weights – Cement to surface • Intermediate (protective) casing is the next casing after surface casing, normally in size of 9 5/800  1600 . More than one intermediate casing may be used in deep well application. – Used to protect weaker formations and unstable formations – Also used to isolate abnormal pressure and/or problem zones

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Cement to a depth above abnormal pressure and/or problem zones or to the surface • Production casing is the last casing, normally in size of 700  9 5/800 – Used to provide production zone isolation on corrosive fluid, reservoir fluid, and reservoir high pressure – Also used to serve as the second barrier for the well integrity to contain oil and/or gas reservoir pressure, in case of tubing failure (tubing is the smallest pipe set inside production casing to produce oil and/or gas, whose design is similar to casing but is not a subject of this chapter) – Cement to a depth at least above the productive zones or to the surface. An intermediate liner or production liner may be used, which does not extend to the wellhead (or surface) but hang above the preceding casing shoe (typically 300–500 ft. above the preceding casing shoe), like the 700 production liner illustrated in Fig. 2.2. A liner is always cemented to the liner top. In Fig. 2.2, a 3.500 tubing is also shown with a tubing packer at bottom of tubing to seal the tubing annulus.

Wellhead level

20 inch Conductor

13 5/8 inch Surface casing

7 inch Production liner hanger 9 5/8 inch Protective & Production casing 3 1/2 inch Production tubing

7 inch Production liner

Fig. 2.2 A 700 production liner in casing program.

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When a production liner is used, like the 700 liner in Fig. 2.2, the preceding casing will also serve as a production casing, as it will be exposed to the production loads in the production phase. For the 9 5/800 intermediate (protective) casing in Fig. 2.2, it is first exposed to the drilling loads when drilling the next wellbore for setting the 700 production liner, and it is then exposed to the production loads when the well is put on production. The details of drilling loads and production loads are discussed in the later sections. Conductor casing, surface casing, and intermediate casing are also called “drilling casing,” as they are exposed to drilling loads from the drilling of deeper wellbores. However, an intermediate casing may also be exposed to production loads from the production of the well, if a production liner is set below it, as discussed above. This intermediate casing will also serve as a production casing. • Drilling casing (conductor casing, surface casing, and intermediate casing): exposed to drilling loads from drilling operations • Production casing: exposed to production loads from production operations

2.2.2 Casing setting depth Different types of casings are used to set at different well depth in an oil and gas well, and casing setting depth is determined based on the casing application purposes for a safe drilling, completing, and production operation, such as protecting shallow fresh water zone, isolating wellbore pressure/ lost-circulation zone/chemical reactive zone, etc. Setting depth of production casing is generally the well target depth across reservoir formation, serving as the last casing string in a well. Setting depth of intermediate casing is basically determined based on controlling the formation pressure and avoiding formation fracturing in drilling operation. As shown in Fig. 2.3, a minimum drilling mud density profile, normally 0.5 ppg higher than the formation pore pressure gradient profile, is planned to safely control formation pressure with allowing a decrease of effective drilling mud pressure in a trip-up operation (swab); and a maximum mud density profile, normally 0.5 ppg lower than formation fracture pressure gradient profile, is also planned to safely avoid formation fracturing with allowing an increase of effective drilling mud pressure in a trip-down operation (surge). A vertical line, starting from the minimum mud density profile at the well target depth (the production casing setting depth in Fig. 2.3), or Point 1, is drawn to reach the maximum mud density

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Casing string and design

Equivalent density Conductor casing depth

Fracture gradient Surface casing depth

Depth

4

Maximum mud density (Fracture gradient minus surge margin)

Pore Pressure Gradient

Intermediate casing depth

3 2

Minimum mud density (Pore pressure gradient plus trip margin)

1

Production casing depth

Well target depth Fig. 2.3 Intermediate casing setting depth determination.

profile, or Point 2, and this point is the intermediate casing setting depth, to protect the formation above this depth from being fractured by the drilling mud density used in drilling to the well target depth (Point 1). If there will be a problem zone (lost-circulation, chemical reactive, etc.) deeper than Point 2, or if there will be a high risk on casing differential stuck in the wellbore below Point 2, the intermediate casing will need to set deeper to protect the problem zone or to reduce the risk of casing differential stuck. Casing differential stuck risk is considered high when the differential pressure between drilling mud pressure and formation pore pressure is larger than 2000– 3000 psi. This practice of controlling formation pressure and avoiding formation fracturing in drilling operation is repeated to determine the next shallower intermediate casing setting depth until the surface casing depth, which is determined by a different criterion, is reached or passed. In Fig. 2.3, this practice is repeated by drawing a vertical line, starting from

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Jiang Wu

the minimum mud density profile at the intermediate casing depth, or Point 3, to reach the maximum mud density profile, or Point 4. If this Point 4 does not reach or pass the surface casing setting depth, this is the next shallower intermediate casing setting depth; and if this Point 4 reaches or passes the surface casing setting depth, like shown in Fig. 2.3 where this Point 4 just reaches the surface casing setting depth, no more shallower intermediate casing is needed. The determination of intermediate casing setting depth by the above “Point 1 ! Point 2 ! Point 3 ! Point 4” approach is called a “bottomup” method, while a “top-down” method may also be used, to start from the maximum mud density profile at the surface casing setting depth, or Point 4, with a reversed “Point 4 ! Point 3 ! Point 2 ! Point 1” approach. The “top-down” method may result in a deeper intermediate casing setting depth and allow a higher drilling mud density to well target. This will happen when the Point 4 in Fig. 2.3 from the “bottom-up” method reaches a depth shallower than the surface casing setting depth. The “top-down” method may be used in drilling new exploration well with less confidence on reservoir pressure, so that a higher drilling mud density can be allowed in drilling to the well target for controlling possible higher reservoir pressure, though it may result in a higher drilling and casing cost. Setting depth of surface casing is normally governed by local government regulation, to set across the shallow fresh water formation zone and protect it from drilling mud contamination of chemical contents, in drilling the deeper formations below the surface casing. Setting depth of conductor casing relies on the resistance of top formation soil when it is driven into the ground, and the conductor-driving operation will be stopped when the driving rate approaches or reduces to a specified limit (number of driving blows per foot).

2.2.3 Casing size selection Casing is started with the largest diameter (conductor casing) on top in a well, and the subsequent casing sizes are progressively smaller in diameter as they must pass through the inside of the previous casing. A sufficient clearance between casing and wellbore is needed to achieve good cementing quality, and that is the basic consideration on casing size selection. Casing size selection starts with the production casing or production liner (the deepest casing string), to allow accommodation of the production tubing (the producing conduct of oil and gas from the oil and gas reservoir to

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Casing string and design

surface), and to perform any work-over/well-deepening operations. The production tubing size is determined through the production planning and optimization based on oil and gas reservoir characters, such as reservoir formation pressure and permeability, by production engineer and not by drilling engineer and therefore will not be discussed further in this chapter. Once the production casing size is determined based on the above completion and redrilling considerations, the size of the next larger casing (likely intermediate casing) can be determined based on having a sufficient casing internal diameter to allow a drill-bit to pass and drill the deeper open-hole for the production casing. The open-hole wellbore size or the drill bit size needs to be larger than the production casing connection size and have a sufficient wellbore clearance (half of the difference between wellbore size and casing external diameter) for cementing operation. The optimum wellbore clearance is 0.7500 to achieve a good cementing quality based on the previous studies, though a larger or smaller wellbore clearance may also be accepted. Note that casing and drill-bit are normally manufactured by their standard sizes, and the selection of casing and drill-bit size will then need to be based on their standard sizes, unless a special order of nonstandard sizes is needed and achievable. After the intermediate casing size is determined, the size of the next larger casing (surface casing or another intermediate casing) can be selected by the same approach till the largest casing (conductor) size is selected in a well. Table 2.1 lists two examples of commonly used casing size and drill-bit size combinations in on-land well with four casing strings. The casing and bit size combinations listed in Table 2.1 have a 0.7500 or larger wellbore clearance. Sometime, a smaller wellbore clearance may be used, for various reasons such as allowing more casing strings in a well, casing size availability, bit size limitation, or slim-hole well construction. Casing connection selection may need more attention for smaller wellbore Table 2.1 Examples of casing and drill-bit size combinations. Combination Combination 1 (in.)

Combination 2 (in.)

Conductor Drill-bit and wellbore Surface casing Drill-bit and wellbore Intermediate casing Drill-bit and wellbore Production casing

24 20 16 14 3/4 11 3/4 10 3/4 8 5/8

20 17 1/2 13 3/4 12 1/4 9 5/8 8 1/2 7

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Jiang Wu

clearance condition, and a reduced-size casing connection, instead of a fullsize casing connection, may have to be used, to reduce casing running difficulty and help achieve good cementing quality by reducing casing annulus cementing flow friction pressure and avoiding cementing leaking into a weak open formation. More information on casing connection is discussed in a later section. As casing is manufactured with a drift diameter slightly less than casing inner diameter due to casing manufacturing tolerance, it is the casing drift diameter, rather than the casing internal diameter, that needs to be equal to or larger than the next drill bit size so that the next drill bit can pass through the casing and drill the next (deeper) open hole. For example, 9 5/800 53.5# intermediate casing has casing inside diameter 8.53500 and casing special drift diameter 8.500 , which can allow a drill bit of 8 1/200 to pass through and drill the next (deeper) open-hole of 8.500 for a 700 liner, in the “Combination 1” in Table 2.1.

2.3 Casing grades and performance properties Casing is manufactured as tube joint with threaded connection at both ends, to connect casing tube joint to each other and run into oil and gas well as casing string. Casing’s abilities to resist casing loads in the wellbore (wellbore pressure and casing axial load) are called casing strengths or casing performance properties, which are related to casing grade, casing wall thickness or weight per foot, and casing size.

2.3.1 Casing grades Casing grade is a measure of casing material strength, and steel casing grades are specified by the API Spec. 5CT “Specification for Casing and Tubing” and the International Organization for Standardization (ISO) Spec. 11960 “Petroleum and Natural Gas Industries-Steel Pipes for Use as Casing or Tubing for Wells,” as the industry standards for the manufacture, testing, and inspection of the steel casing for use in oil and gas wells. The API 5CT and ISO 11960 documents are essentially the same in format and content, by an agreement between API and ISO, and should always be considered as the minimum acceptable standard when purchasing new casing. API/ISO specifications and proprietary mills’ specifications are also available on corrosive resistance alloy (CRA) casing grades for use in severely corrosive well environment, but they are not in the scope of this Chapter. API 5CT/ISO 11960 specifies the following steel casing grades (API casing grades), as listed in Table 2.2, with the specified minimum material yield

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Casing string and design

Table 2.2 API Casing Grades (API 5CT/ISO11960). Yield strength (ksi)

Tensile strength (ksi)

Group

Grade

min

max

min

1

H40 J55 K55 N80 R95 M65 L80 C90 T95 C100 P110 Q125

40 55 55 80 95 65 80 90 95 110 110 125

80 80 80 110 110 85 95 105 110 120 140 150

60 75 95 100 105 85 95 100 105 115 125 135

2

3 4

strength, maximum material yield strength, and minimum material tensile strength in ksi. API casing grade designation is by “a letter + a number,” such as K55, where the letter helps to differentiate the grade’s chemical requirements, and the number designates the minimum yield strength of casing grade material in ksi units. For example, K55 grade has a minimum yield strength of 55 ksi and has no particular chemical component requirement. The higher the casing material minimum yield strength, the stronger the casing material to resist casing loading. However, casing material with high yield strength may have higher potential risk on material cracking under certain application environments to cause casing failure as discussed below. Not all API casing grades are allowed to use in sour service environment (H2S 0.05 psi) on all temperature, in order to avoid casing premature cracking failure in sour service environment. The National Association of Corrosion Engineers (NACE) has specified the environmental condition (H2S partial pressure and temperature) where the API casing grades can be used for sour service (H2S 0.05 psi), as listed in Table 2.3. N80, R95, C110/P110, and Q125 are generally not acceptable for use in sour service, unless above certain elevated temperatures. 2.3.1.1 Non-API casing grades Casing grade of 140 (140 ksi minimum yield strength) or higher are non-API grades, and are available through some casing manufacturers. Generally, the higher the casing material yield strength, the higher risk the casing material is sensible to cracking failure. Therefore, although casing of those non-API

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Jiang Wu

Table 2.3 API casing grades for use in sour service environment (NACE MR0175). For all temperatures For ≥65°C (150°F) For ≥80°C (175°F) For ≥107°C (225°F)

H40 J55 K55 M65 L80 type 1 C90 type 1 T95 type 1

N80 type Q R95 C100

N80 P110

Q125

Temperatures given are minimum allowable service temperatures with respect to SSC.

casing grades (140 ksi or higher) may provide high resistance to casing loads, they generally need to be evaluated for suitability or cracking sensitivity to the application environment, to prevent a casing premature cracking failure due to their environment sensitivity (including but not limiting to sour environment).

2.3.2 Casing performance properties Casing performance properties are the measures of casing strengths or casing abilities to resist the exposed loads and avoid casing failures. API 5C3 “Calculating Performance Properties of Pipe Used as Casing or Tubing” and its ISO version of ISO 10400 “Formulae and calculations for the properties of casing” have specified the following casing performance properties or casing strengths on casing burst, collapse, tension failure modes: • Casing burst: casing failure under high internal pressure • Casing collapse: casing failure under high external pressure • Casing tension-parted: casing failure under high tension load 2.3.2.1 API casing burst strength (API historical) Casing burst strength (Pb) is defined in API 5C3/ISO 10400 as the maximum internal pressure necessary to start yielding of casing material under internal pressure when the external pressure is zero (also without axial load):
 2YP t Pb ¼ 0:875 (2.1) D where D: casing outside diameter, in. t: casing wall thickness, in. Yp: Specified minimum yield strength of API casing material grade, psi

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Casing string and design

The factor of 0.875 is used to consider the API casing wall thickness tolerance 12.5%, or API casing minimum wall thickness 0.875t. This equation is an approximation of casing material yield at the inner diameter fiber under internal pressure only. The more actuate prediction of casing yield under combined loads, including internal pressure, external pressure, and axial load, will need a triaxial stress analysis, and will be discussed later. A casing rupture strength is also documented in the current API 5C3/ ISO 10400 documents, giving a higher internal pressure necessary to start to rupture (beyond yield) casing, but it may have an application environment limitation, i.e., may not be valid for use in sour service environment, and will not be discussed further in this chapter. 2.3.2.2 API casing collapse strength (API historical) Casing collapse strength (Pc) is defined in API 5C3/ISO 10400 as the maximum external pressure necessary to collapse the casing when the internal pressure is zero (also without axial load). The following four casing collapse strength formulas are developed in API 5C3/ISO 10400 through theoretical derivation and statistical analysis of full-size casing collapse data. Casing collapse strength will be determined by one of the formulas according to casing grade and the value of casing OD-to-wall thickness ratio (D/t), as listed in Fig. 2.4, due to the complicated casing collapse mechanism, which can vary from casing stability loss (elastic collapse, Eq. 2.2) to casing yielding (yield strength collapse, Eq. 2.5): 1. Elastic collapse formula, Pe Pe ¼

46:95  106
2 D D 1 t t

(2.2)

2. Transition collapse formula, Pt 2

3

7 6 F 7
 P t ¼ Yp 6  G 5 4 D t

(2.3)

2. API transition collapse pressure formula range

1. API elastic collapse pressure formula range Grade H-40 J-K-55 N-L-80 C-90 C-95 P-110 Q-125

D/t Range 42.64 and greater 37.21 and greater 31.02 and greater 29.18 and greater 28.36 and greater 26.22 and greater 24.46 and greater

P6 =

46.95*106 D D t

2

–1

t

4. API yield collapse pressure formula range Grade H-40 J-K-55 N-L-80 C-90 C-95 P-110 Q-125

D/t Range 16.40 and less 14.81 and less 13.38 and less 13.01 and less 12.85 and less 12.44 and less 12.11 and less

D/t Range 16.40 to 42.64 14.81 to 37.21 13.38 to 31.02 13.01 to 29.18 12.85 to 28.36 12.44 to 26.22 12.11 to 24.46

F 2.063 1.989 1.998 2.017 2.029 2.053 2.092

G 0.0325 0.036 0.0434 0.0466 0.0482 0.0515 0.0565

Pt = Yp

F –G D t

2. API plastic collapse pressure formula range

D Pyp = 2Yp

Grade H-40 J-K-55 N-L-80 C-90 C-95 P-110 Q-125

–1

t D t

2

Grade H-40 J-K-55 N-L-80 C-90 C-95 P-110 Q-125

D/t Range 16.40~27.01 14.81~25.01 13.38~22.47 13.01~21.69 12.85~21.33 12.44~20.41 12.11~19.63

Fig. 2.4 API casing collapse formula and D/t ranges (API 5C3/ISO 10400).

A 2.95 2.991 3.071 3.106 3.124 3.181 3.239

B 0.0465 0.0541 0.0667 0.0718 0.0743 0.0819 0.0895

C 754 1206 1955 2254 2404 2852 3301

Pp = Yp

A –B –C D t

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Casing string and design

3. Plastic collapse formula, Pp 2

3

6 A 7 7C
 Pp ¼ Yp 6  B 4 D 5 t

(2.4)

4. Yield collapse formula, Pyp 3 D 6 17 7 6 Pyp ¼ 2Yp 6
t 2 7 4 D 5 2

(2.5)

t Therefore, API casing collapse strength (Pc, Eq. 2.6) will be calculated by one of the above four equations based on casing grade and D/t ratio:   (2.6) Pc ¼ Pe , Pt , Pp , or Pyp , by casing grade and D=t ratio The empirical constants of A, B, C, F, and G used in Eqs. (2.3), (2.4) and listed in the Fig. 2.4 are from the statistical analysis of the full-size casing collapse test data under zero axial load and zero internal pressure. When the axial load and internal pressure are present, the above casing collapse strength will be modified based on the triaxial stress analysis and will be discussed later. A new casing collapse strength that incorporates with casing ovality, eccentricity, and residual stress is also documented in the current API 5C3/ISO 10400, likely giving a higher collapse strength, but it has to be based on further statistical analysis of sufficient measurement data on casing ovality, eccentricity, and residual stress, and will not be further discussed in this chapter. 2.3.2.3 API casing tension strength Casing tension strength (Ty) is simply defined in API 5C3/ISO 10400 as the maximum axial tension load necessary to yield the casing under axial tension when the internal pressure and external pressure are zero. Ty ¼

 πYP  2 D  d2 4

(2.7)

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Jiang Wu

where d: casing inside diameter, in. Example calculation of casing strength: What is the API casing burst, collapse, and tension strength on 9 5/800 53.5 lb./ft. (t ¼ 0.54500 ) L80 casing? • API casing burst strength (Eq. 2.1, API historical): Pb ¼ 0.875  (2  80,000  0.545)/9.625 ¼ 7927 psi • API casing collapse strength (Eq. 2.6, API historical): D/t ¼ 9.625/ 0.545 ¼ 17.66 ! Plastic collapse on L80 grade by Fig. 2.4 Pp ¼ 80;000  ð3:071=17:66  0:0667Þ  1955 ¼ 6620psi • API casing tension strength (Eq. 2.7): Ty ¼ 3.14159  80,000  (9.6252 – 8.5352)/4 ¼ 1,243,718 lb. 2.3.2.4 Non-API casing performance properties Some casing manufacturers or mills may produce proprietary casing (nonAPI casing), such as high collapse casing and high burst casing, with higher performance properties than API casing with same grade and same weight. The proprietary casing (non-API casing) may be accepted and used in a well application, as long as the higher performance properties are confirmed or verified with sufficient inspection and test data. (1) High burst casing High burst casing is generally manufactured by tightening the casing wall thickness tolerance to be better than API’s casing wall thickness tolerance of 12.5% (by API 5CT), such as an improved wall thickness tolerance of 10%. It may also involve with lifting casing grade material minimum yield strength slightly above API’s casing grade material minimum yield strength. High burst casing may be accepted and used in a well application, when these stricter casing manufacture practices are confirmed through sufficient inspection and test data. An example of high burst (high performance) casing of 9 5/800 53.5# L80HP from a US casing manufacture has a casing burst strength (internal yield) of 8420 psi, higher than the corresponding API 9 5/800 53.5# L80 casing burst strength (internal yield) of 7930 psi, as listed in Table 2.4. (2) High collapse casing Similarly, high collapse casing is manufactured by controlling casing ovality, eccentricity, and residual stress, which are not specified and controlled by API 5CT (API Casing manufacturing specification). It may also involve with lifting casing grade material minimum yield strength slightly above API’s

Table 2.4 Performance properties of high-burst casing and high-collapse casing. Dimensional and grade designators Collapse resistance

Internal yield API Historical

Lame’—Von Mises

OD size

Pipe body

Threaded and coupled

Open end

Capped end

psi

STC LTC psi psi

psi

psi

in.

Weight

NOM wall

T&C PE lb./ft. lb./ft. in.

NOM ID

API drift

Alternate drift

Product

in.

in.

in.

Grade

9 5/8 53.50 52.90 9 5/8 53.50 52.90

0.545 0.545

8.535 8.379 8.535 8.379

8.500 8.500

9 5/8 53.50 52.90

0.545

8.535 8.379

8.457

9 5/8 53.50 52.90 9 5/8 53.50 52.90

0.545 0.545

8.535 8.379 8.535 8.379

8.500 8.500

9 5/8 53.50 52.90

0.545

8.535 8.379

8.457

L80 L80 HC L80 HP N80 N80 HC N80 HP

psi

BTC psi

6620 7510

7930 7930

– –

7930 7930 7930 7930

7880 7880

8680 8680

8000

8420

–

8420 8420

8370

9220

6620 7800

7930 7930

– –

7930 7930 7930 7930

7880 7880

8680 8680

8480

9420

–

9420 8830

9360

10,310

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Jiang Wu

casing grade material minimum yield strength. High collapse casing may be accepted and used in a well application, when these stricter casing manufacturing practices are confirmed by sufficient inspection and test data. An example of a high collapse casing of 9 5/800 53.5# L80HC from a US casing manufacture has a casing collapse strength (collapse resistance) of 7510 psi, higher than the corresponding API 9 5/800 53.5# L80 casing collapse strength (collapse resistance) of 6620 psi, as listed in Table 2.4. It may also be noticed in the Table 2.4, 9 5/800 53.5# L80HP (highperformance) casing from the same US casing manufacture has an even higher collapse strength (collapse resistance) of 8000 psi. This is likely because the high-performance casing (9 5/800 53.5# L80HP) is manufactured with a tighter wall thickness tolerance (casing wall thickness tolerance 1). In contrast to other non-Newtonian fluids, apparent viscosity of the dilatant fluids increases with an increasing shear rate. Because this shearthickening property is not desirable in the drilling and completion operations, the dilatant fluids are not purposely used as drilling fluids. However,

257

Cementing hydraulics

sometimes pseudoplastic fluids become dilatant fluids when a significant amount of starch-like additives, such as carboxymethyl cellulose, are added to the system.

6.2 Hydraulics models Hydraulics models define the relationship between flow rate and pressure drop for a given geometry of flow conduit and fluid properties. These hydraulics models have been established for all types of Newtonian and Non-Newtonian fluids based on their rheological models. In the well cementing processes, the pressure components are hydrostatic pressure and frictional pressure. For most completion fluids and cement slurries are considered to be incompressible, the hydrostatic and frictional pressure components are independent, making it easy to perform pressure calculations. One of the major issues in cementing hydraulics is the prediction of bottom-hole pressure (BHP) to compare with formation breakdown (fracturing) for preventing the loss of circulation. This pressure prediction involves the calculations of hydrostatic pressure at the bottom hole and frictional pressure loss in the annulus. Another major issue is the prediction of cement slurry injection pressure to compare with the pressure rating of surface equipment for preventing the equipment rupture. This pressure prediction is essentially the calculations of the total frictional pressure loss and hydrostatic pressure differences due to the density variation of fluids.

6.2.1 Hydrostatic pressure Hydrostatic pressure is defined as the weight of a column of fluid per unit area supporting the weight. In the US oil-field units, it is expressed as ph ¼ 0:052ρf H,

(6.5)

where ph is the hydrostatic pressure in psi, ρf is the weight of fluid in ppg, and H is the column height in ft. The column height is usually the change in vertical depth.

6.2.2 Friction pressure Friction pressure is defined as the pressure loss due to flow friction over a length of flow conduit. This pressure component depends upon the flow regime (laminar or turbulent flow), flow rate, conduit geometry, and fluid

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Boyun Guo

properties. The general procedure for calculating the frictional pressure loss is as follows: 1. Calculate the critical Reynolds number based on the fluid type and properties. 2. Calculate the fluid velocity at the point of interest. 3. Calculate the Reynolds number and determine the flow regime (laminar or turbulent flow). 4. Calculate the pressure loss based on theological model and flow regime. This section is divided into two subsections describing the identification of flow regimes and calculation of frictional pressure loss. 6.2.2.1 Flow regimes Flow regimes commonly encountered in well cementing are laminar flow, turbulent flow, and transitional flow. In laminar flow, the fluid behaves as a series of parallel layers moving at a uniform or near-uniform velocity. There is no large-scale movement of the fluid particles between the layers. The fluid layers nearest the center of the pipe or annulus generally move faster than the layers adjacent to the casing wall or wellbore. Turbulent flow is characterized by velocity fluctuations among the fluid stream particles, both parallel and axial to the mean flow stream. These fluctuations break down the boundaries between the fluid layers, resulting in a chaotic flow pattern. Transitional flow exhibits characteristics of both laminar and turbulent regimes. It describes the often hard-to-define region where flow is neither completely laminar nor completely turbulent. Also reported in literature is an additional fluid regime called plug flow. It describes the low-velocity, sublaminar condition of a fluid moving as a homogeneous, relatively undisturbed body. This flow regime has not been found to be dominant in today’s well cementing conditions except in very large holes. Turbulent flow of cement slurry is desirable in well cementing because it promotes the efficiency of cement displacement to drilling fluids. Identification of flow regimes requires Reynolds number analysis for the type of fluid involved. Newtonian fluids

For Newtonian fluids inside the pipe, the Reynolds number is defined as NRe ¼ where ρ ¼ fluid density, kg/m3 d ¼ inside diameter of the pipe, m

ρvd , μ

(6.6)

259

Cementing hydraulics

μ ¼ fluid viscosity, Pa s. and v¼

q , 0:7854d2

(6.7)

where v ¼ average flow velocity, m/s q ¼ flow rate, m3/s For annular flow, the Reynolds number becomes NRe ¼ 0:816 

ρvðd2  d1 Þ , μ

(6.8)

where d2 ¼ hole or casing diameter, m d1 ¼ outside diameter of pipe, m and v¼

q : 0:7854ðd22  d12 Þ

(6.9)

The term 0.816(d2  d1) in Eq. (6.8) is the equivalent circular diameter of a slot representation of the annulus (Bourgoyne et al., 1986). In the US field units (where ρ is given in ppg, v in ft/s, q in gpm, d, d1, and d2 in in. and μ in cP), Eqs. (6.6) through (6.9), respectively, become: NRe ¼ 928 

ρvd μ

q 2:448d 2 ρvðd2  d1 Þ NRe ¼ 757  μ q v¼ 2:448ðd22  d12 Þ v¼

(6.10) (6.11) (6.12) (6.13)

As a general guideline, Reynolds numbers of less than 2100 indicate laminar flow, while Reynolds numbers greater than 4000 indicate complete turbulent flow. Between these values, the flow is considered transitional. Unfortunately, determining flow regimes is seldom this straightforward. Laminar flow has been observed under controlled conditions for Reynolds numbers as low as 1200 and as high as 40,000 (Bourgoyne et al., 1986), although we do not usually encounter such extremes in cementing operations.

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Boyun Guo

Illustrative Example 6.1. A 10.5 ppg Newtonian completion fluid with a viscosity of 10 cP is circulating at 500 gpm in an 8 ¾-in. diameter wellbore. Determine the flow regime inside a 5 ½-in. OD, 17 lb/ft casing (4.892-in. ID), and in the casing/hole annulus. Solution Inside the casing: v¼

500 ¼ 8:53ft=s 2:448ð4:892Þ2

NRe ¼ 928

ð10:5Þð8:53Þð4:892Þ ¼ 40, 683 10

Because NRe > 4000, complete turbulent flow exists inside the casing. Annulus: v¼

500 ¼ 4:41ft=s 2:448ð8:752  5:52 Þ

NRe ¼ 757

ð10:5Þð4:41Þð8:75  5:5Þ ¼ 11, 393 10

BecauseNRe > 4000, complete turbulent flow exists in the annular space. Bingham plastic fluids

For Bingham plastic fluids, the equations for the Newtonian fluids need to be modified by defining an apparent viscosity to account for the plastic viscosity and yield point. For pipe flow, the definition is 6:66τy d : v

(6.14)

5τy ðd2  d1 Þ : v

(6.15)

μa ¼ μp + For annular flow, the definition is μa ¼ μp +

Eqs. (6.14) and (6.15) are valid for the US field units. When expressed in SI units, the constant 6.66 becomes 0.1669 and 5 becomes 0.1253. Thus for Bingham plastic fluids, Eqs. (6.6), (6.8), (6.10), and (6.12), respectively, become NRe ¼

ρvd μa

(6.16)

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Cementing hydraulics

NRe ¼ 0:816 

ρvðd2  d1 Þ μa ρvd μa

(6.18)

ρvðd2  d1 Þ μa

(6.19)

NRe ¼ 928 

NRe ¼ 757 

(6.17)

Using these equations, the criterion for turbulent flow is the same as for Newtonian fluids, with laminar flow occurring below a Reynolds number of 2100. Illustrative Example 6.2. A 10.5 ppg Bingham plastic drilling fluid with a plastic viscosity of 20 cP and yield point of 5 lb/100 ft2 is circulating at 500 gpm in an 8 ¾-in. diameter wellbore. Determine the flow regime inside a 5 ½-in. OD, 17 lb/ft casing (4.892-in. ID), and in the casing/hole annulus. Solution Inside the casing: v¼

500 ¼ 8:53ft=s 2:448  ð4:892Þ2

6:66  5  4:892 ¼ 39:09cP 8:53 10:5  8:53  4:892 NRe ¼ 928  ¼ 10, 408 39:09 μa ¼ 20 +

Because NRe > 4000, a complete turbulent flow exists inside the drill pipe. Annulus: v¼

500 ¼ 4:41ft=s 2:448  ð8:752  5:52 Þ

5  5  ð8:75  5:5Þ ¼ 38:42cP 4:41 10:5  4:41  ð8:75  5:5Þ ¼ 2965 NRe ¼ 757  38:42 μa ¼ 20 +

Because NRe > 2100, turbulent flow is expected in the annular space.

262

Boyun Guo

Power-law fluids

The concept of apparent viscosity can also be used for power-law fluids for Reynolds number calculations. Eqs. (6.14) and (6.15), respectively, become
 Kdð1nÞ 3 + 1=n n μa ¼ 96vð1nÞ 0:0416

(6.20)


 K ðd2  d1 Þð1nÞ 2 + 1=n n μa ¼ 0:0208 144vð1nÞ

(6.21)

If Dodge and Metzner’s (1959) correlation is used, the Reynolds number for pipe flow and annular flow can be, respectively, expressed in the US field units as
 ρv2n 0:0416d n NRe ¼ 89,100 (6.22) 3 + 1=n K and   ρv2n 0:0208ðd2  d1 Þ n NRe ¼ 109,000 2 + 1=n K When expressed in SI units, these two equations become
 ρð3:281vÞ2n 1:638d n NRe ¼ 743:5 3 + 1=n K

(6.23)

(6.24)

and NRe ¼ 909:5

  ρð3:281vÞ2n 0:819ðd2  d1 Þ n 2 + 1=n K

(6.25)

The turbulence criterion for power-law fluids is based on a critical Reynolds number (NRec), which depends upon the value of the flow behavior index. A simple correlation for estimating the critical Reynolds number at the upper limit of laminar flow is NRec ¼ 3470  1370n

(6.26)

For the region between transitional and turbulent flow, the critical Reynolds number is NRec ¼ 4270  1370n

(6.27)

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Cementing hydraulics

Illustrative Example 6.3. A 15.5 ppg power-law cement slurry with a consistency index of 20 cP equivalent and flow behavior index of 0.8 is circulating at 500 gpm in an 8 ¾-in. diameter wellbore. Determine the flow regime inside a 5 ½-in. OD, 17 lb/ft casing (3.826-in. ID), and in the casing/hole annulus. Solution Inside the drill pipe: NRecLam ¼ 3470  1370  0:8 ¼ 2374 NRecTur ¼ 4270  1370  0:8 ¼ 3174 500 v¼ ¼ 8:53ft=s 2:448  ð4:892Þ2   10:5  8:53ð20:8Þ 0:0416  4:892 0:8  ¼ 53, 903 NRe ¼ 89,100  3 + 1=0:8 20 Since NRe > 3174, turbulent flow exists inside the drill pipe. Annulus: 500 ¼ 4:41ft=s 2:448  ð8:752  5:52 Þ   10:5  4:41ð20:8Þ 0:0208  ð8:75  5:5Þ 0:8 NRe ¼ 109,000  ¼ 15, 325  2 + 1=0:8 20 v¼

Because NRe > 3174, turbulent flow exists in the annular space. Herschel-Bulkley fluids

For Herschel-Bulkley fluids, the Reynolds number can be calculated using the following equations in US field units. Inside the casing:
n 3 d 7:48ρv 7 2ð3n + 1Þ 6 24 6
n
n 7 NRe ¼ 4 d 3n + 1 5 n τy + 0:0021K 24v nC c 2

ð2nÞ

(6.28)

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Boyun Guo

In the annulus: 3  d2  d1 n 7:48ρv 7 4ð2n + 1Þ 6 24 7 6

  NRe ¼ 7, 6 4 d2  d1 n 2ð2n + 1Þ n 5 n τy + 0:0021K nC ∗a 24v 2




ð2nÞ

where the constants Cc and C∗a are expressed below, respectively,
 τ 1 " y #n Cc ¼ 1  2n + 1 0:0022ð3n + 1Þq τy + 0:0021K nπ ðd=24Þ3

(6.29)

(6.30)

and Ca∗ ¼ 1 




 1 n+1

τy

(

0:0044qð2n + 1Þ τy + 0:0021K   nπ ½ðd2 =24Þ  ðd1 =24Þ ðd2 =24Þ2  ðd1 =24Þ2

)n (6.31)

The critical Reynolds number NRec inside the casing and in the annulus can be estimated, respectively, as   4ð3n + 1Þ 1 1z (6.32) NRec ¼ ny and 

8ð2n + 1Þ NRec ¼ ny



1 1z

(6.33)

where log ðnÞ + 3:93 50 1:75  log ðnÞ z¼ 7 y¼

(6.34) (6.35)

The critical Reynolds number (NRec) is the criterion for the determination of flow regime. The flow becomes turbulent once over the critical Reynolds number; otherwise, it is laminar flow. Illustrative Example 6.4. A 10.5 ppg Herschel-Bulkley fluid with a consistency index of 20 cP equivalent, flow behavior index of 0.8, and yield stress of 5 lb/100 ft2 is circulating at 500 gpm in an 8 ¾-in. diameter

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Cementing hydraulics

wellbore. Determine the flow regime inside a 5 ½-in. OD, 17 lb/ft casing (4.892-in. ID), and in the casing/hole annulus. Solution log ð0:8Þ + 3:93 y¼ ¼ 0:077 50 1:75  log ð0:8Þ ¼ 0:26 z¼ 7 Inside the casing: 500 ¼ 8:53ft=s 2:448ð4:892Þ2   1 4ð3ð0:8Þ + 1Þ 10:26 NRec ¼ ¼ 1537 ð0:8Þð0:077Þ
 1 5 Cc ¼ 1  " #0:8 ¼ 0:75 2ð0:8Þ + 1 0:0022ð3ð0:8Þ + 1ð500Þ 5 + ð0:0021Þð20Þ ð0:8Þð3:14Þð4:892=24Þ3 2 3
0:8 ð20:8Þ 7:892 7:48ð10:5Þð8:53Þ 7 2ð3ð0:8Þ + 1Þ 6 24 6 7 NRe ¼ 6

 7 ¼ 5827 4 0:8 4:892 0:8 3ð0:8Þ + 1 0:8 5 5 + 0:0021ð20Þ 24ð8:53Þ ð0:8Þð0:75Þ v¼

Because NRe > 1537, turbulent flow is expected inside the casing. Annulus: v¼

Ca∗ ¼ 1 




 1 0:8 + 1

500  ¼ 4:41 ft=s 2:448 8:752  5:52

" # 1 8ð2ð0:8Þ + 1Þ 10:26 NRec ¼ ¼ 2737 ð0:8Þð0:077Þ (

5

0:0044ð500Þð2ð0:8Þ + 1Þ 5 + 0:0021ð20Þ   ð0:8Þð3:14Þ½ð8:75=24Þ  ð5:5=24Þ ð8:75=24Þ2  ð5:5=24Þ2 2 3
0:8 8:75  5:5 6 7 7:48ð10:5Þð4:41Þð20:8Þ 6 7 4ð2ð0:8Þ + 1Þ 6 7 24 6 7 ¼ 2140 NRe ¼ ! ! 6 0:8 0:8 7 0:8 4 8:75  5:5 5 2ð2ð0:8Þ + 1 5 + 0:0021ð20Þ ð0:8Þ0:65 24ð4:41Þ

)0:8 ¼ 0:65

Because NRe < 2737, laminar flow is predicted in the annular space.

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6.2.2.2 Frictional pressure loss Frictional pressure loss of fluid in conduit depends upon the type of fluid and flow regime. Different flow equations have been used in the industry to calculate pressure losses inside the casing and in the annuli. Based on Fanning equation (Bourgoyne et al., 1986), the gradient of frictional pressure drop in a conduit is expressed as: dpf f ρf v2 ¼ dL 25:8d

(6.36)

where pf ¼ frictional pressure, psi or kPa L ¼ pipe length, ft or m f ¼ Fanning friction factor, dimensionless. v ¼ the average velocity, ft/s or m/s d ¼ equivalent pipe inner diameter, in. or m. The constant 25.8 in the US units is 519 in the SI units. In laminar flow, the friction factor f relates to Reynolds number NRe by f ¼ N16Re . In turbulent flow, the friction factor is a function of Reynolds Number and the relative roughness of conduit wall. The relative roughness is defined as the ratio of the absolute roughness to the pipe diameter where the absolute roughness represents the average depth of pipe wall irregularities. Table 6.1 shows the absolute roughness of some pipe surfaces. Several empirical correlations for the determination of friction factor for fully developed turbulent flow in circular pipe have been presented, including those by Colebrook (1938):
 1 δ 1:255 pffiffiffi pffiffiffi ¼ 4 log 0:269 + (6.37) d NRe f f Table 6.1 Absolute roughness of some pipe surfaces. Absolute roughness Type of pipe

(in.)

(mm)

Riveted steel Concrete Cast iron Galvanized iron Asphalted cast iron Commercial steel Drawn tubing

0.00025–0.0025 0.000083–0.00083 0.000071 0.000042 0.000033 0.000013 0.0000004

0.00635–0.0635 0.0021–0.021 0.0018034 0.0010668 0.0008382 0.0003302 0.00001016

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Cementing hydraulics

where the Reynolds number is defined as NRe ¼

928ρf vd μ

(6.38)

The constant 928 in the US units is 1 in the SI units. The δ is the absolute roughness of the pipe surface in in. or m. The selection of an appropriate absolute roughness for a given application is often difficult. Fortunately, in cementing applications involving the use of relatively viscous completion fluids and cement slurries, for most casing strings, the relative roughness is usually less than 0.0004 in all sections. For these conditions, the friction factor for a smooth pipe can be applied for most cementing calculations:  pffiffiffi 1 pffiffiffi ¼ 4 log NRe f  0:395 f

(6.39)

For smooth pipes, the Colebrook’s (1938) friction factor function degenerates to Blasius’ (1913) equation: f¼

0:0791 0:25 NRe

(6.40)

However, the wall of an open hole is not considered as smooth. Its roughness varies from 0.05 to 0.3 in. depending upon the types of drill bit used. Frictional pressure loss calculations for the open hole section of annulus should consider both the roughness of casing wall and borehole wall. Wall-surface area-weighted average roughness can be used in rigorous calculations. Chen’s (1979) correlation for rough pipes has an explicit form and gives a similar accuracy to Colebrook-White equation (Gregory and Fogarasi, 1985), which was employed for generating the friction factor chart widely used in the petroleum industry. Chen’s correlation takes the following form: (

" #)!2
 ε 5:0452 ε1:1098 7:149 0:8981 f ¼ 4log log  + 3:7065 NRe NRe 2:8257 (6.41) where the relative roughness is defined as ε ¼ dδ.

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Boyun Guo

Newtonian fluids

If the friction factor in Eq. (6.36) is replaced by f ¼ N16Re , the frictional pressure loss under laminar flow inside the casing and in the annulus can be estimated using the following approximate equations, respectively: μv ΔL 1500d 2 μv ΔL Δpf ¼ 1000ðd2  d1 Þ2 Δpf ¼

(6.42) (6.43)

where Δpf ¼ pressure loss, psi or kPa ΔL ¼ length of conduit, ft or m. These two equations are valid in the US field units. When expressed in SI units, the constant 1500 becomes 0.0313 and 1000 becomes 0.0209. Use of Chen’s friction factor correlation allows for an accurate prediction of frictional pressure loss in turbulent flow. However, in many cases, use of Blasius’ correlation gives a result that is accurate enough for frictional pressure calculations. Substituting Eq. (6.40) into Eq. (6.36) and rearranging the latter yields the pressure loss expressions for inside the casing and in the annulus, respectively, as follows: ρ0:75 v1:75 μ0:25 ΔL 1800d1:25

(6.44)

ρ0:75 v1:75 μ0:25 ΔL 1396ðd2  d1 Þ1:25

(6.45)

Δpf ¼ and Δpf ¼

These two equations are valid in the US field units. When expressed in SI units, the constant 1800 becomes 631.8 and 1396 becomes 490. Illustrative Example 6.5. A 10.5 ppg Newtonian completion fluid with a viscosity of 10 cP is pumped at 500 gpm down a 10,000 ft, 5 ½-in. OD, and 17 lb/ft casing (4.892-in. ID). Predict the frictional pressure loss. Solution 500 v¼ ¼ 8:53ft=s 2:448ð4:892Þ2 ð10:5Þð8:53Þð4:892Þ ¼ 40, 683 NRe ¼ 928 10

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Cementing hydraulics

BecauseNRe > 4000, complete turbulent flow is expected inside the casing. Eq. (6.44) gives Δpf ¼

10:50:75 8:531:75 100:25 ð10, 000Þ ¼ 338psi ð1800Þ4:8921:25

Bingham plastic fluids

For Bingham plastic fluids, the pressure loss under laminar flow inside the casing and in the annulus, respectively, can be estimated using the following equations:  μv τy p Δpf ¼ + ΔL (6.46) 1500d 2 225d and

"

# τy ΔL + Δpf ¼ 1000ðd2  d1 Þ2 200ðd2  d1 Þ μp v

(6.47)

These two equations are valid in the US field units. When expressed in SI units, the constants 1500, 225, 1000, and 200 become 31.33, 187.5, 20.88, and 166.7, respectively. The pressure loss under turbulent flow inside the casing and in the annulus can be estimated using the following equations: Δpf ¼

ρ0:75 v1:75 μ0:25 p 1800d1:25

ΔL

(6.48)

and Δpf ¼

ρ0:75 v1:75 μ0:25 p 1396ðd2  d1 Þ1:25

ΔL

(6.49)

respectively. These two equations are valid in the US field units. When expressed in SI units, the constant 1800 becomes 6320 and 1396 becomes 4901. The apparent viscosity is defined as μa ¼ μp +

5τy ðd2  d1 Þ v

(6.50)

Illustrative Example 6.6. A 10.5 ppg Bingham plastic drilling fluid with a plastic viscosity of 20 cP and yield point of 5 lb/100 ft2 is displaced by a

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Boyun Guo

cement slurry at 500 gpm in an 8 ¾-in. diameter wellbore outside a 5 ½-in. OD, 17 lb/ft casing (4.892-in. ID) at a depth of 9000 ft. Predict the frictional pressure loss in the annulus. Solution 500 v¼ ¼ 4:41ft=s 2:448  ð8:752  5:52 Þ 5  5  ð8:75  5:5Þ ¼ 38:42cP μa ¼ 20 + 4:41 10:5  4:41  ð8:75  5:5Þ ¼ 2965 NRe ¼ 757  38:42 Because NRe > 2100, turbulent flow is expected in the annular space. Eq. (6.49) gives Δpf ¼

10:50:75 4:411:75 38:420:25 9000 ¼ 288psi: 1396ð8:75  5:5Þ1:25

Power-law fluids

For power-law fluids, the pressure loss under laminar flow inside the casing and in the annulus, respectively, can be estimated using the following equations: 

 96v 3n + 1 n K Δpf ¼ ΔL (6.51) d 4n 300d and


Δpf ¼

144v d2  d1




 2n + 1 n K ΔL 3n 300ðd2  d1 Þ

(6.52)

Eqs. (6.51) and (6.52) are valid in the US field units. When expressed in SI units, they take the following form 

 8v 3n + 1 n K Δpf ¼ 0:0019152 ΔL (6.53) d 4n d and



 12v 2n + 1 n K ΔL Δpf ¼ 0:0019152 d2  d1 3n ðd2  d1 Þ

(6.54)

There is no simple correlation found to estimate friction factor for pressure loss under turbulent flow of power-law fluids. Therefore the original form of

271

Cementing hydraulics

friction loss equation has to be used. The following equations are employed for the pipe flow and annular flow, respectively f ρv2 ΔL 25:8d

(6.55)

f ρv2 ΔL: 21:1ðd2  d1 Þ

(6.56)

Δpf ¼ and Δpf ¼

Illustrative Example 6.7. A 16 ppg power-law cement slurry with a consistency index of 30 cP equivalent and flow behavior index of 0.8 is pumped at 500 gpm into an annulus section of 1000 ft. The annulus is between an 8 ¾-in. diameter wellbore and a 5 ½-in. OD, 17 lb/ft casing (4.892-in. ID). Assuming borehole wall roughness of 0.2 in. and casing wall roughness of 0.004 in., predict the frictional pressure loss over this annulus section. Solution 500 v¼ ¼ 4:41ft=s 2:448  ð8:752  5:52 Þ   16  4:41ð20:8Þ 0:0208  ð8:75  5:5Þ 0:8 NRe ¼ 109,000  ¼ 15,568 2 + 1=0:8 30 NRecTur ¼ 4270  1370ð0:8Þ ¼ 3174 Because 15,568 > 3174, turbulent flow is expected. The relative borehole wall roughness is εhole ¼

0:2 ¼ 0:062 8:75  5:5

The relative casing wall roughness is εcsg ¼

0:0004 ¼ 0:000123 8:75  5:5

The average relative wall roughness is ε¼

0:000123½ð3:14Þð5:5Þ + 0:062½ð3:14Þð8:75Þ ¼ 0:0375 ð3:14Þð5:5Þ + ð3:14Þð8:75Þ

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Boyun Guo

The friction factor for the borehole wall is ( " #)!2
 0:0375 5:0452 0:03751:1098 7:149 0:8981 f ¼ 4 log  log + 3:7065 15, 568 15, 568 2:8257 ¼ 0:016 The pressure loss is Δpf ¼

0:016  16  4:412  1000 ¼ 170psi 21:1  ð8:75  5:5Þ

Herschel-Bulkley fluids

For Herschel-Bulkley fluids, the pressure losses inside the casing and in the annulus under laminar flow can be calculated in the US field units using the following equations:



   
476:2τy 7  106 K 3n + 1 9:81q n Δpf ¼ ΔL (6.57) + d nC c d3 K 



n   
476:2τy 7  106 K 192ð2n + 1Þ 0:1q ΔL Δpf ¼ + ðd2  d1 Þ K n  Ca∗ ðd2  d1 Þ d22  d12 (6.58) Under turbulent flow conditions, the pressure losses inside the casing and in the annulus, respectively, are estimated as: Δpf ¼

6:5  103 fc q2 ρ ΔL d5

(6.59)

and Δpf ¼

6:5  103 fc q2 ρ ðd2  d1 Þðd22  d12 Þ

2 ΔL

(6.60)

The friction factors fc inside the casing and fa in the annulus, respectively, are calculated as:

and

fc ¼ yðCc NRe Þz

(6.61)

 z fa ¼ y Ca∗ NRe

(6.62)

Cementing hydraulics

273

Illustrative Example 6.8. A 12 ppg Herschel-Bulkley spacer fluid with a yield point of 5 lb/100 ft2, consistency index of 10 cP equivalent, and flow behavior index of 0.9 is placed at 500 gpm in an annulus section of 100 ft. The annulus is between an 8 ¾-in. diameter wellbore and a 5 ½-in. OD, 17 lb/ft casing (4.892-in. ID). Predict the frictional pressure loss over this annulus section. Solution log ð0:9Þ + 3:93 ¼ 0:07769 50 1:75  log ð0:9Þ z¼ ¼ 0:2565 7 1 " # 8ð2ð0:9Þ + 1Þ 10:2565 ¼ 2346 N Rec ¼ ð0:9Þð0:07769Þ 500  ¼ 4:41 ft=s v¼ 2 5:52 2:448 
8:5   1 5 Ca∗ ¼ 1  ( )n ¼ 0:6479 0:9 + 1 0:0044ð500Þð2ð0:9Þ + 1Þ 5 + 0:0021ð10Þ   ð0:9Þπ ½ð8:75=24Þ  ð5:5=24Þ ð8:75=243Þ2  ð5:5=24Þ2 2
 8:75  5:5 0:9 7 6 7:48ð12Þð4:41Þð20:9Þ 7 6 4ð2ð0:9Þ + 1Þ 6 7 24 7 ¼ 2498 > 2346 6 NRe ¼ ! ! 6 0:9 0:9 7 0:9 5 4 8:75  5:5 2ð2ð0:9Þ + 1Þ 5 + 0:0021ð10Þ 24ð4:41Þ ð0:9Þð0:6479Þ y¼

Therefore turbulent flow is expected. fa ¼ 0:07769½ð0:6479Þð2498Þ0:2565 ¼ 0:01167 6:5  103 ð0:01167Þð500Þ2 ð12Þ Δpf ¼ 2 ð100Þ ¼ 3:3psi ð8:75  5:5Þð8:752  5:52 Þ

6.3 Flowing BHP BHP is always a major concern in cementing operations. An excessive BHP can fracture (break down) wellbore, resulting in the loss of cement slurry into formation and failure of cementing job. Even though the wellbore is not fractured, a high BHP causes high water loss of cement slurry into reservoir due to filtration and damage to the reservoir permeability. Fig. 6.3 shows a schematic of primary well cementing process. The column (a) illustrates a fluid profile when the spacer fluid and cement slurry are completely injected inside a casing string. Column (b) depicts a situation where the bottom plug reaches the float collar. Column (c) shows a

274

Boyun Guo

Top Plug

Cement Top Plug Released Bottom Plug

Displacement Fluid

Spacer Fluid

Drilling Fluid Float Collar

Bottom Plug Ruptured

Shoe Joint

Plug Bumped

Float Shoe

(A)

(B)

(C)

Fig. 6.3 Sketch of well cementing process.

condition where the top plug bumps the float collar at the end of fluid displacement. The peak BHP usually occurs at the end of fluid displacement because the density of cement slurry is higher than that of drilling fluid in the annulus. The BHP at the end of fluid displacement can be predicted using the hydraulics models presented in the previous section. It constitutes of hydrostatic pressure components and frictional pressure losses in the annulus: BHP ¼

N X i¼1

phi +

N X

Δpfi

(6.63)

i¼1

where i is the index of annulus with different types of fluids and/or different geometries, and N is the number of annular sections. Illustrative Example 6.9. Fig. 6.4 shows a schematic of a vertical well cementing. A 7-7/8-in. hole is drilled to a TD of 10,000 ft through an intermediate 8-5/8-in., 32 lb/ft (7.921-in. ID) casing set at 7000 ft. The drilling fluid in the open hole is Bingham plastic fluid of 11 ppg, PV 5 cP, and PY 5 lb/100 ft2. A 5-1/2-in., 17 lb/ft (4.892-in. ID) production casing is set from the TD to surface. A 16 ppg power-law cement slurry with a consistency index of 20 cP equivalent and flow behavior index of 0.8 is to be

Drilling Fluid 11 ppg (1.38 SG)

HOLE SIZE

CASING DEPTH

DRILL PIPE OD

24”

6 5/8”

(610mm)

(168mm)

MUD WEIGHT

CASING SIZE

120’(37m) 1400 ’

MUD VISCOSITY

20”,94 lb/ft

9.2 ppg

20 cp

(508mm,140 kg/m)

(1.10SG)

(0.020Pa-s)

(427m)

17 1/2”

6 5/8”

7000 ’

(445mm)

(168mm)

(2134m)

12 1/4”

5”

(318mm)

(127mm)

Spacer 12 ppg (1.44 SG)

13 3/8 ”,48 lb/ft

9.6 ppg

15 cp

(339.7mm,71.4 kg/m)

(1.15SG)

(0.015Pa-s)

85/8 ”,32 lb/ft

10.4 ppg

10 cp

(219.1mm,47.6 kg/m)

(1.25SG)

(0.01Pa-s)

10000 ’ (3048m)

7 7/8”

5”

(200mm)

(127mm)

10000 ’

11 ppg

5 cp

(3048m)

(1.38SG)

(0.005Pa-s)

Cement 16 ppg (1.92 SG)

Cement 20 cp (0.02 Pa-s)

Comple on Fluid 9.5 ppg (1.14 SG)

10,000 7-7/8” hole (200mm)

Fig. 6.4 Schematic of a vertical well cementing.

10,000’ (3,048m)

5-1/2”, 17 lb/ (139.7mm, 25.3kg/m)

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Boyun Guo

placed in the annulus up to 400 ft above the casing shoe. A 9 ppg Newtonian spacer fluid with a 5 cP viscosity will be used to cover 100 ft of annulus. Assuming a borehole roughness of 0.2 in. and smooth casing wall, predict the maximum BHP induced by a fluid displacement rate of 500 gpm. Also predict the dynamic pressure gradient and equivalent circulation density. Solution The maximum BHP occurs at the end of fluid displacement. Fig. 6.4 indicates that there will be four annular sections with different fluids and/ or geometries at the end of fluid displacement. They are (1) 6500-ft cased-hole with drilling fluid (2) 100-ft cased-hole section with spacer fluid (3) 400-ft cased-hole section with cement slurry (4) 3000-ft open-hole section with cement slurry Hydrostatic pressure of the drilling fluid in the 6500-ft cased-hole section: ph ¼ 0:052ð11Þð6500Þ ¼ 3178psi Hydrostatic pressure of the spacer fluid in the 100-ft cased-hole section: ph ¼ 0:052ð9Þð100Þ ¼ 47psi Hydrostatic pressure of the cement slurry in the 400-ft cased-hole section: ph ¼ 0:052ð16Þð400Þ ¼ 333psi Hydrostatic pressure of the cement slurry in the 3000-ft cased-hole section: 4 X

ph ¼ 0:052ð16Þð3000Þ ¼ 2496psi phi ¼ 3178 + 47 + 333 + 2497 ¼ 6055psi

i¼1

Frictional pressure loss in the 6500-ft cased-hole drilling fluid section: 500 ¼ 6:29ft=s 2:448  ð7:9212  5:52 Þ 5  5  ð7:921  5:5Þ μa ¼ 20 + ¼ 14:63cP 6:29 11  6:29  ð7:921  5:5Þ ¼ 8663 NRe ¼ 757  14:63 v¼

Because NRe > 2100, turbulent flow is expected in the annular space.

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Cementing hydraulics

Δpf ¼

110:75 6:291:75 14:630:25 6500 ¼ 455psi: 1396ð7:921  5:5Þ1:25

Frictional pressure loss in the 100-ft cased-hole spacer fluid section: 500 ¼ 6:29ft=s 2:448  ð7:9212  5:52 Þ 9  6:29  ð7:921  5:5Þ ¼ 20,737 NRe ¼ 757  5

v¼

Because NRe > 2100, turbulent flow is expected in the annular space. Δpf ¼

90:75 6:291:75 50:25 100 ¼ 6psi 1396ð7:921  5:5Þ1:25

Frictional pressure loss in the 400-ft cased-hole cement slurry section: 500 ¼ 6:29ft=s 2:448  ð8:752  5:52 Þ   16  6:29ð20:8Þ 0:0208  ð8:75  5:5Þ 0:8 NRe ¼ 109,000  ¼ 28, 230  2 + 1=0:8 20 v¼

NRecTur ¼ 4270  1370ð0:8Þ ¼ 3174 Turbulent flow is expected in the annular section. Assuming smooth walls of the casing, the friction factor for the casing wall is f¼

0:0791 ¼ 0:0061 28,2300:25

Pressure loss is Δpf ¼

0:0061  16  6:292  400 ¼ 80psi 21:1  ð8:75  5:5Þ

Frictional pressure loss in the 3000-ft cased-hole cement slurry section: 500 ¼ 6:43ft=s 2:448  ð8:752  5:52 Þ   16  6:43ð20:8Þ 0:0208  ð7:875  5:5Þ 0:8 ¼ 28, 565 NRe ¼ 109,000   2 + 1=0:8 20 NRecTur ¼ 4270  1370ð0:8Þ ¼ 3174 v¼

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Boyun Guo

Turbulent flow is expected in the annular section. The relative borehole wall roughness is εhole ¼

0:2 ¼ 0:084 7:875  5:5

The relative casing wall roughness is εcsg ¼

0:0004 ¼ 0:000168 7:875  5:5

The average relative wall roughness is ε¼

0:000168½ð3:14Þð5:5Þ + 0:084½ð3:14Þð7:875Þ ¼ 0:0495 ð3:14Þð5:5Þ + ð3:14Þð7:875Þ

The average friction factor is ( " #)!2
 0:0495 5:0452 0:04951:1098 7:149 0:8981 f ¼ 4 log  log + 3:7065 28, 565 28, 565 2:8257 ¼ 0:018 Pressure loss is Δpf ¼

0:018  16  4:412  3000 ¼ 1961psi 21:1  ð7:875  5:5Þ

The total pressure loss in the annulus is 4 X

pfi ¼ 455 + 6 + 80 + 1961 ¼ 2502psi

i¼1

The BHP is BHP ¼ 6055 + 2502 ¼ 8557psi The dynamic BHP gradient is GBH ¼

8557 ¼ 0:8557psi=ft 10,000

The equivalent circulation density is EMW ¼

8557 ¼ 16:46ppg 0:052ð10, 000Þ

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Cementing hydraulics

which should be checked with formation pressure gradient for preventing the loss of circulation.

6.4 Displacement pressure Displacement pressure (DP) is a major concern in cementing operations for the safety of field personnel and equipment. An excessive DP can cause rupture of the surface equipment, resulting in personnel injury and failure of cementing job. Leak of cement slurry to the well site can induce environmental issues. As shown in Fig. 6.3C, the peak DP occurs prior to plug bumping before pumping speed is slowed down. At this moment, the BHP reaches its peak value due to the high columns of heavy fluids in the annular space, and the hydrostatic pressure inside the casing reaches its lowest value due to the low density of displacement fluid. The maximum DP can be predicted using the hydraulics models presented in the previous section. It constitutes of hydrostatic pressure components and frictional pressure losses in the annulus and inside the casing. If the BHP has been calculated, it can be used for predicting the DP: DP ¼ BHP  phPipe + Δpf Pipe ,

(6.64)

where ph-Pipe and pf-Pipe are the hydrostatic pressure and frictional pressure loss of the displacement fluid inside the pipe (casing and drill string, if any), respectively. Illustrative Example 6.10. Fig. 6.5 shows a schematic of a horizontal well cementing. A 8¾-in. hole is drilled to a total depth (TD) of 12,756 ft through a 10-3/4-in., 51 lb/ft (9.850-in. ID) intermediate casing set at 5000 ft. The kick-off-point is at 6000 ft, radius of curvature is 800 ft, and the true vertical depth at the TD is 7256 ft. The drilling fluid in the open hole is Bingham plastic fluid of 10 ppg, PV 10 cP, and PY 10 lb/100 ft2. A 5½-in., 17 lb/ft (4.892-in. ID) production liner is held at 4500 ft by a 5in., 25.6 lb/ft (4-in. ID) drill string. A 15 ppg power-law cement slurry with a consistency index of 25 cP equivalent and flow behavior index of 0.85 is to be placed in the annulus up to 400 ft above the intermediate casing shoe. A 9 ppg Newtonian spacer fluid with a 5 cP viscosity will be used to cover 100 ft of annulus. A 9.5 ppg Newtonian displacement fluid with a 2 cP viscosity will be utilized. Assuming a borehole roughness of 0.2 in. and smooth casing wall, predict the maximum DP induced by a fluid displacement rate of 500 gpm.

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Drilling Fluid 11 ppg (1.38 SG)

13 3/8” 48lb/Ō (12.715” ID) surface casing set at 500’

10 ¾” 51 lb/Ō (9.850” ID) intermediate casing set at 5,000’

KOP 6,000’ 5 ½” 17 lb/Ō (4.892” ID) producƟon casing set to TD 00 Lateral length 5,500’

TD 12,756’

Fig. 6.5 Schematic of a horizontal well cementing.

Solution The maximum DP occurs at the end of fluid displacement. Fig. 6.5 indicates that there will be four annular sections with different fluids and/or geometries at the end of fluid displacement. They are (1) 4500-ft cased-hole with drilling fluid. (2) 100-ft cased-hole section with spacer fluid (3) 400-ft cased-hole section with cement slurry (4) 8156-ft open-hole section with cement slurry Hydrostatic pressure of the drilling fluid in the 4500-ft cased-hole section: ph ¼ 0:052ð10Þð4500Þ ¼ 2340psi Hydrostatic pressure of the spacer fluid in the 100-ft cased-hole section: ph ¼ 0:052ð9Þð100Þ ¼ 47psi Hydrostatic pressure of the cement slurry in the 400-ft cased-hole section: ph ¼ 0:052ð15Þð400Þ ¼ 312psi Hydrostatic pressure of the cement slurry in the 8156-ft cased-hole section is calculated based on the column height of 2656 ft: 4 X i¼1

ph ¼ 0:052ð15Þð2656Þ ¼ 2072psi phi ¼ 2340 + 47 + 312 + 2072 ¼ 4771psi

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Frictional pressure loss in the 4500-ft cased-hole drilling fluid section: 500 ¼ 2:84ft=s 2:448  ð9:852  52 Þ 5  10  ð9:85  5Þ ¼ 96cP μa ¼ 20 + 2:84 10  2:84  ð9:85  5Þ NRe ¼ 757  ¼ 1090 96 v¼

Because NRe < 2100, laminar flow is expected in the annular space. " # ð95Þð2:84Þ 10 ð4500Þ ¼ 98psi + Δpf ¼ 1000ð9:85  5Þ2 200ð9:85  5Þ Frictional pressure loss in the 100-ft cased-hole spacer fluid section: 500 ¼ 3:06ft=s 2:448  ð9:852  5:52 Þ 9  3:069  ð9:85  5:5Þ ¼ 18,131 NRe ¼ 757  5 v¼

Because NRe > 2100, turbulent flow is expected in the annular space. Δpf ¼

90:75 3:061:75 50:25 ð100Þ ¼ 0:6psi 1396ð9:85  5:5Þ1:25

Frictional pressure loss in the 400-ft cased-hole cement slurry section: 500 ¼ 3:06ft=s 2:448  ð9:852  5:52 Þ   15  3:06ð20:85Þ 0:0208  ð9:85  5:5Þ 0:85 ¼ 11, 492 NRe ¼ 109,000   25 2 + 1=0:85 NRecTur ¼ 4270  1370ð0:85Þ ¼ 3106 v¼

Turbulent flow is expected in the annular section. Assuming smooth walls of the casing, the friction factor for the casing wall is f¼

0:0791 ¼ 0:0076 11,4920:25

The pressure loss is Δpf ¼

0:0076  15  3:062  400 ¼ 4:7psi 21:1  ð9:85  5:5Þ

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Frictional pressure loss in the 8156-ft cased-hole cement slurry section: 500 ¼ 4:41ft=s 2:448  ð8:752  5:52 Þ   15  4:41ð20:85Þ 0:0208  ð8:75  5:5Þ 0:85  ¼ 13, 662 NRe ¼ 109,000  2 + 1=0:85 25 NRecTur ¼ 4270  1370ð0:85Þ ¼ 3106 v¼

Turbulent flow is expected in the annular section. The relative borehole wall roughness is εhole ¼

0:2 ¼ 0:061 8:75  5:5

The relative casing wall roughness is εcsg ¼

0:0004 ¼ 0:000123 8:75  5:5

The average relative wall roughness is ε¼

0:000123½ð3:14Þð5:5Þ + 0:061½ð3:14Þð8:75Þ ¼ 0:0375 ð3:14Þð5:5Þ + ð3:14Þð8:75Þ

The average friction factor is ( " #)!2
 0:0375 5:0452 0:03751:1098 7:149 0:8981 f ¼ 4 log  log + 3:7065 13, 662 13, 662 2:8257 ¼ 0:016 The pressure loss is Δpf ¼

0:018  15  4:412  8156 ¼ 562psi 21:1  ð8:75  5:5Þ

The total pressure loss in the annulus is 4 X

pfi ¼ 98 + 0:6 + 4:7 + 562 ¼ 665psi

i¼1

The BHP is BHP ¼ 4771 + 665 ¼ 5436psi

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The dynamic BHP gradient is GBH ¼

5436 ¼ 0:75psi=ft 7256

The equivalent circulation density is EMW ¼

5436 ¼ 14:41ppg 0:052ð7256Þ

which should be checked with formation pressure gradient for preventing the loss of circulation. The hydrostatic pressure of the displacement fluid inside the drill string and casing is phPipe ¼ 0:052ð9:5Þð7256Þ ¼ 3584psi As shown in Fig. 6.5, there will be two pipe sections with different geometries at the end of fluid displacement. They are as follows: (1) 4500-ft drilling string and (2) 8256 ft 5 ½-in. casing. Frictional pressure loss inside the 4500 ft drilling string: v¼

500 ¼ 12:77ft=s 2:448ð4Þ2

NRe ¼ 928

ð9:5Þð12:77Þð4Þ ¼ 225,082 2

Because NRe > 4000, complete turbulent flow is expected inside the drill string. Δpf ¼

9:50:75 12:771:75 20:25 ð4500Þ ¼ 245psi ð1800Þ41:25

Frictional pressure loss inside the 8256-ft casing: v¼

500 ¼ 8:83ft=s 2:448ð4:892Þ2

NRe ¼ 928

ð9:5Þð8:53Þð4:892Þ ¼ 184,041 2

Because NRe > 4000, complete turbulent flow is expected inside the drill string.

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Δpf ¼

9:50:75 8:531:75 20:25 ð8256Þ ¼ 173psi ð1800Þ4:8921:25

The maximum DP is predicted to be DP ¼ 5436  3584 + ð245 + 173Þ ¼ 2270psi which should be checked with equipment pressure rating for preventing rupture.

6.5 Surge and swab pressure In the downward motion of a casing string, the string forces the drilling fluid and cement slurry up the annulus and out of the flowline. At the same time, the fluids immediately adjacent to the casing is dragged downhole. The resultant piston effect generates surge pressures that are added to the hydrostatic pressure. Excessive surge pressures can increase the borehole pressure to such a high level as to induce lost circulation. Conversely, in an upward motion of casing string, fluid flows down the annulus to fill the resulting void. This causes a suction effect, generating a swab pressure that can possibly bring formation fluid into the borehole. Calculating surge and swab pressures can be a complex undertaking depending upon the casing string configuration and hole geometry. Burkhardt (1961) developed a relationship between hole geometry and the effect of the fluid being dragged by a pipe. Based on Burkhardt’s (1961) work, the effective annular velocity is equal to ve ¼ vf  κvp

(6.65)

where ve ¼ the effective annular velocity, ft/s or m/s vf ¼ fluid velocity, ft/s or m/s vp ¼ pipe upward velocity, ft/s or m/s and κ is referred to as the clinging constant, which is a function of annular geometry. Burkhardt (1961) presented a chart for determination of the value of κ in both laminar flow and turbulent flow. Guo and Liu (2011) found that the chart can be replaced by the following correlations with minimal error. For laminar flow, the correlation is
 dp κ ¼ 0:275 + 0:25 (6.66) dh

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where dp ¼ outer diameter of pipe, in. or mm. dh ¼ hole diameter, in. or mm. For turbulent flow, the correlation is
 dp κ ¼ 0:1 + 0:41 dh

(6.67)

For closed-end pipes such as casing string with float shoe, the fluid velocity can be calculated by

vf ¼ vp

dp2

!

dh2  dp2

(6.68)

For open-end pipes, the fluid velocity can be calculated by 0

1  2 4dp2 dh  dp  3dp4 A: vf ¼ vp @  2  2 2 2 4 4dp dh  dp dh  dp + 6dp

(6.69)

Illustrative Example 6.11. Calculate the surge pressure generated by a 10 ¾ in. casing string under the following conditions, and predict whether the total borehole pressure will exceed the formation fracture gradient. Assume that the casing is effectively “closed” with a float shoe and laminar flow in the annulus.

Casing depth: Fracture gradient: Hole diameter: Average fluid weight: Plastic viscosity: Yield point: Pipe velocity:

6400 ft (1951 m) TVD 0.82 psi/ft 14 ¾ in. 15.5 ppg 37 cP 6 lb/100 ft2 110 ft/min (the negative sign denotes downward velocity)

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Solution
 110 10:752 vf ¼  ¼ 2:08ft=s 60 14:752  10:752
 10:75 κ ¼ 0:275 + 0:25 ¼ 0:45 14:75
 110 ve ¼ 2:08  0:45 ¼ 1:25ft=s 60 Annular flow pressure loss for laminar flow: " # ð37Þð1:265Þ 6 ð6400Þ ¼ 67psi Δpf ¼ + 1000ð14:75  10:75Þ2 200ð14:75  10:75Þ The equivalent mud weight (EMW): EMW ¼ 15:5 +

67 ¼ 15:7ppg 0:052ð6400Þ

The EMW of fracture gradient (EMWf): EMWf ¼

0:82 ¼ 15:8ppg > 15:7ppg 0:052

Therefore the borehole will be safe during downward motion of the casing. Illustrative Example 6.12. Using the Bingham plastic model, calculate the swab pressure generated by a 10 3/4 in. casing string under the following conditions, and predict whether the total borehole pressure will be lower than the formation pore gradient. Assume that the casing is fully opened and laminar flow in the annulus.

Casing depth: Pore pressure gradient: Hole diameter: Average fluid weight: Plastic viscosity: Yield point: Pipe velocity:

6400 ft (1951 m) 0.78 psi/ft 14 3/4 in. 15.5 ppg 37 cP 6 lb/100 ft2 110 ft/min

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Solution " # 110 4  10:752  ð14:75  10:75Þ2  3  10:754  vf ¼  ¼ 0:0718ft=s  60 4  10:752  ð14:75  10:75Þ2  14:752  10:752 + 6  10:754 k ¼ 0:275 

10:75 + 0:25 ¼ 0:45 14:75

ve ¼ 0:0718 + 0:45 

110 0:90ft=s 60

Annular flow pressure loss for laminar flow: " # 37  0:90 6  6400 ¼ 61psi + Δpf ¼ 1000  ð14:75  10:75Þ2 200  ð14:75  10:75Þ 61 EMW ¼ 15:5  ¼ 15:32ppg 0:052  6400 The EMW of pore gradient (EMWP): EMW P ¼

0:78 ¼ 15ppg < 15:32ppg 0:052

Therefore the borehole will be safe during the movement of casing string.

6.6 Summary This chapter reviews fundamentals of hydraulics applied well cementing. Cement slurry and drilling fluids are characterized on the basis of their rheological properties. For incompressible cement slurry and drilling fluids, hydrostatic pressure and frictional loss pressure components can be calculated independently. Mathematical models for predicting bottom pressure, DP, and surge and swab pressures are presented. Example calculations are illustrated.

Exercise problems 6.1 A 11 ppg Bingham plastic drilling fluid with a plastic viscosity of 20 cP and yield point of 15 lb/100 ft2 is circulating at 600 gpm in a 7-7/8-in. diameter wellbore. Determine the flow regime inside a 5½-in. OD, 17 lb/ft casing (4.892-in. ID), and in the casing/hole annulus.

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6.2 A 15 ppg power-law cement slurry with a consistency index of 20 cP equivalent and flow behavior index of 0.85 is circulating at 600 gpm in a 7-7/8-in. diameter wellbore. Determine the flow regime inside a 5½-in. OD, 17 lb/ft casing (3.826-in. ID) and in the casing/hole annulus. 6.3 A 11.5 ppg Bingham plastic drilling fluid with a plastic viscosity of 15 cP and yield point of 15 lb/100 ft2 is displaced by a cement slurry at 600 gpm in a 7-7/8-in. diameter wellbore outside a 5½-in. OD, 17 lb/ft casing (4.892-in. ID) at a depth of 6000 ft. Predict the frictional pressure loss in the annulus. 6.4 A 16 ppg power-law cement slurry with a consistency index of 30 cP equivalent and flow behavior index of 0.85 is pumped at 600 gpm into an annulus section of 1200 ft. The annulus is between an 8-3/4 in.diameter wellbore and a 5 ½-in. OD, 17 lb/ft casing (4.892-in. ID). Assuming borehole wall roughness of 0.2 in. and casing wall roughness of 0.004 in., predict the frictional pressure loss over this annulus section. 6.5 A 7-7/8-in. hole is drilled to a TD of 9000 ft through an intermediate 85/8 in., 32 lb/ft (7.921-in. ID) casing set at 6000 ft. The drilling fluid in the open hole is Bingham plastic fluid of 10 ppg, PV 10 cP, and PY 10 lb/100 ft2. A 5-1/2 in., 17 lb/ft (4.892-in. ID) production casing is set from the TD to surface. A 15 ppg power-law cement slurry with a consistency index of 25 cP equivalent and flow behavior index of 0.85 is to be placed in the annulus up to 500 ft above the casing shoe. A 9.5 ppg Newtonian spacer fluid with a 5 cP viscosity will be used to cover 100 ft of annulus. Assuming a borehole roughness of 0.2 in. and smooth casing wall, predict the maximum BHP induced by a fluid displacement rate of 500 gpm. Also predict the dynamic pressure gradient and equivalent circulation density. 6.6 An 8¾-in. hole is drilled to a TD of 12,756 ft through a 10-3/4 in., 51 lb/ft (9.850-in. ID) intermediate casing set at 6000 ft. The kickoff-point is at 6500 ft, radius of curvature is 800 ft, and the true vertical depth at the TD is 7756 ft. The drilling fluid in the open hole is Bingham plastic fluid of 11 ppg, PV 15 cP, and PY 15 lb/100 ft2. A 5½-in., 17 lb/ft (4.892-in. ID) production liner is held at 5500 ft by a 5-in., 25.6 lb/ft (4in. ID) drill string. A 15.5 ppg power-law cement slurry with a consistency index of 25 cP equivalent and flow behavior index of 0.85 is to be placed in the annulus up to 400 ft above the intermediate casing shoe. A 9.5 ppg Newtonian spacer fluid with a 5 cP viscosity will be used to cover 100 ft of annulus. A 9.0 ppg Newtonian displacement fluid with

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17 1/2”

Hole Size

Casing 4,022’ 20” 94lb/ft (19.124” ID) surface casing

7,525’ 13 3/8” 48lb/ft (12.715”

12 1/4”

ID) intermediate casing

8 3/4”

20,606’ 9 5/8” 36 lb/ft (8.921” ID) intermediate casing

Fluids for Cementing 7” Casing

12.7 ppg Bingham Plastic mud PV = 5 cp, YP = 5 lb/100 ft^2

10 ppg Newtonian spacer m = 5 cp

14.5 ppg Power Law cement K = 20 cp, n = 0.80 23,650’

7” 20 lb/ft (6.456” ID) casing

Fig. 6.6 Schematic of an exploration well before well cementing.

a 2 cP viscosity will be utilized. Assuming a borehole roughness of 0.2 in. and smooth casing wall, predict the maximum DP induced by a fluid displacement rate of 600 gpm. 6.7 Fig. 6.6 shows a schematic of an exploration well before cementing the 7-in. casing. Cement is to be placed in the annulus up to 500 ft above the casing shoe. Spacer fluid will be used to cover 100 ft of annulus. Assuming a borehole roughness of 0.2 in. and smooth casing wall, predict the maximum BHP and DP induced by a fluid displacement rate of 500 gpm. Also predict the dynamic pressure gradient and equivalent circulation density.

References Blasius, H., 1913. Das Aehnlichkeitsgesetz bei Reibungsvorgangen in Flussigkeiten. VDL Forsch, p. 131. Bourgoyne Jr., A.T., Millheim, K.K., Chenevert, M.E., Young Jr., F.S., 1986. Applied Drilling Engineering. SPE Textbook Series, Society of Petroleum Engineers International, Dallas. Burkhardt, J.A., 1961. Wellbore pressure surges produced by pipe movement. Trans. AIME 222, 595–605. Chen, N.H., 1979. An explicit equation for friction factor in pipe. Ind. Eng. Chem. Fundam. 18, 296. Colebrook, C.F., 1938. Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws. J. Inst. Civ. Eng. 11, 133–156. Dodge, D.G., Metzner, A.B., 1959. Turbulent flow of non-Newtonian systems. AIChE J 5, 189–196.

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Gregory, G.A., Fogarasi, M., 1985. Alternate to standard friction factor equation. Oil Gas J. 83, 120–127. Guo, B., Liu, G., 2011. Applied Drilling Circulation Systems. Gulf Professional Publishing, Burlington. Herschel, W.H., Bulkley, R., 1926. Konsistenzmessungen von Gummi-Benzollosungen. Kolloid-Zeitschrift 39, 291–300.

CHAPTER SEVEN

Job simulation and design Gunnar DeBruijn Progressive Talent Solutions Inc., Calgary, AB, Canada

Abbreviations API AZIM BHCT BHST BOP BVOB BVOC BWOB BWOC BWOW CSGS ECD ED FPR GMS HGS ID INCL LGS MD MRR MSL N2 OBM OD PDL PFZ RT RWF SBM SG STO SVF TIE TMD TOC TVD

American Petroleum Institute Azimuth bottom hole circulating temperature bottom hole static temperature blow out preventer by volume of blend by volume of cement by weight of blend by weight of cement by weight of water critical static gel strength equivalent circulating density equivalent density formation productivity risk gas migration severity high gravity solids internal diameter inclination low gravity solids measured depth mud removal risk mean sea level nitrogen oil-based mud outer diameter pressure decay limit potential flow zone rotary table recommended workflow synthetic-based mud specific gravity standoff solid volume fraction third interface echo total MD top of cement total vertical depth

Applied Well Cementing Engineering https://doi.org/10.1016/B978-0-12-821956-0.00013-4

Copyright © 2021 Elsevier Inc. All rights reserved.

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292 UCS WBM WOC

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unconstrained compressive strength water-based mud wait on cement

Units ft. gal h lb. m3 min ppg psi sk

feet gallon hours pound cubic meters minutes pounds per gallon pounds per square inch sack

7.1 Introduction Computer-assisted design of primary cementing is the main tool for the cementing engineer to ensure the success of the zonal isolation objectives. Once the objectives are clearly defined, the cement simulation software can be used to calculate and predict volumes, pressures, temperatures, centralization, fluid flow regimes, and fluid placement. The simulation may be used to visualize the cement job and may be useful after the cement job to evaluate how the objectives have been met.

7.2 Cement job objectives in the context for simulation The objective of the cement job should be clearly stated and understood. The objectives will drive the engineer’s use of simulation to demonstrate that the objective(s) can be met. Top of cement (TOC) is a typical objective for a cement job. TOC is also typically a regulatory requirement for all casing strings. A cementing simulator may use a volume calculation and a hydrostatic calculation to demonstrate that this objective will be met. Isolation of potential flow zones may be another objective of the cement job. This is a more complex requirement and requires several simulations to determine that this objective will be met. The engineer will have to consider casing centralization, fluid properties, displacement efficiency, and job execution parameters such as pump rates and casing movement.

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293

A physical barrier provided by the set cement is often an implied objective. Laboratory tests, discussed in Chapter 5, provide evidence of compressive strength of the cement. Simulations can be used to provide temperature and pressure schedules for laboratory testing. Simulations may also be used to estimate possible contamination of the cement in a casing annulus or a cement plug application.

7.3 What is a cement job simulation? Computer-assisted design of primary cementing is the main tool for the cementing engineer to ensure the success of the cementing and zonal isolation objectives. It is a computer program that can be used to understand many aspects of the cement job. There are several computer cementing simulations that are currently available. Examples of commercially available cement simulations used by cementing service providers are CEMENTICS*,a CemFACTS*,b CemPRO+*,c and iCEM*.d Each of the cementing simulators may also include branded modules and stand-alone modules as part of the software package. The software providers’ web pages provide links and information about the submodules and their capabilities. Examples of submodules and standalone modules are as follows: CEMLab*,c CEMLife*,c CemSTRESS*,a CEMVIEW*,c CentraDesign*,c LCPRO*,c Plug Cement Wizard*,b PlugPRO*,c Set for Life*,b WELLCLEAN III*,a and WellTemp*.b Many other numerical simulators exist that are useful for the cementing engineer in designing a cement job. Cement jobs are of short duration, and the simulations are more transient than steady state. The simulators may generically be thought of as hydraulic (including U-tubing) and temperature simulators. Other useful simulations are stress simulations, various drilling simulations, casing and drill string simulations, and acoustic properties simulations.

7.3.1 Overall recommended workflow: Cement job simulation A cement job simulation is essentially a process that can be described as a workflow. The cement job simulation can be performed as part of the well design process, it can be revisited during the drilling of the well, and may be a b c d

Mark of Schlumberger. Trademark of Baker Hughes, a GE Company, LLC. Mark of Pegasus Vertex, Inc. Registered mark of Halliburton.

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performed after the cement job and performed again as a job evaluation process. The workflow described later is adaptable for most cementing simulation exercises. The recommended workflow (RWF) for a cement simulation can be described as: RWF 1. Collect and input the well description and available well data. RWF 1.1. Surface equipment description RWF 1.2. Tubular description RWF 1.3. Hole size RWF 1.4. Directional details RWF 1.5. Formation data RWF 1.6. Temperature details RWF 1.7. Centralizer(s) description RWF 2. Collect and input all the known fluids data RWF 2.1. Define each fluid RWF 2.2. Define drilling fluid RWF 2.3. Define spacer(s) and wash(es) RWF 2.4. Define slurry(s) RWF 2.5. Define displacement fluid RWF 3. Design additional fluids. RWF 3.1. Design fluid based on density RWF 3.2. Design fluid based on rheological properties RWF 3.3. Design fluid based on compatibility RWF 3.4. Design fluid based on component availability RWF 3.5. Design fluid based on set cement properties RWF 4. Design fluid volumes, pump schedule, and fluids preparations requirements. RWF 4.1. Fluids volumes RWF 4.2. Pump schedule RWF 4.3. Fluid and blend preparation RWF 5. Perform hydraulics and temperature simulation. RWF 5.1. Simulate prejob well circulation RWF 5.2. Simulate cementing operations RWF 5.2.1. Run the hydraulic simulation using the planned pump schedule RWF 5.2.2. Confirm that design parameters are met including well security. Review the security checks, that well control is maintained, and cement losses (if simulated) are manageable. Use the charts available in the program to review.

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RWF 5.2.3. Check minimum hook load to ensure that the risk of casing pump out is not present RWF 5.2.4. Check pump horsepower requirement against available capacity RWF 5.2.5. Verify key temperature values against laboratory test conditions. Detailed pressure and temperature results may be used to prepare or update laboratory test requests. RWF 5.3. Iterate by adjusting the pump schedule as necessary RWF 5.4. Standalone calculation aids RWF 6. Perform casing centralization simulation RWF 6.1. Centralization standoff calculations RWF 6.2. Running force RWF 6.3. Surge and swab RWF 6.4. Casing stretch RWF 6.5. Hook load and surface torque during cementing RWF 6.6. Iterate on the centralizer design RWF 7. Perform annular displacement simulation. RWF 7.1. Perform displacement simulation RWF 7.2. Compare the simulation results to the job objectives RWF 7.3. Iterate on the design to meet the job objectives, by modifying (in order of difficulty) the pump schedule, centralizer placement, fluids volumes, or even fluid design) RWF 8. Perform special case simulations RWF 8.1. Critical static gel strength RWF 8.2. Gas migration risk RWF 8.3. Plug placement RWF 8.4. Cement sheath stress calculations RWF 8.5. Foam cement calculations RWF 9. Generate cement program documentation RWF 10. Perform postjob simulations for job evaluation. RWF 10.1. Import wellsite recorded data RWF 10.2. Define the job sequence RWF 10.3. Perform pressure match and form conclusions RWF 10.4. Additional comparisons Cement simulation is often thought of as only hydraulics simulation, however detailed data input is required for accurate hydraulic simulation. The cement job objectives will determine which steps are required in addition to the hydraulic simulation. Often cement job design and simulation requires an iterative process that may require designing additional fluids

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or redesigning the pump schedule so that all of the cement job objectives can be met. Results from the simulation can be visualized, or plotted, versus time, or versus depth in the wellbore. Computer capabilities impact the detail of the simulation and visualization that is available. Typical simulators include plots of pressures, equivalent circulating densities, centralization, and annular displacement in the wellbore. These plots can be used to understand how the cement job objectives are met. Visualization can be in plots and 3D renderings and graphics. Early computer simulations gridded the well into 100 cells; modern simulations can simulate, calculate, and plot parameters every foot of depth in the wellbore and every second of time. High definition monitors with almost infinite color possibilities allow 3D representation of many of the parameters along the entire wellbore length. Gridding, human machine interface, and computer performance (both CPU and graphics cards) are important topics for software design. It is anticipated that computer performance will continue to increase. The result of the cement job simulation is a cement job design document. This document typically includes all the design assumptions and the final iteration of the centralization program and pump schedule that is intended to be executed at the wellsite. Material requirements, a pump schedule, required equipment pressure ratings and expected pressures are all calculated from the simulation. A cement program and simulation may also include additional rig activity details such as pipe movement, drilling fluid tank management schedule, expected cement returns, and rig pump schedule. Simulation may be used after the cement job to compare original assumptions, compare wellsite observations to the simulation, and even compare downhole measurements such as cement evaluation logs to the annular displacement simulations. This chapter focuses on what the engineer will consider for inputs and how they will use the outputs of the simulation.

7.4 Cement job simulation outputs: What are they used for? Cement job simulation provides useful outputs that can be used for job planning and job evaluation.

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Volumes calculations provide material details for the cement job. Storage and delivery for each of the following materials can then be planned: - Cement volume - Dry additives quantities - Mix water volume - Liquid additive(s) quantities - Displacement fluid volume Surface pressure simulation allows proper planning for the following surface equipment: - Cement head pressure rating - Cement pump pressure rating - Pump (cement pump and rig pump) horsepower requirement - Treating iron (or hose) pressure rating - Rig equipment (standpipe and rig pump) pressure rating Hydraulic simulations are used to ensure that the cement job pressures at any depth in the wellbore stay within the following wellbore equipment pressure limitations: - Casing burst and collapse—discussed in Chapter 2, Casing String and Design - Blowout preventer (BOP) - Casing equipment—discussed in Chapter 3
Float equipment
Stage tool equipment
Liner/casing hanger Hydraulic simulations are used to ensure that well control is maintained throughout the cement job. A cement job typically consists of at least four different fluids in the wellbore, and a computer simulation is especially useful to calculate the dynamic and hydrostatic pressures throughout the job, ensuring that the pressures are between the pore and fracture pressure at all depths in the wellbore. Well control is a primary responsibility during all operations and the engineer must determine that there is no risk of formation fluid influx during the cement job. If losses are indicated by the simulation, the engineer needs to appropriately understand and mitigate the risk associated with the losses. Simulations are used to provide laboratory testing schedules. Deepwater and directional wells require simulation to estimate the temperature and pressure schedule for cement laboratory testing. Cement simulations are also performed to plan centralizer schedules for the casing. The centralization schedule is planned so that cementing

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objectives can be met. The simulator can assist in predicting the hook load while running casing, ensuring that the casing can be run to bottom without getting stuck. The centralization schedule is also used to simulate the casing position in the wellbore so that annular displacement models can be calculated, and fluid positions are visualized. Simulations may be used to visualize the fluid placement. Simulators provide visualization of where the fluids are in the wellbore, radial position in the annulus, mixing inside the pipe on the way down the wellbore, and mixing in the annulus as the cement rises in the annulus. Simulations are very helpful to understand the U-tubing effect with the use of different density of fluids in the wellbore. Cement job simulation is very useful for job evaluation. Well site recorded pressures can be compared with simulations. A match of the recorded pressure and the simulated pressure may be used as evidence that the cement was placed as designed. Similarly, annular fluid displacement simulations may be compared with recorded cement evaluation logs to help understand features that may be observed in the evaluation logs. Long-term well integrity objectives may also be supported by cement job simulation. The prejob and postjob simulations may be kept in the wellbore record as evidence of the design and placement of the cement in the well. Simulations are also developed to understand special cases. Cement plug placement is an example of a special case. Simulations that calculate stresses in the cement sheath are another example of a special case.

7.5 Recommended workflow for cement job simulation The overall RWF for cement job simulation was introduced in Section 7.3. The remainder of this chapter will expand and explain each one of the steps in the RWF. Steps in the workflow are preceded with the designation “RWF.” Sections of the RWF that are provided courtesy of Schlumberger have been adapted from the help screens that are available in the CEMENTICS software package.

7.6 Collect and input the well description and any available well data RWF 1. Collect and input the well description and available well data

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The first fundamental step of simulation is to collect all of the well data. Well details that need to be collected are as follows: - Surface equipment description - Tubular(s) description - Hole size - Directional details - Formation - Temperature details - Centralizer The well details and assumptions will affect the simulation; thus it is important to perform simulations with assumptions that are as accurate as possible. It may also be possible to perform sensitivity analysis and iterations of the simulations with changes to any one of all of these inputs. Each of the inputs and assumptions will affect the output of the simulation, the significance of each of the inputs is described later.

7.6.1 Surface equipment description RWF 1.1. Surface equipment description. Surface equipment details include rig details, treating line details, and returns depths. Fig. 7.1 describes surface equipment details that may be included in the simulation. The reference point for many well details is the rotary table (RT). Because the RT is the reference, all depths and measurements to RT need to be accurate. The operating environment determines whether the cement job take place on land or offshore. Rig setup will then require different parameters, depending on your selection. For land operations, to improve simulation accuracy, the basic rig setup should be described: • RT/mud return depth: The point where the mud returns are taken, relative to the rig floor. Conductor and surface casing are usually cemented with returns taken to the cellar, but once the blow out preventer (BOP) is installed, the return depth is just below the RT. • Rig floor elevation: The height of the rig floor (RT) from the ground. For offshore operations, the sea and rig environment need to be described: • RT/mud return depth: The point where the mud returns are taken, relative to the rig floor. For conductor casing, if it is cemented, returns are typically taken at the sea floor. For surface casing, the depth of the returns will depend on the rig type, drill ships and semi-submersible rigs will take

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Fig. 7.1 Surface equipment details. (Credit: Schlumberger.)

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returns at the seabed, platform and jack up rigs will take returns just below the rig floor. For all other casings and liners, returns are taken at the rig return line. • RT/seabed depth: The measured depth (MD) corresponding to the seabed. It is the sum of the air gap and the water depth. • Water depth: The average water depth, that is, the distance between the mean sea level (MSL) and the seabed. • Water density: The density of the (sea)water at the operating location. This value will be used for pressure calculations. Surface lines from the cement pump and rig pumps also need to be specified. Cement simulations are typically done from the RT, and then the effects of the surface lines to the pumps are added. Total vertical depth (TVD) elevation from the pumps to the RT is important when simulating pump pressures. In addition, the length (L) and inner diameter (ID) of the surface lines from the pumps to the cement head at RT also affect the final simulation. In Fig. 7.1, the total surface line is depicted as L1 + L2 + L3 + L4 + L5. Surface treating line definitions are important because they are part of the circulating system. Friction pressure will occur in the surface lines, from the cement pump during cementing, and from the rig pump or cement pump when displacing. When the cement is U-tubing forward and the pressure at the cement head is zero, the friction pressure in the surface lines is the only pressure that will be observed. Proper definition of the surface lines allows the simulation to predict what will be observed at the pumps.

7.6.2 Tubular(s) description RWF 1.2. Tubular description. Tubular description includes the casing being cemented as well as the casing previously installed in the wellbore. In a liner configuration, the drill pipe will also be specified. Many simulators also allow the description of wellbore equipment. When the tubulars are defined, they are assigned several properties such as dimensions and mechanical resistance. Tubulars may be selected from databases, where these data are already available for most world-distributed tubular brands and standard API pipe. The data selected on the tubular page will be used in various places in the software: • These parameters are used as a primary source when the well dimensions are required. Simulators rely on the string diameters and section intervals to define well geometry. Casing collars may also be considered for volume and hydraulics calculations.

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• The security checks use the pressure ratings for the current string to check burst and collapse security margins. • The temperature simulator takes the insulated riser dimensions and thermal properties when it takes into account the cooling effect of the seawater. Simulations require a definition of the casing previously installed in the wellbore. This describes the annular flow path as fluids are expected to return to surface between the current and previous casing string. Liner hangers and associated liner hanger packers may be specified in great detail, with dimensions of both the inner flow path and external body. Dimensions should be specified to match the flow path at the time of cementing, for example, with the packer unset. The outer diameter is used to characterize the restriction in the annulus, caused by the slips and the eventual packer. The inner diameter describes the flow path restriction in the pipe, usually attributed to the running tool. This diameter is used by the software only if it is smaller than the ID of the drill pipe. All of the dimensions of the tubulars that are specified are part of the flow path of the fluids in the well and contribute to the friction pressure in the entire system. API Standard 65 – Part 2 (2010) “Isolating Potential Flow Zones During Well Construction” indicates that close tolerance and other flow restrictions should be considered. To consider these, the engineer should closely describe tools such as liner hangers, liner top packers, polished bore receptacles, stage tools, external casing packers and expandable tubulars. The more accurate the inputs, the more confidence there will be in the outputs. Components of significant length and small flow area will impact the simulations the most.

7.6.3 Hole size RWF 1.3. Hole size. Hole size is the most important factor when calculating cement volumes and simulating the cement job. Cementing volumes are typically determined by using the hole diameter, either estimated with the bit size or measured with a caliper, and then adding excess. Excess slurry volumes are typically included as part of the cementing program but should be considered carefully in the simulation. Cement excess is typically calculated as an annular excess. The engineer must understand how the excess is calculated in the simulator as annular excess and open hole excess are different values. Many simulators will display an equivalent open hole diameter to clarify how the volume is calculated.

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Hole size and excess volume are significant to the accuracy of the cement simulation. Volumes for cement slurries are typically determined by calculating the annular volume and adding cement excess. Simulations may use and equivalent hole diameter to reflect this excess. For the simulations to be accurate, it is prudent to use an accurate hole size and the fluids volumes, including excess.

7.6.4 Directional survey RWF 1.4. Directional details. Directional survey (or well trajectory) is another critical input for simulation. Simulators mostly use the directional survey to correlate MD and TVD. However, the actual 3D well shape is used for centralization, fluid displacement simulations and other 3D visualizations. Directional data are typically provided by the drilling engineer and may be entered using different types of input data: • MD, INCL, AZIM: 3D trajectory definition based on measured depth, inclination, and azimuth. Recommended and default option. • MD, INCL: 2D trajectory definition, with measured depth and inclination (no azimuth data). • MD, TVD: 2D trajectory definition, with measured depth and true vertical depth (no azimuth data). The well trajectory is typically reconstructed using the minimum curvature algorithm.

7.6.5 Formation data RWF 1.5. Formation data. The complete formation pressure profile, including pore and fracture pressures, for the well and the corresponding lithology should be defined. Outputs from the hydraulic simulations can be compared with the pore and fracture pressures at each depth to ensure that well control are maintained. The lithology data are used by the temperature simulator. All measurement points that share the same lithology, formation name, and formation fluid will correspond to the same formation stratum (layer). 7.6.5.1 Formation pressures The primary objective of cementing simulations is to make sure no well security incidents occur during the job and that losses to the formation are kept to minimal. Formation pore pressures should be known for the

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former, and formation fracture pressures for the latter. This is why the most important inputs are the formation pressures. Formation pressures may be defined by one of several methods: • Absolute: All pressures are input and displayed as gauge pressure. • Equivalent density (ED): Pressures are input as equivalent density, relative to the selected reference depth. • Gradient: Pressures are input as pressure gradient, relative to the selected reference depth. 7.6.5.2 Formation fluids The formation may be named and the fluid that fills up the pore space may also be selected. If a potential flow zone is identified that formation stratum may be marked as a potential flow zone, and the corresponding permeability and skin may also be recorded. 7.6.5.3 Lithology Formation lithology is used mainly for the temperature simulations, where the associated thermal properties are a significant component. If there is only basic data on the well geology, with only a single pressure data for each formation layer (stratum), defined by MD, formation pressures and lithology may be entered by depth. Operators often ask the geologists to provide the formation data. In this case, they frequently provide data correlated with true vertical depth (TVD). Also, they may provide a complete pressure profile, with more pressure points along all strata, what is either the result of models or measured using logging tools. In these cases, the workflow may need to be adjusted: Recommended workflow: Formation data entry (Courtesy: Schlumberger) RWF 1.5.1. Update the directional survey to match the pressure data RWF 1.5.2. Select the pressure input mode RWF 1.5.3. Select the reference depth, in case gradient or ED is selected as the pressure input mode RWF 1.5.4. Import the text file (LAS file) that contains the data RWF 1.5.5. In the Import dialog, select the data channels. Make sure the following are selected correctly: RWF 1.5.5.1. Check whether the depths are given as MD or TVD RWF 1.5.5.2. Check whether the input mode (absolute pressures, gradient, or ED) corresponds to the selection RWF 1.5.5.3. Check the order of pore and fracture pressure channels

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RWF 1.5.6. Once the import is complete, assign the pressure data to formation strata RWF 1.5.7. To evaluate risks related to gas migration, select the potential flow zones RWF 1.5.8. To estimate the formation productivity risk, fill in the data for each gas zone

7.6.6 Temperature details RWF 1.6. Temperature details. Temperature simulation is one of the most significant outputs from a cement job simulation. Formation temperatures, surface temperatures, and sea temperature profiles are important assumptions for the simulations. Detailed formation temperature profiles may not be available during the cement job design phase; in most of the cases only a bottom hole static temperature (BHST) is provided. For this reason, most simulators only require a few temperature points. Recommended workflow: Temperature data entry (Courtesy: Schlumberger) RWF 1.6.1. Surface temperature RWF 1.6.2. BHST RWF 1.6.3. In addition, for offshore wells: RWF 1.6.3.1. Sea Surface temperature RWF 1.6.3.2. Seabed temperature If there are more data points for the sea or the rock temperature, they can increase simulation precision, but are not necessarily required. 7.6.6.1 Temperature input mode Downhole temperatures are often defined based on geothermal gradients rather than temperature values. To facilitate this type of data entry, you can choose between different input modes: • Absolute: enter temperature values directly. • Gradient: enter gradients with reference temperature at the surface. Surface temperature is typically specified in the first line of the table. • Relative gradient: enter relative gradients, meaning that the reference temperature and depth for a data point is the previous data point provided. • Despite the different entry formats, many simulators convert the data to absolute temperatures indexed against MD.

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Fig. 7.2 Temperature versus water depth Gulf of Mexico. (Credit: G DeBruijn, Data from National Centers for Environmental Information, National Oceanic and Atmospheric Administration.)

Offshore operations: Seawater temperature and sea currents play a very important role in simulating well temperatures for deepwater operations. The design engineer is encouraged to obtain this data with the greatest accuracy possible. Once the rig is on location, the subsea contractor should be able to provide very detailed information on both of these parameters. However, during the planning phase, database values may be utilized. The National Oceanic and Atmospheric Administration - National Centers for Environmental Information (NOAA NCEI) databases may be utilized for seawater temperature profiles. These database values may be included in the simulator program. Note that sea currents also can have a significant influence on temperature simulation results. Fig. 7.2 is a plot of water depth vs temperature typical of the Gulf of Mexico.

7.6.7 Centralizer RWF 1.7. Centralizer(s) description. Centralization design is key to a successful cement job; good standoff will minimize cement contamination during placement and ensure the mechanical durability of the cement sheath. In addition, proper centralization can decrease running forces, in contrast with the common perception that centralizers increase the risk of casing getting stuck. The iterative process for

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designing centralizer placement will be discussed in Section 6 but for initial setup of the simulation some centralizer information is necessary. To properly calculate the standoff and running forces, centralizers and their properties are required for the simulation. Cement simulators typically include a centralizer’s database, with several types of centralizer in stock. Simulation programs also provide a method for the design engineer to create and assign centralizer properties for locally available centralizers. A stock centralizer table lists all the centralizers already added to the stock, with a few basic properties: • Alias: The name given to the centralizer model. • Casing OD: Casing outer diameter where the centralizer can be mounted on. • Min. OD: Min. diameter where the centralizer can pass (minimum compressed diameter of the centralizer). • Max. OD: Maximum uncompressed diameter of the centralizer. • Type: Rigid or Bowspring. For bowspring centralizers, additional information can be entered. Properties for bowspring centralizers can be referenced in API Specification 10D (2002) – Specification for Bow-Spring Casing Centralizers. These properties include. • Starting Force: the maximum force required to insert a centralizer into a specified diameter. • Running Force: the maximum force required to move a centralizer through a specified diameter. • Restoring Force: force exerted by a centralizer on the casing to keep it away from the wellbore wall. Load deflection information. Some centralizer manufacturers may be able to provide load deflection information which includes details of load forces versus deflection of the bow-spring centralizer. Cementing simulators vary in their capacity to utilize this load-deflection information.

7.7 Collect and input all the known fluids data RWF 2. Collect and input all the known fluids data Fluid selection for cementing operation has been thoroughly discussed in Chapter 5, Fluids. Fluids properties are critical for simulation, so they are discussed briefly here as well.

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The fluid definitions bring together all the fluid properties that are used by the software in various contexts: recipe, composition, density, and rheology. These properties can be modified to adjust important parameters. Note that for the compressible mud, fluid properties depend on pressure and temperature. Density is a critical component of hydraulic simulations. For incompressible fluids, the density of the fluid is typically considered to be the same throughout the simulation. When compressible fluids are included in the design, such as synthetic- or oil-based drilling fluids, the density may vary with the temperature and pressure conditions throughout the simulation. Density of the fluids is the most important factor for simulating the vertical component of the hydrostatic pressure. Rheology is another important component of hydraulic simulations. Chapter 6 discusses the many rheological models that can be used. The more deviated the well, the more important the rheological properties of the fluid becomes in the overall simulation. Rheological properties for each of the fluids may change with temperature, pressure, and time. Early simulators used bottom hole conditions for the rheology definitions, but with more powerful computers, changes in rheology are considered more often. For compressible fluids, changes in rheology may also be significant, and can be considered. Temperature simulations utilize the composition of fluid. Base fluid and solids content are critical components of the fluid’s definition. It is easy to understand that a water-based fluid such as a cement slurry will conduct and transport heat differently than an oil-based fluid such as a synthetic base drilling fluid. Recommended workflow for defining fluids RWF 2.1. Define each fluid Each fluid must be defined in the simulation so that the simulator can use the properties that are assigned. RWF 2.1.1. Base fluid Base fluid for cement simulation will be used for volume calculations, and also for assigning thermal properties for temperature simulation. Most cementing preflushes, including washes and spacers, are water-based fluids. Water may be freshwater, seawater, or some sort of brine. Freshwater is typically used for land operations. Offshore operations often use seawater for shallower sections and drill water, such as freshwater from a water plant, for deeper hole sections. Brines may also be incorporated in fluids as the base fluid. Drilling fluids may use water, oil, or synthetic fluids as a base fluid.

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RWF 2.1.2. Solids content and density The solids component of each fluid is important for cement simulation. The solids content and the density of the solids’ component together with the base fluid will define the overall density of the fluid. Typically referred to as weighting agents, solids for spacer fluids may be made up of silica, fly ash, calcium carbonate, barite, or hematite. The solids in the cement slurry include the cement itself, silica components, and any dry additives. The solids component of the fluids will be used to calculate the solids component of the slurry and can also be used to calculate the yield and mix water requirements for a given fluid. RWF 2.1.3. Rheological properties The rheological properties of the fluid will be used together with the density of the fluid for the hydraulic calculations. Rheological models are discussed in Chapter 6. Computer simulators will use laboratory measurements and assign a rheological model to the fluid. It is important to have laboratory measurements at downhole and surface conditions. Additionally, for compressible fluids there should be rheological properties measurements for at least three pressure and temperature conditions. The rheological properties of cementing fluids (washes, spacers, and cement slurry) are required to complete the fluid characterization before running any simulations. It is not only used to calculate friction pressures for the hydraulic simulations but also it plays a large role when heat transfer is calculated by the temperature simulator. Note that shear stress and model parameters calculated based on API tables or manufacturer formula may not exactly match those calculated by the simulation software. For more details on rheological models and related calculations (including model fits), consult the following literature “Well Cementing (Nelson et al., 2006), Chapter 4, Rheology and Flow of Well Cement Slurries”. RWF 2.1.4. Noncompressible/compressible Fluids should be defined as noncompressible or compressible. Traditionally, most cementing fluids have been considered to be noncompressible as they are water-based fluids that contain solids. An oil- or synthetic-based drilling fluid may be considered compressible because the volume of the base fluid will change with temperature and pressure. Defining the compressibility of the fluid will aid in calculating displacement volumes, especially for deep water offshore wells. For some wells the compressibility factor may be assumed to be small (and therefore negligible), and subsequently not considered in the simulation. Foamed fluids that include nitrogen should be considered to be compressible as there are significant volume changes within.

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7.7.1 Define drilling fluid RWF 2.2. Define drilling fluid. In the most basic scenario, when fluids are created for a cement job, the drilling mud is described as an incompressible fluid. For these incompressible drilling fluids, their properties (composition and rheological properties) are defined quite simply. The simulators will use the density to calculate hydrostatic pressures. The thermal properties are calculated based on the subtype of drilling fluid, the exact volume fraction and the fluid density. Simulators are able to use many of the drilling fluid properties that are reported on the daily drilling report including the following: - Density: Density of the drilling fluid (mud weight). If the data are coming from the field, it is recommended to use values measured using pressurized mud balance. - Mud Type—The following types are typically referred to:
Brine: Clear brine (solution of a salt) with minimal solid content, usually used as completion fluid.
Oil-based mud (OBM): Drilling fluid where mineral oil is the continuous (outer) phase of the emulsion.
Synthetic-based mud (SBM): Drilling fluid where synthetic oil is the continuous (outer) phase of the emulsion.
Water-based/fresh water (WBM): Drilling fluid that is completely fresh water based (i.e., without oil content) or where the oil is the dispersed (inner) phase.
Water-based/salt water (WBM): Drilling fluid that is completely salt water based (i.e., without oil content) or where the oil is the dispersed (inner) phase. Additionally the actual ratio of the components can be defined based on the following volume fractions which may also be included in the daily drilling report and mud report: - LGS volume fraction: The volume fraction (percentage) of the low gravity solids (LGS). This would include bentonite used to viscosify/ inhibit the drilling fluid, natural clays and most formation cuttings (sands/ shales/limestone). - HGS volume fraction: The volume fraction (percentage) of the high gravity solids (HGS). This would usually mean the weighting agent (barite, hematite, etc.) added to the drilling fluid. - Oil volume fraction: The volume fraction (percentage) of the oil/synthetic oil included in the drilling fluid. - Water volume fraction: The volume fraction (percentage) of the water (or brine) in the drilling fluid.

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7.7.2 Define spacer/wash RWF 2.3. Define spacer(s) and wash(es). Simulators may allow the choice between two modes to calculate the composition for spacers and slurries, depending on the target that is specified. If density is specified, the SVF (solid volume fraction) will be adjusted to achieve the density. If the SVF is specified, the simulator will keep the solid–liquid ratio constant in the composition and calculate the resulting density. The base fluid, weighting agents, and additives may all be specified.

7.7.3 Define slurries RWF 2.4. Define slurry(s). 7.7.3.1 Slurry composition When designing a slurry, one of the most important steps to define its recipe. The simulator will help in this task with different calculations as the fluid compositions are entered. Chapter 5, Fluids, provides detail on the selection of cement and additives for the design of a cement slurry. The following paragraphs describe the slurry definition and simulation results. The slurry composition is calculated based on the density or SVF target for the calculations; the additive concentrations; the composition of the mix water, including base fluid selection; the blend composition; and the concentration of additives, whether they are dry-blended or added to the mix fluid. 7.7.3.2 Sack sizes All slurry additive concentrations are typically referenced to a sack of cement or blend in standard oilfield practice. This practice assumes that the sack weight is known, standardized, and agreed. Simulators allow the user to edit the cement and blend sacks based on cement weight or blend weight. Cement Weight: The reference sack weight for concentrations provided for a sack of cement. Default value for normal cement is 94 pounds. For operations that use the international system of units (SI) the sack weight is typically set to 1000 kg or 1 metric tonne. Blend Weight: The reference sack weight for concentrations given for a sack of blend. The default value is 94 pounds for neat cement. Specialty blends may have the equivalent sack weight set to 100 pounds. Pozzolanic blends may have the equivalent sack weight set to the weight of one cubic foot of blend.

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7.7.3.3 Calculation results Simulators then provide several calculations based on the slurry composition. These calculations are related to the composition itself, produced from the recipe which was created to achieve the specified target. These calculation results are useful for operational planning, especially for cement blending and storage, mix fluid requirements, and liquid additive management. 7.7.3.4 Blend properties Blend density: Calculated absolute blend density, including dry additives. The weighted average of the blend components’ absolute densities. Bulk density: Calculated minimum bulk density. 7.7.3.5 Concentrations Base fluid: Calculated concentration of the base fluid (fresh water or sea water). Base fluid concentration is expressed as a volume ratio to either the cement or the blend, for example, by volume of cement (BVOC) or by volume of blend (BVOB). Units are typically gal/sk or m3/tonne. Mix water: Calculated concentration of the mix water (base fluid with added salt). Mix water ratios are expressed similarly to base fluid either BVOC or BVOB. Mix fluid: Calculated concentration of the mix fluid (mix water with all additives, the liquid phase). Mix fluid ratios are expressed either BVOC or BVOB in units of gal/sk or m3/tonne. 7.7.3.6 Mixing parameters Yield: The volume of slurry that can be prepared with a given amount of cement or blend. SVF: The calculated solids volume fraction of the slurry. 7.7.3.7 Silica ratio The silica ratio is the calculated ratio of reactive silica to the cement mass. This ratio is calculated because long-term set cement properties can be affected by the silica ratio when the set cement is exposed to temperatures above 110°C (230°F). 7.7.3.8 Post addition Post addition calculations allow the user to select an additive that will be added to the slurry itself, once the slurry is mixed.

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The calculation for postaddition can be performed based on a target density or a preset concentration of the additive. It will calculate the other parameter, assuming that a base slurry was mixed to the designed density. Post addition calculations provide the following answers: - Final density: The density once the post addition is done. - Concentration: The concentration of the additive added to the slurry. - Final volume: The volume of the slurry in the laboratory after the post addition is completed. - Per 600 mL: The amount of additive required to be added to the base slurry in the laboratory. 7.7.3.9 Additive breakage This calculation is available only when the blend contains at least one additive susceptible to breakage (such as Litefil). Selecting the additive breakage option lets the user check the effect of crushing, after selecting the additive from the dropdown menu. The calculation can be performed either based on a measured density after exposing the slurry to the downhole pressure or based on a theoretical crush rate. Additive breakage calculations yield the following answers: - Density at P: The density of the slurry at downhole pressure - Crushed: The percentage of the particles crushed - Crushed additive SG: The specific gravity (SG) of the crushed component at downhole pressure
Volume reduction factor: Reduction of the slurry volume when crushability taken into account.
Blend yield at P: The yield of the slurry at downhole pressure.
Downhole SVF: The SVF of the slurry at downhole pressure. 7.7.3.10 Laboratory tests Many simulators include a section where the laboratory test results may also be reported. Slurries may be tested according to practices specified in API RP 10B-2 (2013)—Recommended Practice for Testing Well Cements. Simulators may include reporting for the following tests: - Slurry preparation - Slurry density - Well-simulation compressive strength tests - Nondestructive sonic determination of compressive strength - Well-simulation thickening time tests - Static fluid-loss tests

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- Rheological properties - Well-simulation slurry stability tests - Compatibility of wellbore fluids - Arctic cement slurries tests

7.7.4 Define displacement fluid RWF 2.5. Define displacement fluid. The displacement fluid may be water or drilling fluid. If it is water it may be defined similar to a wash, if it is a drilling fluid, it can be described as the drilling fluid previously. Often cement jobs are displaced with the drilling fluid that will be used in the next section of the wellbore. If the drilling fluid that will be used for the next section is different than the current section (e.g., the rig is changing to nonaqueous drilling fluid), then both the original fluid in the well and the displacement fluid need to be specified. Each fluid will have its own specific density, compressibility, and thermal properties.

7.8 Design additional fluids RWF 3. Define additional fluids. Additional fluids and slurries may be needed to meet all of the design criteria for the well. In these cases, it may be necessary to add more fluids and iterate on previous fluids to achieve the desired performance. Updates or changes to fluids may be based on density, rheology, compatibility, component availability, or set cement properties. Cost may also be a consideration for changes in fluid design. Once fluids are designed, they may be tested in the laboratory. Fluid selection is discussed extensively in Chapter 5.

7.8.1 Design fluid based on density RWF 10.1. Design fluid based on density. The density of the fluid may not meet the well control requirements. With the fluids in the wellbore, well control must be maintained. If the hydrostatic pressure in the wellbore is below the pore pressure at any time during the cement job, the density of some of the fluids may need to be increased. On the other hand, if the density of the cement column is higher than the fracture pressure of the formation, some of the fluid densities may need to be reduced. If managed pressure cementing will be part of the operation,

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then the back pressure will also have to be considered when designing the fluid density.

7.8.2 Design fluid based on rheological properties RWF 10.2. Design fluid based on rheological properties. The rheological properties of each fluid have a significant impact on the displacement efficiency of that fluid. Higher rheological properties may be required for better displacement of the previous fluid. Conversely, lower rheological properties will allow easier displacement by the following fluid. Typically, a fluid such as a spacer will be required to have a rheology between the drilling fluid and the cement slurry. Chapter 6 discusses rheological models and how they may be used in the design.

7.8.3 Design fluid based on compatibility RWF 10.3. Design fluid based on compatibility. Test procedures for testing compatibility of wellbore fluids are described in API 10B-2 (2013) Recommended Practice for Testing Well Cements in Section 13. Spacers should be compatible with both the drilling fluid and the cement slurry. Cement simulators may provide suggestions for additives or fluid designs to achieve compatibility requirements. The cement design engineer may be able to perform several simulations based on laboratory compatibility tests to understand the effects of the fluid compatibility on the overall design.

7.8.4 Design fluid based on component availability RWF 10.4. Design fluid based on component availability. Substitution of components, additives, or complete fluids is a common engineering challenge. Substitution may be required because of cost, availability, performance or a combination of the three. Cementing simulators allow the design engineer to change components and additives, update the laboratory tests, and rerun the simulation to understand and evaluate the effects of the substitution.

7.8.5 Design fluid based on set cement properties RWF 10.5. Design fluid based on set cement properties. Set cement properties are an important consideration. Regulatory requirements in most jurisdictions include a minimum compressive strength requirement. In some locations where temperatures above 230°F are encountered there may also be a requirement for the cement to be thermally

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stable. Cement simulators allow the analysis of the active silica content to provide confidence that the cement is thermally stable. Permeability of set cement is generally considered to be extremely low or near zero, and this low permeability is the basis for the assumption that cement is a barrier. Other mechanical properties such as Young’s modulus and Poisson’s ratio may also be considered for the cement design. These mechanical properties may be used in finite analysis simulations of the wellbore throughout the life of the well. Expansion and/or shrinkage is another property of the set cement that may be considered in the design.

7.9 Design fluids volumes, pump schedule, and fluids preparation requirements RWF 4. Design fluids volumes, pump schedule, and fluids preparation requirements. Once the fluids are selected, the volumes and pump schedule need to be specified and fluids preparation requirements need to be detailed. Intuitively, when creating a cement program, this step is performed at the same time as selecting and designing the fluids. The steps are separated here because the fluid definition can have a significant impact on the output of the simulation. The fluid volumes and pump schedule are decided after the fluids are specified, and the fluids preparation requirements are based on the fluid design.

7.9.1 Recommended workflow—Fluid volumes RWF 4.1. Fluid volumes. Calculating the fluid volumes, including slurry volume, is one of the most important parts of the cement job design. The volume is critical to ensure that job requirements, such as cement top requirements, are met and these volumes are used for cement job preparation. Fig. 7.3 shows an example of a Well Schematic, along with a table of the fluid’s volumes in both the annulus and the casing, referred to as pipe in the table. RWF 4.1.1. Check and update the well description so that it is current RWF 4.1.2. Check that the fluids to use for the calculations are all defined RWF 4.1.3. Select volumes of fluids based on cement job objectives RWF 4.1.3.1 Annular volume/height for tail cement RWF 4.1.3.2 Annular volume/height for lead cement RWF 4.1.3.3 Spacer volume

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Fig. 7.3 Well schematic with fluids volume table. (Credit: Schlumberger.)

RWF 4.1.3.4 Any additional fluids ahead of the spacer RWF 4.1.3.5 Shoe track fluid RWF 4.1.3.6 Displacement fluid RWF 4.1.4. Check the hydrostatic pressure gradient against the formation pressures using well security plots RWF 4.1.5. If necessary, fine tune the volumes for complex fluid sequences RWF 4.1.6. Proceed to defining the pump schedule

7.9.2 Recommended workflow—Pump schedule RWF 4.2. Pump schedule. Determining the pump schedule is critical for understanding the equipment requirements for the job. The volumes that have been previously calculated must be pumped in a timely fashion with the appropriate pumps. Cement pumps are used to pump cement slurries, and rig pumps or cement pumps may be used for displacement. Pump schedules are typically based on local experience and may be adjusted to meet specific design criteria. Iterations on the pump schedule are typically performed to achieve better mud removal (annular displacement), or to prevent losses near the end of the displacement process. Table 7.1 provides an example pump schedule for a cement job. During the design process, it is common to iterate on the pump schedule after the hydraulics simulation has been completed. RWF 4.2.1. Check and update the well description so that it is current RWF 4.2.2. Set the back pressure for each stage

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Table 7.1 Example of cement job pump schedule. Pumping schedule Pump rate Duration Volume bbl/ min Fluid name h:mn bbl

Injection temperature °F Pumped by

Cumulated time h:min

Spacer

00:16

70.0

00:16

Plug

00:05

Cement pump Drop bottom plug Cement pump Cement pump Drop Top Plug Cement pump

02:34 02:39 02:42

80.0

5.0

Lead slurry 00:21

166.8

8.0

80.0

Tail slurry 00:34

102.0

3.0

90.0

Plug

00:10

Spacer

00:02

10.0

Mud total Schedule below: Mud Pause Mud

01:14

670.2

01:06 00:05 00:03

5.0

70.0

660.2

10.0

80.0

Rig pump

10.0

3.0

80.0

Rig pump

00:21

00:42 01:16 01:26 01:28

RWF 4.2.2.1 If returns are normally to the drilling fluids tanks with no restrictions, the back pressure may be assumed to be zero. RWF 4.2.2.2 If returns are taken at seabed, set up the surface description accordingly RWF 4.2.2.3 If there is a managed pressure device (MPD) select the back pressure appropriately RWF 4.2.3. Use fluids volumes determined in RWF 4.1 RWF 4.2.4. Set up the various stages of the pumping schedule. Initial pump rates may be chosen based on offset wells, experience, or job objectives. Note that selecting the pump rates may be in iterative process. RWF 4.2.4.1 Select rig pump or cement pump for pumping spacer RWF 4.2.4.2 Select cement pump for pumping cement slurry RWF 4.2.4.3 Select rig pump or cement pump for pumping displacement

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RWF 4.2.4.4 Select the pump rates for each stage RWF 4.2.4.5 Add reasonable pauses for operations such as dropping cement plugs RWF 4.2.4.6 The displacement period may be divided with slower pump rates near the end of displacement RWF 4.2.4.7 Optional—add a pause for wait-on-cement (WOC) at the end of the pumping period. Adding a pause at the end of the pumping period is useful for simulating the temperature during the WOC time. This temperature simulation can be used for developing a laboratory test schedule for testing compressive strength to determine when the cement can be counted on as a barrier and the earliest that it can be drilled out.

7.9.3 Recommended workflow—Fluid and blend preparation RWF 4.3. Fluid and blend preparation. Blend preparation will be based on the recipes that are determined in the fluid definition: Recommended workflow: Fluid and blend preparation (Courtesy: Schlumberger) RWF 4.3.1. Select the amount of blend or total fluid volume to prepare. The blending sheet then computes the required quantities for each component. RWF 4.3.2. Specify the measured bulk density (if available). This is used to adjust the required bulk capacity to store the blend. RWF 4.3.3. Specify the batch parameters for the bulk plant operation: the silo capacity available and which practices should be followed when blending. RWF 4.3.4. Select the options for the packaging: how the materials are packaged and whether packages are divisible. RWF 4.3.5. Review the distribution of packages among and within the batches, the blend composition in the batch, and the overall blend properties. If the results are not satisfactory, check possible changes to packaging options for improving the results. RWF 4.3.6. Once satisfied with the results, generate the report with the blending sheet, which can be sent to the bulk plant. Table 7.2 provides an example operator load out sheet that can be provided to the bulk plant.

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Table 7.2 Example operator load out sheet. Volume summary Pumped Prepared fluid Prepared Mix fluid dead volume Silo dead volume volume dead volume fluid bbl tonne Bbl bbl Fluid name bbl

Lead slurry 166.8 Tail slurry 102.0 Spacer 90.0

0.0 0.0 0.0

166.8 102.0 90.0

0.0 0.0 0.0

0 0 0

Material summary Additive

Barite— weighting agent Fresh water Viscosifier Bentonite Lead slurry blend Mix water Salt Antifoam Extender Fluid Loss Control Dispersant Retarder Tail slurry blend

Pumped quantity

Required Loadout quantity quantity

Loadout Pack. Pack. items name size

22,655 lb 22,655 lb 22,655 lb 205.96

sack

110 lb

8883 gal 270 lb 297 lb 59,868 lb

8883 gal 270 lb 297 lb 59,868 lb

8883 gal 270 lb 297 lb 59,868 lb

0.00 5.40 2.70 0.00

sack sack bulk

0 gal 50 lb 110 lb 0 lb

5801 gal 927 lb 57 gal 318 gal 929 gal

5801 gal 927 lb 57 gal 318 gal 929 gal

5801 gal 927 lb 57 gal 318 gal 929 gal

0.00 16.85 11.30 6.37 17.53

sack pail drum drum

0 gal 55 lb 5 gal 50 gal 53 gal

61 gal 61 gal 61 gal 1.16 147 gal 147 gal 147 gal 18.39 46,395 lb 46,395 lb 46,395 lb 0.00

Comment

drum 53 gal pail 8 gal bulk 0 lb

7.10 Perform hydraulics and temperature simulation RWF 5. Perform hydraulics and temperature simulation. Hydraulics simulation is typically considered the main component of cement job simulation. The hydraulics simulations are used to calculate the hydrostatic and friction pressure components of pressure throughout the wellbore and through the entire cement job so that well control can be predicted and maintained. Temperature simulation is typically done at the same time as hydraulic simulation and is critical to provide temperature and pressure schedules to the laboratory for slurry testing.

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Multiple fluids with multiple density and rheological properties add complexity to the simulation. Cement slurries are typically heavier than the drilling fluid and will therefore “U-tube” forward during the cement job. U-tubing is a well-known phenomenon observed at the well site during cement jobs, with returns increasing during cement mixing operations, and then decreasing during displacement until the pumps “catch up” to the cement. This U-tubing simulation is what sets cement simulation apart from other wellbore hydraulic simulators. A cement simulator must take into account the U-tubing effect for both hydraulic and temperature simulation. The entire hydraulics simulation typically includes prejob well circulation and the cement job itself. Wait on cement (WOC) time may be simulated for temperature, and additionally postcementing operations such as circulating cement off a line top may be simulated.

7.10.1 Simulate prejob well circulation RWF 5.1. Simulate prejob well circulation. Prejob well circulation is often called conditioning as this circulation breaks the gels of the drilling fluid and also may be used to reduce the bottom hole temperature. A simulation is used to predict the temperature change in the well before cementing. The simulated pressure may also be compared with the actual pressure during prejob circulation as a verification that all of the wellbore assumptions (including hole size and drilling fluid rheology) are consistent with the observations at the well. A simulation of bottom hole temperature compared with prejob well circulation time is presented in Fig. 7.4. In this case, most of the temperature changes occur in the first 3 h. This knowledge can be used to plan the operations at the well site. An engineer may specify that the well must be circulated at least 3 h before cementing. Alternatively, no prejob circulation is planned, it may be assumed that the bottom hole temperature will be near the geothermal gradient. In any case, the prejob circulation time and pump rate should be used as the starting point for the temperature simulation for the cement job. If no prejob circulation is planned, then the geothermal gradient can be used as the starting point for the cement job temperature simulation. Recommended Schlumberger)

workflow—Prejob

well

circulation

(Courtesy

RWF 5.1.1. Check and update the well description so that it is current RWF 5.1.2. Define the fluids used for the cement job, paying attention to the drilling fluid properties:

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Fig. 7.4 Bottom hole temperature during prejob circulation. (Credit: Schlumberger.)

RWF 5.1.2.1 For accurate temperature predictions, make the correct mud type and composition is entered RWF 5.1.2.2 To run compressible hydraulic simulations, define a compressible drilling fluid RWF 5.1.3. Select the wellbore fluids for the mud circulation If a compressible mud is selected, run the simulation with the corresponding compressible fluid simulator. RWF 5.1.4. Choose the injection temperature model to be used during the simulation RWF 5.1.5. Set up the pumping schedule using the mud circulation table RWF 5.1.6. Run the simulation RWF 5.1.7. Review the security checks RWF 5.1.8. The results of the mud circulation may be used as the initial temperature condition for the cement job simulation.

7.10.2 Simulate cementing operations RWF 5.2. Simulate cementing operations. Pressures and temperatures will be predicted by the cement simulator. The simulation uses all the wellbore and fluid assumptions that have been entered into the simulation. The pump schedule is used to simulate the rates of fluid that are entering the wellbore. If back pressure is applied, it will also be accounted for in the simulation.

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The output of the simulation is pressure and temperature predictions. The pressures can be plotted throughout the wellbore and compared with the pore and fracture pressures in a well security plot. If the pressures on the well security plot are between the pore and fracture pressure, then the engineer can be confident that well control is maintained. Fig. 7.5 is an example of a well security plot, which illustrates that the pressures can be plotted as either pressures or equivalent mud weights. It is customary to show minimum and maximum pressures for the entire cement job. Table 7.3 is an example of a well security check in tabular format, indicating in numerical format how close the simulated pressures are to pore pressure, fracture pressure, casing collapse, and casing burst and the depths where the closest approach is. Iterations to the design may be applied if it is not possible to simulate the pressures between the pore and the fracture pressures. Many iterations may

Fig. 7.5 Example of well security plots. (Credit: Schlumberger.) Table 7.3 Example of well security check table. Well security Status

Description

Min differential pressure psi

At depth ft

At time h:min

Success Success Success Success

Fracturing Production/Influx Burst Collapse

1351 204 4350 3266

5350.0 5350.0 0.0 4200.0

01:30 01:30 01:30 01:30

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be required especially for wells that have a very tight pore pressure/fracture pressure window. One can go back to the fluid design and change the density of the fluids to achieve the desired results. Fluid rheological properties may also be changed by adjusting additive concentrations. The pump schedule may be adjusted to meet the design requirements. Combinations of these changes together with back pressure that can be applied with management pressure cementing equipment may even be contemplated and simulated to ensure that well security is maintained. Surface pressure and return flow rate are also simulated and can be used for operational planning purposes. Recommended workflow—Cement operations hydraulic and temperature simulation (Courtesy: Schlumberger) RWF 5.2.1 Run the hydraulic simulation using the planned pump schedule RWF 5.2.2 Confirm that design parameters are met including well security. Review the security checks, that well control is maintained, and cement losses (if simulated) are manageable. RWF 5.2.3 Check minimum hook load to ensure that the risk of casing pump out is not present RWF 5.2.4 Check pump horsepower requirement against available capacity. RWF 5.2.5 Verify key temperature values against laboratory test conditions. Detailed pressure and temperature results may be used to prepare or update laboratory test requests. RWF 5.3 Iterate by adjusting the pump schedule as necessary Operations can be planned based on the simulated schedule. Fig. 7.6 is an example of the surface pressure prediction for this job. The difference between the cement head pressure and the cement pump pressure is the friction pressure that will occur in the treating line from the cement pump to the cement head. In this simulation, the maximum pressure is simulated to be 527 psi at 2 h 34 min, with the final pressure simulated at just over 500 psi. It is customary to bump the plug at 500psi over the final circulating pressure which will require the cement head and all the surface treating iron to have a pressure rating higher than 1000 psi. The rate and pressure simulation can be used to calculate the maximum pump horsepower (hp) that will be required for the job. The pump rates in Fig. 7.7 combined with the pressure in Fig. 7.6 can be used to estimate that the maximum horsepower required during displacement, in this case 129 hp. The design engineer should check that the pump used for displacement is

Job simulation and design

Fig. 7.6 Surface pressure prediction. (Credit: Schlumberger.)

Fig. 7.7 Pump and return rate simulation. (Credit: Schlumberger.)

325

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capable for this pressure and rate. If the pump is not capable, a different pump may be sourced, or the pump schedule can be changed (slowed down) to match the capability of the pump. A comparison of the pump rate and simulated return rate can also be used to predict the level changes in the drilling fluids pits. Fig. 7.7 shows the return rate compared with the pump rates. At the beginning of the job during mixing operations, the U-tubing effect can be observed with returns up to 10 bbl/min while only mixing at 8 bbl/min. The drilling fluid pits can be configured to accept the returns at this rate. After displacement is started, note that the returns are slower than the pump rate, also due to the U-tubing effect. If the rig pump is displacing the cement job this discrepancy is often misinterpreted as “losses.” In fact, this reduction in pit volume can be entirely predicted by integrating the difference between the pump rate and the return rate during the simulated displacement period. Hydraulic simulation is also useful for complex wells such as horizontal wells. RWF 5.1 and RWF 5.2 can be used for planning cementing operations in extended reach horizontal wells. Fig. 7.8 is the surface pressure simulation for horizontal well with a 7000 ft. horizontal section. Observe that the surface pressure is simulated to be quite low during mixing operations. During displacement, starting at approximately 2 h, the U-tubing effect is

Fig. 7.8 Surface pressure simulation for horizontal well. (Credit: Schlumberger.)

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Fig. 7.9 U-Tubing simulation for a horizontal well. (Credit: Schlumberger.)

quite short, as seen in Fig. 7.9, and pressure increases linearly while displacing the vertical section of the well. There is an inflection at approximately 2 h 30 min indicating the displacement of the horizontal section of the well. The higher pressures for the last 1.5 h of displacement will require 225–400 hydraulic horsepower. Hydraulic simulation is also useful for adjusting the pump schedule for a horizontal well. Fig. 7.10 plots the bottom hole equivalent circulating density (ECD) and compares it with the pore and the fracture pressure. The annular pressure including the friction pressure is plotted. When it approaches the fracturing pressure, at 2 h 46 min, the pump rate can be slowed so that the ECD remains below the fracture pressure. The annular balanced pressure is also plotted, so that if operations need to stop for any reason, well security can be assessed as safe because the annular pressure is higher than the pore pressure. 7.10.2.1 Minimum hook load Owing to pressure and density difference, bouyancy forces may become large enough at the end of displacement that they overcome the casing weight. This is called casing pump out, as the casing can be lifted up at this point, unless it is fixed to the rig floor. Usually this occurs with large diameter and relatively thin casing, and it can be prevented by securing the casing to the rig floor.

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Fig. 7.10 Equivalent circulating density at TD for a horizontal well. (Credit: Schlumberger.)

7.10.2.2 Compressible simulations What we call compressibility encompasses several phenomena. The compressible simulation can consider density variation due to pressure and temperature (compressibility and thermal expansion), as well as rheological property variation to pressure and temperature. However, the simulator relies on fluid models to tell how the density and the rheological properties changes. Compressibility may be considered when calculating the displacement volume if the displacement fluid is a compressible fluid. Depending on the temperature and pressure conditions, the compressibility of the fluid may require additional volume to be pumped to bump the plug. 7.10.2.3 Simulating temperature schedule for cement laboratory testing Temperature simulation is another critical component of cement job simulation which is related to the hydraulic simulation. The hydraulic simulation predicts where the fluids are in the wellbore and for what time period, then temperature simulation calculates the heat transfer between the formation,

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the annular fluids, the casing, and the fluid inside the pipe. Because cementing is a short duration operation with several different fluids, the temperature simulations are transient in nature. Predictions of the temperature can then be used to create a pressure and temperature schedule for laboratory testing of the fluids. Temperature simulation is also useful for understanding the temperature profile in the well during and after the cement job. Fig. 7.11 helps us to visualize the temperature in the horizontal well. The geothermal temperature is plotted as a red line versus total MD (TMD) so that we have our reference. Tubular and annular fluids are plotted so that we can visualize how a fluid, spacer or cement, heats up as it travels down the wellbore and cools off as it comes back up. Returns temperatures may also be monitored and compared with the simulated returns temperature at surface. A laboratory test schedule can be defined by converting the temperature and pressure profile changes to a schedule for the laboratory to test. Fig. 7.12 plots the fluid temperatures at each interface versus the time during the cement job. Fig. 7.13 plots the pressure of the interface versus time. The combination of pressure and temperature will give the schedule for the laboratory test.

Fig. 7.11 Temperature Profile after cementing a Horizontal Well. (Credit: Schlumberger.)

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Fig. 7.12 Temperature versus time for each fluid interface. (Credit: Schlumberger.)

Temperature simulation can also be performed for the wait on cement (WOC) time. This temperature simulation can be used for compressive strength simulation tests at a specific spot in the wellbore. The temperature prediction can also be used for interpreting temperature logs or understanding other temperature-related phenomenon in a wellbore. Fig. 7.14 plots the annular and in pipe temperature near the TOC throughout the entire cement job including the WOC time. The first 3 h of the simulation are during the cement job, followed by 24 h of WOC.

7.10.3 Standalone calculation aids RWF 5.4 Standalone calculation aids. Some simulators include standalone calculators that may assist the design engineer in understanding the friction pressures in the pipe or in the annulus so that they can better choose a pump rate for the hydraulic simulation. The following is an example workflow for a friction pressure calculator:

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Fig. 7.13 Pressure versus time for each fluid interface. (Credit: Schlumberger.)

Fig. 7.14 Temperature simulation through job and WOC time. (Credit: Schlumberger.)

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Recommended workflow—Friction pressure—standalone (Courtesy: Schlumberger) RWF 5.4.1. Specify the geometry to calculate the friction pressures (annulus or pipe) RWF 5.4.2. Specify whether to sensitize by flow rate or by geometry RWF 5.4.3. Specify the fixed parameters for geometry or flow rate, as applicable RWF 5.4.4. Enter the range of parameters for sensitizing RWF 5.4.5. Review the calculation result in the friction pressures table or chart that is displayed RWF 5.4.6. Compare the results with both surface and downhole rheological properties Friction pressures compared with shear rates are presented in Fig. 7.15. Other scales may be used in these plots to aid with the design. Another common scale is pump rate on the x-axis versus pressure drop/1000 ft. on the y-axis. In general, it is desirable for displacing fluids to be “thicker” than the displaced fluids, which would be indicated by successively higher lines on this graph. For example, a sequence of fluids from mud to spacer to lead slurry to tail slurry is desirable. This graph may also be used to interpret at

Fig. 7.15 Friction pressure—Stand alone aid. (Credit: Schlumberger.)

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333

what shear rates (or pump rates) the desired friction pressure hierarchy is not met. The design engineer can use this graph to quantify what fluid rheological properties may be required to meet the design requirements.

7.11 Perform casing centralization simulation RWF 6. Perform casing centralization simulation. Centralization design is key to a successful cement job. Good standoff is required to minimize cement contamination during placement and to ensure the mechanical durability of the cement sheath. In addition, centralization can minimize casing buckling and decrease running forces which can aid in casing running. Fig. 7.16 illustrates what needs to be considered in the simulation, from the centralizers themselves, to the forces involved, the position of the pipe in the wellbore and the fluid flow around the pipe.

7.11.1 Centralization standoff calculations RWF 6.1. Centralization standoff calculations. Calculating the standoff, otherwise known as the centralization, is the basis for annular displacement simulations and understanding the cement coverage in the annulus. In general, the closer the pipe is to the center of the wellbore, the easier it will be to displace the drilling fluid and achieve cement

Fig. 7.16 Centralization of casing in a wellbore. (Credit: Pegasus Vertex, Inc.)

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all around the pipe, which may be translated into a better cement job. Circumferential cement placement may even be one of the cementing objectives. Optimizing the centralizer placement and understanding the resulting centralization is critical to achieving a successful job. Centralization or standoff can be calculated for the casing at any point in the wellbore. It can be calculated at the centralizer, or at the midway point between the centralizers. The formula for standoff given in Eq. (7.1) will result in a number between 0 and 1 which can also be converted to a percentage between 0% and 100%. Fig. 7.17 translates the variables in Eq. (7.1) to the wellbore configuration. Standoff equation STO ¼ C=ðA  BÞ

(7.1)

where STO is the Standoff (%); A is the radius of the actual borehole (units must be the same as B and C); B is the radius to outside of casing (units must be the same as A and C); and C is the distance from the casing to the borehole wall on the narrow side of the annulus (units must be the same as A and B). Many cementing engineers set a minimum standoff as the design criteria. It is more important to understand what the centralization is in the wellbore, and how it will affect the cement placement. There are several models for calculating the centralization. The most common are soft string and stiff string. Soft and stiff imply how the forces are applied along the casing string. Factors that are considered in all models of centralization calculation are the deviation of the wellbore, the weight of the casing, buoyancy of the casing, restoring force of the centralizer and dimension of the centralizers.

Fig. 7.17 Standoff calculation. (Credit: Pegasus Vertex, Inc.)

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Fig. 7.18 Soft string or hinged end centralization model. (Credit: Pegasus Vertex, Inc.)

Soft string centralization calculation details can be found in API 10D-2 (2004)—“Recommended Practice for Centralizer Placement and Stop-collar testing” Section 4. The equations are used to calculate the casing deflection between two identical centralizers, and they assume that the casing is in tension. Fig. 7.18 illustrates the assumptions made in the soft string model, especially that the moment forces are not transmitted through the casing string. A soft string model assumes that the casing deflection will be to the lower side of the wellbore, due to gravitational forces. This model may also be referred to as a “hinged end model.” One of the models to calculate casing deflection between centralizers is developed by Juvkam-Word and Wu (1992). This model considers the fixed-ends boundary for one span of casing between two centralizers. The fixed-ends approach is more realistic than the hinged-ends assumption used in some of the old software because it simulates the casing string as a continuous beam. In fact, the hinged-ends boundary assumes a casing string that transmits no bending moment across centralizers, which results in the prediction of excessively high casing deflection. Stiff string centralization models are similar to the fixed-ends approach and have been developed to consider the effects of casing forces including compression and tension, lateral loads on the casing, and highly deviated wellbores. Where a soft string model assumes that the deflection of the casing will be to the lower side of the hole, a stiff string model may simulate that the casing can deflect in any direction in the wellbore depending on the combinations of gravitational forces and axial forces along the wellbore. More details comparing stiff and soft string centralization calculations can be found in SPE 163424 “Comparing Soft-String and Stiff String Method used to Compute Casing Centralization”(Gorokhova et al., 2013). Fig. 7.19 illustrates the fixed end or stiff string approach to calculating centralization.

Fig. 7.19 Stiff string centralization model. (Credit: Pegasus Vertex, Inc.)

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Recommended workflow—Centralization standoff calculations (Courtesy: Schlumberger) RWF 6.1.1. Check and update the well description so that it is current. At the planning stage, it is a good practice to plan based on the expected tortuosity, once a well is drilled, the actual trajectory may be used. RWF 6.1.2. Run the hydraulic simulator, as centralization calculations rely on placement pressures to obtain buoyancy forces. RWF 6.1.3. Select the centralizers planned for the job and add them to the centralizers stock on the centralization page. RWF 6.1.4. Define the centralizer placement RWF 6.1.4.1. Placement may be described as a placement pattern RWF 6.1.4.2. The exact depth for each centralizer may be specified RWF 6.1.5. Select a centralization model for the standoff calculation RWF 6.1.6.1. Soft string RWF 6.1.6.2. Stiff string RWF 6.1.6. Run standoff calculations. The standoff calculation can be performed for three different stages of the cement job to understand the maximum and minimum standoff during cementing. The standoff will change because the density difference between the fluids inside the pipe and in the annulus affects the buoyancy of the casing. The three cases to simulate are as follows: RWF 6.1.6.1. Just before cementing, only drilling fluid in the well (pipe neutral simulation) RWF 6.1.6.2. Just as cement turns the shoe (pipe heavy simulation) RWF 6.1.6.3. At end of displacement (pipe light simulation) RWF 6.1.7. Review the standoff results RWF 6.1.8. Use standoff results for annular displacement simulation 7.11.1.1 Optimizing the centralization design The workflow above may be adjusted to design the centralizer placement. First, check the limitations regarding the type and the number of centralizers available. Second, establish initial standoff objectives for the different intervals within the well. These can be modified, depending on the objectives and the results of the displacement simulations. An iterative design process can be used, where an initial centralizer placement is assumed, the standoff is calculated, casing the centralizer placement is

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modified, and the standoff is recalculated. The centralizer plan can be changed based on the following: - If the standoff ratio is poor between the centralizers, add more centralizers to decrease the distance between them. Note that there are limits to improving standoff by increasing the number of centralizers. Standoff generally is not improved when increasing centralizer density to more than two centralizers per joint of casing. - If the standoff ratio is poor between centralizers and is not improved by adding centralizers, consider changing the type or model of centralizer. - If the standoff ratio is poor at a bow-spring centralizer, it can be improved up to a certain point by adding more centralizers, as this will distribute the load on the centralizers, decreasing their compression. - The general suggestion to improve the standoff ratio at centralizers is to change the centralizer type: - in the case of rigid centralizers, higher standoff is achieved with larger diameter centralizers not to exceed the minimum drift diameter in the well. - in the case of bow-spring centralizers, the choice is more complicated as the dimensions and the restoring forces both affect the standoff ratio at the centralizer. While performing the iterations, it is necessary to check the centralizers’ stock table to see that the limitations on the number of centralizers are respected. A comparison of the soft string and stiff string calculations is shown in Figs. 7.20 and 7.21. This well is a horizontal well, the vertical section is approximately 6500 ft. with a horizontal lateral length of 8000 ft. The casing size is 5 ½” run in an 8 ½” hole section. The plots show standoff in percentage on the x-axis versus MD on the y-axis. The blue  is the calculated standoff at the centralizers. The red line is the calculated standoff at the midpoint between the centralizers. For this simulation, the centralizer schedule is presented in Table 7.4 where rigid or positive standoff centralizers are run at various densities in the horizontal section for comparison. An example of the centralization calculation using a soft string calculation is shown in Fig. 7.20 for a horizontal well. There are several observations: - 100% standoff is not achieved at any depth - Standoff at the centralizers’ “blue x” is determined by centralizer geometry - The pipe does not touch the borehole wall in the vertical section of the wellbore

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Fig. 7.20 Soft string centralization simulation in a horizontal well. (Credit: Schlumberger.)

Fig. 7.21 Stiff string centralization simulation in a horizontal well. (Credit: Schlumberger.)

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Table 7.4 Centralization schedule used to simulate standoff in Figs. 7.20 and 7.21.

-

1 centralizer 1 centralizer 1 centralizer 1 centralizer 1 centralizer 1 centralizer

per joint near the casing shoe every 2 joints from every 3 joints from every 4 joints from per joint around the bend every 4 joints vertical section

14,500–13,000 ft 11,000–13,000 ft. 9000–11,000 ft 7000–9000 ft 5000–7000 ft 0–5000 ft

- Standoff in the vertical section is generally greater than 80% - In the horizontal section, only centralizer density of one per joint or greater can keep the casing off the borehole wall (red line > 0%) - The casing touches the borehole wall between the centralizers for centralizer density less than one per joint. An example of the centralization calculation using a stiff string calculation is shown in Fig. 7.21 for a horizontal well. The green line in this plot helps to visualize the standoff along the entire casing string. There are several observations: - Calculated standoff at the centralizers’ “blue x” is similar to the calculated standoff using the soft string model. - The minimum standoff between the centralizers is also similar to the soft string model. - The green line helps to visualize the deflection of the pipe from the centralizer to the midpoint between the centralizers. If the stiff string model is used, other plots to aid in visualization may be used. The azimuth and magnitude of the deflection may be plotted. Threedimensional plots may also be used. These centralization simulations are then used to inform the running forces and annular displacement simulation. 7.11.1.2 Fluid positions It is commonly believed that standoff depends on two factors, the geometry (given with the well definition) and the centralizer placement. However, there is a third factor that can play an important role— buoyancy forces. To make matters more complicated, buoyancy forces change during the job, as fluid positions are changing too. The standoff will be different when the string is full of heavy fluids, compared with when the string is full of light fluids because of buoyancy effects. To take this difference into account, the stage of the cement job can be specified for the standoff calculation:

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- Cement turns—When heavy fluids are inside the pipe (also called pipe heavy), considered to be worst case scenario. It is the suggested choice to run annular simulations. - Start of job—The well is filled with only the original fluid (drilling fluid). This is the assumption also used for running force calculations. - End of job—The cement is in its final position (also called pipe light). The results may be used to compare results between software, to evaluate stresses in set cement, and to compare results to cement evaluation logs such as Isolation Scanner measurements. - Custom—User can enter a custom stage or time during the cement job.

7.11.2 Running forces RWF 6.2. Running forces. Once the standoff calculations are acceptable, the running forces calculation needs to be executed to check if the casing can be run with the planned centralizer placement. The driller will need assurance that the casing can be run to bottom without getting stuck. It is also important to understand how much rig capacity (hook load) will be required to pull the casing out of the hole if required for any reason. Casing running is discussed in detail in Chapter 4. Centralizers, especially bow spring centralizers should be considered for casing running forces. The following few paragraphs detail considerations for centralizers. The running forces calculation will estimate the forces acting on the string at different depths, while running the casing, to calculate the hook load. Recommended workflow—Casing running forces (Courtesy: Schlumberger) RWF 6.2.1. Select a centralization model for the running forces calculation. RWF 6.2.1.1 Soft String RWF 6.2.1.2 Stiff String RWF 6.2.2. Select the friction factors that will be used for running forces RWF 6.2.2.1 In previous casing RWF 6.2.2.2 In open hole RWF 6.2.3. Perform running forces calculation with the required parameters RWF 6.2.4. Compare hook load with available rig capacity and traveling block weight RWF 6.2.5. Compare simulated torque with casing connections if casing rotation is planned

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Fig. 7.22 Simulated running forces for casing in horizontal well. (Credit: Schlumberger.)

Simulated running forces are plotted for a horizontal well in Fig. 7.22. The well configuration is the same as used in the previous section. The green line indicates the weight of the casing in the drilling fluid. This may also be referred to as the rotating weight. The blue line indicates the hook load while running the casing into the ground “hook load down” which is sometimes referred to as the slack-off weight. If the slack-off is calculated below the traveling block weight, caution should be observed, as it could be possible that the casing will not make it to bottom with this centralizer program. The red line “hook load up” is the pick-up weight, which is the load required if the casing were to be pulled out of the wellbore. This should be compared with the rig capacity to understand if the casing can be pulled out of the wellbore.

7.11.3 Surge and swab RWF 6.3. Surge and swab. Surge and swab considerations during running casing are also discussed in Chapter 4. Some cementing simulators include surge and swab calculations in simulation.

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The dimensions of the casing in the wellbore, the drilling fluid properties, and the speed of running the casing will generate surge and swab pressures. These pressures can be compared with the pore and fracture pressures to ensure that well security is maintained.

7.11.4 Casing stretch RWF 6.4. Casing stretch. Casing stretch is the axial elongation of a casing string in the well before and during a cementing job. There are two main causes of casing stretch. One is the axial tension due to its own weight and forces from cement slurry and wellbore fluids, and frictional force from the wellbore in case of directional wells. The other is thermal stretch induced by temperature change of the casing. There are other contributions, but they are often less significant. Prediction of casing stretch involves simple engineering calculations, but it is an important consideration for engineers before actually performing a cement job. If there is not sufficient distance between the casing shoe and well bottom, a casing can possibly stretch into the bottom of the well during pumping, causing a blockage of the flow path and a sudden increase of pump pressure. Fig. 7.23 shows a casing stretch history of a cementing job for a

Fig. 7.23 Computer calculated casing stretch during cementing (CEMPRO +). (A) Without thermal effect and (B) with thermal effect. (Credit: Pegasus Vertex, Inc.)

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vertical well predicted by a simulator. In the Fig. 7.23, line (a) is the result by axial force only and line (b) is the result including both axial force and temperature effect. Here the stretch is relative to the original length of the casing on the ground, therefore, the value of stretch at the beginning of pumping is not zero. The change of stretch is more important than its absolute value. The largest stretch is seen at about 172 min, when the 12.20-ppg spacer reaches the shoe as shown in the wellbore schematic, corresponding to the time with highest buoyant casing weight. As the spacer runs into annulus and a lighter displacement (10 ppg) is pumped in, the tension force is reduced, causing a decrease of casing stretch. As shown in the figure, without thermal effect, there is a 16-in. stretch increase from the beginning of pumping to the moment of maximum stretch. When thermal effect is considered, this number is reduced to 8 in.. This is because pumped fluids can cool down the casing string, therefore help to reduce the amount of stretch and provide more safety. The maximum casing stretch should be added to the casing length and compared with the total MD of the open hole to ensure that the casing will not stretch into the bottom of the well. If there is a risk of the casing stretching into the bottom of the well, consideration should be made to slightly shortening the casing string or lengthening the rat hole.

7.11.5 Hook load and surface torque during cementing RWF 6.5. Hook load and surface torque during cementing. During cementing operation, pumping cement and displacement fluid can lift the casing. As the mud is displaced by spacer, cement slurries and displacement fluid, the positions of fluids inside pipe and annulus are continuously changing. This affects the buoyant force on casing and hook load during the cementing. When heavy cement slurries are in annulus while displacement fluid occupies most of casing interior, the density differential creates much greater buoyant force. The force from pump pressure also adds to the uplifting force. These forces will reduce the hook load. If the hook load becomes negative, the casing will be lifted out of the hole. Predicting the hook load variation during the cementing job helps cementing engineers to identify this problem, which could occur when light weight yet large diameter casing, heavy cement slurry and light displacement fluid are present. Fig. 7.24 illustrates the hook load change during a cementing job. Rotating casing during cementing will significantly improve displacement efficiency. However, the casing rotation causes increased surface

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Fig. 7.24 Hook load during cementing. (Credit: Pegasus Vertex, Inc.)

torque and torque at the top of liner, especially for a highly deviated well. Simulating and predicting the torque will allow the engineer to determine whether rotation is possible within the limits of the wellbore equipment. Surface torque can also be monitored during a cement job and compared with the simulated torque. Fig. 7.25 shows a simulated surface torque variation during a cementing job. The simulated torque should be compared with the torque ratings of the string being cemented. The torque rating of the liner hanger components, the casing connections, and the cement head connections are critical. If the simulated torque at any of these components exceeds the torque rating, then the design should be iterated to either reduce the simulated torque or increase the torque capacity of the components.

7.11.6 Iterate on the centralizer design RWF 6.6. Iterate on the centralizer design. Iteration of centralization design will ensure that the casing can be run to bottom and the cement job can be completed. Additional iteration may be required after performing annular displacement simulations. Table 7.5 details design parameters and changes that may be considered. Many of these

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Fig. 7.25 Surface torque during cementing. (Credit: Pegasus Vertex, Inc.) Table 7.5 Design iterations for centralizer program. Design parameter Condition Iteration possibility

Standoff (centralization) at centralizers Standoff (centralization) midpoint between centralizers Standoff (centralization) midpoint between centralizers Simulated hook load (running in hole— RIH)

- Less than required

- Change centralizer type

- Less than required

- Increase density of centralizers - Change centralizer type

- More than required

- Reduce density of centralizers - Change centralizer type

- Less than block weight - Change centralizer type - Reduce density of centralizers - Rotate casing down Simulated hook load - Less than block weight - Secure (Chain) casing down (during cementing) during cementing - More than rig capacity - Prepare contingency for one way casing trip Continued

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Table 7.5 Design iterations for centralizer program—cont’d Design parameter Condition Iteration possibility

Simulated hook load—(pulling out of hole - POOH) Casing stretch

- More than casing connection capacity

Torque at top of casing string

-

-

-

Torque at top of liner -

- Upgrade casing connection capacity - Change casing program Casing length + stretch - Lengthen rat hole longer than total - Ensure casing off bottom by measured depth more than simulated casing stretch - Shorten casing Greater than casing - Upgrade casing connections connection rating - Upgrade cement head Greater than cement - Remove rotating casing from head rating cement program Greater than casing - Upgrade liner connections connection rating - Monitor torque during Greater than liner cementing and stop rotating if hanger rating torque limit exceeded - Remove rotating liner from cement program

changes include components of well design parameters such as casing design, rig capability, and rat hole depth. An initial centralization plan should be simulated during the well design phase to identify possible significant changes. Program details such as centralizer density and placement which are relatively easy to change during the drilling phase should be simulated based on actual well conditions and updated within a few days of the cement job.

7.12 Perform annular displacement simulation RWF 7. Perform annular displacement simulation. Annular displacement simulations allow the engineer to visualize how fluids are displaced, if there is any channeling, and where the cement slurry will ultimately end up in the annulus. Visualizing the fluids in an annulus is often done using the color gray for cement slurries, green for spacer, and brown for drilling fluid. There are several simulations available to simulate and visualize the annular displacement. These simulators typically have brand names associated

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with them and they are optimized to match computer performance. They may include finite element analysis, two-dimensional, or three-dimensional computation models or combinations of these to converge on a solution. One example of an annular simulator is WELLCLEAN III. It is a displacement simulator to model fluid contamination in the well during a cement job. The simulator is actually two components packaged together: one for the pipe and another for the annulus. This simulator was designed to help the cementing engineer come up with a robust design in the shortest possible time: it is relatively fast, and it tends to take into account worst case scenarios and provides some safety margins.

7.12.1 Perform the annular displacement simulation RWF 7.1. Perform displacement simulation. When simulating annular displacement, the engineer should consider the interval for simulation, fluid mixing inside the casing or drill pipe as the fluids is traveling down the pipe, and fluid mixing due to the pipe configuration in the annulus as the fluid is traveling up the annulus. The engineer may consider each of these individually as they are designing, and then tie all of the components together for the final simulation. 7.12.1.1 Top of simulation The top of the simulation. Setting the top deeper in the well allows the simulation to “focus” more on the zone of interest. 7.12.1.2 Type of simulation Selection of where the WELLCLEAN III simulation should run to evaluate fluid contamination. There are three choices: - Annulus only—Run the simulator on the annulus only. The simulation assumes that fluids that exit the pipe at the shoe are uncontaminated. - Pipe only—Run the simulator inside the pipe only for the fluid traveling down the inside of the casing. - Both—Run linked pipe and annulus simulations. The simulator uses the pipe simulation results and feeds them to the annulus simulation as input. 7.12.1.3 Mechanical separators When bottom and top plugs are used in cementing operations, they will separate the fluids and prevent them from mixing in the pipe while traveling

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down the wellbore. This is an obvious use for the top plug and when the plug is bumped the cement is on the outside of the casing, and the displacement fluid is on the inside. When a bottom plug is used, it will separate those fluids as they travel down the pipe, and the simulator will keep the fluids separate until the bottom plug lands, and bursts letting the fluids pass to the annulus. If there is no bottom plug at a fluid interface, those fluids may mix due to gravitational and frictional forces as the fluids are traveling down the pipe. The simulator can be used to assess the mixture as the fluids are traveling down the pipe, and then use that mixture for the annular displacement simulations. A design engineer may try several simulations with and without bottom plugs to assess the volume of spacer that may be required to keep the slurry and drilling fluid separate. 7.12.1.4 Imposed standoff Instead of running the displacement simulation with a standoff ratio calculated based on the centralization, the standoff can be specified explicitly. This can be useful either at an early stage of the design, when the centralization placement is not known yet, or when the centralization design and simulations are provided by a different centralizer simulation. Recommended workflow—Annular displacement (Courtesy: Schlumberger) RWF 7.1.1. Perform hydraulic simulation RWF 7.1.2. Perform centralizer standoff simulation RWF 7.1.3. Set simulator options and launch the simulation RWF 7.1.4. Review the simulation results in different forms: RWF 7.1.4.1. Concentration curves RWF 7.1.4.2. Maps of the results RWF 7.1.4.3. Fluid concentration map Fig. 7.26 is graph of the fluid concentration in the pipe. Because the displacement fluid is mud, it is intuitive that the fluid inside the pipe is 100% mud. In this simulation a small volume of spacer was pumped after the top plug, and that is seen to be mixed with the drilling fluid on top of the plug inside the casing. At the landing collar where the top plug has separated the slurry from the displacement fluids, one can see that there is 100% tail slurry below the landing collar. Fig. 7.27 graphs the results of an annular displacement simulation as an average percentage of each fluid in the annulus. Note that the interface

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Fig. 7.26 Average fluid concentration in pipe. (Credit: Schlumberger.).

Fig. 7.27 Average fluid concentration in the annulus. (Credit: Schlumberger.)

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between the lead and the tail is simulated to stretch over 3000 ft. from 6000 to 9000 ft. It may be easier to visualize the annular concentration as a fluid concentration map. These maps of the annulus are typically displayed in twodimensional (2D) form. The maps are generated to contain color-coded values for each of the cells in the simulation mesh. Maps display depth along the vertical axis, and annulus maps add the azimuthal distribution along the horizontal axis. The bottom of the well (0 degrees azimuth) is displayed in the middle, with azimuth angle increasing toward the right (this ensures easy correlation with the standoff azimuth charts.) It can be visualized as cutting the wellbore on the top and folding it down or looking at the simulation results from the inside. The low side of the annulus is typically mapped in the center of the plot, and the high side on the outside of the track. Fig. 7.28 illustrates how the annular simulation can be converted to a 2D map. Fig. 7.29 is an example where each fluid is given a color and mapped in the annulus, generated from the same simulation that was used to generate the graphs in Figs. 7.26 and 7.27. Simulators may have several maps that are available for analysis. Some available maps are included in Table 7.6 below: Recommended workflow—Annular displacement—with casing movement Precise definitions of the wellbore and current computing capacity have allowed many more detailed cementing models of annular displacement. Another brand of annular displacement model is the 3D Aperture model

Fig. 7.28 Converting annular image to 2D map. (Credit: Pegasus Vertex, Inc.)

Fig. 7.29 Fluids concentration map example. (Credit: Schlumberger.)

Table 7.6 Maps for analysis of cement simulation. Map name Description

Velocity Normalized fluid velocity Fluid Concentration of the majority fluid at the given point. concentrations This serves mostly illustration purposes, and great care should be taken when interpreting this map—high concentration of a light gray fluids will appear the same as the lower concentration of a dark gray. Mud on the wall Color-coded risk prediction for mud on the wall, based on the risk expected thickness of mud layer left behind the fluid interfaces. This estimation will account for annular dimensions, fluid rheological properties, flow rates, and gel strength of the original fluid. Contact time A contact time “counter” based on the time: - A displacing fluid is in turbulent flow at the given point. - While the concentration of displacing fluids is higher than a threshold value (90%). Flow regime The flow regime of the fluids in the annulus, determined by comparing Reynolds numbers against the calculated critical Reynolds number for each fluid.

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which can take into account the effects of casing movement on fluid displacement. The 3D Aperture model requires a detailed well trajectory as well as stiff string calculation of standoff. A casing movement schedule also needs to be defined. The model can consider either casing string rotation, reciprocation, or no casing movement. There are situations where casing is landed in the wellhead during cementing operations, and no casing movement is possible. Recommended workflow—Annular displacement—with casing movement (Courtesy Schlumberger) RWF 7.1.5. Perform hydraulic simulation The hydraulic simulation is discussed in RWF 5.2, but is reiterated here as the hydraulic simulation must be current to simulate the displacement with casing movement. RWF 7.1.6. Perform centralizer standoff simulation (RWF 6.1) using stiff string method RWF 7.1.7. Run the in-pipe simulation (choosing pipe only or both options for the simulation) to take into ac7count the contamination that occurs while the fluids are traveling down the string RWF 7.1.8. Define a timeline for casing string movement, if the plan is to reciprocate or rotate the string during the cement job. RWF 7.1.9. Set simulator options and launch the simulation. RWF 7.1.10. Review the simulation results in different forms: RWF 7.1.10.1. Concentration curves RWF 7.1.10.2. Maps of the results RWF 7.2. Compare the simulation results with the job objectives RWF 7.3. Iterate on the design to meet the job objectives, by modifying (in order of difficulty) the pump schedule, centralizer placement, fluids volumes, or even fluid design. Results from a 3D aperture simulation of a horizontal well are pictured in Fig. 7.30. This simulation utilizes the centralization calculated using the stiff string method for the horizontal well presented earlier in this chapter. No casing movement is applied, and the wellbore is divided into 3-ft intervals. This gridding of the wellbore allows finite element type simulation along the wellbore and gives a much more granularity to the resulting map. This simulation and resulting map support the idea that cement will be around the entire annulus at the centralizer, and that there could be drilling fluids pockets on the low side of the well midway between the centralizers.

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Fig. 7.30 Fluids concentration and mud on wall risk from 3D aperture simulation— horizontal well. (Credit: Schlumberger.)

It may be useful to compare these simulations to cement evaluation logs to better interpret the logs. Planning stimulation treatments and stages based on the simulated isolation may also be considered. For the engineer who prefers the data to be presented in graphical format, an average fluid concentration graph is presented in Fig. 7.31. Casing movement such as casing rotation may also be applied. Figs. 7.32 and 7.33 are the result of simulations of a horizontal well, where rotation of ten revolutions per minute was simulated through the cement job. This simulation supports the idea that casing rotation is beneficial for the objective of achieving cement around the entire annulus. Note in the fluids map that there may be some diagonal features. These features are consistent with the idea that rotating the casing imparts rotational movement to the fluid traveling up the annulus.

Fig. 7.31 Annular fluid average concentration. (Credit: Schlumberger.)

Fig. 7.32 Casing rotation applied. (Credit: Schlumberger.)

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Fig. 7.33 Horizontal well with casing rotation applied. (Credit: Schlumberger.)

Presenting the data in different formats will help the engineer visualize how fluids move in the annulus. The results of a cement job simulation can be presented in various formats with today’s powerful computers and excellent graphics displays. A simulation can include many calculated parameters presented on a finely gridded wellbore. Fig. 7.33 is an image of a horizontal well with cementing fluids imposed on the wellbore. In these images the aspect ratio may be significantly modified. The length of the well is thousands of feet reduced to just a few inches on the page while the diameter of the wellbore is reduced by a factor less than 20. Well survey details compressed over the 8000 ft. lateral make the well appear somewhat like an accordion in the image.

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7.13 Perform special case simulations examples RWF 8. Perform special case simulations. Cement simulators can be used for special case simulations because they already include significant definition of the wellbore and cement. The special cases can also be calculated using pressures and temperatures that have already been calculated with the simulator. Special cases that are discussed are critical static gel strength, gas migration risk, plug placement, cement sheath stress calculations, and foam cement calculations.

7.13.1 Critical static gel strength RWF 8.1. Critical static gel strength. Critical static gel strength (CSGS) is a property that is calculated and considered when thinking about gas migration or other flow potential. Two API documents: API Recommended Practice 65 (2002) “Cementing Shallow Water Flow Zones in Deepwater Wells” and API Standard 65 – Part 2 (2010) “Isolating Potential Flow Zones During Well Construction” discuss managing (e.g., shortening) the critical static gel strength period as a method for minimizing the risk of influx into the cement during the setting time. The equation for critical static gel strength is defined in the following equation: CSGS ¼

ðOBPÞð300Þ ðL=Deff Þ

(7.2)

where OBP is the hydrostatic overbalance pressure (psi); 300 is the conversion factor (lb/in); and L is the length of the cement column (ft) above the potential flow zone. The effective diameter Deff is calculated using the following equation: Deff ¼ DOH  Dc

(7.3)

where DOH is the diameter of the open hole (in) and Dc is the diameter of the casing. The critical static gel strength is actually NOT a cement property, but instead is a wellbore design property that can be calculated along the entire wellbore. Rather than hand calculate this property, it is useful to use a simulator for this calculation. Fig. 7.34 is an example of the critical static gel

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Fig. 7.34 Example critical static gel strength plot. (Credit: Schlumberger.)

strength calculated along the wellbore. Note that the critical static gel strength is calculated to the top of each slurry. The critical static gel strength can then be used to determine the critical static gel strength period which is a cement slurry property that can be determined in the laboratory using static gel strength testing procedures. The critical static gel strength period is the time that it takes for the cement slurry to develop gel strength from the critical static gel strength to 500 lbs./100 ft2. Larger critical static gel strength values generally result in a shorter critical static gel strength period, reducing the risk of gas migration into the cement sheath. Gas migration is a significant concern for the cement design engineer, and simulators may include additional factors to assess gas migration risk. One simulator uses a value called the “pressure decay limit” (PDL) which is similar to the CSGS calculation but also takes into account 10-min gel strength of a fluid.

7.13.2 Gas migration RWF 8.2. Gas migration risk. Gas migration is a significant concern for the driller. The cement job objective will often include an objective to minimize the risk of gas migrating into the cement column. Minimizing the gas migration risk includes managing many of the factors related to the cement job including, but not limited to,

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wellbore geometry, spacer design, slurry design, prejob circulation, centralization, and pump schedule. The formation flow potential is also a significant factor. The cement engineer can use a simulator to evaluate all the components of the cement job and assess the associated risk. A cement simulator can be used to quantify the risks of gas migration (short-term annular fluid migration) associated with the cement job design. The simulator can calculate a set of risk factors for each potential flow zone (PFZ) and generate the composite Gas Migration Severity risk. Based on the results and suggestions coming from the software, a plan to minimize the risk of fluid migration can be implemented. These calculations do not typically consider physical and chemical phenomena that occur in the cement slurry itself such as chemical shrinkage due to cement hydration, fluid loss, or fluid exchange with the formation. 7.13.2.1 Gas migration risk factors Short-term fluid migration occurs when cement becomes self-supporting and does not transmit enough hydrostatic pressure to hold the fluids (including gas) in the formation. Knowing the well and placement geometry, the critical pressure loss can be translated to the equivalent CSGS. Based on the value of the CSGS or the PDL parameter, the software will assign a related risk. Failure to completely displace the mud from the annulus may jeopardize zonal isolation and may lead to short-term gas migration. To capture this, the software uses the results from the annular displacement simulation such a WELLCLEAN III or 3D Aperture to calculate a Mud Removal Risk (MRR). This value takes into account the simulated cement coverage at the flow zone and above. The severity of a possible gas migration incident will depend largely on how much fluid will migrate into, and up the annulus. The Formation Productivity Risk (FPR) is used by the simulation program to capture this factor. The FPR is calculated only for gas zones, based on the volume of gas that can be produced by the formation. For this estimation, additional data are required such as permeability, the skin of the formation and the critical static gel strength period of the cement slurries. Based on the PDL and the MRR risk values, the software estimates the gas migration severity (GMS) risk. The level of the gas migration severity can be used to select a cement system to control or mitigate the gas migration risk. Fig. 7.35 illustrates how the simulation components contribute to the determination of the overall gas migration severity risk.

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Fig. 7.35 Simulation components for gas migration risk determination. (Credit: Schlumberger.)

Recommended workflow—Gas migration (Courtesy: Schlumberger) RWF 8.2.1. Select and describe the potential flow zones (PFZs). For gas zones, formation permeability and skin factor may also be entered, if the data are available, for the calculation of the formation productivity risk RWF 8.2.2. Ten-minute gels may be considered

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RWF 8.2.3. Run the hydraulic simulator to obtain the pressures at the end of placement. This is will be the basic input for the critical static gel strength calculation RWF 8.2.4. After running standoff calculation, run a displacement simulator. The resulting cement coverage and concentration results will be the input for the mud removal risk RWF 8.2.5. Enter the applied backpressure, if pressure is kept on the annulus while the cement is setting (as a method to prevent gas migration) RWF 8.2.6. Set slurry critical period RWF 8.2.7. Indicate applicable special well conditions before running the calculation for gas migration risks RWF 8.2.8. Launch the calculation RWF 8.2.9. Review the details of the calculation for each PFZ 7.13.2.2 Special well conditions There is an industry consensus that certain well conditions significantly increase the risks associated with gas migration. When any of these conditions are present, the simulators should automatically set the gas migration to a high level and provide a reminder to design the slurry according to this severity: - Cement job is in a well section where shallow gas zones are a risk - A liner top packer, or external casing packer, is set directly after slurry placement To take one of these conditions into account, mark the checkbox next to them. 7.13.2.3 Liner top and external casing packers A liner top packer increases the risk of gas migration below the packer because it isolates the annulus below the packer from the pressure of the hydrostatic column above. If the packer is set immediately after cementing, the cement will still be in the process of hydration. Shrinkage and fluid loss can decrease the slurry volume, which will reduce the annular pressure and provide space for fluids to enter the wellbore, enabling annular fluid migration. This fluid migration can create a channel to the packer, thus compromising zonal isolation. The actual pressure and volume decrease during cement hydration cannot be accurately predicted as it depends on many factors. For this reason, the

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associated risk is difficult to quantify and the worst-case scenario should be assumed—this is why gas migration severity is set to high. Liner top packers can be useful for operational purposes. The risk of gas migration can be assessed against other benefits of the packer. The simulation of gas migration risk is useful to assess the risk of gas migration and to understand cement evaluation log results after the cement job. 7.13.2.4 Shallow gas well Shallow gas is defined as a gas zone encountered in sections when a blowout preventer is not installed yet on the wellhead. Shallow gas is not related to any depth in particular, rather to the condition that there is no way to shut in the well, should an influx occur. If formation fluids start flowing under these conditions, the cement will set around an active (producing) channel, and thus the GMS risk is set to high. 7.13.2.5 Iteration on the design Gas migration is an important consideration in the design of the cement job, and there are many components to consider. A simulator is very useful for considering various approaches and understand how each of these approaches may change the risk: If the CSGS, or PDL contributes to the risk, consider: - Changing density (increase) of the fluids above the PFZ - Changing the wellbore configuration (larger hole diameter) - Add back pressure - Change fluid column lengths If mud removal contributes to the risk, consider: - Changing the centralizer program - Adding casing movement (rotation or reciprocation) - Changing the spacer volume - Adding mechanical separators (plugs) between fluids - Adjusting any or all of the fluid designs to change rheological properties If potential flow zones contribute to the risk, consider: - Better definition of the PFZ (seismic, logs, offset wells, etc.) Optimizing a cement job design to minimize the risks of gas migration can be a significant challenge because of all of the factors involved. A simulator can be very useful for comparing options, assessing the components of gas migration risk including PFZ details, MRR and CSGS and thus assisting in evaluating and mitigating overall gas migration risk.

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7.13.3 Plug design RWF 8.3. Plug placement. Cement plugs are usually placed using the balanced plug method where the cement is placed in the annulus and the pipe in a way to leave a continuous cemented section in the well when the pipe is pulled out of the hole. Chapter 12, Plug and Abandonment, provides detail on well abandonment design, this section demonstrates the usefulness of simulation for a cement plug job. If the cementing string is a simple pipe, the balanced plug calculations are straight forward. However, when a tailpipe is used (to decrease the risk of swabbing), the interfaces in the annulus and in the drill-pipe may not move together, and the related calculations become too complex to be done manually. The volumes can be optimized using a simulator to build the placement design. Prejob well circulation should be simulated similar to a casing job. This prejob circulation can be used to simulate temperature and rheology conditioning before the cement job. Once the volumes are optimized, the hydraulic and temperature simulations can be run similar to a casing cement job to check that well control is maintained, and to obtain simulated temperature and pressure schedules for laboratory testing which will predict when compressive strength will develop in the plug cement. 7.13.3.1 Recommended workflow—Plug—Volume optimization Optimizing the volume of the cement, spacer and displacement volume can significantly improve cement plug placement results. Several papers have been written about how simulators can be used to improve cement plug results. Bogaerts et al. (2012) discusses setting plugs in Deepwater in SPE 155736 and Yabin Guo et al. (2014) discusses the use of a cement plug simulator for HPHT wells in SPE 171395. Several options are available for optimizing the volumes of cement spacer and displacement volumes. The most intuitive option is to calculate the volumes so that all of the interfaces are at the same depth inside and outside the pipe, however, this may lead to significant contamination at the fluid interfaces. Better results will be achieved by optimizing spacer and slurry volumes. Four optimizations and their characterizations are described as follows: - Level slurry and spacer—Construct a placement according to the traditional balanced plug calculation, with slurry and spacer interfaces level

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before POOH. Typically, such a placement will end up with slurries and spacers at different levels after POOH, resulting in slurry contamination. - Level slurry only—Construct a placement with only the slurry interfaces level at the end of placement, before POOH. Such as placement is typically unbalanced. - Optimize slurry and spacer—Construct a placement such that the slurry and spacer interfaces are at the same level in the pipe and in the annulus when the end of the string reaches them, so contamination would be minimal between the different fluids. - Optimize slurry only—Construct a placement where the slurry interfaces are optimized for POOH, so contamination of the slurry would be minimal. Under displacement is another important consideration for improving cement plug results by minimizing contamination. The under displacement is the difference between the actual displacement and the theoretical displacement calculated using the level-interface (“traditional” balanced plug) method. Recommended workflow—Plug—Volume optimization (Courtesy Schlumberger) RWF 8.3.1. Enter the well data for the cement job, making sure that well geometry is as accurate as possible RWF 8.3.2. Define the fluids used for the cement job. Describe all fluid properties, although the volume optimization uses only the density of the fluids RWF 8.3.3. Set an optimization criterion (options) for the volume balance algorithm RWF 8.3.4. Select the wellbore fluids placed in different parts of the well. Indicate if the trip tank is connected to fill up the annulus during POOH RWF 8.3.5. Choose the fluids placed to be pumped and specify how much of each fluid will be placed in the well, using the fluid and volume selection tools RWF 8.3.6. Launch the optimization RWF 8.3.7. Review the generated design for the annulus and pipe in the placement design tables RWF 8.3.8. Compare the hydrostatic pressure against the formation pressures, ensuring that well control is maintained RWF 8.3.9. If fine-tuning is required to realize complex fluid sequences, it can be done using custom pages

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Fig. 7.36 Optimized volumes for cement plug placement. (Credit: Pegasus Vertex, Inc.)

RWF 8.3.10. Validate the optimized volumes by simulating the pull out of hole (POOH) RWF 8.3.11. Proceed in the workflow to define the pumping schedule once satisfied with the placement design Once the simulation is performed the engineer can observe where the cement top is before and after POOH and check that the plug will meet the design objectives. Fig. 7.36 illustrates the positions of the optimized fluids after the cement is placed (before POOH) and after the plug placement string is pulled above the top of the spacers (after POOH).

7.13.3.2 Recommended workflow—Plug—POOH fluid mixing simulation In addition to volume optimization, the fluid mixing in the pipe and in the annulus can be simulated using the hydraulic and annular displacement simulations that have been described for casing cementing operations. In addition, the fluid mixing can be simulated as the pipe is being pulled out of the cement plug.

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Mechanical separators, such as foam balls, may also be considered in these simulations. The engineer can determine whether the use of mechanical separators will improve (by minimizing contamination) the results of the cement plug. Please refer to Chapter 12, Plug and Abandonment, for an in-depth discussion of factors affecting plug design. Fluid mixing risk can be related to the success of the cement plug and where the driller can expect to tag the TOC if that is the objective. A simulation may assign a “green” or low risk color to sections where the cement slurry makes up more than 90% of the fluid volume. Where the slurry is simulated to be a lower concentration of the total fluid the simulator may assign a “yellow” or “red” color. The engineer can use this simulation together with the knowledge of the slurry performance to predict if the cement plug will meet the design objectives. Recommended workflow—Plug—POOH fluid mixing simulation (Courtesy: Schlumberger) RWF 8.3.12. Before designing fluid placement, select whether the annulus will be kept full during POOH RWF 8.3.13. Design the fluid placement for the cement job RWF 8.3.14. Set a final depth for the pull out of hole if the postplacement circulation will occur below the top of the spacer RWF 8.3.15. Run the displacement simulation to evaluate the contamination while the fluids are pumped. RWF 8.3.16. For running contingency simulations, or for certain placement methods, select the options that match the contingencies (e.g., pulling wet, including mechanical separators, filling the annuls) RWF 8.3.17. Launch the calculation RWF 8.3.18. Review the results of the simulation RWF 8.3.19. Iterate as necessary for the design Cement slurry mixing and fluid contamination simulation are illustrated in Fig. 7.37. Hydraulics simulations are used to simulate mixing of fluids during placement. The results are presented graphically as a percentage in the graph on the left, visually as fluids in the wellbore in the middle, and with risk colors on the right side. Cement slurry mixing and fluid contamination simulation are illustrated both before and after POOH in Fig. 7.38. After the hydraulics simulation during placement, a POOH simulation is performed. The resulting fluid mixtures are presented graphically as a percentage in the graph on the left,

Fig. 7.37 Slurry placement and risk of contamination after placement before POOH. (Credit: Schlumberger.)

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Fig. 7.38 Slurry position and simulated risk of contamination before and after POOH. (Credit: Schlumberger.)

and with risk colors on the right side. The engineer may use the percentage of the fluid mixtures to consider laboratory testing using the procedures detailed in API 10B-2 “Recommended Practice for Testing Well Cements” Section 13 Compatibility of Wellbore fluids. These mixtures could be used as an example for compressive strength testing of a mixture of cement slurry, spacer and mud to predict when the mixture might achieve compressive strength to meet the design requirements. Iterations on the design are typically performed to increase the top of the cement plug so that the plug can meet the objectives. Typical options that may be considered to increase the height of the “green zone” are as follows:

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- Increase slurry volume - Add mechanical separators (foam balls) - Before spacer - Before slurry - After slurry - Increase spacer volume - Adjust the pump schedule - Change the pipe/tailpipe configuration

7.13.4 Cement sheath stress simulation and calculation RWF 8.4. Cement sheath stress calculations. Cement sheath stress calculations are performed to quantify the risk of cement failure which could lead to a zonal isolation issue. The cement sheath stress calculations may be performed to simulate and compare the performance of cement systems in a wellbore annulus when subjected to temperature and pressure changes. The cement sheath stress calculations may also be used to sensitize on and design a cement system with specific mechanical properties such as Young’s modulus and Poisson’ ratio. Cement sheath stress calculations are based on well-known mechanical properties calculations such as stress and strain, Young’s modulus, Poisson’s ratio, and thermal expansion coefficients. However, there is considerable debate in the industry about the initial state of stress in the cement sheath. These calculations and simulations are best used to compare cement system performance in the wellbore for a specific section of the wellbore. Additional reading is recommended for a full understanding of the calculations and the models used. SPE papers 56,536, 56,535, and 87,195 are quite useful for exploring these. Recommended workflow for cement sheath stress simulation RWF 8.4.1. Options—set options such as units for the calculations RWF 8.4.2. Geometry—set the number of casing strings RWF 8.4.3. Formation—specify open hole diameter and formation mechanical and thermal properties RWF 8.4.4. Casing—specify casing dimensions and material. Mechanical and thermal properties are typically assumed for steel RWF 8.4.5. Cement—specify the cement system—these are the properties that may be compared between systems. Simulators may include a database that includes (and assumes) the following: RWF 8.4.5.1. Density

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RWF 8.4.5.2. Compressive strength—typically unconstrained compressive strength (UCS) RWF 8.4.5.3. Tensile strength—typically 1/10 of the compressive strength if the measured tensile strength is not available RWF 8.4.5.4. Young’s modulus—modulus of elasticity RWF 8.4.5.5. Poisson’s ratio RWF 8.4.5.6. Chemical expansion coefficient (if expanding agent is used) RWF 8.4.5.7. Thermal properties—include thermal conductivity, specific heat capacity and thermal expansion factor RWF 8.4.6. Specify the dynamic conditions for the section. Include both temperature and pressure in these dynamics: RWF 8.4.6.1. Pressure schedule—specify the change in pressure and the schedule. The change may be due to fluid density changes in the wellbore, pressures due to completion operations, pressures due to production of the wellbore, and or pressure due to injection RWF 8.4.6.2. Temperature schedule—specify the change in temperature and the schedule. Temperature changes may occur because of completion, production, or injection operations RWF 8.4.7. Perform stress analysis. Analysis may include several layers of detail RWF 8.4.7.1. Section analysis summary—overview of the results of stress calculations RWF 8.4.7.2. Output plots—plots of stress, displacement, temperature, and microannular sizes RWF 8.4.7.3. Sensitivity analysis—analysis of sensitivity of cement failure risks to parameter variation RWF 8.4.8. Iterate on the design as necessary RWF 8.4.8.1. Change the pressure schedule RWF 8.4.8.2. Change the temperature schedule RWF 8.4.8.3. Change the cement properties 7.13.4.1 Section analysis and possible failure modes Section analysis screen displays the summary of the stress calculations and whether cement failure is simulated to occur. Three cement failure types are calculated: compression, traction, and microannulus. Fig. 7.39 illustrates the cracks and possible flow paths for each of the failure modes.

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Fig. 7.39 Failure modes in cement sheath stress analysis. (Credit: Schlumberger.)

7.13.4.2 Compression failure mode CemSTRESS uses the Mohr-Coulomb compression failure criterion. Compression failure is predicted to occur when Compressive Failure Stress (computed from radial and tangential stresses) in cement exceeds compressive strength (UCS). Compression failure is usually caused by large radial compressive stresses due to well pressure and/or temperature increase. Typically, such type of failure produces radial cracks in the cement sheath. 7.13.4.3 Traction failure mode Traction failure is said to occur when the tangential tensile stress exceeds Tensile Strength of the cement. Traction failure is usually caused by well pressure or temperature increase in a weakly constrained cement sheath. Typically, traction failure will generate radial cracks that will propagate through the cement parallel to the well axis and may lead to zonal isolation problems. 7.13.4.4 Microannulus failure mode Microannulus occurs when the cement debonds from either the casing (inner microannulus) or the formation (outer microannulus). Microannulus is caused by casing or cement contraction due to well pressure or temperature decrease.

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7.13.4.5 Output plots may be used to understand the stresses and when they occur Graphs and plots are useful for understanding how and when the failures are simulated. The stresses in the cement sheath may be plotted by dimension, and they may also be plotted over time. 7.13.4.6 Compressive stress plot Calculated compressive stresses are plotted through the cement sheath. Fig. 7.40 indicates the compressive stresses plotted as a red line versus the radius in the wellbore. Mohr-Coulomb stresses are on the y-axis and well radius is on the x-axis with the center of the well on the left of the graph. The casing is shown as a blue bar and the formation is shown as an orange area for reference. If the red line extends into the compressive failure zone (green fill) the simulation indicates that possible failure could occur. In this case the compressive failure may happen next to the casing. Simulation through the entire pressure and temperature cycle is also useful. This plot may be created with time as a variable. It may be best contemplated as a video, so that the exact time, pressure, and temperature that are related to the simulated failure can be understood.

Fig. 7.40 Compressive stress in the cement sheath. (Credit: Schlumberger.)

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Fig. 7.41 Tensile stress in the cement sheath. (Credit: Schlumberger.)

7.13.4.7 Tensile stress plot Tensile stresses can also be plotted through the cement sheath similar to the compressive stresses. Fig. 7.41 indicates the tensile stresses plotted as a red line versus the radius in the wellbore. Tensile stresses are on the y-axis and well radius is on the x-axis with the center of the well on the left of the graph. Casing and formation are shown as blue and orange areas for reference. If the red line extends into the compressive failure zone (brown fill), the simulation indicates that possible failure could occur. In this case the tensile failure may happen next to the casing. Simulation through the entire pressure and temperature cycle is also useful to understand the time and condition that can lead to the failure of the sheath. 7.13.4.8 Microannulus plot The magnitude of the microannulus can be plotted through the simulated time. Fig. 7.42 is an example simulation of both an inner and outer microannulus next to the cement sheath. Time is on the x-axis and the microannulus dimension is on the y-axis. Once the micro annulus is greater than 10 μm, it may be considered to be a flow path for gas. If dimension

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Fig. 7.42 Simulated microannulus. (Credit: Schlumberger.)

of the microannulus is simulated, the user can determine what the flow potential could be for gas, oil, or water through the gap. The user can also adjust the schedule to determine what pressure or temperature change may be used to close the microannulus. 7.13.4.9 Sensitivity analysis The cement sheath stress is related to all of the input parameters. To understand how close to the failure the cement sheath may be, it is useful to sensitize on some parameters. Various methods for presenting sensitivity analysis may be used. Fig. 7.43 illustrates how a design and schedule may be optimized between all of the different parameters that are investigated. 7.13.4.10 Iteration on the cement design based on cement sheath stress calculations Iteration on the cement design based on cement sheath stress calculations is challenging because simulated failures depend on the cement properties, the initial cement installation and the pressure and temperature cycle in the well. This means that the cement engineer, the driller, and the well operator all contribute to the success (or failure) of the cement sheath. Cement sheath stress simulations are useful to investigate failures where the well details, and the temperature and pressure history are known and

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Fig. 7.43 Sensitivity of cement sheath stress to various parameters. (Credit: Schlumberger.)

have been measured. Sensitivities may be performed and changes may be made to prevent future failures. Changes may be as simple as changing a pressure test schedule or an injection schedule to minimize the stresses caused by pressure or temperature. Cement properties may also be changed so that the cement sheath may be robust for which ever temperature and pressure cycles may happen in the well. The most challenging wells have very large pressure or temperature changes or both at the same time. If these changes occur in very “soft” formations, arriving at a solution may become very challenging. Examples are steam injection wells (large temperature changes), or HTHP wells that require fracturing stimulation (large pressure changes). In general, more flexible cements, those with lower Young’s modulus and higher tensile strengths, with sufficient compressive strength, tend to perform best when simulating cement sheath stresses. Adjusting the pressure and temperature schedule so that the stresses are spread over time also helps to mitigate risk of failure. The objective for analyzing the cement sheath stresses and optimizing the cement system is to ensure that the cement will withstand all the stresses through the life of the well. Fig. 7.44 indicates that the cement sheath can withstand all of the simulated stresses. This simulation indicates that the cement will not fail in compression or in tension for the simulated conditions. A microannulus is also not anticipated from the simulation.

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Fig. 7.44 Cement passes simulated stresses. (Credit: Schlumberger.)

Fig. 7.45 Magnified foam cement slurry. (Credit: Schlumberger.)

7.13.5 Foam cement simulation and design RWF 8.5. Foam cement calculations. Foam cement is challenging to design because of the compressibility of the nitrogen in the cement slurry. Fig. 7.45 is a magnified picture of a foamed cement slurry including nitrogen and slurry. The nitrogen will undergo significant volume changes and will compress up to five times as it travels down the pipe, and then will expand as it travels up the annulus, due to the pressure and temperature changes. When designing foam jobs, it is challenging to account for all the pressure and temperature changes affecting the final volumes. However, using a computer and a simulation, it is possible to design the fluid density and foam quality between limits. Industry standards also include requirements to use computer simulations when designing foam cement jobs. API Standard 65—Part 2 “Isolating Potential Flow Zones During Well Construction” (Section 5.6.5.9) recommends the use of engineering software for the design and placement of foamed cement.

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7.13.5.1 Foam cement design Foamed cement has variable density and foam quality in a well as downhole temperature and pressure change. To design a foam job, one will determine a schedule of nitrogen loading ratios together with pumping rates of liquid fluids. Given a temperature profile in the well, required nitrogen loading ratios during pumping can be calculated based on final fluid positions and foamed slurry densities or operation methods such as constant nitrogen rate, constant density or “hybrid” (a combination of both). The time dependent foam density during the entire job at any depth can be predicted in a computer simulation. Fig. 7.46 shows an example of constant density design generated by a computer program. Computer programs can give profiles of the pressure, foam quality, and nitrogen ratio distribution in the annulus and help engineers determine whether the design objective is met. 7.13.5.2 Temperature selection As the density (and volume) of the foamed fluids depends significantly on the well temperature, there are three choices of which temperature will be used by the calculator that generates the placement simulation: - Temperature from geothermal: this option can be chosen when no prejob circulation is run, and the initial temperature for the hydraulic simulation is also taken from the geothermal temperature profile. - Temperature from mud circulation: this option can be chosen if a prejob circulation is expected. The temperature profile at the end of the prejob circulation is used as the initial temperature the placement simulation. The same choice can be made when the hydraulic simulation is initialized. - Temperature from placement simulation: Once the hydraulic simulation is run, the final temperature profile at the end of the job may be used to run the placement simulation. 7.13.5.3 Nitrogen ratio selection The nitrogen (N2) ratio selection methodology impacts how many stages are written into the cement program. The N2 ratio selection may also be called the foam objective because this is how the foam stages are designed. The operational method that will be used to perform the cement job should be considered when creating the foamed cement program. One or two stages would generally be considered to be easy to execute manually. If the operations include computer controlled foamed cementing equipment, then the number of stages will not impact the complexity of the cement job, and in fact the automated control systems may enable a complex design of a foamed cement job that can meet tight wellbore constraints. Four methods

Fig. 7.46 Designing a constant density foam job using a computer program (CEMPRO +). (Credit: Pegasus Vertex, Inc.)

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are typically considered when selecting the nitrogen ratio stages to program into the cement job: - Fixed N2 ratio, also called constant ratio: the N2 ratio is fixed for the fluid that will be pumped downhole. The placement calculation will recalculate how the foam will compress during the job and establish fluid density based on the downhole pressures and temperatures. Fixed N2 ratio is considered to be the least complex for operations. - Min/max Density: The final slurry density range after placement is set as the objective. The calculation will obtain the N2 ratio required to achieve these densities at downhole conditions. If a single ratio cannot keep the density within the range, it will automatically split the fluid into multiple sections to respect the limits. Because well design parameters typically require specific fluid density ranges, the min/max density method is considered to be the easiest method to meet well design requirements. - Constant Density: The final slurry density after placement is set as the objective. The N2 ratio will be varied through the slurry stage to achieve this density at downhole conditions. Using the min/max density method and setting a small range is effectively the same as the constant density method. This method will result in the most stages but computer controlled automated foamed cementing equipment can be used to easily execute this type of design. - Min/max Quality: The foam quality range is set as the objective. The calculation will find the corresponding N2 ratio, based on the downhole conditions. If a single ratio cannot keep the quality within the range, the algorithm will automatically split the fluid into multiple sections to respect the limits. This method is used when the foam quality is the most important design criteria for the well. 7.13.5.4 Back pressure Back pressure is an important parameter for foamed cement simulation. It can be applied back pressure when returns are taken at surface, or hydrostatic pressure when returns are taken at the seabed. In the latter case the default value is calculated based on seawater depth and density. Recommended workflow: Initial foam cement selection (Courtesy: Schlumberger) RWF 8.5.1. Define the well data for the cement job, just like a normal primary cement job

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RWF 8.5.2. Describe the fluids used for the job. For the fluids to be foamed this means defining the base fluid, including foamer and stabilizer additives RWF 8.5.3. Select the original fluids in the well before the cement job starts RWF 8.5.4. Select the foam objective type to use initially to characterize the foamed stages RWF 8.5.5. Setup the required final fluid positions in the annulus and the pipe, using the placement tables: add the fluids to the tables and define for each of them the depth interval that it should cover at the end of the job RWF 8.5.6. In the placement tables, provide initial objectives for the fluid stages that will be foamed RWF 8.5.7. Select the temperature profile that the software should use for the placement calculation. As the foam density depends on pressure and temperature conditions, this will have a significant impact on the results. RWF 8.5.8. Launch the calculation RWF 8.5.9. Once the calculation is finished, review the generated placement design on the placement result page 7.13.5.5 Foam placement simulation After running the placement calculations after the initial workflow with the foam objectives that are provided, the calculation results can be reviewed. A placement simulation can be run again, and the design can be iterated. Recommended workflow—Foam placement (Courtesy: Schlumberger) To create a pumping schedule from the placement objectives, follow the workflow below: RWF 8.5.10. Set up the placement objectives: select the original wellbore fluids, the required position of each fluid stage and the corresponding objectives. RWF 8.5.11. Run the placement calculation RWF 8.5.12. Review the placement results in the annulus and pipe placement tables RWF 8.5.13. The design may be iterated at this point RWF 8.5.14. The original foam objectives may be changed. For example, constant ratio may be used for the first iteration, and then min/max density, or constant density may be used for the second iteration

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Fig. 7.47 Deepwater foam cement design. (Credit: Schlumberger.)

RWF 8.5.15. If fine-tuning of the placement results is desired, the fluid stages with the corresponding N2 ratio can be copied back into the placement objectives for another iteration RWF 8.5.16. Verify the downhole pressure at the end of placement to ensure that the pressure is within the design limits Once satisfied with the results, update the pumping schedule. This will reinitialize the pumping schedule with a fluid sequence based on the placement results. In addition to listing which section of the well is covered by which fluid stage, it lists the basic properties for all foamed and unfoamed stages: N2 ratios, foam quality, density, and the base fluid volume to be pumped at the surface. Results of the foam simulation can be presented in graphical format. Fig. 7.47 illustrates a deep water foamed cement design after several iterations. The graph indicates that the foamed cement slurry designed for a constant density of 11 ppg. The slurry is divided into five stages each with a downhole density between 10.75 and 11.25 ppg, with the calculated foam quality and apparent density plotted at the end of placement.

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7.14 Generate job program and reports RWF 9. Generate cement program documentation. Generating a job program and reports is an obvious statement but so important that it deserves a section in this chapter. Engineers often perform many simulations and sensitivity analysis when designing a cement job for a specific casing string. For traceability, it is imperative that a final program is generated, or a file saved, that includes all of the assumptions that contributed to the design. This cement program may be referred to during the performance of the cement job, and may also be referred to throughout the life as the well for insights into the cement that is placed in the well. Cement program and design files range from very simple one-page programs to complex 100 + page programs. The length and complexity of the cement program depends on the complexity of the well and the regulatory, reporting and design requirements for the well operator, the driller, and the service provider. While difficult to propose a “standard” program, the operator, driller, and service provider should agree what type of summary, hard copy and digital files will be in the cement program. The cement program, together with the cement job data and the laboratory tests define the cement system and how it has been installed in the well.

7.15 Simulation for job evaluation Perform postjob simulations to compare wellsite observations to simulations. RWF 10. Perform postjob simulations for job evaluation. Comparison of well site data with simulation data are recognized as one method for determining that the cement job has met the objectives. This is a logical step after performing all the prejob simulations. Comparing job data with simulation is not the only way, however, to evaluate a cement job. Please also refer to Chapter 11, Job Evaluation, for more details on cement job evaluation. There are several significant components in the workflow for comparing job data to the simulations. First the data must be collected and entered into the simulator. The fluid sequence needs to be set, and then the simulated

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pressure may be compared or “matched” with wellsite observations. Additional assumptions about the well configuration and any flow paths also need to be defined in the simulator. Once the hydraulics simulation is performed along with any other simulations such as centralization and annular displacement, the results can be compared with wellsite observations and conclusions may be formed. Confirming TOC by comparing wellsite pressure observations to simulated pressures is one of the first indications that a job has gone well. This is done by using the recorded fluid densities and pump rates, performing the hydraulic simulation, and comparing the recorded pressure with the simulated surface pressure. If the pressures do not exactly match, some assumptions (e.g., hole size or fluid rheology) may be updated in the simulation to facilitate the pressure match. The user must be aware that there is not necessarily a unique solution for a pressure match. Confirming other wellbore parameters by comparing wellsite observations with simulations is also possible. Centralization and annular displacement simulations may be compared with cement evaluation logs to affirm wellsite observations such as centralizer placement and hook loads. As cement evaluation logs become more sophisticated, the results of a stiff string centralization may be compared with a cement evaluation log with a measured third interface echo (TIE). The reader is encouraged to review Chapter 11, Job Evaluation, for cement job evaluation and may also consult API 10TR1 (2008) for more details on cement sheath evaluation including details on cement evaluation logs.

7.15.1 Recommended workflow—Placement evaluation— Importing data RWF 10.1. Import wellsite recorded data After the cement job, the job data will need to be imported into the simulator using the following steps: Recommended workflow—Placement evaluation—Importing data (Courtesy: Schlumberger) RWF 10.1.1. Set the job boundaries to remove unwanted data from the start and the beginning of the job RWF 10.1.2. Review imported messages in the job events list RWF 10.1.3. Add custom messages to the job events list if important events are not marked RWF 10.1.4. Select the messages to be displayed on the chart.

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RWF 10.1.5. Add the events to mark the start and end of the displacement, to correct the displacement volume for the inaccuracies related to pump efficiency RWF 10.1.6. Select the channels to be imported RWF 10.1.6.1. Required: RWF 10.1.6.1.1. Time RWF 10.1.6.1.2. Pump rate (cement pump and rig pumps if used) RWF 10.1.6.1.3. Pumped fluid density RWF 10.1.6.2. Optional: RWF 10.1.6.2.1. Returns rate RWF 10.1.6.2.2. Returns density RWF 10.1.6.2.3. Returns temperature RWF 10.1.6.2.4. Back pressure RWF 10.1.6.2.5. Hook load RWF 10.1.6.2.6. Additional rig data as available

7.15.2 Recommended workflow—Placement evaluation— Setting the job sequence RWF 10.2. Define the job sequence Before starting the job schedule reconstruction, import the data acquired during the cement job, set the job boundaries, and optionally add markers to the acquired data chart to indicate timing of key job events. Fig. 7.48 is an illustration of recorded data during a cement job which includes acquired pressure, acquired pump rate and acquired density all measured at the pump truck. The time that each of the fluids is pumped is highlighted by a different shading on the graph. After this data preparation, the pumped fluid sequence map may be defined: Recommended workflow—Placement evaluation—Setting the job sequence (Courtesy: Schlumberger) RWF 10.2.1. Initialize the pumping schedule with the designed fluid sequence RWF 10.2.2. Update when fluid stages were pumped, either by manually entering the start and end times, or using the markers on the acquired data chart RWF 10.2.3. Add and remove fluids in the pumping schedule table as required if different fluids were pumped on the job compared with the design

Fig. 7.48 Recorded data and job sequence for a horizontal cement job. (Credit: Schlumberger.)

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RWF 10.2.4. Override fluid density to correct its value if the fluid was not pumped through the densitometer during any stages of the job RWF 10.2.5. Override fluid rate if the recorded pump rate does not match actual values (e.g., when rig displacement is not recorded, or fluids pumped by gravity feed did not pass through a flowmeter, or pump rate from proximity switch is wrong due to severe cavitation or U-tubing) RWF 10.2.6. Update injection temperature for a correct temperature simulation RWF 10.2.7. Enter back pressure manually if it was applied and not recorded during the job RWF 10.2.8. Select the treating line used to pump each fluid stage to make sure the simulated pump pressure reflects the correct surface pressure losses

7.15.3 Recommended workflow—Job evaluation—Pressure matching RWF 10.3. Perform pressure match and form conclusions. Pressure matching is a method for comparing actual job parameters to simulated ones. If the recorded parameters match the simulated parameters, then there is a high degree of confidence that the assumptions for the design were realized for the actual job. Below is the workflow for performing the pressure match: RWF 10.3.1. Perform quality assurance checks and compare the measured density of the slurry to the design density of the slurry RWF 10.3.2. Run the hydraulic simulation RWF 10.3.3. Compare the recorded surface pressure (cement head or cement pump pressure) with the simulated pressure RWF 10.3.4. Compare the recorded returns rate (if available) with the simulated returns rate RWF 10.3.5. Iterate and adjust assumptions (such as hole diameter, surface lines, or fluids rheological properties), and rerun the hydraulic simulation. RWF 10.3.6. Describe and explain anomalies in the recorded data RWF 10.3.7. Describe and explain differences between the recorded data and simulated data

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Fig. 7.49 Pressure match for a horizontal well cement job. (Credit: Schlumberger.)

RWF 10.3.8. Describe and explain what conclusions can be made. One example of a conclusion is that the pressure match is consistent with the programmed TOC An example pressure match is shown in Fig. 7.49. The acquired pressure for a horizontal well cement job is compared with the simulated pump pressure on the plot. The plot also includes a simulated cement head pressure, which will differ from the cement pump pressure by the pressure drop in the surface lines. Because the acquired pump pressure closely matches the pump pressure (simulated), there is a high degree of confidence that all the assumptions in the simulation are reasonable. A conclusion may be formed that the TOC that is achieved is similar to the TOC in the simulation. Because TOC is typically a regulatory requirement, it is useful to use the pressure match technique as one method to demonstrate where the TOC is located. Note that the workflow does NOT indicate to set the TOC, and then change the assumptions to match the pressure. It is a subtle difference to iterate on the assumptions, compare the pressure, and then draw conclusions. When iterating on the assumptions, all of the iterations should be within reasonable limits. For example, it is not reasonable to select a hole size smaller than bit size unless there is some other data to support this assumption. Many wellbore parameters are measured, therefore measured data

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should be included, and assumptions should only change according to the possible error in those measurements. Some of the assumed parameters may include changes during the cement job (such as cement slurry rheology), which may require sensitivity analysis and judgment to arrive at which assumptions should be used in the final pressure match report. Anomalies between the recorded data and simulations are also useful and should be explained. These anomalies may be due to downhole or surface events. It is particularly useful to note pressure events associated with plugs that are used in cementing. Other anomalies such as pack-offs or losses may be noted.

7.15.4 Recommended workflow—Job evaluation—Additional comparisons RWF 10.4. Additional comparisons. Wellsite data and observations may be compared with simulations for several other sets of data. Each matching data set gives more confidence that all the assumptions in the simulation are correct. A procedure for running other comparisons is listed below: RWF 10.4.1. Run hydraulic simulations with recorded data RWF 10.4.2. Perform centralization calculations with actual centralizers that were installed RWF 10.4.3. Compare recorded hook load to actual hook load RWF 10.4.3.1. During casing running RWF 10.4.3.2. During the cement job RWF 10.4.4. Perform annular displacement simulation RWF 10.4.5. Compare cement evaluation log (if run), to annular displacement simulation RWF 10.4.6. Compare cement evaluation log to centralization calculation RWF 10.4.7. Describe and explain any conclusions Simulated returns rates and recorded (acquired) pump rates are included in Fig. 7.50. It is useful to compare simulated returns with actual returns to confirm that there were no losses during the cement job. The workflow presented here for postjob evaluation can also be performed in real time during the cement job. With the continuing development of data recording and real time data transmission, together with increased data transmission capabilities and computing capacity, it is possible to imagine collecting the data, setting the fluid sequence and comparing the simulations to actual data in real time. Comparison of simulations with wellsite data is useful for confirming all the assumptions in the simulation, including the assumed TOC.

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Fig. 7.50 Pump rate and simulated return rate used for pressure match simulation. (Credit: Schlumberger.)

7.16 Detailed workflow described in this chapter To conclude this chapter, the process for cement job simulation is described as a series of recommended workflows that have been described in this chapter. The detailed workflow, including all the subsets is collected here for reference: RWF 1. Collect and input the well description and any available well data RWF 1.1. Surface equipment description RWF 1.2. Tubular description RWF 1.3. Hole size RWF 1.4. Directional details RWF 1.5. Formation data Recommended workflow: Formation data entry RWF 1.5.1. Update the directional survey to match the pressure data RWF 1.5.2. Select the pressure input mode RWF 1.5.3. Select the reference depth, in case you have chosen gradient or ED as the pressure input mode RWF 1.5.4. Import the text file (LAS file) that contains the data

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RWF 1.5.5. In the import dialog, select the data channels. Make sure the following are selected correctly: RWF 1.5.5.1. Check if the depths are given as MD or TVD RWF 1.5.5.2. Check if the input mode (absolute pressures, gradient, or ED) corresponds to the selection RWF 1.5.5.3. Check the order of pore and fracture pressure channels RWF 1.5.6. Once the import is complete, assign the pressure data to formation strata RWF 1.5.7. To evaluate risks related to gas migration, select the potential flow zones RWF 1.5.8. To estimate the formation productivity risk, fill in the data for each gas zone Recommended workflow: Temperature data entry RWF 1.6. Temperature details RWF 1.6.1. Surface temperature RWF 1.6.2. BHST RWF 1.6.3. In addition, for offshore wells: RWF 1.6.3.1.Sea surface temperature RWF 1.6.3.2.Seabed temperature RWF 1.7. Centralizer(s) description RWF 2. Collect and input all of the known fluids data. Recommended workflow for defining fluids: RWF 2.1. Define each fluid RWF 2.1.1. Base fluid RWF 2.1.2. Solids content and density RWF 2.1.3. Rheological properties RWF 2.1.4. Noncompressible/compressible RWF 2.2. Define drilling fluid RWF 2.3. Define spacer(s) and wash(es) RWF 2.4. Define slurry(s) RWF 2.5. Define displacement fluid RWF 3. Design additional fluids RWF 3.1. Design fluid based on density RWF 3.2. Design fluid based on rheological properties RWF 3.3. Design fluid based on compatibility RWF 3.4. Design fluid based on component availability RWF 3.5. Design fluid based on set cement properties

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RWF 4. Design fluid volumes, pump schedule, and fluids preparations requirements RWF 4.1. Fluid volumes Recommended workflow—Fluid volumes RWF 4.1.1. Check and update the well description so that it is current RWF 4.1.2. Check that the fluids to use for the calculations are all defined RWF 4.1.3. Select volumes of fluids based on cement job objectives RWF 4.1.3.1. Annular volume/height for tail cement RWF 4.1.3.2. Annular volume/height for lead cement RWF 4.1.3.3. Spacer volume RWF 4.1.3.4. Any additional fluids ahead of the spacer RWF 4.1.3.5. Shoe track fluid RWF 4.1.3.6. Displacement fluid RWF 4.1.4. Check the hydrostatic pressure gradient against the formation pressures using well security plots RWF 4.1.5. If necessary, fine tune the volumes for complex fluid sequences RWF 4.1.6. Proceed to defining the pump schedule RWF 4.2. Pump schedule Recommended workflow—Pump schedule RWF 4.2.1. Check and update the well description so that it is current RWF 4.2.2. Set the backpressure for each stage RWF 4.2.2.1. If returns are normally to the drilling fluids tanks with no restrictions, the back pressure may be assumed to be zero RWF 4.2.2.2. If returns are taken at seabed, set up the surface description accordingly RWF 4.2.2.3. If there is a managed pressure device (MPD) select the back pressure appropriately RWF 4.2.3. Use fluids volumes determined in RWF 4.1 RWF 4.2.4. Set up the various stages of the pumping schedule. Initial pump rates may be chosen based on offset wells, experience, or job objectives. Note that selecting the pump rates may be in iterative process

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RWF 4.2.4.1. Select rig pump or cement pump for pumping spacer RWF 4.2.4.2. Select cement pump for pumping cement slurry RWF 4.2.4.3. Select rig pump or cement pump for pumping displacement RWF 4.2.4.4. Select the pump rates for each stage RWF 4.2.4.5. Add reasonable pauses for operations such as dropping cement plugs RWF 4.2.4.6. The displacement period may be divided with slower pump rates near the end of displacement RWF 4.2.4.7. Optional—add a pause for wait on cement (WOC) at the end of the pumping period RWF 4.3. Fluid and blend preparation Recommended workflow—Blend preparation RWF 4.3.1. Select the amount of blend or total fluid volume to prepare. The blending sheet then computes the required quantities for each component. RWF 4.3.2. Specify the measured bulk density (if available). This is used to adjust the required bulk capacity to store the blend. RWF 4.3.3. Specify the batch parameters for the bulk plant operation: the silo capacity available, and which practices should be followed when blending. RWF 4.3.4. Select the options for the packaging: how the materials are packaged and whether packages are divisible. RWF 4.3.5. Review the distribution of packages among and within the batches, the blend composition in the batch, and the overall blend properties. If the results are not satisfactory, check possible changes to packaging options for improving the results. RWF 4.3.6. Once satisfied with the results, generate the report with the blending sheet that can be sent to the bulk plant. RWF 5. Perform hydraulics and temperature simulation RWF 5.1. Simulate prejob well circulation Recommended workflow—Prejob well circulation RWF 5.1.1. Check and update the well description so that it is current

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RWF 5.1.2. Define the fluids used for the cement job, paying attention to the drilling fluid properties: RWF 5.1.2.1.For accurate temperature predictions, make the correct mud type and composition is entered RWF 5.1.2.2.To run compressible hydraulic simulations, define a compressible drilling fluid RWF 5.1.3. Select the wellbore fluids for the mud circulation If a compressible mud is selected, run the simulation with the corresponding compressible fluid simulator. RWF 5.1.4. Choose the injection temperature model to be used during the simulation. RWF 5.1.5. Set up the pumping schedule using the mud circulation table. RWF 5.1.6. Run the simulation RWF 5.1.7. Review the security checks RWF 5.1.8. The results of the mud circulation may be used as the initial temperature condition for the cement job simulation RWF 5.2. Simulate cementing operations Recommended workflow—Cementing operations hydraulic and temperature simulation RWF 5.2.1. Run the hydraulic simulation using the planned pump schedule RWF 5.2.2. Confirm that design parameters are met including well security. Review the security checks, that well control is maintained, and cement losses (if simulated) are manageable. RWF 5.2.3. Check minimum hook load to ensure that the risk of casing pump out is not present RWF 5.2.4. Check pump horsepower requirement against available capacity. RWF 5.2.5. Verify key temperature values against laboratory test conditions. Detailed pressure and temperature results may be used to prepare or update laboratory test requests RWF 5.3. Iterate by adjusting the pump schedule as necessary RWF 5.4. Standalone calculation aids

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Recommended workflow—Friction pressure—Standalone RWF 5.4.1. Specify the geometry to calculate the friction pressures (annulus or pipe). RWF 5.4.2. Specify whether to sensitize by flow rate or by geometry RWF 5.4.3. Specify the fixed parameters for geometry or flow rate, as applicable. RWF 5.4.4. Enter the range of parameters for sensitizing RWF 5.4.5. Review the calculation result in the friction pressures table or chart that is displayed RWF 5.4.6. Compare the results with both surface and downhole rheological properties RWF 6. Perform casing centralization simulation. RWF 6.1. Centralization Standoff Calculations Recommended workflow—Centralization standoff calculations RWF 6.1.1. Check and update the well description so that it is current. At the planning stage it is a good practice to plan based on the expected tortuosity, once a well is drilled, the actual trajectory may be used RWF 6.1.2. Run the hydraulic simulator, as centralization calculations rely on placement pressures to obtain buoyancy forces RWF 6.1.3. Select the centralizers planned for the job and add them to the centralizers stock on the Centralization page RWF 6.1.4. Define the centralizer placement RWF 6.1.4.1. Placement may be described as a placement pattern RWF 6.1.4.2. The exact depth for each centralizer may be specified RWF 6.1.5. Select a centralization model for the standoff calculation RWF 6.1.5.1. Soft String RWF 6.1.5.2. Stiff String RWF 6.1.6. Run standoff calculations. The standoff calculation can be performed for three different stages of the cement job to understand the maximum and minimum standoff during cementing. The standoff will change because the density differences between the fluids inside the pipe and in the annulus affect the buoyancy of the casing. The three cases to simulate are as follows: RWF 6.1.6.1. Just before cementing, only drilling fluid in the well (pipe neutral simulation)

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RWF 6.1.6.2. Just as cement turns the shoe (pipe heavy simulation) RWF 6.1.6.3. At end of displacement (pipe light simulation) RWF 6.1.7. Review the standoff results RWF 6.1.8. Use standoff results for annular displacement simulation RWF 6.2. Running forces Recommended workflow—Casing running forces RWF 6.2.1. Select a centralization model for the running forces calculation RWF 6.2.1.1. Soft String RWF 6.2.1.2. Stiff String RWF 6.2.2. Select the friction factors that will be used for running forces RWF 6.2.2.1. In previous casing RWF 6.2.2.2. In open hole RWF 6.2.3. Perform running forces calculation with the required parameters RWF 6.2.4. Compare hook load to available rig capacity and traveling block weight RWF 6.2.5. Compare simulated torque to casing connections if casing rotation is planned. RWF 6.3. Surge and Swab RWF 6.4. Casing Stretch RWF 6.5. Verify hook load, torque and drag parameters during cementing RWF 6.6. Iterate on the centralizer design RWF 7. Perform annular displacement simulation RWF 7.1. Perform displacement simulation Recommended workflow—Annular displacement RWF 7.1.1. Perform hydraulic simulation RWF 7.1.2. Perform centralizer standoff simulation RWF 7.1.3. Set simulator options and launch the simulation RWF 7.1.4. Review the simulation results in different forms: RWF 7.1.4.1. Concentration curves RWF 7.1.4.2. Maps of the results RWF 7.1.4.3. Fluid concentration 3D map Recommended workflow—Annular displacement with casing movement RWF 7.1.6. Perform hydraulic simulation

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RWF 7.1.7. Perform centralizer standoff simulation (RWF 6.1) using stiff string method RWF 7.1.8. Run the in-pipe simulation (choosing pipe only or both options for the simulation) to take into account the contamination that occurs while the fluids are traveling down the string RWF 7.1.9. Define a timeline for string movement if the plan is to reciprocate or rotate the string during the cement job RWF 7.1.10. Set the simulator options and launch the simulation RWF 7.1.11. Review the simulation results in different forms: RWF 7.1.11.1. Concentration curves RWF 7.1.11.2. Maps of the results RWF 7.2. Compare the simulation results with the job objectives RWF 7.3. Iterate on the design to meet the job objectives by modifying (in order of difficulty) the pump schedule, centralizer placement, fluids volumes, or even fluid design RWF 8. Perform special case simulations RWF 8.1. Critical static gel strength RWF 8.2. Gas migration risk Recommended workflow—Gas migration RWF 8.2.1. Select and describe the potential flow zones (PFZs). For gas zones, formation permeability and skin factor may also be entered, if the data are available, for the calculation of the formation productivity risk RWF 8.2.2. Ten-minute gels may be considered RWF 8.2.3. Run the hydraulic simulator to obtain the pressures at the end of placement. This is will be the basic input for the critical static gel strength calculation. RWF 8.2.4. After running standoff calculation, run a displacement simulator. The resulting cement coverage and concentration results will be the input for the mud removal risk (MRR). RWF 8.2.5. Enter the applied backpressure, if pressure is kept on the annulus while the cement is setting (as a method to prevent gas migration). RWF 8.2.6. Set slurry critical period RWF 8.2.7. Indicate applicable special well conditions before running the calculation for gas migration risks

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RWF 8.2.8. Launch the calculation RWF 8.2.9. Review the details of the calculation for each PFZ. Recommended workflow—Plug—Volume optimization RWF 8.3. Plug placement RWF 8.3.1. Enter the well data for the cement job, making sure that well geometry is as accurate as possible RWF 8.3.2. Define the fluids used for the cement job. Describe all fluid properties, although the volume optimization uses only the density of the fluids RWF 8.3.3. Set an optimization criterion (options) for the volume balance algorithm RWF 8.3.4. Select the wellbore fluids placed in different parts of the well. Indicate if the trip tank is connected to fill up the annulus during POOH RWF 8.3.5. Choose the fluids placed to be pumped and specify how much of each fluid will be placed in the well, using the fluid and volume selection tools RWF 8.3.6. Launch the optimization RWF 8.3.7. Review the generated design for the annulus and pipe in the placement design tables RWF 8.3.8. Compare the hydrostatic pressure against the formation pressures, ensuring that well control is maintained RWF 8.3.9. If fine-tuning is required to realize complex fluid sequences, it can be done using the custom placement page RWF 8.3.10. Validate the optimized volumes by simulating the pull out of hole (POOH) RWF 8.3.11. Proceed in the workflow to define the pumping schedule once satisfied with the placement design Recommended workflow—Plug—POOH simulation RWF 8.3.12. Before designing fluid placement, select whether the annulus will be kept full during POOH RWF 8.3.13. Design the fluid placement for the cement job RWF 8.3.14. Set a final depth for the pull out of hole if the postplacement circulation will occur below the top of the spacer RWF 8.3.15. Run the displacement simulation to evaluate the contamination while the fluids are pumped

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RWF 8.3.16. For running contingency simulations, or for certain placement methods, select the option that match the contingencies (e.g., pulling wet, including mechanical separators, filling the annuls) RWF 8.3.17. Launch the calculation RWF 8.3.18. Review the results of the simulation RWF 8.3.19. Iterate as necessary for the design RWF 8.4. Cement sheath stress calculations Recommended workflow for cement sheath stress simulation RWF 8.4.1. Options—set options such as units for the calculations RWF 8.4.2. Geometry—set the number of casing strings RWF 8.4.3. Formation—specify open hole diameter and formation mechanical and thermal properties RWF 8.4.4. Casing—specify casing dimensions and material. Mechanical and thermal properties are typically assumed for steel RWF 8.4.5. Cement—specify the cement system—these are the properties that may be compared between systems. Simulators may include a database that includes (and assumes) the following: RWF 8.4.5.1. Density RWF 8.4.5.2. Compressive strength—typically unconstrained compressive strength (UCS) RWF 8.4.5.3. Tensile Strength—typically 1/10 of the compressive strength if the measured tensile strength is not available RWF 8.4.5.4. Young’s modulus—modulus of elasticity RWF 8.4.5.5. Poisson’s ratio RWF 8.4.5.6. Chemical expansion coefficient (if expanding agent is used) RWF 8.4.5.7. Thermal properties—include thermal conductivity, specific heat capacity and thermal expansion factor. RWF 8.4.6. Specify the dynamic conditions for the section. Include both temperature and pressure in these dynamics: RWF 8.4.6.1. Pressure schedule—specify the change in pressure and the schedule. The change may be due to fluid density changes in the wellbore, pressures due to completion operations, pressures due to production of the wellbore, and or pressure due to injection.

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RWF 8.4.6.2. Temperature schedule—specify the change in temperature and the schedule. Temperature changes may occur because of completion, production, or injection operations. RWF 8.4.7. Perform stress analysis. Analysis may include several layers of detail. RWF 8.4.7.1. Section analysis summary—overview of the results of stress calculations. RWF 8.4.7.2. Output plots—plots of stress, displacement, temperature, and microannular sizes. RWF 8.4.7.3. Sensitivity analysis—analysis of sensitivity of cement failure risks to parameter variation. RWF 8.4.8. Iterate on the design as necessary RWF 8.4.8.1. Change the pressure schedule RWF 8.4.8.2. Change the temperature schedule RWF 8.4.8.3. Change the cement properties Recommended workflow: Initial foam cement selection RWF 8.5. Foam cement simulation and design RWF 8.5.1. Define the well data for the cement job, just like a normal primary cement job RWF 8.5.2. Describe the fluids used for the job. For the fluids to be foamed, this means defining the base fluid, including foam and stabilizer additives RWF 8.5.3. Select the original fluids in the well before the cement job starts RWF 8.5.4. Select the foam objective type to use initially to characterize the foamed stages RWF 8.5.5. Setup the required final fluid positions in the annulus and the pipe, using the placement tables: add the fluids to the tables and define for each of them the depth interval that it should cover at the end of the job RWF 8.5.6. In the placement tables, provide initial objectives for the fluid stages that will be foamed RWF 8.5.7. Select the temperature profile that the software should use for the placement calculation. As the foam density depends on pressure and temperature conditions, this will have a significant impact on the results. RWF 8.5.8. Launch the calculation

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RWF 8.5.9. Once the calculation is finished, review the generated placement design on the placement result page Recommended workflow—Foam placement RWF 8.5.10. Set up the placement objectives: select the original wellbore fluids, the required position of each fluid stage and the corresponding objectives RWF 8.5.11. Run the placement calculation RWF 8.5.12. Review the placement results in the annulus and pipe placement tables RWF 8.5.13. The design may be iterated at this point RWF 8.5.14. The original foam objectives may be changed. For example, constant ratio may be used for the first iteration, and then min/max density, or constant density may be used for the second iteration RWF 8.5.15. If fine-tuning of the placement results is desired, the fluid stages with the corresponding N2 ratio can be copied back into the placement objectives for another iteration RWF 8.5.16. Verify the downhole pressure at the end of placement to ensure that the pressure is within the design limits RWF 9. Generate cement program documentation RWF 10. Perform postjob simulations to compare wellsite observations to simulations. Recommended workflow—Placement evaluation—Importing data RWF 10.1. Import wellsite recorded data After the cement job, the job data will need to be imported into the simulator using the following steps: RWF 10.1.1. Set the job boundaries to remove unwanted data from the start and the beginning of the job RWF 10.1.2. Review imported messages in the job events list RWF 10.1.3. Add custom messages to the job events list, if you find that important events are not marked RWF 10.1.4. Select the messages to be displayed on the chart RWF 10.1.5. Add the events to mark the start and end of the displacement, to correct the displacement volume for the inaccuracies related to pump efficiency RWF 10.1.6. Select the channels to be imported

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RWF 10.1.6.1. Required RWF 10.1.6.1.1. Time RWF 10.1.6.1.2. Pump rate (cement pump and rig pumps if used) RWF 10.1.6.1.3. Pumped fluid density RWF 10.1.6.2. Optional RWF 10.1.6.2.1. Returns rate RWF 10.1.6.2.2. Returns density RWF 10.1.6.2.3. Returns temperature. RWF 10.1.6.2.4. Back pressure RWF 10.1.6.2.5. Hook load. RWF 10.1.6.2.6. Additional rig data as available Recommended workflow—Placement evaluation—Setting the job sequence RWF 10.2. Define the job sequence Before starting the job schedule reconstruction, import the data acquired during the cement job, set the job boundaries, and optionally add markers to the acquired data chart to indicate timing of key job events. After these preparations, the pumped fluid sequence map may be defined: RWF 10.2.1. Initialize the pumping schedule with the designed fluid sequence RWF 10.2.2. Update when fluid stages were pumped, either by manually entering the start and end times, or using the markers on the acquired data chart RWF 10.2.3. Add and remove fluids in the pumping schedule table as required if different fluids were pumped on the job compared to the design RWF 10.2.4. Override fluid density to correct its value if the fluid was not pumped through the densitometer during any stages of the job RWF 10.2.5. Override fluid rate if the recorded pump rate does not match actual values (e.g., when rig displacement is not recorded, or fluids pumped by gravity feed did not pass through a flowmeter, or pump rate from proximity switch is wrong due to severe cavitation or U-tubing.) RWF 10.2.6. Update injection temperature for a correct temperature simulation RWF 10.2.7. Enter back pressure manually if it was applied and not recorded during the job

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RWF 10.2.8. Select the treating line used to pump each fluid stage to make sure the simulated pump pressure reflects the correct surface pressure losses Recommended workflow—Job evaluation—Pressure matching RWF 10.3. Perform pressure match and form conclusions Pressure matching is a method for comparing actual job parameters to simulated ones. If the recorded parameters match the simulated parameters, then there can be a high degree of confidence that the assumptions for the design were realized for the actual job. RWF 10.3.1. Perform quality assurance checks and compare the measured density of the slurry to the design density of the slurry RWF 10.3.2. Run the hydraulic simulation RWF 10.3.3. Compare the recorded surface pressure (cement head, or cement pump pressure) to the simulated pressure RWF 10.3.4. Compare the recorded returns rate (if available) to the simulated returns rate RWF 10.3.5. Iterate and adjust assumptions (such as hole diameter, surface lines, or fluids rheological properties), and rerun the hydraulic simulation RWF 10.3.6. Describe and explain anomalies in the recorded data RWF 10.3.7. Describe and explain differences between the recorded data and simulated data RWF 10.3.8. Describe and explain what conclusions can be made. One example of a conclusion is that the pressure match is consistent with the programmed TOC Recommended workflow—Job evaluation—Additional comparisons RWF 10.4. Additional comparisons Several other items may be compared between actual data and recorded data. RWF 10.4.1. Run hydraulic simulations with recorded data RWF 10.4.2. Perform centralization calculations with actual centralizers that were run RWF 10.4.3. Compare recorded hook load with actual hook load RWF 10.4.3.1. During casing running RWF 10.4.3.2. During the cement job RWF 10.4.4. Perform annular displacement simulation

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RWF 10.4.5. Compare cement evaluation log (if run), to annular displacement simulation RWF 10.4.6. Compare cement evaluation log with centralization calculation RWF 10.4.7. Describe and explain any conclusions that can be made

7.17 Summary of the overall workflows in this chapter Computer-assisted design of primary cementing is the main tool for the cementing engineer to ensure the success of the cementing and zonal isolation objectives. The results of the simulations are utilized for well planning and operational planning so that the cement job execution can be performed to meet those objectives. After the cement job, the comparison of simulations to well site data is useful for confirming all the assumptions in the simulation, including the assumed TOC. Recommended workflow: Overall cement job simulation RWF 1. Collect and input the well description and any available well data. RWF 2. Collect and input all the known fluids data RWF 3. Design additional fluids RWF 4. Design fluid volumes, pump schedule, and fluids preparations requirements RWF 5. Perform hydraulics and temperature simulation RWF 6. Perform casing centralization simulation RWF 7. Perform annular displacement simulation RWF 8. Perform special case simulations RWF 9. Generate cement program documentation RWF 10. Perform postjob simulations for job evaluation All these workflows can be considered to be cement job simulation which is the main tool for the cementing engineer to ensure success in achieving the cementing and zonal isolation objectives. Cement job simulation is a numerical calculation performed by a computer program that can be used to understand almost all aspects of the cement job. These simulations can be performed during the design process. Simulation can also be used during the evaluation process to confirm that the

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cement job execution met the objectives and met the zonal isolation requirements.

Acknowledgments This work was possible because of the support of many people. The author thanks Schlumberger for his career development and providing the practice and skills that allowed him to write this chapter. Participation through industry conferences and meetings, especially those organized by the Society of Petroleum Engineers (SPE) and the American Petroleum Institute (API) standards committees also informed and refined these ideas. The author especially recognizes Nicolas Flamant who has worked on cementing simulation within Schlumberger for decades and developed the software that generated many of the figures included in this chapter. Finally, he thanks his wife Sheri, who provides unwavering support through all his endeavors.

References API Standard 65 – Part 2, 2010. Isolating Potential Flow Zones During Well Construction, second ed. American Petroleum Institute, Washington, DC. API Recommended Practice 65, 2002. Cementing Shallow Water Flow Zones in Deepwater Wells, first ed. American Petroleum Institute, Washington, DC (reaffirmed 2012). API Recommended Practice 10D-2, 2004. Recommended Practice for Centralizer Placement and Stop-Collar Testing, first ed. American Petroleum Institute, Washington, DC (re-affirmed 2010). API Recommended Practice 10B-2, April 2013. Recommended Practice for Testing Well Cements, second ed. American Petroleum Institute, Washington, DC. API Specification 10D, 2002. Specification for Bow-Spring Casing Centralizers, sixth ed. American Petroleum Institute, Washington, DC (re-affirmed 2010). API Technical Report 10TR1, September 2008. Cement Sheath Evaluation, second ed. American Petroleum Institute, Washington, DC. Nelson, et al., 2006. Well cementing. In: Chapter 4: Rheology and Flow of Well Cement Slurries of the Well Cementing Book Schlumberger, Houston, TX, USA, second ed. Bogaerts, M., et al., 2012. Challenges in setting cement plugs in deepwater operations. In: SPE 155736, The Society of Petroleum Engineers Deepwater Drilling and Completions Conference, June. Gorokhova, L., Parry, A., Flamant, N., March 2013. Comparing soft-string and stiff string method used to compute casing centralization. SPE 163424, SPE/IADC Drilling Conference and Exhibition. Guo, Y., et al., 2014. Successful placement of cement plugs in HP/HT wells using an innovative computer-aided simulator. In: SPE 171395, The Society of Petroleum Engineers Asia Pacific Oil & Gas Conference, October. Juvkam-Word, H.C., Wu, J., December 1992. Casing deflection and centralizer spacing calculations. In: SPE Drilling Engineering, pp. 268–274.

Software CEMENTICS “Version 2019” (Software) “2019”. Schlumberger, Sugar Land TX. CemSTRESS “Version 2014” (Software) “2014”. Schlumberger, Sugar Land TX.

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Web pages Schlumberger. https://www.slb.com/drilling/drilling-fluids-and-well-cementing/wellcementing/cement-software/cementics-zonal-isolation-software. Pegasus Vertex, Inc. https://www.pvisoftware.com/cempro+-cementing-job-model.html. Baker Hughes, A GE company, LLC. https://www.bhge.com/system/files/2018-06/ cemfacts-slsh.pdf. Halliburton. https://www.halliburton.com/en-US/ps/cementing/cementing-software-solutions/ job-design/icem-reg-service.html. Anon. https://www.ncei.noaa.gov/access/data/coastal-water-temperature-guide/.

Further reading API Recommended Practice 96, March 2013. Deepwater Well Design and Construction, first ed. American Petroleum Institute, Washington, DC.

CHAPTER EIGHT

Temperature prediction Hu Dai Pegasus Vertex, Inc., Houston, TX, United States

Abbreviations BHCT BHST CFD ID LWD MD MWD OD PV TD YP

bottom-hole circulation temperature bottom-hole static temperature computational fluid dynamics internal diameter logging while drilling measured depth measurement while drilling outer diameter plastic viscosity total depth yield point

8.1 Introduction Resulting from the Earth’s interior heat, the geothermal temperature (i.e., static formation temperature) generally increases with the vertical depth. The world average geothermal gradient is about 1.5°F/100 ft. Based on that, a 10,000-ft vertical well will be 150°F hotter at the bottom than on the ground. A well can be cooled down by pumping in cold fluids because of heat exchange between the surrounding formation and wellbore fluids and across different depths by fluid flow. After a sufficiently long period of circulation, the temperature distribution will appear stable, when the temperature at the well bottom is called bottom-hole circulating temperature (BHCT). After the circulation stops, the temperature profile will gradually recover to the geothermal temperature. Wellbore temperature is important in cementing engineering for many reasons. First, cement slurries are designed to have proper thickening time under downhole conditions; in other words, wellbore temperature must be in an expected range to avoid an early or a delayed setting. Second, because gel strength and compressive strength of cement are largely affected

Applied Well Cementing Engineering https://doi.org/10.1016/B978-0-12-821956-0.00001-8

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by temperature, knowledge of the wellbore temperature helps to predict gas migration and well integrity. Third, the properties of spacer and drilling fluid are subject to change under higher temperatures; thus their formulation may need to be modified according to the expected bottom-hole temperature at higher temperature zones. In the case of lost circulation, lost circulation materials are likely designed to function under a certain temperature range. Furthermore, temperature is a factor that changes the fluid density and rheology and consequently affects the bottom-hole pressure. Casings, pipes, downhole tools, and valves may fail under high temperatures. As technology evolves, drilling high temperature, high pressure wells requires accurately predicting and monitoring the extreme downhole temperature, a crucial aspect for a successful well development.

8.2 Temperature logging Temperature logging is a procedure of measuring and recording the geothermal temperature or the circulating temperature. In producing wells, temperature logging is often conducted to locate gas entry. Temperature measurement can be made by measurement while drilling and logging while drilling techniques during drilling or by running wireline or free fall tool before the cementing job. Bottom-hole static temperature (BHST) and BHCT are measured during shut-in and during circulation, respectively, both of which are referred to in the cementing job design. However, the wellbore temperature during cementing is expected to be different from that of during drilling because a sequence of fluids with different properties pumped in that has an impact on the wellbore temperature. Temperature measurements during actual cementing jobs are rarely performed and often too late to be useful; therefore predicting the temperature ahead of the job has a great significance in cementing engineering. Methods of predicting the temperature by theoretical approaches or simulations are desired.

8.3 The physics In theory, depth and time-dependent wellbore temperature is predictable by solving mathematical equations developed from basic principles of thermal physics. In this process, the concept of energy conservation is applied, and different forms of heat transfer in formation and in fluids must be evaluated.

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8.3.1 Physical principals Heat exchange at solid-fluid interface induced by fluid flow, named heat convection, occurs at the inner and outer surfaces of casing or drilling pipe and at the borehole wall. The rate of this heat flow is proportional to the surface area, heat transfer coefficient, and the temperature difference between the solid and fluid, as expressed in Newton’s law of cooling (Incropera et al., 2007):
 (8.1) Q ¼ AU Ts  Tfl , where Q is the heat flow rate, A is the area of heat exchange, and U is the heat transfer coefficient. Ts and Tfl are the temperatures of the solid and fluid, respectively. Internal heat flow within the casing material and the formation is heat conduction, the latter of which will affect the rate of heat flow feeding into a wellbore. Conductive heat rate is related to the heat conductivity of the media, the surface area, and the temperature gradient, as described in Fourier’s law, which has the form of the following equation in one dimension:   dT Q ¼ kA , (8.2) dx where Q is the heat flow rate, k is the heat conductivity, A is the area,
 and dT dx is the temperature gradient. A system with conserved energy is observed by enclosing the wellbore fluids inside both the casing and the annulus, the casing itself and the formation extended to the far field. The formation sufficiently far from the borehole, that is, at a radius greater than the scale of thermal influence, can be assumed undisturbed. Cold fluids are pumped in and heated fluids flow out, where the gained thermal energy was received from the formation boundary, which is the same physical system as a geothermal well that retrieves geothermal energy from the Earth. In drilling problems, because of a large measured depth (MD)-to-diameter ratio, the temperature gradient along the MD is much smaller than the radial gradient; hence axial heat conduction in the rock and inside the casing steel is often neglected. The radial temperature gradient in the pipe and in the annulus is also neglected; thus only mean fluid temperature is considered at a depth, which substantially simplifies the problem. As given in Raymond (1969), the system can be described by the following equations: AD ρνD Cp

∂TD ðZ, tÞ ∂TD ðZ, t Þ + 2πrD U ½TD ðZ, t Þ  TA ðZ, t Þ ¼ ρAD Cp ∂Z ∂t (8.3)

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  ∂TA ðZ, tÞ + 2πrD U TD ðZ, t Þ  TAðZ , tÞ ∂Z   ∂TA ðZ, t Þ + 2πrB hf Tf ðrw , Z, tÞ  TA ðZ, tÞ ¼ ρAA Cp ∂t  ∂Tf ðrw , Z, t Þ kf 1 ∂ ∂Tf ðrw , Z, tÞ ¼ r ∂t ∂r ρf Cpf r ∂r AA ρνA Cp

   ∂Tf ðrw , Z, tÞ 2πrB hf Tf ðZ, t Þ  TA ðZ, t Þ ¼ 2πrB kf , ∂r r¼rB

(8.4)

(8.5)

(8.6)

where rw is a variable representing the wellbore radius in formation, and rB is the borehole radius. The first two equations, Eqs. (8.3) and (8.4) describe the energy conservation of the fluid inside the pipe and the fluid in the annulus, where AD and AA are the cross-sectional areas inside the pipe and the annulus, TD and TA are the mean temperature of fluids in the pipe and in the annulus, vD and vA are the flow velocities in the pipe and in the annulus, respectively, Cp is the heat capacity of the fluid, and U is the total heat transfer coefficient, including the inner and outer surfaces of the pipe. Eq. (8.5) describes the heat diffusion inside the formation. Eq. (8.6) is the heat flux condition at the borehole wall. In the equations, hf is the heat transfer coefficient at the borehole wall, Tf is the temperature in the formation which is dependent k on the MD, radial distance, and time, and α ¼ ρ Cf pf is the heat diffusivity of the f

formation, a combined parameter, including heat conductivity kf, density ρf, and heat capacity Cpf. Including proper boundary conditions at the inlet and the undisturbed formation boundary, this system is closed and can be solved numerically to find the time-dependent temperature distribution in the pipe, annulus, and formation. An analytical solution of pseudo-steady-state temperature profile in the pipe and annulus in terms of borehole wall temperature Tf(rB, Z, t) can be derived by dropping the transient terms in Eqs. (8.3) and (8.4). Detailed expressions can be found in Raymond (1969). On the other hand, the solution of heat diffusion equation in formation, Eq. (8.5), with fixed wall temperature is found as follows (Kutasov and Eppelbaum, 2015) T¼

T ðr, t Þ  Tf ln r ¼1 ,1  r  Rin , T ðrB , tÞ  Tf ln Rin

(8.7)

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where r ¼ rrB ,t ¼ αt ,Rin ¼ rrinB , and rin is the radius of thermal influence in forr2 B

mation. The radius of thermal influence is estimated as (Kutasov, 1999): pffi Rin ¼ 1 + 2:184 t :

(8.8)

As time elapses, the thermal influence boundary in the formation is continuously expanding to the far field; therefore true steady status is never reached in this thermal system, when temperature keeps dropping in an infinitely long time. As an example, pseudo-steady formation temperature evolution for up to 24 h predicted by Eq. (8.7) is shown in Fig. 8.1 for a borehole of 8.725 in. in diameter. The borehole wall temperature is assumed fixed at 100°F cool, and the undisturbed formation temperature is 180°F. The thermal influence after 24 h reaches 23.3 in. The fluid temperature and the formation temperature are coupled at the borehole wall; therefore the borehole wall temperature T(rB, t) can be found through Eq. (8.6) by matching the heat flux associated with both sides. However, the pseudo-steady solution is only an approximation and may not accurately capture time-dependence of the temperature development, which especially becomes an issue for cementing, because early stage temperature development is important since the start of pumping. Therefore the full unsteady system described by Eqs. (8.3)–(8.6) is often solved by computer. When multiple fluids flow in the wellbore, which is the case during cementing, properties of different fluids corresponding to the depths are applied. Fig. 8.2 is a typical temperature profile of a well under circulation

Fig. 8.1 Evolution of radial temperature distribution in the formation. Tw ¼ 100°F, Tf ¼ 180°F. The thermal diffusivity of the formation α ¼ 3.15 in.2/h. (Credit: Pegasus Vertex, Inc.)

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Fig. 8.2 Simulated temperature in the pipe and annulus after circulating a 20,000 ft vertical well for one and four bottom-ups (simulated in CEMPRO). (Credit: Pegasus Vertex, Inc.)

predicted by solving the system with numerical method implemented in CEMPRO. The formation temperature gradient is 1.6°F/100 ft and surface temperature is 80°F. The fluid enters the well at 135°F. The bottom temperature, after four bottom-ups of circulation, was cooled to about 285°F, the annulus temperature at the outlet was slightly heated to 143°F. The highest temperature in the annulus, known as hotspot, is not at the bottom, instead found at about 17,800 ft where the temperature is 292°F.

8.3.2 Contributing factors Factors of influence on the wellbore temperature can be identified by observing the Eqs. (8.4)–(8.6), in addition to the boundary and initial conditions. Initial temperature field at the beginning of pumping, inlet fluid temperature or surface tank condition, and the undisturbed geothermal temperature must be considered in predicting the well temperature. Flow rate takes effect in Eqs. (8.3) and (8.4) through velocity and heat transfer coefficient hf and U. To account for convective heat transfer coefficient, a dimensionless parameter Nusselt number is used, which is defined as Nu ¼ hD/kf, where D is the hydraulic diameter, kf is the heat conductivity of the fluid, and h is the heat transfer coefficient. Nusselt number is often related to Reynolds number and Prandtl number by experimentally determined correlations. Most of these correlations are developed for Newtonian fluids; however, they are widely

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applied to non-Newtonian fluids through effective viscosity. Two relations for turbulent flow are given as 4 1 Nu ¼ 0:023Re5 Pr3

 0:14 μ μs

(8.9)

and   f ðReD  1000Þ Pr 8 Nu ¼ ,  1  2 2 f ð1 + 12:7 Pr3  1 8

(8.10)

where Prandtl number Pr ¼ μCp/k and Reynolds number Re ¼ ρDv/μ. Eq. (8.9) is good for Reynolds number greater than 104, while Eq. (8.10) is believed applicable for Re > 2300, which covers the transitional regime. If the flow is laminar, Nu ¼ 4.36 is used with restrictions, which is developed for steady Newtonian flow (Incropera et al., 2007). A different formula developed from experimental study by Seider and Tate (1936) is recommended:  1   D 3 μ 0:14 Nu ¼ 1:86 RePr , L μs

(8.11)

where f is the friction factor, μ and μs are fluid viscosities measured at the mean fluid temperature and wall surface temperature. Fig. 8.3 shows correlations of the Nusselt number and Reynolds number proposed from the two

Fig. 8.3 Nusselt number (Nu) versus Reynolds number (Re) from Gnielinski (1976, red line) and Seider and Tate (1936, blue line) (Pr ¼ 100). (Credit: Pegasus Vertex, Inc.)

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references at a typical Prandtl number. The rate of heat exchange in laminar regime at low Reynolds number is much lower than in the turbulent regime. The density and heat capacity of fluids appear in Eqs. (8.3) and (8.4), which will influence the temperature solution; other parameters, including heat conductivity and viscosity, have contributions by changing the convective heat transfer coefficient [Eqs. (8.9)–(8.11)]. Three cases are simulated to estimate the influence of density and heat capacity of circulating fluid on the bottom-hole temperature for a vertical well, and the results are listed in Table 8.1. Note the same viscosity is used for these cases. The BHST is 400°F. The 18-ppg mud cools the bottom to 260 F, 25°F, lower than that of 10-ppg mud, and the annulus return temperature is 7°F higher than 10-ppg mud. The temperature change from the bottom to outlet, Tbtm  Tout, is reduced by more than 30°F. From Eqs. (8.3)– (8.4), we notice the combined fluid property ρCp, that is, volumetric heat capacity, instead of density or specific heat capacity alone, has contribution to the results. High volumetric heat capacity causes less temperature changes along the annulus, lower hotspot temperature, and is likely to bring the hotspot location to a shallow depth. Intuitively, this is because the annulus fluid with higher heat capacity can hold more heat. Cases II and III have the same volumetric heat capacity; however, they display different bottom temperatures, caused by distinct heat transfer coefficients. Consider Reynolds number dominating the Nusselt number (because Prandtl number is usually less than a few hundred and to the power of 1/3), 18-ppg mud has a higher Reynolds number and, thus, higher Nusselt number, which leads to an increased heat transfer. Consequently, with 18-ppg mud, the bottom has a temperature closer to the near formation than with 10-ppg mud. Table 8.2 gives rough values of properties for oil, water, and mud and estimated Prandtl number and Reynolds number at a flow rate of 200 gpm (or 1.5 ft/s). Table 8.1 Influence of heat capacity and density of the circulating fluid after circulating for four bottom-ups in a well of 20,000 ft in depth and 8.625 in. in diameter. Cp MD (Btu/lbm/°F) MW (ppg) CpMW Tbtm (°F) Tout Thot hot (ft) Tbtm 2 Tout

I 0.61 II 0.61 III 1.09

10 18 10

6.1 10.98 10.9

285 260 246

146 153 157

292 266 254

18,000 138.9 17,500 107 17,000 89

The rheology parameters used for the simulations are plastic velocity (PV) ¼ 40 cP, yield point (YP) ¼ 20 lbf/100 ft2.

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Table 8.2 Thermal parameters of water, oil, and mud (water-based). μ Cp (Btu/ Density k (Btu/ μ (lb s/ (lb/ft3) (cP) lb/F) ft h °F) Pr 100 ft2)

Re

Water-based 0.2089 mud Water 0.0021 Oil 0.0104

48,347.9 7674.3

100 0.61

110

0.39

378.3 844.2

1 5

63 50

0.3 0.1

8.1 60.5

1 0.5

As heat transfer rate in the solid formation is governed by heat diffusivity k of the formation (α ¼ ρ Cf pf ), therefore when lithology’s effect on the rock f

temperature is evaluated, the conductivity, density, and heat capacity should be accounted for in a combination, except on the borehole wall. At deep depths, high diffusivity in the formation implies quick heat propagation from the neighboring formation to the borehole and, thus, helps to increase the bottom-hole temperature. This will be further discussed in the following sections. In addition, a larger hole has an increased solid-fluid interface area between the annulus and formation; thus the heat transfer from the formation to the annulus fluids is enhanced, which increases the bottom-hole temperature. Furthermore, a low fluid viscosity also increases the convective heat transfer via increased Reynolds number.

8.4 Numerical modeling Numerical method is the approach of solving mathematical or physical equations using computers. This is done by converting differential equations defined in continuous space and time to a large system of equations in discretized domain. Numerical procedures have been developed to solve the wellbore temperature problem since decades ago (e.g., Keller et al., 1973; Santoyo, 1997), which is described by Eqs. (8.3)–(8.6) or similar equations. A typical method is discussed in this section. As illustrated in Fig. 8.4, two-dimensional mesh is predefined to describe the physical space of an axis-symmetric wellbore in cylindrical coordinates. One direction is along measured depth and the other is in radial direction. The radial mesh points are distributed in the pipe, on the pipe, in the annulus, and in the formation. Multiple mesh points are needed in the formation because the thermal influence can reach tens of times farther than the wellbore radius. Mesh size in the MD direction is of the order of 100 ft, which is adjustable according to the resolution requirement. Each mesh

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Fig. 8.4 Wellbore schematics with the mesh points in the depth and radial directions for temperature calculations. The red dots show the grid points for temperature, and the blue lines show the mesh along the MD. (Credit: Pegasus Vertex, Inc.)

point represents a 3D finite volume in which the integral form of energy equation is described to correlate the heat flux of each faces and the temperature variation in the volume. Numerical solution could not achieve 100% accuracy because of the errors coming from the input data uncertainty, the discretization scheme, mesh and temporal sizes, empirical formulae, and assumptions made to simplify the physical problem. If uniform temperature and properties are assumed in each finite volume cell, the error of calculated temperature is estimated to be at least as large as the temperature difference across two adjacent cells. For example, in the case of 1.6°F/100 ft geothermal gradient, discretization of 100 ft mesh size leads to at least 1.6°F error. The actual error can be greater. For example, numerical diffusion in fluids may cause artificial temperature influence not reflecting the reality. On the other hand, a significant error comes from the formula of Nusselt number, a dimensionless parameter indicating convective heat transfer coefficient. Investigations on field data reveal that using conventional values of film heat transfer

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coefficients in predicting wellbore temperatures during drilling are very questionable (Kutasov and Eppelbaum, 2015; Sump and Williams, 1973). This is possibly due to strong dependence of the effective viscosity on temperature. Heat transfer of drilling fluids is greatly enhanced at a high temperature in the downhole, when fluids become much thinner. If this is ignored, the bottom temperature can be significantly underestimated. A comparison of temperature calculated by CEMPRO and by the leading computational fluid dynamics software ANSYS Fluent was made by Wang and Dai (2019) in predicted BHCT for a vertical well of 1200 ft depth in cementing scenario. The BHCT history displays a satisfactory agreement (Fig. 8.5). The largest difference between the two was seen around 10 min from the start of pumping, which was approximately 2°F. The results predicted by the same solver (CEMPRO) were also compared with the field data from Chen and Novotny (2003) for an offshore well of 5778 ft with a water depth of 3780 ft. As shown in Fig. 8.6, the results are compared at three locations, and the percentage errors ranged from 1% up to 11.5%. Compared to temperature logging, numerical modeling is especially good at predicting temperature trend, while its accuracy of predicted

Fig. 8.5 Comparison results of bottom-hole temperature between the numerical simulations in CEMPRO and ANSYS Fluent solver. (Credit: Wang, Yanfang, Dai, Hu, 2019. CFD Analysis and Model Comparisons of Circulating Temperature During Cementing Job, AADE-19-NTCE-004.)

Fig. 8.6 Measured and simulated temperatures at circulation depth of 5721 ft, at depth of 4786 ft, and at return surface. (Credit: Wang, Yanfang, Dai, Hu, 2019. CFD Analysis and Model Comparisons of Circulating Temperature During Cementing Job, AADE-19-NTCE-004.)

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temperature values remains an issue. When using computer simulations to predict wellbore temperature, it is very important to have a sense of order of accuracy and to know the source of errors. Solely relying on a single simulator without any other references could introduce risks. Improving the accuracy of input parameters feeding into the solver, as well as conducting grid convergence and sensitivity studies, is helpful in predicting the wellbore temperature.

8.5 Circulating temperature When neither measurement nor simulation is possible, an estimating method of circulating bottom-hole temperature is available by API RP10B. The API method is based on drilling data of limited areas with a typical surface temperature of 80°F. This method is not recommended for untypical wells and not directly applicable to predicting temperature during the cementing jobs. Many numerical solutions for wellbore temperature in circulation are developed. Based on a series of simulations, charts can be created and used for an easy prediction of BHCT for oil- and water-based mud of different densities for wells of different depths. For example, Raymond (1969) presented charts of temperature change of annulus fluid, defined as Tbhf  Toutlet, versus flow rate from 150 to 450 gpm. It was shown that the difference of temperature reduces as the circulating rate increases. As annulus outlet temperature is often measurable on the rig, the chart can be used for estimating BHCT. The temperature change of oil-based mud is 220°F at 150 gpm and quickly reduces to around 100°F if increasing the flow rate to 450 gpm for a deep well of 25,000 ft. This temperature difference becomes small for 10,000-ft well and in which case the change of flow rate shows less impact because heat exchange between formation and the wellbore fluid is insufficient owing to short of travel distance. It is also observed that low-density oil-based mud displays apparently lower temperature difference than the heavier mud. This conclusion is reversed for water-based mud, in which case, the difference between 10- and 18-ppg water-based mud is mainly found at a low pumping rate and for deeper wells, and low-density fluid has greater temperature change. By the previous discussion, we may consider all water-based mud have similar volumetric heat capacity; therefore the difference is possibly contributed by convective heat transfer coefficient. Lighter water based mud is thinner and has higher Reynolds number and, thus, higher heat transfer coefficient at the borehole face; therefore a higher

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temperature at the bottom and a lower temperature at the outlet are seen. However, when the pumping rate or Reynolds number is high enough, low fluid viscosity does not enhance convective heat transfer further.

8.5.1 Flow rate and temperature evolution Temperature in a vertical well of 10,000 ft under circulation was simulated, and the BHCT history is plotted in Fig. 8.7 under 2, 6, and 10 bpm. The casing outer diameter (OD) is 9.875 in., and the open hole inner diameter is 12 in. A drilling fluid (13 ppg, PV ¼ 25 cP, YP ¼ 15 lbf/100 ft2) and water are considered. The initial temperature is the geothermal temperature, which is 68°F at the surface and 218°F at the bottom. In the case of mud, the bottom hole was quickly cooled to 150°F in the first two bottom-ups, and the temperature goes down below 130°F when further circulating to eight bottomups, in a much reduced slope. A pumping rate of 10bpm gives a slower decrease of temperature than 2 bpm in the first three bottoms-up but eventually brings the bottom temperature to a lower value. On the other hand, if water is circulated in the well, the bottom-hole temperature is much higher. Note flow rate affects the temperature by two opposite effects: increasing heat transfer coefficient at the borehole wall and reducing the travel time of fluids throughout the well. The former will increase the bottom temperature and the latter will work on the contrary because of short of heat exchange time. Because after a couple of bottom-ups, the formation temperature achieves a relative stable temperature, heat exchange at the borehole face is less significant; consequently, the latter role dominates. Therefore a higher flow rate always lowers the bottom-hole temperature. For a thicker fluid, because of lower Nusselt number, a higher flow rate does help to enhance convective heat exchange for the first few bottom-ups, as seen in Fig. 8.7A.

Fig. 8.7 History of bottom-hole circulating temperature during eight bottom-ups of circulation at different pump rates for (A) mud and (B) water. (Credit: Pegasus Vertex, Inc.)

Fig. 8.8 Annular temperature profiles at the end of two bottom-ups of circulation at 6 bpm for vertical well (blue and black lines) and a directional well (red line). (A) Section view of well paths and (B) temperatures. The fluid is 13 ppg in density, with PV ¼ 25 cP and YP ¼ 15 lbf/100 ft2, for all three cases. (Credit: Pegasus Vertex, Inc.)

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8.5.2 Well inclination The temperature profiles in a vertical well and a horizontal well of the same vertical depth after circulating for two bottom-ups are compared in Fig. 8.8. Two wells have the same BHST of 152.5°F at 5636 ft (TVD). The annulus temperature of the horizontal well is much higher than the vertical well because of much greater length available for heat exchange between the fluid and formation. The vertical well has a BHCT of 106°F, compared to 134°F in the horizontal well. Presented together is a vertical well of the same total depth (TD) as the horizontal well, the BHCT of which is at 155°F because it reaches a deeper formation with a higher temperature.

8.5.3 Pipe diameter Simulated BHCT history during eight bottom-ups of circulation in the same well with three different pipe ODs are shown in Fig. 8.9. The flow rate is kept the same at 6 bpm. The simulation shows that the bottom temperature by 9.875-in. pipe is about 25°F higher than 6.625-in. pipe after eight bottom-ups. Because the borehole face area has not changed for all pipe sizes, the convective heat transfer rate is mainly controlled by fluid velocity. The smallest pipe has the lowest annulus flow, resulting in the weakest heat exchange and lowest bottom temperature. Although the annulus flow is slower with the smaller pipe, allowing a longer time for heat exchange between the annulus fluid and the formation, in fact, the overall traveling

Fig. 8.9 BHCT history during circulation with different sizes of pipes. The borehole ID is 12 in. The same drilling fluid is used. (Credit: Pegasus Vertex, Inc.)

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Fig. 8.10 Temperature versus fluid viscosity in a 20,000-ft vertical well after four bottomups of circulation at 200 gpm. The hole and pipe size are 8.625 in. and 4.5 in., respectively. Mud weight is 10 ppg. The formation lithology is shale. Heat conductivity of the fluid is 0.392 Btu/ft h °F, and heat capacity is 0.61 Btu/lbm/°F. (Credit: Pegasus Vertex, Inc.)

time, which should also include the time through inside the pipe, is similar in the three cases.

8.5.4 Fluid viscosity As discussed in Section 8.5.1, circulating a well with a more viscous fluid can greatly reduce the temperature at the bottom, resulting from reduced convective heat transfer or smaller Nusselt number. We observe this trend in Fig. 8.10 by running a series of simulations. It is found that increasing fluid viscosity only slightly increases temperature at the annulus outlet; hence the overall annulus temperature change (ΔT ¼ Tbhct  Treturn) also drops. In addition, the influence of changing fluid viscosity become less significant when the viscosity is very large.

8.6 Temperature in cementing The temperature during cementing involves more variations with time and depth than in drilling scenario. This is concerned in three stages: during conditioning, during pumping, and waiting on cement. In addition to bottom-hole temperature, the temperature at fronts and trails of cement slurries are especially concerned.

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Fig. 8.11 Temperature profiles in the pipe and in annulus after two bottom-ups of circulation at 6 bpm. (A) Water and (B) mud. (Credit: Pegasus Vertex, Inc.)

8.6.1 Prejob circulation Before pumping cementing fluids, a well is first conditioned by circulating for a certain amount of time. In addition to removing cuttings and mobilizing gelled mud, this process also helps to cool down the bottom-hole temperature. The temperature of wellbore fluid before circulation is the same as static temperature. A well is circulated by often less than two bottom-ups; the bottom temperature may not get as low as the BHCT under drilling condition. Fig. 8.11 shows the temperature profiles after two bottom-ups of circulation at 6 bpm in a well of 10,000 ft. Drilling fluid at bottom is cooled down to 150°F from 214°F (BHST). In contrast, the same well circulated with water is cooled down to approximately 200°F only because the heat transfer with the formation is more intensive. To estimate the bottom temperature after a few bottom-ups of circulation and before cementing, one can refer to the methods for predicting BHCT in drilling condition, when the rate of temperature evolution must be considered.

8.6.2 Temperature during cementing Temperature during a cementing job is based on similar physics to that of during mud circulation, except in the following aspects. First, there is a sequence of fluids flowing in the wellbore with distinct densities, viscosities, and thermal properties, making it more difficult to predict temperature than

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in the drilling scenario when a single fluid is involved. Second, cement placement is often done within less than a couple of hours; the temperature during this period is time-dependent, which is different from during drilling when pseudo-steady state can be assumed. Finally, cement slurries can generate heat from hydration, which will affect the well temperature. A primary cementing job is simulated for a 12,345-ft vertical well, with spacer, lead, and tail slurries and displacement pumped in sequence. BHST is 245°F. The well has a 12.5-in. open hole and 9.625-in. pipe. A smaller hole and casing configuration with 6.625-in. casing and 9.5-in. hole is also simulated for comparison. The job starts with two bottom-ups of circulation before pumping. As seen in Fig. 8.12, when the tail slurry enters the annulus, the hotspot depth is already shift up to 10,000 ft at approximately 150°F, about 5°F higher than the bottom. After both slurries enter the annulus, the hotspot is further moved up and the temperature is increased,

Fig. 8.12 Slurry temperature profiles when tail slurry enters annulus and at the end of job. Label (S) indicates smaller open hole and casing size (6.625 in. casing in 9.5 in. hole). (Credit: Pegasus Vertex, Inc.)

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Fig. 8.13 Temperature history during a typical cementing job with two slurries. Front of the first slurry, front of the tail slurry, and trail of the tail slurry, with and without prejob circulation. (Credit: Pegasus Vertex, Inc.)

while the bottom temperature is reduced to 140 °F. When the same job is performed in the smaller well, lower temperature is obtained. This is because of less heat exchange through the borehole face due to a smaller surface area. Fig. 8.13 shows the slurry temperature variation at the leading and trailing edges in the same cementing job. The temperature at leading edge of the lead slurry is increased to a maximum of 150°F at about 180 min, when it reaches the hotspot at approximately 11,000 ft. As it further moves upward, its temperature drops. The temperature of the front of tail slurry experiences a similar, but delayed, temperature increase to approximately 150°F and does not drop until the job end. The trail of tail slurry was heated to about 140°F inside the casing and remains at that temperature when it stops at the float collar. Great differences are seen by introducing prejob circulation. If no precirculation is performed before pumping, the temperature of lead slurry reaches a maximum of 30°F higher. The tail slurry will also see 20°F higher at both the front and the trail. The annular hotspot temperature and its location are shown with the time in Fig. 8.14. Hotspot temperature starts to drop from 170°F, which results from two bottom-ups circulation. Meanwhile, the hotspot depth gradually moves up from 10,000 to 9600 ft. Later on, resulting from an increased flow rate, the temperature reduces more quickly and touches a

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Fig. 8.14 Hotspot temperature and locations during a cementing job. (Credit: Pegasus Vertex, Inc.)

150°F low at 212 min, when the pumping rate was decreased. The hotspot location was also brought to a deeper depth of 11,200 ft, at approximately 200 min, before it comes back to around 9600 ft at the end of job. 8.6.2.1 Effect of flow rate In a series of numerical simulations of the same cementing job, different pumping rates are applied. All other conditions are kept the same. The

Fig. 8.15 Peak temperature of the fronts of lead and tail slurries during the cementing job by changing the pumping rate of displacement fluid, predicted by simulations. (Credit: Pegasus Vertex, Inc.)

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relationship between maximum slurry temperature (at front and at tail of the first slurry) and flow rate is found as in Fig. 8.15. Increasing flow rates greatly reduces the slurry temperature when the flow rate is relatively low. This effect becomes weaker as the flow rate increases. 8.6.2.2 Effect of lithology In estimating the impact of different types of formation lithology, the thermal diffusivity of formation should be examined. Thermal parameters of common types of lithology are listed in Table 8.3. Numerical simulations of cementing jobs with four types of formations, that is, shale, granite, limestone, and sandstone are performed. As given in Fig. 8.16, at the end of job, the temperature profiles show about 10°F difference on the hotspot temperature and 5°F difference on the bottom temperature. The granite gives the highest temperature of 160°F, and limestone gives the lowest. Although we notice the diffusivity of granite is the highest among the four, 7.11 in.2/h, the simulated results of the other three do not support a simple correlation between diffusivity and annulus temperature. This is because of the differences of heat exchange rates on the borehole face. 8.6.2.3 Water temperature In offshore wells, especially deepwater wells, the seawater temperature could apparently change the temperature in the wellbore below the seabed. A typical water temperature profile is shown in Fig. 8.17A, where the water temperature drops from 72°F to below 40°F at 3000 ft. Actual water temperature profile should differ from site to site. Because of the Table 8.3 One-dimensional diffusion length. Density Conductivity (lb/ft3) (Btu/ft h °F)

Heat capacity (Btu/lbm/°F)

Diffusivity (in.2/h)

Shale Granite Limestone Sandstone Coal Ice Basalt Rock salt Slate Marble

0.3 0.2 0.22 0.17 0.3 0.46 0.21 0.21 0.18 0.21

3.153610 7.118336 3.169609 6.568233 0.854295 7.029748 8.069682 9.518428 6.718535 5.874297

140.03 164.87 154.88 139.28 84.28 57 98.57 138.03 174.8 168.56

0.92 1.63 0.75 1.08 0.15 1.28 1.16 1.916 1.468 1.444

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Fig. 8.16 Annulus temperature profile of well in different lithology types at the end of a cementing job. (Credit: Pegasus Vertex, Inc.)

Fig. 8.17 (A) Ambient water temperature profile in offshore wells and (B) temperature profiles affected by 2000-ft water depth. In the legend, “L” labels the land well. The surface water is 60°F, and the temperature at seabed is 48°F. This negative gradient of approximately 0.6°F/100 ft causes nearly 40°F reduction of annular temperatures down to the bottom of the hole. The sea current speed has a little influence. (Credit: Pegasus Vertex, Inc.)

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cooling effect of water on the wellbore fluid, opposite to the geothermal heating effect, the hole temperature is reduced. Comparing an offshore well of the 12,345 ft with 2000-ft water depth with a land well of the same TD, the formation temperature at the seabed is 40°F lower. A similar temperature difference is seen on the wellbore fluid temperature at the bottom, as in Fig. 8.17B. The profile of annulus temperature maintains a similar shape below the seabed except a shift; however the annulus fluid is cooled down dramatically when it comes to the riser, and later, it reaches a temperature very close to seawater before it returns to the annulus top. This is because of a strong convective heat transfer between the annulus fluid and seawater. In a land well, the annulus outlet temperature is often higher than the formation temperature because of a slow conductive heat transfer with the formation.

8.6.3 Temperature recovery When the wellbore flow ceases, during shut-in in the middle of cementing job, or during wait on cement after the cementing job is completed, the forced convective heat transfer in the well also stops. Although natural convection still exists, it is a much weaker form of heat transfer. The heat conduction in the formation dominates heat flow until the wellbore temperature reaches the geothermal temperature. In the upper section of the well, when shut-in begins, the fluid temperature is usually higher than the formation; therefore the fluid will recover to a lower temperature. In the lower section, the direction of heat flow is opposite. Temperature during shutin may be estimated by the following equation (Kutasov, 1999)   
 rw2 (8.12) Ts ¼ Tf  Tf  Tm 1  exp  , 4ats where Tm is the wellbore fluid temperature, Tf is the formation temperature, a is the formation diffusivity, rw is the borehole radius, and ts is the shut-in time. The temperature of formation is assumed undisturbed, and the thermal diffusivity of fluid is assumed the same as that of formation. Fig. 8.18 shows a comparison of temperature development at 20,000 ft and at surface during a 16-h circulation followed by a 16-h shut-in between numerical simulation and calculation from Eq. (8.12). The temperature at the bottom was reduced to 270°F by circulation and then recovered during shut-in. The outlet temperature was increased from 80°F to 150°F and then drops during shut-in. The simulation by Raymond (1969) neglected heat conduction in the

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Fig. 8.18 A comparison of wellbore temperature during 16-h shut-in time predicted by the analytical solution and numerical results from CEMPRO and from Raymond (1969). (Credit: Pegasus Vertex, Inc.)

wellbore fluid and assume annulus temperature equal to the borehole wall temperature, which may overestimate the temperature. The analytical solution assumes that the formation temperature is undisturbed during the first 16 h of circulation; as a result, the predicted temperature is the highest.

8.6.4 Heat of hydration Liquid slurry experiences a hydration process after mixed and pumped down the well. This process involves not only changes of chemical and mechanical

Fig. 8.19 Hydration heat during cement setting. (Credit: Pegasus Vertex, Inc.)

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properties but also energy transform in the form of heat generation. Fig. 8.19 shows a typical history of heat generation rate and cumulative heat during the curing time. After an initial peak over 5 mW/g, the rate of heat generation quickly drops to a minimum in the first few hours, when the overall generated heat is small. Given that the cement placement is usually finished in the first few hours after mixing, the effect of the hydration heat on the temperature change is negligible. However, in the following 24 h, a significant amount of heat is generated. The cumulative heat may reach over 200 J/g, during which time the temperature of cement slurry in the annulus is gradually recovered to geothermal temperature. Temperature recovery discussed in the previous section does not consider the effect of hydration heat. Here, we consider a 18-ppg slurry column in 8.625-in. hole /4.5-in. pipe, whose temperature is recovered by 50°F in 16 h. Heat capacity is 0.6 Btu/lbm/°F. Therefore the total heat absorbed from the formation by 1 ft long slurry is Q ¼ CpVρ ΔT ¼ 1639 Btu. We assume that heat generation within the 16 h is 150 J/g, that is, 2564 Btu, greater than total heat received from formation. If the direction of heat flow is not reversed by excessive heat generation, then all heat of hydration is used to increase the temperature of the slurry, which will greatly speedup the process of temperature recovery.

8.6.5 Predicting slurry temperature Numerical simulations using physics-based models are recommended in predicting the slurry temperature after cement placement and during wait on cement. When simulation is unavailable, the following procedures may guide a rough estimation. First, obtain the BHST through measurement or local drilling experience. Then BHCT under drilling condition should be acquired through measurement or charts. Next, one can refer to the history chart of BHCT to estimate a transient bottom temperature, determined at a time of precirculation time plus cementing time. Apply a correction specifically contributed by cement through higher density and rheology than drilling fluid. Finally, estimate hotspot temperature by referring to bottom temperature, and evaluate the contribution of hydration heat when temperature recovery is to be predicted during waiting on cement.

8.7 Using simulators Computer simulators are useful tools for planning drilling and cementing jobs. When using a simulator to predict wellbore temperature,

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reliability of the results depends upon both the accuracy of the simulator and quality of input data. Providing accurate input data is essential in modeling. However, in many cases, not all input parameters are available due to lack of either field information or laboratory procedures. Estimation of those data could still be good to be applied in simulations.

8.7.1 Thermal parameters When a numerical simulator developed from physical model is used for temperature prediction, thermal properties of fluids are pulled out from a fluid database or provided by user input. When neither database nor laboratory measurement is available, parameters may be roughly estimated from the compositions. If a fluid comprises oil, water, and solid, such as in drilling fluid, then the heat capacity in the US oil field unit can be estimated as: Cp ¼ 0:5  woil + 1:0  wwater + 0:2  wsolid Heat conductivity of fluid mixture of two species is found by Dul’nev and Zarichnyak (1966):  λ ¼ λ1

 p 1 , 1=ð1  νÞ  ð1  pÞ=3

where p is the volume concentration of the second component, λ1and λ2 are the heat conductivities of the first and second components, and ν ¼ λ2/λ1. For three-component mixtures, the same formula may be used by first finding the combined conductivity of any two components. The following conductivity values for oil, water, and solid may be used: λo ¼ 0.1 Btu/ft h °F, λw ¼ 0.3 Btu/ft h °F, λs ¼ 1.08 Btu/ft h °F. The thermal parameters for cement slurries are difficult to predict because of complex chemical components and microstructures formed during the hydration process. Data should be obtained from laboratory testing. The experimental study by He et al. (2000) shows the heat capacities of drilling fluids and cement slurries increase with temperature. As temperature increases by 100 F, heat capacity can increase by 20%. Low-density fluid has higher heat capacity, but it apparently depends upon the fluid compositions. Typically, heat conductivity increases with density, as presented in Wen et al. (2008).

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8.7.2 Fluid viscosity Temperature solution based on classic equations of heat transfer may be sensitive to fluid viscosity. Rheological data measured at high temperature are required to rectify the calculation of lower sections of the well. It is common that fluid viscosity drops greatly as the temperature increases; however, the temperature–viscosity relations are replying on fluid compositions. Assuming a constant viscosity of surface condition may cause a discrepancy of up to 60°F for deep wells. Fluids’ rheological data at different temperatures are obtainable in a standard laboratory test, and they must be fed to the simulator for better accuracy.

8.7.3 Sensitivity study When using simulators, a sensitivity study can be conducted by running multiple simulations of similar cases by changing certain parameters and comparing the results. Manual sensitivity study is necessary when an input parameter is only estimated, therefore, not accurately known. Changing the value of an interested parameter within a range of uncertainty and running several simulations, one can obtain from the simulator a variation of temperatures corresponding to possible uncertainty. In other cases, although the interested parameter can be accurately measured, it only represents the true value at ground surface condition; therefore it is still necessary to estimate a variation resulting from change of downhole environment. For example, the fluid rheology is largely variable as discussed in the preceding section. Other parameters such as formation conductivity, density, and heat capacity can also be greatly altered by downhole temperature, pressure, porosity, formation fluid, and so forth. Not all simulators will surely produce simulation results agreeing with each other, including those popular in the cementing industry. It is not rare when a simulator fails to provide reliable results for particular types of jobs. Knowing the influences of input data on the temperature is also helpful in ruling out erroneous simulation results. On the other hand, when there is no built-in optimization capability in a simulator, sensitivity study is a necessary process toward optimization of job designs. A good understanding of the physical model can benefit the job design.

References Chen, Z., Novotny, R.J., 2003. Accurate prediction wellbore transient temperature profile under multiple temperature gradients: finite difference approach and case history.

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In: SPE 84583. SPE Annual Technical Conference and Exhibition, October, Denver, Colorado, pp. 5–8. Dul’nev, G.N., Zarichnyak, Y.P., 1966. Thermal conductivity of liquid mixtures. J. Eng. Phys. 11, 400–402. https://doi.org/10.1007/BF00829337. Gnielinski, V., 1976. New equations for heat and mass transfer in turbulent pipe and channel flow. Int. Chem. Eng. 16, 359–368. He, S., Xu, B., He, P., et al., 2000. Laboratory study on heat capacity of cement slurry and drilling fluids. J. Southwest Pet. Inst. 22 (4), 65–69. Incropera, F.P., DeWitt, D.P., Bergman, T.L., et al., 2007. Fundamentals of Heat and Mass Transfer. John Wiley & Sons. Keller, H.H., Couch, E.J., Berry, P.M., 1973. Temperature distribution in circulating mud columns. Soc. Pet. Eng. J. 13 (1), 23–30. Kutasov, I.M., 1999. Applied Geothermics for Petroleum Engineers. Elsevier. Kutasov, I.M., Eppelbaum, L.V., 2015. Wellbore and formation temperatures during drilling, cementing of casing and shut-in. In: Proceedings World Geothermal Congress 2015, April, Melbourne, Australia, pp. 19–25. Raymond, R., 1969. Temperature distribution in a circulating drilling fluid. J. Petrol. Tech. 21 (03), 333–341. Santoyo, E.R., 1997. Transient Numerical Simulation of Heat Transfer Processes During Drilling of Geothermal Wells (Ph.D. thesis). Seider, E.N., Tate, G.E., 1936. Heat transfer and pressure drop of liquids in tubes. Ind. Eng. Chem. 28, 1429. Sump, G.D., Williams, B.B., 1973. Prediction of wellbore temperatures during mud circulation and cementing operations. J. Eng. Ind. 95 (4), 1083–1092. Ser. B. Wang, Y., Dai, H., 2019. CFD Analysis and Model Comparisons of Circulating Temperature During Cementing Job, AADE-19-NTCE-004. American Association of Drilling Engineers. Wen, Q., Liang, D., Ren, M., et al., 2008. Laboratory study on drilling fluid heat conductivity. Pet. Drill. Tech. 36 (1), 30–32.

CHAPTER NINE

Displacement efficiency Hu Dai Pegasus Vertex, Inc., Houston, TX, United States

Abbreviations CBL CFD HTHP ID MD MW OD PV RSS TD TOC UCA VDL YP

cement bond log computational fluid dynamics high temperature high pressure internal diameter measured depth mud weight outer diameter plastic viscosity required shear stress total depth top of cement ultrasonic cement analyzer variable density log yield point

9.1 Introduction In a primary cementing job, casing string is run into the hole, and then, pumps are used to displace the native mud and place cement slurry in the wellbore annulus. After the cement sets, the bond between the set cement and casing and the borehole wall is created to prevent zonal communication. Mud removal efficiency and slurry contaminations are major concerns in a cementing job because they affect the cement bond quality and set cement quality. Poor cement bond and failure of fill-up of cement to planned annulus level will cause zone communication and possibly blowout in severe cases. Cement job quality is a safety issue and closely related to well life. Predicting fluid displacement using theoretical approach is not an easy task. It is easy only in ideal or unrealistic situations, such as when the fluid interfaces can maintain flat; hence simple volume calculations will determine fluid interface positions during displacement (Fig. 9.1A). In general, the fluid front in one side of the annulus falls behind the other because of velocity Applied Well Cementing Engineering https://doi.org/10.1016/B978-0-12-821956-0.00006-7

Copyright © 2021 Elsevier Inc. All rights reserved.

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Fig. 9.1 Side views of annular fluid displacement: (A) ideal scenario, (B) elongated interface, (C) broken or isolated interface, (D) scattered mixing, and (E) diffusive mixing. (Credit: Pegasus Vertex, Inc.)

difference, and the interface can have locally curved shapes resulting from frictional drag from the walls (Fig. 9.1B). Real flow can create more complex topology changes of the interface, such as breaking down and scattering (Fig. 9.1C and D). When two fluids are miscible, dissolution-induced mixing occurs near the interface (Fig. 9.1E). For all these cases, bad cement length should be defined as the distance from the top position where cement or contaminated cement presents to the bottom where mud exists. In Fig. 9.1A, bad cement length is zero, and all other scenarios have nonzero lengths. Displacement efficiency in cementing engineering is used as an evaluation of mud removal effectiveness, which can be considered from different respects, such as bad cement length, severity of fluid channeling, thickness of mud cakes, and amount of mixed or contaminated fluids. The goal of a cement job is to place uncontaminated slurries to the planned depth while minimizing mud risk on the wall. In the case that a cementing job was poorly done, the defect is found in the form of poor cement bonding and zone communication; consequently, a costly remedial job has to be performed to establish zonal isolation. Essential concepts in this subject and their definitions are made clear in the following. Displacement efficiency (E): volume fraction of displacing fluid divided by the total volume. Bad cement length (Lbd): distance between the very top where cement or contaminated cement is present and very bottom where mud exists. Strictly, this is not the same as mixing length.

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Planned top of cement (TOC): TOC if displacement is perfect, as shown in Fig. 9.1A. Actual TOC: Actual TOC that good cement reaches. TOC would be lower than planned TOC if all fluid volumes are pumped as planned. Fluid mixing: Two fluids come into each other driven by convection or diffusion. Macroscopic mixing of fluids is caused by inertia-induced instability or turbulence. Microscopic mixing of miscible fluids is driven by molecular diffusion. Immiscible fluids have an interface or mix to form an emulsion, for which surface tension is an important parameter. Miscible fluids do not have a clear interface, unless diffusion is small. Contaminated cement: When mud and cement are brought into contact, they mix up and form complex chemical compositions. Contaminated cement has altered rheology, thickening property and stability, and may lead to pumping issue, formation fracture, weak bonding strength, and compressive strength. Mud channel: A continuous presence of mud along the depth within cemented interval. Filter cake (mud cake): Solid mud residue deposited on and inside the borehole wall, formed by forcing fluid against permeable formation when filtrate can pass through the pores. This process is also named “fluid loss.” There are internal (inside formation) and external (on the wall) cakes. Generally, external mud cake is helpful during drilling in protecting formation, and it should be removed during cementing to ensure acceptable bonding with the formation. In general, displacement efficiency can be quantified as the volume fraction of displacing fluid inside the casing or annulus. This is equivalent to the volume of displaced fluid removed from the space divided by the total volume: E ðtÞ ¼ 1 

Vn ðtÞ V

(9.1)

where Vn(t) is the volume of native fluid remaining in the pipe or annulus, V is the total volume, and E(t) is the efficiency. When the displacement efficiency is concerned at interest depths, it can be defined as an area fraction of displacing fluid, Eðx, tÞ ¼ 1 

An ðx, tÞ AðxÞ

(9.2)

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where x, t are the depth and time, respectively, An is the area occupied by native fluid (displaced fluid), and A is the total area of cross-section. The foregoing volumetric efficiency will be derived by integrating the area efficiency over the total annulus. When mud removal is not effective, various forms of bonding failure could be created after cement sets. Fig. 9.2 is an illustrative schematic showing the issues in a cross-sectional view. Gas migration during and after cement placement can create compromised cement. Contaminated cement will have a higher risk of bonding failure or integrity issue at later stages when a well event takes place. Rheology hierarchy: Rheology relationships between two or more fluids or within a fluid train. A rule of thumb from conventional cementing jobs is to use thicker fluids to displace thinner fluids to achieve better displacement efficiency. This topic is highly important and understudied. Interface instability: Interface of two immiscible fluids is not stable if they mix by irregular convection. An example is gravity-induced RayleighTaylor (R-T) instability. When a heavy fluid is on the top or by the side of a light fluid, the former fluid is inclined to find a way to fall. Interface instability may increase the mixing length and reduce the displacement efficiency. A sequence of fluids with increasing densities is pumped as a common practice. However, interface instability in horizontal

Fig. 9.2 Illustration of various forms of poor cement coverage (a plan view): (a) mud channel, (b) poor bond to the pipe, (c) poor bond to formation, and (d) compromised cement. (Credit: Pegasus Vertex, Inc.)

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Fig. 9.3 Illustration of different forms of mud existing near the formation and casing inside the well. In the figure, the letters a, b, c, and d represent displacing fluid, flowing mud, gelled mud, and mud cake, respectively. (Credit: Pegasus Vertex, Inc.)

wells can drive the transverse mixing and prevent flow segregation and, thus, help to improve displacement efficiency. Displacement efficiency is affected by different forms of mud existing in the wellbore, as depicted in Fig. 9.3, including moving mud, gelled mud, and mud cakes. Under high pressure, mud is forced against the formation, and liquid component is filtered through the formation, while a hard layer is left sticking on the wall. Chemical washes can be used to clear mud cakes. Next to the mud cake, a static gelled mud layer may exist, when viscous shear stress is not high enough to mobilize it. Here, erodibility is introduced to quantify the mud property of whether or not the mud can be easily removed. Only the removed mud (or flowing mud) actually participates in the displacement flow. However, the mud is subject to form changes, and they influence the effective geometry and wall condition of the flow passage; therefore they should be considered in the prediction of displacement efficiency. Required shear stress (RSS): The minimum shear stress required to start eroding a gelled mud or mud cake. Erodibility: It describes how easy a mud is eroded by displacing fluid, the value of which is equal to 600/RSS, when RSS is in the unit of lbf/100 ft2. Gel strength: A time-dependent property of a static fluid. Gel is developed when the fluid is in rest and it resists flow. Yield point (YP): y-intercept of the rheology curve relating shear stress and shear rate. Actual fluid displacement in oil wells involves chemical process at the fluid interfaces and wellbore wall, which makes the displacement process

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further complicated and difficult to model. Mud and cement are incompatible because of detrimental interface reactions that create complex materials with high viscosity and gel strength. Incompatibility causes altered cement properties such as thickening time, fluid loss, compressive strength, and bonding strength; hence it must be prevented. Wiper plugs, chemical washes, and spacer are used to minimize the contact between mud and cement. Compatibility: Two fluids are incompatible if their mixture flocculates and reacts to form highly viscous materials. Compatibility test is usually done on a mixture of two or three fluids at certain percentages for rheology readings. It is possible that a mixture of cement and mud can have significantly higher viscosity than either 100% mud or 100% cement. Spacer: A barrier fluid compatible with both mud and cement. Spacer should have appropriate suspending capacity, density and rheology, fluid loss control, and be environmentally safe. Chemical washes: Fluids used to assist mud removal by dispersing, diluting, and thinning mud. They effectively clear the mud on the casing and formation wall to create better cement bond. Fluid influx: Fluid (liquid or gas) flows into wellbore when formation pressure exceeds the pressure in the wellbore, which is also known as kick. Fluid flux alters annular fluid column and changes annulus pressure. Failure of early detection and control of influx may cause a serious blowout. Although important, mathematical or numerical models of mud displacement rarely consider the existence of influx. Loss of flow: Loss of flow happens when wellbore pressure exceeds formation pressure during drilling or cementing. This causes loss of return fluid, drop of annulus top, and reduction of pressure. Serious loss can cause reversed annular flow. Predicting loss relies on the information of formation and well condition. P/T dependence: Variable temperature and pressure in wells can alter fluid property significantly. Assuming constant fluid density and rheology in a model will lead to significant loss of accuracy for high pressure/high temperature wells. Fluid viscosity, density, and their contrast of different fluids are critical factors affecting displacement efficiency; hence considering these fluid property changes in a model is important. Hole geometry: An actual wellbore has irregular shape and variable hole sizes as caliper logs can show. Washout happens and further alters the well size. These factors introduce uncertainty in displacement efficiency prediction.

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In-pipe displacement: Most interests of research are placed in the process of the annulus displacement. This is mainly because the common usage of bottom and top plugs helps to separate the fluid train inside casing and, therefore, nearly eliminate fluid contamination. However, in many situations, the displacement inside casing or drill pipe is still a big concern. Contaminations that happen inside the pipe will be remained and further developed after the fluids enter annulus. Therefore in addition to the annulus displacement, it is also necessary to model the displacement flow inside the pipe to predict realistic job results. Mechanical parts: Not just fluids are existing inside a well. Cement plugs, centralizers, cement baskets, and so forth are often used in cement jobs, and these mechanical parts will have influence on the flow, and therefore a displacement model may need to account for it.

9.2 Cement logs Postjob cement logging is a popular method to evaluate cement job quality and reveal the true displacement efficiency. Various cement logs can be acquired through applications of logging tools after cement hardens to assess the job quality and cement bond. Although modern tools are capable in advanced logs or maps, cement bond log (CBL) is the most basic and inexpensive one that provides useful information of the bond between the external casing wall and the cement. This log takes the first pulse received at the receiver and records the variation of amplitude of acoustic signal, and it is displayed as a single line versus depth in the chart. Because the acoustic signal will be more attenuated in the presence of cement than free or poorly cemented casing, a low signal represents a good bond. Attenuation of sound (α) is a measure of energy loss while it travels in media. Therefore the attenuation of media is related to signal strength at the receiver: E ¼ Eo eα x

(9.3)

where Eo is the energy at the source, and x is the traveled distance. Transit time is the travel time of acoustic wave in media. In the formation acoustic logs, transit time or slowness is recorded to reveal formation porosity or calibrate seismic data. This transit time is also measured for hardened cement in ultrasonic cement analyzer (UCA) laboratory test, which can be used to calculate compressive strength precisely. Once sound speed c is found from transit time, the impedance is derived from z ¼ ρc, where ρ is density.

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Although CBL provides signal amplitude, attenuation, bond index, and cement compressional strength, its disadvantage is obvious that it lacks detailed information on azimuthal and radial distribution of cement. Radials log and variable density log (VDL) are used to overcome these limitations. VDL is derived from entire sonic waveform from first arrival to up to 1200 μs and displayed as white-black strips. Due to different distance and medium slowness, arrival time of the wave traveling through casing, mud, and formation are differentiable. Fig. 9.4 shows an example of simulated annulus fluid maps and simulated CBL and VDL logs for a well. In this well, the casing is not centralized in the horizontal section near the bottom, although centralizers are used, and there is no casing rotation applied during cementing. As a result, mud channel is clearly present. The fluid maps are generated from displacement efficiency simulation on three dimensional (3D) grid. The VDL is not generated from actual logging but simulated by a numerical model of acoustic wave propagation, with two tracks corresponding to narrow side and wide side. In reality, to identify mud channeling and obtain azimuthal view, radial logs are used to record tracks for different azimuthal directions.

9.3 The physics The physics of fluid displacement is addressed in fluid dynamics based on which the present discussion is expanded. Knowing the 3D velocity field and pressure field in the wellbore, and how they are formed, is the key step toward a good understanding of displacement efficiency. After the velocity field is found, fluid transport can be solved. In parallel flow, the interface between displacing and displaced fluids will resemble the shape of velocity profile because the distance traveled by fluid particles is equal to velocity times the elapsed time. Displacement efficiency would be perfect if flat and sharp fluid interface is always maintained during displacement. In that case, efficiency will be 100%, and spacer would be unnecessary. This ideal situation is not possible when we consider the actual physical, chemical, and mechanical process, as explained in the following discussion.

9.3.1 Nonuniform axial velocity Axial velocity is nonuniform across the annulus gap because of shear stress on the wall and inside fluid. Flows of different rheological models will display various shapes of velocity profiles. Fig. 9.5 depicts axial velocity profiles of a pure fluid of four rheology models within two parallel plates. The flow near

Fig. 9.4 Simulated CBL and VDL logs for a well section from 5000 to 7000 ft. From left to right, (A) side view of annulus cement concentration (cut off vertically) revealing the narrow side on the left and wide side on the right, (B) unwrapped view of cement concentration, (C) calculated CBL, and (D) and (E) simulated VDL’s responding to narrow side and wide side. (Credit: Pegasus Vertex, Inc.)

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Fig. 9.5 Velocity profile of different rheological models under laminar flow in the narrow gap. (A) Newtonian fluid, (B) Bingham plastic, (C) power low (n ¼ 0.3), and (D) HB model (n ¼ 0.3). (Credit: Pegasus Vertex, Inc.)

the casing and formation walls is slower, so the boundary fluid falls behind much more than the central fluid, and the lag is more significant as time elapses. Actual fluid interface will have more complex shapes than the displayed velocity profiles because two fluids of different rheology have contributions. Selection of density and rheology hierarchy for displacement is aiming at creating flat and stable interfaces. The velocity profiles suggest that the fluid near the borehole wall and casing wall may be left undisplaced. On the other hand, casing eccentricity creates nonevenness of axial velocity along the azimuth in the annulus. When the pipe is not centralized, the flow in the narrow side is slowed down or blocked, resulting from high drag from the walls. Consider single fluid in the annulus and without gravity effect, the velocity at the center of wide side is greatest because it departs from the wall furthest, as the wall creates the highest viscous shear drag. Fig. 9.6A shows the calculated velocity distribution in a cross-section with

Fig. 9.6 (A) Simulated axial velocity distribution in a 28% standoff annulus and (B) comparison of velocities in narrow side and wide side of an annulus with a standoff of 55%, in which the experimental result is from Moran and Savery (2007), and the numerical result is from Dai and Liu (2017). (Credit: Pegasus Vertex, Inc.)

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zero yield fluid. When yield stress exists, there will be an unyielded plug zone at the center. Velocities at wide side and narrow side versus flow rate are shown in Fig. 9.6B, which is also a comparison of experimental and calculated results in an annulus of 55% standoff, with Bingham plastic fluid (plastic viscosity (PV) ¼ 74.5 cP and YP ¼ 33 lb./100 ft2).

9.3.2 Flow irregularity Fluids in a long and narrow space move in the same direction (Fig. 9.7A) as one-dimensional (1D) parallel flow. However, the actual flow path in the well is 3D because of well and casing geometry change and wellbore irregularities, in addition to multiple-fluid interactions. In Fig. 9.7B, local hole size increase produces an expanded space by which the flow loses parallelization and possibly develops a recirculation zone (Fig. 9.7C). A contracted space can generate the opposite phenomenon. As in Fig. 9.7D, local high resistance (e.g., in the narrow side) may cause fluid moving to the other side through developing an azimuth velocity. A wellbore is often assumed circular shaped with uniform diameter; it actually has a significant size and shape variation along its length, including cavity and washout. These irregularities are found to cause differences on the velocity and pressure profiles (Kiran et al., 2019) and can have a noticeable impact on fluid displacement (Renteria et al., 2018; Skadsem et al., 2019). For example, fluids with yield stress tend to reside in local cavities or corners and are hard to remove. Thus using realistic caliper log data to build up realistic wellbore geometry is necessary in an accurate computer modeling. In addition, local blockage or slowdown by cuttings, tools, or gelled mud are also contributors to displacement efficiency results.

Fig. 9.7 (A) Parallel flow in narrow gap; (B) nonparallel flow by change of gap width; (C) recirculation zone is formed at expanding space, and (D) nonparallel flow due to azimuthal velocity. (Credit: Pegasus Vertex, Inc.)

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9.3.3 Transverse flow One-dimensional axial flow is often assumed to calculate basic hydraulics, such as predicting frictional pressure loss, which is a reasonable assumption, because the nonaxial velocity components are often much smaller than the axial component. However, the real displacement flow is always 3D; therefore 1D assumption does not work for modeling displacement efficiency. Transverse flow includes azimuthal and radial flows. Buoyancy is an important cause of transverse flow in an inclined well. In addition, variation of standoff along the pipe, or circumferential coexistence of different fluids, will create azimuth flows in annulus. In a large clearance annulus, radial segregation of interfaces and width change of flow path will create a radial flow, which, although small, may contribute to an interface evolution and a fluid mixing across the gap. In particular, when casing rotation is included, annular transverse flow in azimuthal direction becomes significant. In combination with an axial velocity, the resulted flow becomes helical. With a nonslip boundary condition, the angular velocity at the casing wall (inner boundary) is the pipe rotating speed Ω, while the velocity at the outer boundary is 0, which creates Couette flow. With an axial flow, however, it is difficult to find azimuthal velocity even in a concentric annulus filled with a single non-Newtonian fluid because of coupling of velocity components. Without considering a transverse pressure gradient, an analytical solution is possible only for Newtonian fluid in concentric annulus, as expressed by Deawwanich (2013):
2 R 1 r (9.4) ωðr Þ ¼ Ω 1 1 κ2 where r is the radial coordinate, R is the radius of outer wall, and κ is the ratio of radius of inner wall to outer wall. In Couette flow between two parallel plates, tangential velocity is linearly distributed in the case of Newtonian fluid, which is not true for concentric annulus, as seen in this equation.

9.3.4 Flow transition Three types of flow regimes are differentiated: plug flow, laminar flow, and turbulent flow, as illustrated in Fig. 9.8A. When predicting displacement efficiency, the flow regime has to be determined, because different patterns lead to distinct flow field and pressure distribution. The flow regime is often determined by checking Reynolds number, Re ¼ uD/ν, where u is the mean

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Fig. 9.8 Different velocity patterns in the channel and flow regime distributions in the eccentric annulus. (Credit: Pegasus Vertex, Inc.)

velocity, D is the diameter, and v is the kinematic viscosity. Reynolds number higher than the critical value indicates a turbulent flow. Turbulent flow is the most common but challenging to solve. Turbulent flow develops eddies that are very helpful in mobilizing the solid particles and gelled mud near the wall of borehole; thus it is preferred in cementing jobs whenever the formation condition permits. Laminar flow has nicely distributed flow lines, and it can be accurately solved by standard analytical or numerical methods. Plug flow is a low Reynolds number flow of non-Newtonian fluid. Plug flow has the advantage of maintaining flat fluid front to achieve better displacement efficiency than a laminar flow. In some cases, low rate displacement is preferred if plug flow is established (Parker et al., 1965). Different flow patterns may coexist in an eccentric narrow annulus at different azimuthal angle, as illustrated in Fig. 9.8B, because of the variable flow velocity created by different gap sizes. At a low flow rate, plug zone exists at the narrow side, and as the flow rate increases, the turbulent zone expands from the wide side to narrow side and eventually occupies the entire annulus.

9.3.5 Multiple non-Newtonian fluid system Displacement flow can develop many phenomena different from a singlefluid system; from a modeling perspective, this is because additional

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parameters are involved in the system, that is, the number of parameters describing fluids are doubled (in two-fluid displacement). The flow near the interface or at the mixed regions displays more complexity than the regions occupied by uniform fluid, where the major question of displacement efficiency arises. Thus rheology contrast or hierarchy closely relates to displacement efficiency. Depending upon the rheological parameters of displacing and displaced fluids, viscosity ratio is defined as:
 k1 U n1 n2 (9.5) m¼ k2 D Newtonian fluid is the simplest fluid model with linear stress-strain rate relation. A single parameter (viscosity) fully represents its rheological characteristics. As most of the wellbore fluids are non-Newtonian, two or more parameters are involved for each. For a yield stress fluid, we define a dimensionless group, Bingham number, as τy Bn ¼
n U k D

(9.6)

which describes the ratio of yield stress to viscous stress. For Bingham plastic fluid, this leads to Bn ¼ PVYPU D. This number has physical meanings; for example, for drilling mud, it relates to the capability of cuttings transport. Herschel-Bulkley (HB) model has one more parameter than Power law (PL) and Bingham plastic (BP) models. In a multiple non-Newtonian fluid system, the degree of rheological complexity is literally the sum of the number of model parameters of each fluid, leading to a very complicated flow. However, as the well displacement flow takes place in a long pipe or an annulus and each fluid has adequate volume, it is reasonable to consider the fluid train only by pairs of displacing-displaced fluids; in other words, the interface interactions of more than two fluids are assumed absent.

9.3.6 Buoyancy driven flow (gravity-induced flow) One result of multiple-fluid-induced complexity is the buoyancy effect, responding to two densities. When two fluids with different densities are involved, which presents in any cementing displacement flow, buoyancy will give a major influence on the flow development and interface evolution. Buoyancy forces create an axial and a transverse component in a directional well, contributing to fluid redistribution along depth

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direction and within cross section. Depending upon the inclination angle β, the role of each component changes. For example, transverse buoyancy force in a horizontal well may cause flow segregation, while axial buoyancy force in a vertical well contributes to instability. Buoyancy has its impact in both exchange flow (without imposed velocity) and displacement flow (with imposed velocity). Exchange flow is a convective fluid interpenetration. When buoyancy-induced inertia dominates in an unstable configuration, fluid interface is distorted and not well maintainable, which is R-T instability. To describe the R-T instability, a Rayleigh number Ra is defined as Ra ¼

At g D3 ν Dm

(9.7)

where D is the pipe diameter, ν is the viscosity (¼μρ), g is the acceleration due to gravity, and Dm is diffusivity, and At is Atwood number, which is defined as At ¼

ρh  ρl ρh + ρl

(9.8)

where, ρh and ρl are the densities of the heavy fluid and light fluid, respectively. The influences of buoyancy, viscosity, and diffusion are incorporated in the Rayleigh number. Debacq et al. (2003) suggests macroscopic diffusivity being roughly 200 times of viscous diffusivity ν for At up to 5  103 and then increasing linearly with At for larger At. The viscosity of two fluids is assumed equal or close, hence a single value of viscosity ν is used.The critical Ra number of RT instability is 67.8, the value above which indicates an instability. Viscosity contrast should also be of significant influence, whereas its impact is not discussed here. In a nondiffusive exchange flow, buoyancy-induced inertia force will compete with viscous force, described by a Reynolds number based on inertial velocity, Ret ¼

ut D ν

where ut is the buoyancy-induced inertial velocity, defined as pffiffiffiffiffiffiffiffiffiffiffi ut ¼ AtgD

(9.9)

(9.10)

Here, the Reynolds number represents the ratio of buoyancy to viscous force. In well cementing, displacement flow with a nonzero imposed

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velocity, often driven by a pump, is of most interest, when another parameter named Froude number comes to play, which is Fr ¼

uo uo ¼ pffiffiffiffiffiffiffiffiffiffiffi ut AtgD

(9.11)

where uo is the imposed velocity. Froude number tells which is in dominance: the imposed inertia or the buoyancy-induced inertia. In displacement flow, Reynolds number is often defined using imposed velocity instead of buoyancy-induced inertial velocity ut: Re ¼

u0 D ν

(9.12)

Displacement flow can be a noninstantaneous displacement (when there is a part of fluid flowing backward) or an instantaneous displacement, when a diffusive or nondiffusive counter-flow is possible. Studies show that viscous sustained back flow exists in a low Froude number regime (Amiri et al., 2016). In a cementing job, back flow and stationary residual layers are most undesired. Thus efforts should be made to prevent the flow falling onto or near the noninstantaneous displacement regime.

9.3.7 Diffusion and instability In displacement flow, fluid diffusion, or mixing, is an important transport phenomenon different from convection. Convection is a bulk fluid transport, driven by macro flow, while diffusion represents random motions of internal fluids. Diffusion contributes to blurring the fluid interfaces, the strengths of which relative to convection can be described by a dimensionless parameter Peclet number: Pe ¼

u0 D Dm

(9.13)

where u0 is the velocity, D is the diameter, and Dm is the diffusivity. Although molecular diffusion can be a contributor for miscible fluid mixing, the effect is often very small because the molecular diffusivity Dm can be as low as 109 m2/s, while the macro diffusion coefficient can be in the order of 104 to 103 m2/s for many displacement flow in pipe, according to experimental studies. The macroscopic diffusion results from convective mixing or turbulent mixing. Flow instability is a reason for fluid mixing in relatively low Reynolds number. Different types of interface instability

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exist. One is the R-T instability, driven by buoyancy force, when fluids with different densities exist, and the other is the Kelvin-Helmholtz instability due to shear at the fluid interface where vortices are created. When only axial diffusion is considered, transverse concentration is averaged; thus 1D diffusion equation is solved to find the axial concentration profile: ∂c ðx, tÞ ∂2 c ðx, tÞ ¼ Dm ∂t ∂x2

(9.14)

where Dm is the coefficient responding to macroscopic diffusivity. In a sufficiently long pipe with displacing and displaced fluids, the solution is found with similarity scaling, which leads to a form of error function as
 Δc x c ¼ c + erf pffiffiffiffiffiffiffiffiffiffi (9.15) 2 4Dm t where c and Δc are the medium and the difference of concentration at the interface in the beginning and ð 2 x 2 erf ðxÞ ¼ pffiffiffi eξ dξ (9.16) π o is the error function. Evaluation of the mixing length responding to fully diffusive flow is possible only after the diffusivity Dm is estimated. Analytical determination of this coefficient is difficult; instead, this can be pursued by experimental studies. For example, Debacq et al. (2003) performed studies in vertical tubes, and Alba et al. (2013) did in inclined tubes.

9.3.8 Casing movement A majority of studies of displacement flow consider stationary boundary only. Casing movement creates more complications in the flow. Casing rotation and reciprocation are the two forms of movement that are commonly applied in cementing jobs. Although modern well cementing software can simulate fluid displacement process with casing movement to a reasonable accuracy and reveal the impact of rotating and reciprocating pipes, a logical understanding of the effect of rotation and reciprocation is still largely unknown. The rotating pipe introduces substantial azimuthal flow, which is otherwise much weaker when compared to axial flow. The benefit of the rotating pipe is breaking the mud channel by bringing

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mud to the wide side so it can be displaced forward much easier. The actual effects are multifold and much more complicated. Fig. 9.9 is a demonstration of the simulation results of three-fluid displacement in the annulus with 10-rpm rotation compared with the same case but without rotation. Displacement efficiency is markedly improved by the rotating pipe. The effect of reciprocation is even more mysterious. At least three effects are brought in by reciprocation: induced instantaneous flow rate variation due to surge and swab, fluid inertial force induced by axial acceleration, and fluid velocity change contributed by casing wall velocity. Detailed mechanism of rotating and reciprocation is yet to be carefully studied because: (1) simplified numerical model may not precisely solve the flow field with stronger 3D effects; (2) experimental studies with carefully selected parameter groups are limited,

Fig. 9.9 Final distribution of fluids in the annulus simulated by the displacement efficiency model in CEMPRO +. (A) Casing is stationary and (B) casing rotates at 10 RPM. The casing outer diameter (OD) is 8.7 in., and the wellbore is 9.625 in. The well is vertical, and the total depth is 7000 ft. Only half of the annulus is visualized. The gray fluid is cement, the green fluid is spacer, and the brown fluid is mud. (Credit: Pegasus Vertex, Inc.)

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which cannot assist in interpreting the physical mechanism. In the case of rotating pipe, a dimensionless parameter, Rossby number, is defined as Rb ¼

2U ωD

(9.17)

where U is the pumping velocity, and ω is the rotating angular velocity. This number implies a competition between inertia force and Coriolis force. Although it is largely unknown what rotating speed will optimize displacement efficiency in a real job, cementing engineers should pay attention to the ratio of rotating speed to the pumping velocity instead of trusting or sticking to a fixed rotating speed on the basis of experience.

9.4 Methods This section discusses the models applicable for the analysis and simulations of displacement flow in the well. Equations that fully and precisely describe the physical system exist, but solving them is a challenge. Owing to the complexity of the displacement problem and multiple mechanisms involved, all solutions come with a certain degree of simplifications and assumptions, leaving accuracy and reliability an issue calling for extra cautions. Proper application of these methods in engineering may require a good understanding of the modeling processes.

9.4.1 Equations The working fluids in a cementing well are often incompressible or weakly compressible under high temperature and pressure wells; thus incompressible Navier-Stokes equations are often introduced to describe the flow and pressure field in a well, which have the following form: ∂u 1 + u  ru ¼  rp + g + νr2 u ∂t ρ ru¼0 ∂c + u  rc ¼ Dm r2 c ∂t

(9.18) (9.19) (9.20)

where u is the velocity vector, ρ is the density, ν is the kinematic viscosity, and g is the gravity vector. The first equation describes momentum conservation, and the second describes mass conservation. The last is a concentration transport equation for each phase of fluids, where Dm is the diffusivity of

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the fluid. This equation says the concentration change of a fluid in a location is caused either by fluid flow (convection) or by diffusion. The above equation can be written in the form of three components in a 3D space:
2  ∂u ∂u ∂u ∂u 1 ∂p ∂ u ∂2 u ∂2 u + + +u +v +w ¼ + gx + ν 2 ∂t ∂x ∂y ∂z ρ ∂x ∂y2 ∂z2
∂x 2 ∂v ∂v ∂v ∂v 1 ∂p ∂ v ∂2 v ∂2 v (9.21) + 2+ 2 +u +v +w ¼ + gy + ν 2 ∂t ∂x ∂y ∂z ρ ∂y ∂x ∂y ∂z
2  ∂w ∂w ∂w ∂w 1 ∂p ∂ w ∂2 w ∂2 w + + +u +v +w ¼ + gz + ν ∂t ∂x ∂y ∂z ρ ∂z ∂x2 ∂y2 ∂z2 ∂u ∂v ∂w + + ¼0 (9.22) ∂x ∂y ∂z It is useful to derive a dimensionless form of the equation. This is done by introducing the following conversion: u0 ¼

u 0 x 0 t p , x ¼ ,t ¼ U, p0 ¼ 2 U L L ρU

where U is the characteristic velocity and L is the characteristic length. For displacement flow, U is often selected to be the mean imposed velocity, and L is the pipe diameter or other geometric scale. The equations are now written as: ∂u0 gL ν 2 0 + u0  ru0 ¼ rp0 + 2 + ru 0 ∂t U UL r  u0 ¼ 0 One can further define p00 , which satisfies rp00 ¼ rp0 

gL , or p00 ¼ U2

gx L 0 gy L 0 gz L 0 x  2 y  2 z , to eliminate the gravity term in the equation U U2 U ν and replace using Reynolds number Re, then UL p0 

∂u0 1 2 0 + u0  ru0 ¼ rp00 + ru 0 ∂t Re

(9.23)

Therefore the Reynolds number Re is the only dimensionless group appearing in the equation. Thus to create an equivalent out-of-scale model representing the prototype, one only has to keep the Reynolds number, besides the geometry similarity. For a multiple fluid system, this process is different because the viscosity and density of fluids are not constant in the Eulerian description. For example,

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in a two-fluid system with one native fluid and one displacing fluid, with the same viscosity and different densities ρ1 and ρ2, we have p00 ¼

 p gx L 0 gy L 0 gz L 0 1   x  y  z ¼ p  ρ g x  ρ g y  ρ g z x y z m m m U2 ρm U 2 U 2 U2 ρm U 2

where ρm ¼ (ρ1 + ρ2)/2. Note p00 here does not fully eliminate the gravity U 1 pffiffiffiffiffiffiffi , term in the original equation. With ϕ ¼ 1  2c, At ¼ ρρ2 ρ + ρ , Fr ¼ AtgL 2

1

and egbeing the unit vector in gravity direction, the equation is transformed to the following:
0  ∂u 1 2 0 ϕ 0 0 ð1 + ϕAt Þ + u  ru ¼ rp00 + (9.24) r u + 2 eg 0 ∂t Re Fr ∂c 1 (9.25) + u0  rc ¼ r2 c 0 ∂t Pe In the first equation, the last two terms are the two competing forces (viscous force and inertial force) we had discussed in Section 9.3. The ratio of the two x ¼ Re /Fr2 defines the slope of the line separating the viscous region from the inertia region. In the second equation, the Pe number is usually much >1; hence the diffusive term is often ignored in modeling the sharp interface evolution. Displacement flows in real wells often have more than two fluids, and each of the fluids has different non-Newtonian rheology; thus more parameters are involved. The derivation of dimensionless equations leads to equations that are further complicated, which is not discussed here.

9.4.2 Semiempirical approach Semiempirical approaches referred here were developed from extensive experimental studies using laboratory models and through analysis of the physical models described with dimensionless groups. For example, when predicting buoyancy-induced R-T instability that drives interface interpenetration, the Rayleigh number can be introduced, as discussed in Section 9.3.6. In a horizontal well without imposed flow or in a vertical well with an unstable configuration, when a heavy fluid is present on top of a light fluid, an exchange flow takes place, when Reynolds number based on buoyancy-induced inertia is introduced to describe the correlations discovered from experiments. A flow regime diagram for iso-viscous displacement flow attributed to previous research work is presented in Fig. 9.10 in the form of Ret cos β vs Fr, where β is the inclination angle.

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Fig. 9.10 Diagram of buoyant flow regimes in inclined pipes, presented as Ret cos β vs Fr, where Froude number Fr ¼ uo/ut, Ret ¼ utD/ν, and β is the inclination angle. The red line divides the plane into a mixing regime and nonmixing regime. The green line separates the viscous regime and inertial regime. The yellow shaded zone represents noninstantaneous displacement regime with back flows. (Credit: This illustrative plot is reproduced from Alba, K., Taghavi, S.M., Frigaard, I.A., 2013. Miscible density-unstable displacement flows in inclined tube Phys. Fluids 25, 067101. https://doi.org/10.1063/1. 4808113, with the permission of AIP Publishing.)

A line given by χ c ¼ 2 ReFrt cosβ  116 divides the plane into viscous on the bottom and inertia regime above it (Alba et al., 2013). Above the line, there is a regime of back flows, which results from strong buoyant inertia and weak viscous force insufficient to drive the fluid forward; thus a part of fluid in a diffusive or segregated form flows to the opposite direction as the imposed flow. When Fr number is low, this line represents a critical regime with a stationary top layer with constant height and zero mean flow, as seen in Fig. 9.3, and below the line is the instantaneous displacement viscous flow regime, which is stable because of a weak convective mixing, thus maintaining a clear interface. Another line in the figure divides the diagram into a mixing regime and nonmixing regime. Fluid mixing is driven by different mechanisms, including diffusion caused by miscibility, convective mixing from instability, and turbulent mixing. For miscible fluids under the cementing displacement   context, Peclet number ¼ uD0 D is commonly high, implying the influence m

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Displacement efficiency

of molecular diffusion is negligible. Thus the mixing zone here, in the diagram, is a result of convective and turbulent instabilities. Displacement flow can be an instantaneous or a noninstantaneous displacement. Noninstantaneous displacement is depicted in the figure by a shaded triangle area, which is largely located in the nonmixing inertia zone. Mixing counter flow is possible, as found in the top of the triangle. Example 9.1 13 -ppg fluid is pumped at 5 bpm into a casing (OD ¼ 9.625 in., ID ¼ 8.9 in.) to displace the 11 -ppg mud in a directional well. The hole diameter is 12 in. Predict the displacement flow regime inside the casing and in the annulus at both vertical and horizontal sections. Assume both the fluids are Newtonian, and the viscosities are 80 cP (displacing fluid) and 60 cP (mud). Solution: Velocity inside the casing Q 5  0:159 m3 = min u0, i ¼
2 ¼
2 ¼ 0:33m=s ID 8:9 π 3:14  0:3048m 2 24 Velocity in the annulus u0, a ¼ 4.6m/s Viscosity of the cement νh ¼

80 cp 0:08 Pa:s ¼ 5  105 m2 =s ¼ 13 ppg 13  119:8 kg=m3

Viscosity of the mud νl ¼

60 cp ¼ 4:5  105 m2 =s 11 ppg

Atwood number At ¼

13  11 ¼ 0:083 13 + 11

Reynolds number in casing Re ¼

u0 D 0:33  0:226 ¼ 1570 ¼ ν 4:75  105

Viscous velocity uν ¼

At gD2 0:2262 ¼ 0:083  10 ¼ 892 m=s ν 4:75  105

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Inertia velocity ut ¼

pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi AtgD ¼ 0:083  10  0:226 ¼ 0:43 m=s

Modified Reynolds number Ret ¼

ut D ¼ 0:43  0:226=4:75  105 ¼ 2046, ν

and the Froude number is Fr ¼

uo 0:33 ¼ ¼ 0:77 ut 0:43

In vertical section, β ¼ 0°. In the flow regime diagram in Fig. 9.10, the flow falls into the top left corner at (0.77, 2046) in the mixing zone. In fact, with the relatively large Reynolds number, the flow is possibly turning to turbulent. Thus an instantaneous displacement is expected inside the casing in the vertical section with a length of turbulent mixing. In the horizontal section, if using β ¼ 89°, then Retcosβ ¼ 2046  0.017  36. Therefore χ¼

2Ret cos β ¼ 93 < χ c ¼ 116 Fr

which suggests a stable viscous flow without backflow. In the annulus, the hydraulic diameter Dh ¼ 0:816  129:625 12 0:3048 m ¼ 0:049m

u0 Dh 4:6  0:049 ¼ 4745 ¼ ν 4:75  105 pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ut ¼ AtgD ¼ 0:083  10  0:049 ¼ 0:2 m=s Re ¼

Ret ¼

ut D ¼ 210 ν

Still using β ¼ 89°, then Retcosβ ¼ 210  0.017  3.6 Fr ¼

uo 4:6 ¼ ¼ 23: ut 0:2

Here, a very low modified Reynolds number reveals that viscous force dominates over the buoyant inertial force. In addition, by high pumping velocity, imposed convection is much stronger than buoyant flow,

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indicated by a high Fr number. Therefore here, the relevant parameter is the regular Reynolds number, 4745, which implies turbulent flow. Thus displacement is expected to be instantaneous. Up to the vertical section, because stable density contrast is present (a heavy fluid displaces a lighter fluid upward), Fig. 9.10 is not applicable. One can consider the buoyancy force is of little influence, turbulent mixing will be the only process occurring at the interface. It has an engineering value to estimate the fluid front velocity in displacement flow. On the basis of experimental data and analysis, Taghavi et al. (2012) give the following expression to predict the front velocity of nonmixing flow from Froude number for near horizontal pipes: uf ¼ 0:7 + 0:595Fr + 0:362Fr 2 ut

(9.26)

Alba et al. (2013) proposed the following expression to predict the front velocity from Reynolds number and Froude number with the inclination angle involved:
   uf Re cosβ ¼ Fr  0:002337 + 50Fr  500 1  0:98Fr + 1:03Fr 2 ut Fr (9.27) Example 9.2 Predict the front velocity of the displacement flow inside the casing in the horizontal section in the previous example. Solution: Inside the casing in the horizontal section, we have uf ¼ 0:7 + 0:595  0:77 + 0:362  0:772 ¼ 1:37 ut Then, uf ¼ 1.37  0.43 ¼ 0.59 m/s, which is 1.78 times of the pumping velocity. Using Eq. (9.27) uf ¼ 0:77  0:002337  ð50  0:77  500Þ ut    1  0:98  0:77 + 1:03  0:772 ¼ 1:69 u f ¼ 1.69  0.43 ¼ 0.72 m/s, which is 2.2 times of pumping velocity.

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Example 9.3 Estimate the mixing length of the two fluids inside the casing in the vertical section after 1000 ft. of displacement in the previous example. Solution: In the previous example, the vertical section inside the casing has Ret ¼ 2074 and Fr¼ 0.77, which corresponds to the fully diffusive region in the diagram of Fig. 9.10. The Froude number suggests that buoyant flow and imposed flow are comparable. At¼ 0.083 and Viscosity ν ¼ 4.75  105m2/s refer to the paper by Alba (2013) in Fig. 9.11A or B. Although the flow falls out of the diagram due to higher Reynolds number, a rough extrapolated estimate of the macroscopic diffusivity would be Dm 1 u0 D 2 Hence Dm  0:33  8:9 12  0:3048m ¼ 0:07m =s: As a reference, the Taylor Dffi dispersion coefficient (DT ¼ 1:785u0 p ) for turbulent pipe ,where f ¼ 0:266 Re1=4 f

flow was estimated to be 0.026 m2/s. If we use 90% concentration of the displacing fluid as the front of mixed interval, according to Eq. (9.15), then we want to have
 x erf pffiffiffiffiffiffiffiffiffiffi ¼ 0:8 4Dm t or x pffiffiffiffiffiffiffiffiffiffi ¼ 0:9 4Dm t s ¼ 923s The elapsed time for 1000 ft. of displacement is t ¼ 10000:3048m 0:33 Therefore pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x ¼ 0:9  4  0:07m2 =s  923s ¼ 14 m

Fig. 9.11 Schematic of an eccentric pipe and a dual-pipe representation. (Credit: Pegasus Vertex, Inc.)

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If we assume diffusive transport develops forward and backward symmetrically, then the mixing length is estimated to be 28 m.

9.4.3 A simple dual-pipe model Hydraulics calculations for in-pipe and annular flow using familiar 1D analysis are useful in well engineering in finding pressure, velocity, flow pattern, and so forth. However, solving displacement efficiency requires much more complicated calculations. In some cases, hydraulics analysis may still be used for the purpose of rough evaluation of displacement efficiency. Here, a dualpipe model for annular displacement is discussed. In an eccentric annulus, the narrow side and wide side could have distinct flow velocity and fluid presence. Although the velocity continuously varies along the azimuth, only estimating a mean narrow side velocity and a mean wide side velocity may obtain useful information. We divide the annulus into a wide half channel and a narrow half channel, with a plane passing through the casing axis, and then we perform hydraulics analysis in each of them. Each channel is regarded as an equivalent pipe with different diameters. The hydraulic diameter used for frictional pressure calculations is found as: Dh ¼

4A Pw

where A is the cross-sectional area, and Pw is the wet perimeter. To find divided flow rates into each of the two “pipes,” an iterative process is needed to enforce equal pressure drop, that is, the pressure must be the same in both pipes at the same depth. The following example illustrates this process. Example 9.4 Estimate the mud channel length in a 70% standoff annulus in a 3000 ft. vertical well after 1 bottom up. Hole ID ¼ 8.500 and pipe OD ¼ 700 . The flow rate is 5 bpm. Use Bingham Plastic model for both the displacing fluid (PV ¼ 60 cP, YP ¼ 50 lb./100 ft2, mud weight (MW) ¼ 14 ppg) and native mud (PV ¼ 40 cP, YP ¼ 30 lb./100 ft2, MW ¼ 13 ppg). Solution: The annulus cross-sectional area Aa ¼ π4 ðID2  OD2 Þ ¼ 18:26 in:2 As illustrated in Fig. 9.11, the eccentric distance e ¼ IDOD  2 ð100  STOÞ ¼ 0:225 in: 2e ¼ 0:0529,θ ¼ 3° ID ID L ¼ cos ðθÞ ¼ 4:244 in: 2

sin θ ¼

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Due to eccentricity, the area of the narrow half is 7.24 in.2 and the wide half is 11.02 in.2
 ID OD ID Pw, w  π + + 2 θ ¼ 24:347 + 0:45 ¼ 24:797 in: 2 2 2
 ID OD ID +  2 θ ¼ 24:347  0:45 ¼ 23:897 in: Pw,n  π 2 2 2 4A D h, w ¼ ¼ 1:777 in: Pw 4A D h, n ¼ ¼ 1:215 in: Pw By basic hydraulics calculation, it is found that when the divided flow rates are Qn ¼ 1.3 bpm and Qw ¼ 3.7 bpm, the frictional pressure drop in both the pipes are made equal, assuming either of mud or displacing fluid in the pipes (Table 9.1). Therefore the mean velocities in the wide side and narrow side, respectively, are 3:7 bpm ¼ 4:52 ft=s 11:02 in:2 1:3 bpm un ¼ ¼ 2:42 ft=s 7:24 in:2

uw ¼

The total displacement time Δt is 13.6 min, when the fluid front reaches L ¼ unΔt ¼ 1975 ft. A mud channel in the length of Lm ¼ 3000 – 1975 ¼ 1025 ft. is still overestimated because transverse flow is not accounted. An additional step within the transition interval (where the native fluid flows in the narrow side and the displacing fluid in the wide side), the flow rate at the wide side is reduced. To enforce a mass conservation, a transverse flux Qt is estimated as: Table 9.1 Calculated flow rate in the dual-pipe model with different fluids. Wide/narrow fluids Qw (bpm) Qn (bpm)

Native/native Displacing fluid/displacing fluid Displacing fluid/native Displacing/native (with hydrostatic ΔP)

3.7 3.7 3.60 3.57

1.3 1.3 1.4 1.43

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Qt ¼ 3:7  3:6 ¼ 0:1bpm Thus the volume of the displacing fluid flowing to the narrow side is calculated as Vol ¼ Qt  dt ¼ 0:1bpm  13:6 min ¼ 1:36bbl L ¼ 1:36bbl=A ¼ 1:36bbl=7:24in:2 ¼ 152ft The adjusted mud channel length is L 0 ¼ 1025  152ft ¼ 873ft In fact, the difference of hydrostatic pressure owing to density difference will further reduce the length; consequently, the true length should be lower than the estimated value. It is possible to improve the result by including the hydrostatic pressure difference into the estimate of the flow rate distribution for the mixing interval. If there is an 875-ft long mixing interval, then Δp ¼ 0:052 Δρ Ltvd ¼ 0:052  1  873 ¼ 45 psi With this additional pressure difference consider, it is found the split flow rates are now 3.57 bpm for the larger pipe and 1.43 bpm for the smaller pipe. Δun ¼

ð1:43  1:4Þ bpm ¼ 0:056 ft=s 7:24 in:2 ΔLn ¼ 46 ft

Therefore the mixing length is corrected to L ¼ 873  46 ¼ 827 ft. It must be noted that the simplified dual-pipe model discussed here is a quite rough estimation and not applicable if the pipe rotates, when the flow in the annulus is no longer separable.

9.4.4 Lubrication model Lubrication model or film model is a simplified model derived from NavierStokes equations by dropping out the insignificant terms, which is suitable to describe the flow within a film. In displacement flow, the length scale is often thousands of times larger than the diameter. When the flow is stable and well stratified with a clear interface, it is appropriate to consider the problem with the lubrication model by assuming the axial flow is dominant, while the transverse flow is neglected. Lubrication model is not applicable to unstable and diffusive flow.

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In Eq. (9.21), we assume x is the axial coordinate, β is the inclination angle, and z is the horizontal (thus gz ¼ 0), and remove the transient and small terms in the momentum equation; then we have
2  1 ∂p ∂ u ∂2 u + + g cos β + ν 0¼ ρ ∂x ∂y2 ∂z2 1 ∂p (9.28) 0¼ + g sin β ρ ∂y 1 ∂p 0¼ ρ ∂z In a two-fluid system, we assume fluids are separated by the interface into upper and lower layers, as depicted in Fig. 9.12A. The equations are satisfied in both the layers with different densities. Applying continuity condition in both the layers will lead to the following interface evolution equation (Taghavi et al., 2011): ∂AðhÞ ∂Q + ¼0 ∂t ∂x

(9.29)

in which, h and A(h) are the height and the cross-sectional area of the lower heavier fluid, and Q is the flow rate through the lower layer that can be expressed as the integration of velocity. In the work done by Taghavi et al. (2011), this model is solved to relate Q to h and dh/dx, which leads

Fig. 9.12 Illustrative schematics of a two-fluid buoyant displacement flow in an inclined pipe. Top: Heavy fluid flows downward to displace the light fluid. Bottom: The velocity profile in a lubrication model assuming stable interface, where back flow exists on the top. (Credit: Pegasus Vertex, Inc.)

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to a finding of critical status with χ ¼ 2Ret cos β/Fr¼116 and h/D ¼ 0.72 for near horizontal pipes, when a stationary interface is sustained with zero flux through the top fluid layer. The same status is found for vertical pipes at χ ¼ 230, h/D ¼ 0.377 in the work done by Amiri et al. (2016). The lubrication model may be applied to solve the whole history of the segregated flow and interface evolution and extendable to more layers of fluids. However, because well displacement flow can easily develop instability, a more sophisticated model is often desired.

9.4.5 Reduced CFD model Reduced CFD model is a numerical approach based on simplified NavierStokes (N-S) equations. It is different from full CFD model by introducing substantial simplifications to reduce model complexity and improve computational efficiency (see Table 9.2). This category of models includes 2D or quasi-3D models. Different forms of models exist (for example, Aranha et al., 2012; Chen et al., 2014; Tardy et al., 2017; Dai and Liu, 2017), and some of them are implemented in commercial simulators. Quasi-3D models often carry out numerical calculations in 3D spatial grid; however, 3D flow field is not fully resolved in the space domain. Navier-Stokes equations describe coupled axial, azimuthal, and radial velocities, whereas a model may neglect the radial velocity because that is usually the most insignificant one. The popular narrow-gap assumption is of this type, which requires the ratio of annular gap to hole diameter far 2 ppg over the mud weight. Consider multiple pills to maintain the