Modelling Oilfield Scale Squeeze Treatments: From Core to Reservoir 3319718517, 9783319718514

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SPRINGER BRIEFS IN PETROLEUM GEOSCIENCE & ENGINEERING

Oscar Vazquez

Modelling Oilfield Scale Squeeze Treatments From Core to Reservoir 123

SpringerBriefs in Petroleum Geoscience & Engineering Series Editors Jebraeel Gholinezhad, School of Engineering, University of Portsmouth, Portsmouth, UK Mark Bentley, AGR TRACS International Ltd, Aberdeen, UK Lateef Akanji, Petroleum Engineering, University of Aberdeen, Aberdeen, UK Khalik Mohamad Sabil, School of Energy, Geoscience, Infrastructure and Society, Heriot-Watt University, Edinburgh, UK Susan Agar, Oil & Energy, Aramco Research Center, Houston, USA Kenichi Soga, Department of Civil and Environmental Engineering, University of California, Berkeley, USA A. A. Sulaimon, Department of Petroleum Engineering, Universiti Teknologi PETRONAS, Seri Iskandar, Malaysia

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Oscar Vazquez

Modelling Oilfield Scale Squeeze Treatments From Core to Reservoir

Oscar Vazquez Institute of Petroleum Engineering Heriot-Watt University Institute of Petroleum Engineering Edinburgh, UK

ISSN 2509-3126 ISSN 2509-3134 (electronic) SpringerBriefs in Petroleum Geoscience & Engineering ISBN 978-3-319-71851-4 ISBN 978-3-319-71852-1 (eBook) https://doi.org/10.1007/978-3-319-71852-1 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Susana and Nubia. Keep moving forward.

Preface

In this book, I have attempted to provide an overview of modelling squeeze treatments, commonly associated to the bullhead of threshold scale inhibitors to prevent injectivity and productivity disruptions, due to the deposition of mineral oilfield scale. Although there is a very healthy literature about squeeze treatments, no comprehensive materials focusing on this matter were available, at the time of preparing the manuscript. Therefore, I decided to put this together, although I am sure others could have done better job writing this book. This is my humble contribution. This book is primarily a handbook for the modelling of squeeze treatments, which has several aspects that I thought anyone involved in this business should have some notion, such as mineral scale, scale inhibitors, squeeze treatment modelling, reservoir scale management and finally optimisation of squeeze treatments. It is intended as reference, which provides an overview of scale management with a focus on squeeze treatment modelling. I believe operators, service companies and chemical suppliers might find it useful, including university students wishing to study scale management. This book is divided into eight chapters, which may be read independently, but there is a logic of the sequence as they appear in the manuscript. Chapter 1 is a general introduction to oilfield mineral scale, the main problem we are dealing with. Chapter 2 describes aspects of scale management, although scale precipitation might be considered as near wellbore problem, it is related to the water composition, therefore basic notion of thermodynamics is necessary to predict the problem, including the type of scales and where the deposition will occur, which will determine the scale control options available. Chapter 3 contains a description of the common inhibitors, the chemical selection process, factors affecting the effectiveness and delivery options. Chapter 4 includes a general description of squeeze treatments, including non-aqueous and combined squeeze treatments. Chapter 5 introduces the modelling of squeeze treatments, which includes the mathematical description of the physical processes involved in squeeze treatments. Chapter 6 introduces the concept of life cycle of a field squeeze treatment, which describes all aspects to be considered in the designing process. Chapter 7 presents the concept of reservoir scale management, scale deposition is perceived as production issue, however reservoir processes are critical, the chemical equilibrium of brines contained within the reservoir may be vii

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Preface

disrupted by changes in brine composition and/or reservoir pressure and/or temperature, which will result in the deposition of scale. Finally, last but by no means least, optimisation of squeeze treatments, considering operational constraints, the introduction of new concept “Iso-Lifetime” curve, and finally squeeze treatment lifetime prediction uncertainty quantification. Finally, I would like to express my most sincere appreciation to all the people who I spent some or a lot of time discussing aspects of modelling squeeze treatments, among many others, Eric Mackay, Ken Sorbie, Gill Ross, Myles Jordan, Clare Johnston, Alan Beteta, Lorraine Boak, Mike Singleton, Robin Shields, Olav Selle, Ross McCarney, Terje Østwold, Kari Ramstad, Salima Baraka-Lokmane, Alistair Strachan, Baard Kaasa, Gordon Graham, the sponsors of the FAST group, and all the engineers that have been in one of the many Squeeze courses I run in the last few years. Special gratitude to the SPE for organising the Scale Conference in Aberdeen, and Tekna and specially to Lise Olaussen for organising year after year the Oilfield Chemistry Symposium, my favourite conference in Geilo, which combines science, ski and networking. And specially to my first Ph.D. student Vahid Azari, who coined the concept of “Iso-Lifetime” curve. My email address for comments: [email protected] Edinburgh, UK

Oscar Vazquez

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Definition of Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Problems Caused . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Types of Oilfield Mineral Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 pH Independent Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 pH Dependent Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 2 3 4 6

2 Scale Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Predicting the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Equilibria in Water and Solubility . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Thermodynamics of Mineral Scale . . . . . . . . . . . . . . . . . . . . . 2.1.3 Sulphate Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Carbonate Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Sulphide Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.6 Sodium Chloride (Halite) Scale . . . . . . . . . . . . . . . . . . . . . . . . 2.1.7 Silicate Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.8 Kinetics of Mineral Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Life-Cycle Management of Scale Control . . . . . . . . . . . . . . . . . . . . . . 2.2.1 General Process to Quantify Inorganic Scale Risk . . . . . . . . . 2.2.2 Quantify Scale Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Scale Control Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 8 8 9 11 11 16 17 19 19 22 24 26 27 30

3 Scale Inhibitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Type of Scale Inhibitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Carbonate and Sulphate Scales . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Sulphide Scale Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Halite Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Silicate Scale Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Chemical Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Static Inhibitor Efficiency Test . . . . . . . . . . . . . . . . . . . . . . . . .

35 36 37 38 39 40 41 42 ix

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3.2.2 3.2.3 3.2.4 3.2.5

Dynamic Inhibitor Efficiency Test . . . . . . . . . . . . . . . . . . . . . . Static Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Static Formation Damage Test . . . . . . . . . . . . . . . . . . . . . . . . . Inhibitor/Formation Brine Compatibility Phase Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.6 Thermal Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.7 Mechanisms of Scale Inhibition . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8 Relevance to Test Methodology . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Factors Controlling Scale Inhibitor Effectiveness . . . . . . . . . . . . . . . 3.3.1 pH and pKa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Calcium Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Magnesium Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Scale Inhibitors Delivery Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Continuous Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Squeeze Treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Solid Chemical Inhibitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42 43 43

4 Scale Inhibitor Squeeze Treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Squeeze Treatment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Preflush . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Main Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Overflush . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Retention Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.5 Formation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.6 Placement Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Non-aqueous Scale Inhibitor Squeeze Treatments . . . . . . . . . . . . . . . 4.2.1 Oil Soluble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Invert/reverse Emulsions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Amphiphilic Solvent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Microemulsions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Water Free Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Part-Aqueous Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.7 Encapsulated Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Combined Scale Inhibitor Treatments . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Squimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Squeeze Treatment/Tracer Programme . . . . . . . . . . . . . . . . . . 4.4 Treatment Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57 57 59 59 60 60 61 63 64 64 64 64 65 65 65 65 66 66 66 67 67

5 Modelling Scale Inhibitor Squeeze Treatments . . . . . . . . . . . . . . . . . . . . 5.1 Characteristics of Inhibitor Adsorption . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Scale Inhibitor Aqueous Phase Transport and Adsorption . . . . . . . . . 5.3 Scale Inhibitor Non-aqueous Phase Transport and Adsorption . . . . . 5.3.1 Two Phase Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73 73 75 75 75

43 44 44 44 45 45 46 47 47 47 48 50 50 50

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5.3.2 Two-Phase Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Adsorption Isotherm Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Placement: Partitioning of Flow Between Layers . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77 78 79 81

6 Life Cycle of a Field Squeeze Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 From Coreflood to Field Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Derivation of Inhibitor-Rock Adsorption Isotherm . . . . . . . . 6.1.2 Squeeze Treatment Sensitivity Calculations . . . . . . . . . . . . . . 6.2 Pseudo-adsorption Isotherm Matching . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Estimating Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Analytical Expression for the Partitioning of Flow . . . . . . . . 6.3.2 Squeeze Treatment/Tracer Programme Designs . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83 84 85 87 87 89 94 96 98 99

7 Reservoir Scale Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Reservoir-Simulation Process for Inorganic Scale Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Reservoir Scale Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Estimation of Scale Deposition Through Reservoir History Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Produced Water Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Produced Water Chemistry (PWC) History Matching Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Seawater Mixing Front Uncertainty Maps . . . . . . . . . . . . . . . 7.3 Non-aqueous vs Aqueous Overflush Scale Inhibitor Squeeze Treatment in an Oilfield Offshore Norway . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Near Wellbore Squeeze Simulation . . . . . . . . . . . . . . . . . . . . . 7.3.2 Sensitivity on Splitting the Overflush . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8 Optimisation of Oilfield Scale Inhibitor Squeeze Treatments . . . . . . . . 8.1 Operational Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 SI Neat Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 SI Injection Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.3 Total Injected Water Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Single-Well Squeeze Design Optimization . . . . . . . . . . . . . . . . . . . . . 8.2.1 Squeeze Lifetime Criticality/Reliability . . . . . . . . . . . . . . . . . 8.2.2 Operational Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Chemical Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.4 Squeeze Optimization with Fixed Target Lifetime . . . . . . . . . 8.2.5 Global Squeeze Treatment Optimization . . . . . . . . . . . . . . . . . 8.3 Multi-well Squeeze Design Optimization . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Gradient Descent Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Multi-objective Optimization Algorithm (MOPSO) . . . . . . .

117 118 118 118 119 119 120 120 120 120 122 126 127 127

103 104 106 108 109 109 111 111 114 114

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8.3.3 Field Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Squeeze Treatment Lifetime Prediction Uncertainty Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Isotherm Matching Non-uniqueness . . . . . . . . . . . . . . . . . . . . 8.4.2 Uncertainty Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

127 128 129 129 132

Chapter 1

Introduction

1.1 Definition of Scale Oilfield scale is commonly known as the solid deposits due to the precipitation of inorganic mineral scale in producing wells, which is one of the biggest production challenges of the oil and gas industry, (Vazquez et al. 2012). Possibly next to corrosion and gas hydrates, scale is probably the one of the most important water-related flow assurance problems. Oilfield scale is defined as a hard crystalline deposit resulting from the precipitation of mineral compounds present in the aqueous phase, which typically consist of one of more inorganic deposit along with other debris, such as organic precipitates (naphthenate, aslphaltene, wax), sand, corrosion products, etc. The crystalline deposits are formed due to the minerals adhering to solid surfaces, which may be in the reservoir, the production tubing, or the surface facilities. The problems caused by scale deposits are many, such as reservoir formation damage, blockage in perforations and/or gravel packs, safety valves and choke failure, pump wear, and corrosion underneath deposits. The most common inorganic scales that can be found in oilfields worldwide are sulphate and carbonate scales, which are formed by two different mechanisms. Sulphate scales, namely Barium Sulphate (BaSO4 ), Strontium Sulphate (SrSO4 ) and Calcium Sulphate (CaSO4 ), precipitate as the result of mixing of incompatible brines, specifically injected seawater, and formation brine. Carbonate scales, on the other hand, precipitate due to the pressure reduction in the production wells, which releases the dissolved CO2 . Also, NaCl salt precipitation is becoming more common; this is due to the cooling of well fluids and evaporation of saturated brines. Finally, previously termed “exotic” scales, such as iron, Lead and Zinc Sulfide, nowadays are becoming more common as the number of HPHT (high pressure high temperature) reservoirs being produced is currently increasing. Scale deposition must be anticipated in advance to identify the best scale management strategy (Kelland 2014), to tackle not only individual wells, but the field.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 O. Vazquez, Modelling Oilfield Scale Squeeze Treatments, SpringerBriefs in Petroleum Geoscience & Engineering, https://doi.org/10.1007/978-3-319-71852-1_1

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1 Introduction

Mackay and Jordan (2005) in proposed an integrated risk analysis of scale management particularly focused on deepwater developments, where the cost of remedial treatments may be prohibitive. This type of analysis should be performed at the front-end engineering design (FEED) stage, where several options for scale management are still available, such as changes to the design of the production system to prevent scale deposition. The study included the following steps, identification of maximum scale potential, evaluation of best suited chemistry by laboratory testing, modification of full reservoir simulation model to predict seawater breakthrough and finally, near wellbore squeeze modelling, based on the flow profiles derived from the reservoir model simulations.

1.2 Problems Caused There are a great variety of problems caused by scale deposition, they may be categorised by the problems caused by mineral deposits, and suspended particles. Scale deposits adhere to surfaces, if the scale adheres to the formation pore walls it will lead to formation damage, where the formation permeability will be reduced. Scale may adhere to perforation or gravel packs resulting in blockage. If it occurs in the flow lines walls, the internal diameter will be reduced resulting in restriction of flow; finally, it can also damage Sub Surface Safety Valves (SSSVs), compromising key safety equipment. Suspended particles can result in the plugging of filtration equipment and in the reduction of oil/water separator efficiency.

1.3 Types of Oilfield Mineral Scales In oilfield scale, water is of primary importance, scale will only deposit when water is produced. Water is a good solvent and can carry large quantities of scaling compounds (Crabtree et al. 1999). Reservoir formation water, commonly known as formation brine, contained dissolved components due to the exposure to mineral phases present in the reservoir formation. Therefore, formation brines are complex fluids, rich in ions. Seawater is rich in ionic composition that are by-products of marine life and evaporation, on the other hand, formation brine ion composition depends on mineral diagenesis and other geochemical processes, as formation brines flow and mix over geological times. Scale will start forming when the fluid natural equilibrium is perturbed, as consequence the solubility limit of several components is reduced, and the brine becomes supersaturated. Generally, mineral solubility in water increases with temperature and decreases with higher pressure, but not all minerals follow this trend, for example calcium carbonate and anhydrite increases solubility with decreasing temperature. Additionally, carbonate minerals solubility depends on the presence of acid gases, such as carbon dioxide and hydrogen sulphide, generally, as pressure decreases carbon dioxide evolves from the water phase, resulting in an

1.3 Types of Oilfield Mineral Scales

3

increase of the pH, which leads to calcium carbonate precipitation. Thus, it seems reasonably to classify oilfield scales respect the pH dependency.

1.3.1 pH Independent Scales This type of scale deposits when two incompatible brines mix, namely seawater and formation brine, resulting in the deposition of sulphate scales, such as among others barium, calcium, and strontium sulphate. Divalent ions, such as barium, calcium, and strontium (Ba2+ , Ba2+ and Sr2+ ) are commonly found in reservoir formation brine, their composition will depend on the geological history of the oilfield, and seawater is rich is sulphate ions. Sulphate scales can deposit when the following equilibrium moves to the right: Ba2+ (Ca2+ or Ca2+ ) + SO42− ↔ BaSO4(s) (SrSO4(s) or CaSO4(s) ) Among the sulphate scales, barium sulphate is the most insoluble and hardest to control, the solubility in pure water at 25 °C is just 2.3 mg/l, which makes it the most difficult scale to control, as it is very hard and only dissolvable at a reasonable rate in only the best dissolvers. In addition, due to the low solubility, low concentration of barium in the formation brine may result in barium sulphate deposition. Calcium and Strontium sulphate are the easiest scales to treat, since they are slightly soluble in water, 2,000 and 114 mg/l respectively, and soluble in many chelate dissolvers, which make scales easier to control. In addition, some scales might be radioactive, formation brines might contain low concentration of radioactive radium, which may co-precipitate in the lattice of barium and strontium mixed sulphate scales (Kelland 2014). As mentioned before, sulphate scale deposition is due to the mixing of incompatible brines, therefore scale potential will depend on the seawater fraction (i.e., the ratio injected seawater to the total produced water). The maximum potential will normally occur around 50% seawater fraction, where the optimum ratio between divalent and sulphate ions occurs. Thermodynamic modelling is routinely used to calculate the scaling potential, where the input data compromises the ionic composition of the formation brine and the injected seawater, and the corresponding thermodynamic solubility product of the mineral salts likely to precipitate. This approach represents the simple mixture of injection and formation brines. However, there is increasing evidence that several geochemical reactions occur when seawater is injected and transported through the formation. Deep in the reservoir the mixing of injected, connate and aquifer results in sulphate salts precipitation, (Bertero et al. 1988; Sorbie and Mackay 2000). Therefore understanding the geochemistry in the reservoir provides invaluable information to identify an optimum scale management strategy (Mackay and Jordan 2005; Webb and Kuhn 2004). Ion stripping has been observed in reservoirs under water flooding, particularly when the formation brine is rich in Barium concentration, such as the

4

1 Introduction

Gyda field, where formation brine is rich in barium, resulting in sulphate stripping, which resulted in a lower barium sulphate scaling tendency, as a consequence the adequate concentration of scale inhibiotr to control scale was lower, (Mackay and Jordan 2003). Sodium chloride (Halite) scales are much more soluble than the sulphate and carbonate scales. Some formation brines contain very hign concentration of sodium and chloride, particularly in HPHT (high pressure high temperature) reservoirs. Since the solubbility increases with increasing temperature, some formation brine might become saturated with sodium chloride, and when the temperature decreases, sodium chloride may precipitate out. In addition, water flash evaporation when the pressure reduces, may result in higher concentrations which may lead to Halite deposition.

1.3.2 pH Dependent Scales Carbonate, sulphide, and silicate scales are pH dependent, in other words are acid soluble. Thus, a change in pH will disrupt the brine equilibrium, resulting in the deposition of scales.

1.3.2.1

Carbonate Scales

Controlling carbonate scale deposition is not as difficult as barium sulphate, since it is more soluble than sulphate scales, approximately 2,000 mg/l in pure water at 25 °C, and in addition they are acid soluble. To calculate the scaling tendency of CaCO3 , the concentration of carbon dioxide is of particular importance, in the presence of a gas phase the equilibrium can be written as follows, where calcium carbonate will deposit if equilibrium moves to the left (Atkinson 1997; Cowan and Weintritt 1976): 2+ − CaCO3(s) + CO2(g) + H2 O ↔ Ca(aq) + 2HCO3(aq)

The presence of CO2(g) is the main complication, the molar volume of carbon dioxide gas depends greatly in the pressure and temperature. If the pressure drops the reaction will move to left to try to increase the pressure by forming more CO2(g) by Le Chatelier’s principle, resulting in the precipitation of CaCO3 . On the other hand, if the partial pressure of carbon dioxide increases and partitions to the water phase the pH will decrease, resulting in the dissolution of CaCO3 .

1.3.2.2

Sulphide Scales

Sulphide scales are not as common as carbonate or sulphate scales, in the past they were referred as exotic scales. However, their occurrence is increasing particularly in maturing fields and in HP/HT (High Pressure High Temperature) fields. In the

1.3 Types of Oilfield Mineral Scales

5

last few decades, more emphasis to understand conventional scales (sulphate and carbonate scales) than sulphide scales has been reported, (Chen et al. 2009). Particularly about iron sulphide (FeS), the following reasons were reported: First, some instances iron sulphide deposits are softer than calcium carbonate (Przybylinski 2003), which although will still block the tubing it might not be at the same degree, so it might be considered as a severe problem. Second, study iron sulphide in the laboratory is much more difficult than other conventional scales. And finally, there are a number of iron sulphide crystalline forms with different sulphur to iron ratios result in different solubility in mineral acids (Nasr-El-Din and Al-Humaidan 2001). Sulphide scales forms as the result of the reaction of sulphide ion, sourced from hydrogen sulphide (H2 S), and a metal ion, such as iron (Fe), lead (Pb) and zinc (Zn). Although some H2 S is naturally present in oilfields, the bulk is a consequence of reservoir souring, either biotic and/or abiotic origin, (Seto and Beliveau 2000). Biotic mechanism consists of the production of H2 S due to the activity of sulphatereducing bacteria (SRB). SRB grow in the zone where the seawater mixes with the reservoir formation water, where the components and nutrients that support SRB life are present. Abiotic mechanisms include the production of H2 S by thermochemical sulphur reduction, thermal hydrolysis of organic sulphur compounds, or hydrolysis of metal sulphides. The source of iron ion can be either from the corrosion of steel or from the reservoir, either from the formation/injected waters or dissolution of iron bearing minerals (Wylde 2014). Potential sources of Pb and Zn metal ions are the dissolution of formation minerals such as Galena and Sphalerite; and in addition, Zn is present in heavy brine completion fluids, (Jordan et al. 2000).

1.3.2.3

Silicate Scales

Silicate scales are not as common as other conventional scales, they are associated with geothermal systems, HP/HT reservoirs and ASP (Alkaline Surfactant Polymer) flooding in sandstones reservoirs. Silicate scales are deposited as the result, in the first instance of the dissolution of silica present in the rock formation. The solubility of silica is a very complex process, on one hand is a function of several parameters such as pressure, temperature, particle size and structure of silica and pH of the aqueous solution. And on the other hand, depending on the pH different solute dissolutions are present, which are consequently involved in further hydration and dehydration reactions (Unger 1979),which are catalysed by hydroxide ion, where the hydration reaction results in the synthesis of monosilicic acid, (Chan 1989; Sazali et al. 2015). The base catalyzed reaction shown below, as proposed before, (Amjad and Zuhl 2008; Olajire 2014). 1 Si(OH )4 + OH − → Si(OH )− 3 + H2 O + O2 2 − Si(OH )− 3 + Si(OH )4 → (OH )3 Si − O − Si(OH )3 + OH

Dimer → Cyclic → Colloidal → AmophousSilica(scale)

6

1 Introduction

References Amjad Z, Zuhl RW 2008 An Evaluation of Silica Scale Control Additives. Nace, (8368):1–12 Atkinson G 1997 The chemistry of scale prediction. Journal of Petroleum Science and Engineering, 17:113–121 Bertero L, Chierici GL, Gottardi G, et al 1988 Chemical Equilibrium Models: Their Use in Simulating the Injection of Incompatible Waters. SPE Reservoir Engineering, 1 (February), 288–294 Chan SH 1989 A review on solubility and polymerization of silica. Geothermics, 18(1–2):49–56. https://doi.org/10.1016/0375-6505(89)90009-6 Chen T, Montgomerie H, Chen P, et al 2009 Development of Environmental Friendly Iron Sulfide Inhibitors for Field Application. SPE International Symposium on Oilfield Chemistry. https:// doi.org/10.2118/121456-MS Cowan JC, Weintritt DJ 1976 Water-Formed Scale Deposits. Presented at the Gulf Publishing Company. Knovel Crabtree M, Eslinger D, Fletcher P et al 1999 Fighting Scale — Removal and Prevention. Oilfield Review, 30–45 Jordan MM, Graff CJ, Cooper KN 2000 Development and deployment of a scale squeeze enhancer and oil-soluble scale inhibitor to avoid deferred oil production losses during squeezing lowwater cut wells, North Slope, Alaska. SPE International Formation Damage Control Symposium Proceedings, 149–166. https://doi.org/10.2523/58725-ms Kelland MA 2014 Production Chemicals for the Oil and Gas Industry (2nd ed.). CRC Press, Boca Raton, FL Mackay EJ, Jordan MM 2003 SQUEEZE Modelling: Treatment Design and Case Histories. Presented at the SPE European Formation Damage Conference. Society of Petroleum Engineers Mackay EJ, Jordan MM 2005 Impact of Brine Flow and Mixing in the Reservoir on Scale Control Risk Assessment and Subsurface Treatment Options: Case Histories. Journal of Energy Resources Technology, 127(3):201. https://doi.org/10.1115/1.1944029 Nasr-El-Din H, Al-Humaidan A 2001 Iron Sulfide Scale: Formation Removal and Prevention. Presented at the SPE International Symposium on Oilfield Scale. https://doi.org/10.2523/683 15-MS Olajire AA 2014 Review of ASP EOR (alkaline surfactant polymer enhanced oil recovery) technology in the petroleum industry: Prospects and challenges. Energy, 77:963–982. https://doi.org/ 10.1016/j.energy.2014.09.005 Przybylinski JL, Ruggeri JW, Wakley WD et al 1996 Optimization of Scale Inhibitor Squeeze Treatments in the Cedar Lake Unit. Presented at the NACE International Sazali RA 2018 The development of a test methodology and new findings in Silicate formation and inhibition. Heriot Watt University Seto CJ, Beliveau Da 2000 Reservoir souring in the caroline field. Presented at the SPE/CERI Gas Technology Symposium. https://doi.org/10.2118/59778-ms Sorbie KS, Mackay EJ 2000 Mixing of injected, connate and aquifer brines in waterflooding and its relevance to oilfield scaling. Journal of Petroleum Science and Engineering, 27(1–2):85–106. https://doi.org/10.1016/S0920-4105(00)00050-4 Unger K 1979 Porous Silica. (Elsevier Science, Ed.) Vazquez O, Mackay EJ, Sorbie KS 2012 A two-phase near-wellbore simulator to model non-aqueous scale inhibitor squeeze treatments. Journal of Petroleum Science and Engineering, 82–83:90–99. https://doi.org/10.1016/j.petrol.2011.12.030 Webb P, Kuhn O 2004 Enhanced Scale Management through the Application of Inorganic Geochemistry and Statistics. Proceedings of SPE International Symposium on Oilfield Scale, 1–14. https:// doi.org/10.2118/87458-MS Wylde JJ 2014 Sulfide Scale Control in Produced Water Handling and Injection Systems: Best Practices and Global Experience Overview. SPE International Oilfield Scale Conference and Exhibition, (169776). https://doi.org/10.2118/169776-MS

Chapter 2

Scale Management

Scale management not only consists of combating scale deposition. It also compromises several aspects including the prediction of which type scale will deposit and the maximum scale potential. This information is critical to evaluate the risk assessment and evaluating and selecting solutions. This methodology has been presented a number of times before (Jordan et al. 2001; Graham and Collins 2004; Mackay et al. 2005; Vazquez et al. 2016), in particular related to the increased cost and associated risk of scale management in deep water developments. This methodology suggest that scale control should be included in the asset life cycle management, where changes to the production systems could be implemented to accommodate scale control solutions. Such as an approach allows the implementation of changes in the asset development plan, for example, changes in the water injection strategies, production system and/or completion design. Water production plays an essential role in scale precipitation, scale will only be formed if water is present. The elements on the mineral equilibria presented before are water based. Scale may form in several locations, in injection and production wells, in the topside facilities or in the reservoir. Among these possible locations producing wells and topside facilities are the critical locations, and in addition, it is where most likely scale will be deposited. The prediction and treatment in topside facilities are more manageable than in producing wells, particularly in terms of accessibility and understanding of the system. The information about producing wells, in terms of conditions is somehow limited. Normally, oil producing wells produce a fraction of water, known as water-cut. Oilfield scale will deposit when the water cut is higher than zero, i.e., when water breaks through. To predict scale deposition is critical to know where the water along the well completion interval is produced. This information is of critical importance, to predict the location of scale deposits. If it is a pH dependent scale, considering the pressure profile and a thermodynamic model, the location of scale deposits can be identified. On the other hand, if the reservoir is under water flooding conditions, sulphate scale deposits are expected, the amount and location of deposit depends © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 O. Vazquez, Modelling Oilfield Scale Squeeze Treatments, SpringerBriefs in Petroleum Geoscience & Engineering, https://doi.org/10.1007/978-3-319-71852-1_2

7

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2 Scale Management

on where the mixing between injected seawater and formation brine occurs (Sorbie and Mackay 2000; Mackay and Jordan 2005), where sulphate stripping plays an important role in terms of scale management (Mackay et al. 2006). This is crucially important for long horizontal wells, where for instance, seawater breaks through at the toe of the well, this will imply the whole completion interval will need to be protected. Therefore, adequate placement of scale inhibitor chemical should be achieved, to ensure protection. On the other hand, if seawater breaks through at the heel of the well, mixing will only occur from the heel of the well downstream, and as a result, scale inhibitor will only need to be placed at the heel of the well to achieve full protection.

2.1 Predicting the Problem Scale risk deposition is described by the saturation state, which is calculated by flash calculations to determine the equilibrium in water of the mineral components, the maximum concentration is determined by the solubility of the particular mineral in water. To calculate the saturation state, we need to define the equilibria in water and the solubility, which is used to determine if a solution is supersaturated against any minerals. In this case, to identify which scales will deposit, which will vary with the varying conditions in the producing well, such as temperature, pressure and well water cut. No deposition will occur if water is not present in the well, carbonate scales deposition depends mainly on the pressure and temperature, whereas sulphate scales deposition is function of the degree of mixing between formation brine and injected seawater.

2.1.1 Equilibria in Water and Solubility The law of mass action is fundamental to describe equilibria in water, which states for a general reaction: a A + bB ↔ cC + d D The distribution of species at equilibrium is given by K =

[C]c [D]d [A]a [B]b

where the K is the equilibrium constant, and the bracketed quantities represent activities or “effective concentrations”. Equilibrium aqueous concentrations follows the solubility product, which is a direct application of the law of mass action, with the exception, by definition, that the activity of pure components is equal to one. Since,

2.1 Predicting the Problem

9

the law of mass action is only valid for the activity of ions, which considers the correction to the total concentration due to the electrostatic shielding and the presence of aqueous complexes. In thermodynamic terms, the activity is expressed as fraction relative to a standard state, and as a fraction, the activity is always dimensionless. For aqueous solutes, the standard state is defined as ideal solution with a concentration of 1 molal (1 mol per kg of H2 O). The activity is related to molal concentration, where the activity coefficient corrects for non-ideal behaviour. For aqueous solutes, the activity is defined as: [i] = γi ·

mi m i0

where [i] is the activity of ion i, γ i is the activity coefficient, mi is the molality (mol/Kg of H2 O) and m i0 is the standard state, i.e., 1 mol/Kg of H2 O. The activity coefficients can be calculated using the Hückel theory (Appelo and Postma 1993; Atkins and De Paula 2006). To calculate the state of saturation of a reaction, the solubility product K, which can be calculated using the activities at equilibrium, is compared to the product of activities from water samples, which is commonly known as the Ion Activity Product (IAP). Saturation conditions is terms of saturation state, Ω, is shown below. Ω=

I AP K

where Ω = 1 there is equilibrium between the mineral and the solution, Ω > 1 and Ω < 1 indicates supersaturation and subsaturation, respectively. The saturation index, SI, is the saturation state in logarithm scale. ( S I = log

I AP K

)

where SI = 0 there is equilibrium, SI > 0 and SI < 0 indicates supersaturation and subsaturation, respectively.

2.1.2 Thermodynamics of Mineral Scale The basic concept of thermodynamics of mineral scale, or more precisely chemical thermodynamics is an equation relating standard free energy change for a reaction to the equilibrium constant. The thermodynamic equilibrium constant, K, defined in the previous section. For a given reaction at a given pressure and temperature, reactants form products and the enthalpy H and entropy, S, change; determined by thermodynamic quantity defined by the equation G = H − TS, known as free Gibbs energy, introduced by the

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2 Scale Management

American physicist J. W. Gibbs in 1870s. The changes in H and S, are described by ΔH and ΔS, resulting in change of free energy, ΔG, given by the equation: ΔG = ΔH − ΔS The standard Gibbs free energy change occurs when the reactants in their standard states are converted to products in their standard states, which is given by the equation below: ΔG o = ΔH o − ΔS o The Gibbs energy, which is a thermodynamic function can be used to determine in which direction a process proceeds spontaneously under constant pressure and temperature. The change in Gibbs free energy for a general chemical reaction is given below: ΔG r = ΔG r0 + RT ln

[C]c [D]d [A]a [B]b

where R is the gas constant, and T the temperature. If ΔGr = 0 the reaction is at equilibrium, if ΔGr > 0 the reaction proceeds to the right and if ΔGr < 0 to the left. Using the equation above, it is possible to calculate the solubility in terms of thermodynamic data, from Gibbs energy data, as follows: Σ

ΔG 0f

products

−

Σ

ΔG 0f

reactants

= ΔG r0 = RT ln

[C]c [D]d [A]a [B]b

where ΔG 0f is the free energy of formation, i.e. the energy needed to produce one mole of a substance from pure components (Appelo and Postma 1993). To calculate the solubility as a function of temperature the Van’t Hoff equation could be used, see below: logK T1 − logK T2

) ( 1 1 −ΔHr0 − = 2.303 · R T1 T2

The reaction enthalpy can be calculated using the formation enthalpies, listed in thermodynamic tables. For exothermal reactions, the value is negative, i.e., energy is transferred to the surroundings and positive for endothermal reactions, energy is taken from the surroundings.

2.1 Predicting the Problem

11

2.1.3 Sulphate Scales Sulphate scales precipitate because of the mixing of incompatible brines, in particular seawater and formation brine. Seawater is rich in sulphate ions and formation brine with an excess of divalent ions such as among others barium, calcium, and strontium. Seawater flooding is very common in oil operations, for pressure support, particularly offshore and near coastal reservoirs, which is attributed to its abundance and relative compatibility with formation brines (Vetter et al. 1982; Yuan and Todd 1991; Bader 2006). Consequently, it is expected that some level of sulphate scale deposition will occur in every reservoir under seawater injection. Since the saturation of the sulphate salts depends on the mixing of incompatible waters, i.e., injected seawater and formation brine, it is common to represent the supersaturation as a function of the degree of mixing between seawater and formation brine, where generally the worst scaling conditions occur around 60% seawater percentage, which can be easily shown if we write the mineral equilibrium of sulphate scales: Ba 2+ (Sr 2+ or Ca 2+ ) + S O42− ↔ BaS O4(s) (Sr S O4(s) or CaS O4(s) ) The saturation state can be written as follows: Ω=

[Ba 2+ (Sr 2+ or Ca 2+ )] · [S O42− ] K sp

The barium and strontium sulphate supersaturation of an oilfield reservoir offshore of Norway is shown in Fig. 2.1, the formation and seawater composition can be found in Table 2.1 (Vazquez et al. 2016). The calculations were performed using PHREEQC C, a geochemical model, which accounts for the original acronym-pHREdox-EQuilibrium (Appelo and Postma 1993; Parkhurst and Appelo 1999). Table 2.2 shows the thermodynamic equilibrium constants at 25 °C for some of the most common sulphate salts. Clearly, BaSO4 is much more insoluble that the other sulphate scales. As a consequence, the deposition barium sulphate is one the worst and costly problems encountered in oilfield operations (Vetter 1975; Kelland 2014).

2.1.4 Carbonate Scales Among carbonate scales, the most common is calcium carbonate. Calcium carbonate precipitates due to a pressure drop, which causes the reduction of CO2 in solution, resulting in a lower water pH. The overall reaction between carbon dioxide and calcium carbonate precipitation is shown below: C O2(g) + H O2 + CaC O3(s) ↔ Ca 2+ + 2H C O3−

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2 Scale Management

Fig. 2.1 Barium and strontium sulphate supersaturation versus seawater fraction

Table 2.1 Formation and seawater compositions

Table 2.2 Sulphate scale salts thermodynamic equilibrium constants at 25 °C (Kharaka et al. 1989; Atkinson et al. 1992; Kaasa 1998; Dai et al. 2016)

Formation brine

Seawater

Na (mg/l)

39,600

11,510

K (mg/l)

466

420

Mg (mg/l)

772

1,410

Ca (mg/l)

3,030

Ba (mg/l)

366

Sr (mg/l)

626

SO4 (mg/l)

–

Alkalinity (mg/l)

2,200

435 0 7 2800 150

Value at 25 °C Ksp (BaSO4 )

10–9.96

Ksp (SrSO4 )

10–6.43

Ksp (CaSO4 2H2 O)

10–4.60

Ksp (CaSO4 )

10–4.33

The equation above is fundamental to determine the dissolution or precipitation of calcium carbonate. A decrease of CO2 gas, due to a pressure drop in the reservoir formation, will make the equilibrium to move to the left, resulting in calcium

2.1 Predicting the Problem

13

carbonate precipitation. On the other hand, an increase in CO2 gas results in the dissolution of calcium carbonate. To fully describe the calcium carbonate system, it is recommended to describe the carbonic acid system. When CO2 gas dissolves in water, it associates with water molecules to form carbonic acid H2 CO3 . For practical reasons and facilitate the calculations, and since the CO2 concentration in water is much higher than H2 CO3 , by convention both species are summed up as H2 C O3∗ . When carbonic acid dissociates, it releases two protons, therefore the dissolved carbonate species depends on the pH of solution. The equations to describe the equilibria of carbonic acid is shown below, with the corresponding equilibrium constants at 25 °C (Appelo and Postma 1993): H O2 ↔ H + + O H − , K w = [H + ] · [O H − ] = 10−14.0 [H2 C O3∗ ] C O2(g) + H O2 ↔ H2 C O3∗ , K H = = 10−1.5 [PC O2 ] [H + ][H C O3− ] H2 C O3∗ ↔ H + + H C O3− , K 1 = = 10−6.3 [H2 C O3∗ ] H C O3− ↔ H + + C O32− +, K 1 =

[H + ][C O32− ] = 10−10.3 [H C O3− ]

The distribution of dissolved carbonate species can be calculated in two idealised cases, termed as an open and closed systems with respect to CO2 .

2.1.4.1

Open System

It considers that the partial pressure of CO2 is constant and that [H2 C O3∗ ] is constant and independent of the pH. By taking the logs on the equations presented above, and by adding the last two equations, we obtain the following expressions: log[H2 C O3∗ ] = log[PC O2 ] − 1.5 log[H2 C O3− ] = −6.3 + log[H2 C O3∗ ] + p H Combining the last two equations, applying the law of mass action, and taking the-transformation H2 C O3* ↔ H + + H C O3− , H C O3− ↔ H + + C O32− , H2 C O3* ↔ 2H + + C O32−

K 1 = 10−6.3 +

K 2 = 10−10.3 Π K = 10−16.6

log[C O32− ] = −16.6 + log[H2 C O3∗ ] + 2 p H

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2 Scale Management

Fig. 2.2 Log activity of aqueous carbonate species as function of pH

Figure 2.2 shows the Log activity of aqueous carbonate species as function of pH for a constant gas pressure of CO2 of 0.01 atmospheres.

2.1.4.2

Close System

The system is closed respect to CO2 , where the sum of the dissolved carbonate species is considered constant and defined by the total inorganic carbon (TIC). T I C = [H2 C O3∗ ] + [H C O3− ] + [C O32− ] The distribution of aqueous carbonate species is determined by the fraction of each species, and is shown in Fig. 2.3. H2 C O3∗ [H2 C O3∗ ] = = T IC [H2 C O3∗ ] + [H C O3− ] + [C O32− ] 1+ [H C O3− ] T IC

=

[H C O3− ] [H2 C O3∗ ] + [H C O3− ]

+

[C O32− ]

=

1 K1 [H + ]

+ K1 · K2

1 1+

[C O32− ] [C O32− ] = = T IC [H2 C O3∗ ] + [H C O3− ] + [C O32− ] 1+

[H + ] K1

+

K2 [H + ]

1 [H + ] K2

+

[H + ]2 K 1 ·K 2

2.1 Predicting the Problem

15

Fig. 2.3 Distribution of aqueous carbonate species as a fraction of total inorganic carbon as function of pH

2.1.4.3

Calcium Carbonate System

Finally, to fully describe the calcium carbonate system and the partial pressure of CO2 , the dissociation calcite reaction is combined with the carbonic acid system: CaC O3 ↔ Ca 2+ + C O32− C O32− + H + ↔ H C O3− H2 C O3∗ ↔ H + + H C O3− C O2(g) + H2 O ↔ H2 C O3∗

C O2(g) + H2 O + CaC O3 ↔ Ca 2+ + 2H C O3−

2.1.4.4

K cc = 10−8.5 K 2−1 = 1010.3 K 1 = 10−6.3 K H = 10−1.5 + Π K = 10−16.6

Iron Carbonate System

Iron(II) carbonate is not commonly encountered in the oilfields, but still present (Kriel 1994). Although Iron (II) is common in produced brines, rarely reaches concentration higher than 100 ppm (Patton 1974), other source of iron(II) is corrosion carbon steel pipework. The deposition of iron carbonate in carbon steel pipework is greatly influenced by the corrosion rate in the underlying steel (Barker et al. 2018). The precipitation of iron carbonate is a function of pH and iron content, which follows the reaction below:

16

2 Scale Management

FeC O3 ↔ Fe2+ + C O32− C O32− + H + ↔ H C O3− H2 C O3∗ ↔ H + + H C O3− C O2(g) + H2 O ↔ H2 C O3∗

C O2(g) + H2 O + FeC O3 ↔ Fe2+ + 2H C O3−

K ic = 10−10.5 K 2−1 = 1010.3 K 1 = 10−6.3 K H = 10−1.5 + Π K = 10−8.0

2.1.5 Sulphide Scales Sulphide scales are less common than sulphate and carbonate scales, but if present they cause serious problems (Kelland 2014), they are commonly referred as “exotic” scales. However, occurrence of this type of scales is common in sour fields, where predominantly iron sulphide (FeS) precipitates (Nasr-El-Din and Al-Humaidan 2001). Other sulphide scales such as lead and zinc sulphide (PbS and ZnS respectively) have been observed in high pressure/high temperature fields (Jordan et al. 2000; Collins and Jordan 2001; Baraka-lokmane et al. 2014). Sulphide scales deposition is virtually inevitable due to their low solubility, which increases with salinity and decreases with increasing pH (Al-Harbi et al. 2019). FeS solubility decreases with temperature, whereas PbS and ZnS increases (Barrett and Anderson 1988; Shuler et al. 2000; Verri et al. 2017). Sulphide scales form as the result of the reaction of sulphide ion, sourced from hydrogen sulphide (H2 S), and a metal ion, such as iron (Fe), lead (Pb) and zinc (Zn). The mineral equilibrium of sulphide scales with the corresponding equilibrium constants at 20 °C is described below (Okocha and Sorbie 2013). H O2 ↔ H + + O H − , K w = 10−14.0 H2 S ↔ H + + H S − , K sp = 10−7.0 H S − ↔ H + + S 2− , K sp = 10−17.0 FeS(s) ↔ Fe2+ + S 2− , K sp = 10−18.9 Z nS(s) ↔ Z n 2+ + S 2− , K sp = 10−24.7 PbS(s) ↔ Pb2+ + S 2− , K sp = 10−27.4 Reservoir souring is the main source of hydrogen sulphide, the known mechanisms fall under two main categories, biotic and abiotic (Seto and Beliveau 2000; Cavallaro et al. 2007). Biotic reservoir souring is due to the metabolic activity of SRB (Sulphate Reducing Bacteria) (Maxwell and Spark 2005; Fannir et al. 2008; Thrasher and Vance 2014), which produce H2 S as a reduction product of respiration. There are two main theories about the presence of SRB in reservoirs, in one hand, one theory proposes that SRB are introduced in the reservoir formations by injecting non-biological treated water, forming biofilms on the rock surfaces, which will form colonies capable of

2.1 Predicting the Problem

17

sustaining growth and metabolic activity. The second theory proposes that SRB are native to the reservoirs, and with the injection of nutrients, via water injection, the colonies thrive, grow and initiate sulphate reduction (Sunde et al. 1993). Abiotic reservoir souring, i.e. by inorganic reactions, may occur by one of the following mechanisms reported before: thermochemical sulphate reduction (TSR) (Orr 2003), thermal hydrolysis of organic sulphur compounds (Clark et al. 1983), and finally hydrolysis of metal sulphides, such as pyrite, which is a common constituent of carbonate and clastic reservoir rocks (Marsland et al. 1989). These species can undergo oxidative, non-oxidative and reduction reactions releasing H2 S (Marsland et al. 1989; Hutcheon 1998; Seto and Beliveau 2000).

2.1.6 Sodium Chloride (Halite) Scale Halite scale deposition is normally detected in HPHT (High Pressure High Temperature) gas wells, deposits may be found in the near wellbore area, production lines and/or at surface equipment. Halite precipitation is mainly due to evaporation of the water phase into the gas phase, due to drop in pressure, which is likely to occur in wells with low water cut. Water vaporization depends on the reduction of temperature and pressure, which therefore affects the solubility in the formation brine. Evaporation is a gradual process, as it happens the ionic strength increases, and thus the water vapour pressure decreases, in certain circumstances evaporation might stop before Halite becomes saturated. There are a number of outcomes, depending on the total change in pressure, temperature and water cut (Vazquez et al. 2019): • Evaporation process stops, reaches equilibrium, before halite is saturated. • If Halite is inhibited, the evaporation process can stop, i.e., reach equilibrium, at a higher salinity and the solution is metastable. • Halite precipitates, but vapour becomes water saturated before all water has evaporated. • Evaporation continues, more salts precipitate until all the water has evaporated, resulting in all ions/salts precipitation—complete water evaporation. The solubility of NaCl (Halite) as function of temperature is shown in Fig. 2.4, the solubility increases with temperature, but possibly not as much as expected. The effect of pressure on the solubility is weaker than temperature, as shown in Fig. 2.5, however pressure plays an important role in water evaporation. Formation of NaCl is therefore a complex combination of pressure reduction, resulting in water evaporation, and reduction in temperature leading to less water evaporation, but also lower NaCl solubility.

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Fig. 2.4 Solubility of NaCl in pure water at 1 bar pressure or at water vapour pressure. Exp data Schroeder et al. (1935), Potter et al. (1977), Potter and Clynne (1978), Pitzer et al. (1984), Pinho and Macedo (2005)

Fig. 2.5 Effect of pressure on the solubility of NaCl. Experimental data from Sawamura et al. (2007)

2.1 Predicting the Problem

19

2.1.7 Silicate Scale Silicate scale deposition is triggered by the dissolution of silica present in rock formations. The solubility of silica is a very complex process, on one hand is a function of several parameters such as pressure, temperature, particle size and structure of silica and pH of the aqueous solution. And on the other hand, depending on the pH different solute dissolutions are present, which are consequently involved in further hydration and dehydration reactions (Unger 1979), which are catalysed by hydroxide ion, where the hydration reaction results in the synthesis of monosilicic acid (Chan 1989; Sazali et al. 2015). +O H −

Si O2 + 2H2 O ⮀ Si (O H )4 Although hydrolysis accelerates with increasing pH, the amount of soluble silica in the aqueous phase remains constants for pH between 1 and 9. At pH 9 silicate ions form in addition to monosilicic acid, and above pH 10.7, silica dissolves mainly as silicate ions (Unger 1979). ]− [ Si (O H )4 + O H − ⮀ Si (O H )5 When the concentration is high enough, in particular in supersaturated solutions, condensation occurs yielding polysilicic acids and water, where the reaction rate depends on pH, decreasing at pH above 9 (Chan 1989). Following the reaction below where a dimer is formed (Unger 1979). 2Si (O H )4 ⮀ (H O)3 Si − Si (O H )3 + H2 O Which is the basis to form cyclic, followed by colloidal species resulting in the deposition of amorphous silica scale (Amjad and Zuhl 2008; Arensdorf et al. 2010). In the presence divalent ions such as of magnesium, it can bridge the colloidal silicate particles forming amorphous magnesium silicate scale (Arensdorf et al. 2010).

2.1.8 Kinetics of Mineral Scale The kinetics of a reaction, such as the deposition mineral scale, determine how fast the reaction proceeds to thermodynamic equilibrium. NaCl and sulphate scales, such as BaSO4 and CaSO4 precipitate almost instantaneously if supersaturated, carbonate scales, even if supersaturated, may not precipitate for several hours or days (Kaasa 1998). Consider a simple reaction where a compound A is converted to compound B by a the following reaction (Appelo and Postma 1993):

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A→B Figure 2.6 depicts the concentration of compound A and B recorded with time, t. The reaction rate is the change of compound A with time. The rate, at a given time t, can be calculated as the slope of the tangent at the point (t, Ct ). The reactant, compound A, concentration decreases, therefore the rate is given a negative sign, i.e. the slope of the tangent is negative, while sign for the rate for compound B is positive, as the concentration of B increases with time. The reaction rate depends of the concentration of the reactants, which is referred as the reaction order. Given a generic reaction shown below, where reactants A and B are converted to product C: a A + bB → C, rate = k · C aA · C Bb Experimentally, it is possible to determine that the reaction rate is proportional to the ath power of reactant A and the bth power of the reactant B. The reaction is said to be of the ath and bth power respect compound A and B, with overall order n = a + b. The coefficient k, is the rate constant or specific rate, with units of concentration per time, such as mol/L/s. The effect of the of the reaction orders, i.e., how the concentration varies with time, shown in Fig. 2.7. Temperature has a great influence in most of reactions of reactions rates, the Arrehenius equation can be used to determine the specific rate as a function of temperature. ( k = A · exp

−E a RT

)

Concentration

where A is the pre-exponential factor, particular to each reaction, E a the reaction activation energy, T absolute temperature (Kelvin) and R is the universal gas constant.

B

Ct A t

Time

Fig. 2.6 Concentration of compound A and B as function of time

2.1 Predicting the Problem

21

Second order

Concentration

First order

Concentration

Concentration

Zeroth order

Time

Time

Time

Fig. 2.7 Rate laws for the reaction A → B

The rate of dissolution or growth of minerals depend on a number of processes, including transport of solutes between bulk solution and the mineral surface, and the reaction occurring at the mineral surface (Davis and Hayes 1986). In pure transportcontrolled growth, ions are attached so quickly to the surface of the crystal that the concentration adjacent to the crystal is lowered to the equilibrium or saturation concentration, determined by the solubility product. The rate of growth depends on how fast ions can migrate to the surface by advection and/or diffusion, determined by the hydrodynamic conditions in solution, resulting in faster growth rate in increased flow velocities or increased stirring. Surface-reaction controlled growth occurs when the attachment of ions to the surface is so slow that the concentration surrounding the mineral surface is close to the concentration is solution. If the surface-reaction is fast, the hydrodynamic conditions in solution may prevent the concentration adjacent to the mineral surface to reach the saturation concentration, resulting in an intermediate concentration. In this circumstances, the rate of growth is mixed control, depending on transport and surface-reaction (Berner 1980), see Fig. 2.8. A general rate law for the dissolution/precipitation reactions is presented below (Appelo and Postma 1993): R=k

Transport Control Ceq

Ceq

Csol

Csol 0

r

( ) Ao m n g(C) V mo Surface reaction control

Mixed Control Ceq

Csol 0

r

0

r

Fig. 2.8 Schematic concentration profiles for different rate controlling processes during dissolution. Ceq concentration at equilibrium saturation, Csol concentration in the bulk solution (Berner 1980)

22 Fig. 2.9 Regimes of crystal growth for the reaction A + B → AB, where pA = − log[A] and pB = −log[B] (Nielsen and Toft 1984)

2 Scale Management

1

2

pB

UnderSaturated

3 Metastable

4 Homogeneous nucleation

Heterogeneous nucleation

pA where R is the overall reaction rate, k is the specific rate, Ao is the initial surface area of the solid, V is the volume of solution, mo the initial number of moles of solid, m the number of moles of solid at a given time. The factor (m/mo )n accounts for changes in the surface area, due to changes to crystal size during dissolution/precipitation, changes to the distribution of crystal size population and changes to reactive surface sites. Finally, g(C) accounts for the effects of the solution composition on the rate, such as pH and/or how far the solution is from equilibrium. A rate equation for the dissolution quartz, including the saturation state is shown below (Rimstidt and Barnes 1980): Rquar t z = kquar t z · (1 − Ω) The rate is positive at subsaturation, zero at equilibrium and negative at supersaturation, which accounts for the different regimes of crystal formation, see Fig. 2.9. In region 1, only dissolution may take place (positive, Ω < 1), in region 2, crystals may grow but no nucleation takes place (close to zero, Ω ≈1), region 3 crystal growth may be accompanied by nucleation place (close to zero, Ω ≈1), and in region 4 (negative, Ω > 1), homogenous nucleation is possible at high enough supersaturation.

2.2 Life-Cycle Management of Scale Control Scale control is one of the most important flow assurance challenges faced in the oil industry. The term flow assurance is a relative new term in the oil industry. The term was first used by Petrobras in 1990 (Bai and Bai 2005; Irmann-Jacobsen 2012). Flow assurance may be defined as the ability to produce hydrocarbons economically from the reservoir to the end user over the lifetime of the reservoir (Mackay and

2.2 Life-Cycle Management of Scale Control

23

Jordan 2005). It is most critical in deep-water environments, such as in subsea fields, where deposition of solids will potentially block flowlines, preventing hydrocarbon production. Solids under concern are hydrates, wax, asphaltenes, sand and scale. Among these, possibly hydrates is the most widely recognised flow assurance challenges, followed by organic waxes, and finally inorganic scales (Graham et al. 2002). However, deposition of scale has been observed worldwide, but not exclusively in the North Sea, where seawater injection has been extensively used for pressure support and water flooding enhanced recovery. The challenges in subsea deepwater environments are much greater than those faced in simple vertical platform wells. The complexity of current well completions, particularly, horizontal and multilateral wells, subsea tie backs and comingled flow, present new challenges in terms of scale control, where the corresponding prevention or inhibition treatments are associated with high operational costs (Jordan et al. 2001). Due to the high cost associated to scale control, particularly in subsea deep-water developments, it is essential to evaluate all scale control options at the front-end engineering and design (FEED) stage of the project. At this stage, several techniques to deploy scale inhibitors are evaluated in the Capital Expenditure (CAPEX) phase, which is highly recommended. As opposed to reacting to the problem in the Operating Expenditure (OPEX) phase, where the flexibility to implement particular technologies is critically reduced (Graham et al. 2002). Implementing a scale management at the FEED stage may have an influence on the field development plans. For example, alternative sources of injection water, which are influenced by a number of factors such as water availability, production facility, well accessibility, completion types, type of reservoir and chemical delivery and monitoring options (Jordan et al. 2008). Produced water reinjection (PWRI) has been proposed a number of times (Mackay et al. 2003a; Østvold et al. 2010). Injecting 100% produced brine will minimise the risk of scale deposition, particularly sulphate scales, which are due to the mixing of incompatible brines. In occasions, it might be necessary to inject additional fluids to maintain reservoir pressure, which might not be compatible with the produced brine, and therefore scale might deposit. In other occasions, it has been proposed to reduce the sulphate concentration in the seawater to control the precipitation of barium sulphate (Hardy et al. 1994; Vu et al. 2000; Graham and Collins 2004; Jordan et al. 2008). Sweep patterns, production profiles and well placement can be designed to minimize scale deposition, by minimising equilibrium supersaturation near producing wells. In reservoirs under seawater injection for pressure support, sulphate scales deposit by brine mixing, if the mixing occurs deep in the reservoir, it might result in barium and/or sulphate stripping. As a consequence the scale regime could be potentially significant milder, which may have an important impact on scale management (Sorbie and Mackay 2000; Mackay et al. 2006). Finally, implementing the adequate well completion is important, particularly in circumstances where scale inhibitor continuous injection in producing wells, where chemical is injected via a capillary string or via a gas lift injection system. Continuous injection is necessary when high scaling conditions occur, particularly to prevent

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carbonate scales, which requires high concentration of chemical (Fleming et al. 2007; Goodwin et al. 2012; Hustad et al. 2012).

2.2.1 General Process to Quantify Inorganic Scale Risk As oil production environments are becoming more complex, such as deep water, subsea tiebacks, long horizontal wells, comingled flow and long production lines. The risk of formation damage associated to inorganic scale deposition may be so significant that conventional oil recovery such as water flooding, might become unviable, which could halt reservoir production. Scale precipitation may occur in any location, from water injection points, deep in the reservoir, producing wells, production lines and/or the surface facilities. Therefore, it is highly recommended to be aware of the risk of scale formation damage, and the consequences. The following steps should be follow to quantify the risk that scale deposition poses to a field development, which are outlined below (Mackay and Jordan 2005): 1. Representative brine samples collected from a real formation sampler (RFS) and drill stem test (DST), along with the injection water composition. 2. Identify of the key ions concentration, including accurate measurement of alaklinity and fatty acid content. 3. Determine if there has been any sample contamination. 4. Perform scale prediction calculations using thermodynamic simulator. 5. Asses the nature and location of scale deposits at the producer wells. 6. Study analog fields to identify risk and how they were managed. 7. Asses the economical and technical feasibility of scale control options. 8. Establish monitoring program to evaluate effectiveness of implemented scale technology (Jordan et al. 2005). Scale management need to be part of the asset lifecycle management, therefore any scale formation damage issues can be addresses prior to the field development/production (CAPEX phase) rather than faced with these problems in a reactive manner, once the first signs of formation damage occur during the OPEX phase, where the number of alternatives may be greatly reduced. Scale is a water production issue, therefore scale management within the lifecycle of the asset is directly related to water breakthrough and increasing water cut, as the production wells move from dry production to high water cuts. The types of scale and the severity of the scale regime is associated to the field development phases and production strategies. During natural depletion, the type of scale deposits is normally restricted to carbonate scales, which occurs when the CO2 dissolved in formation brine (connate or/and aquifer water) evolves as the reservoir pressure decreases. If water flooding is injected as secondary recovery, it can result in the precipitation of sulphate scales, which can be severe if barium is present in the formation brine. A scale management strategy selection process has been proposed before (Jordan et al. 2001; Mackay et al. 2005), a schematic flow process is presented in Fig. 2.10.

2.2 Life-Cycle Management of Scale Control

25

This is a multidisciplinary approach, involving the operator company, the service company and on some occasions a research institute. The first step is to analyse the formation brine composition, followed by thermodynamic calculations, to identify the type of deposits and the severity of the scale regime. The next step involves the use of a full field reservoir model, where the objectives are to evaluate on one hand the brine composition at the production wells, and on the other, to predict when water will breakthrough. If seawater injection is planned, reservoir simulation can be used to estimate the degree of mixing of injected seawater and formation brine, if the mixing occurs in deep in the reservoir will result in the deposition of sulphate scales (Sorbie and Mackay 2000). As consequence, barium and/or sulphate stripping might occur, resulting in lower scaling tendency (Mackay et al. 2003b, 2005, 2006). In addition, reservoir simulation can be used to perform placement calculations to evaluate if scale inhibitors could be bull-headed in production wells, via squeeze treatments, to protect the zones under risk of scaling. The final step involves the evaluation of the different scale control options, perform an economic evaluation and identify the most efficient scale control strategy.

Fig. 2.10 Scale management selection process

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2 Scale Management

2.2.2 Quantify Scale Risk Scale deposition can have a very significant impact on field economics, therefore is an important part in terms of scale management to consider the risk and uncertainties of scale control. This is of particular importance in deep-water subsea developments, where several wells production is comingled in a manifold, there is a clear risk that if one of the wells is not successfully protected, the whole production of the manifold could be lost, with the consequent considerable oil deferment and expensive work over operations. Evaluating the risk that scale poses to a development should follow the following steps as reported before (Jordan et al. 2001). First, obtain representative samples of the water chemical composition. Second, determine if during the field lifetime mineral scale will deposit, and assess the magnitude of the scale problem. And finally, review scale control techniques such as well completion design, batch treatment and/or injected seawater sulphate reduction. To quantify scale risk, first it is necessary to determine if scale will be deposited. Next, in order to successfully control scale deposition, the selected inhibition technology has to be effectively deployed A range of BP and industry data has been compiled and plotted in the form of a risk matrix of scale risk against intervention difficulty (Jordan et al. 2001; Collins 2003), which has been adopted by a number of authors to indicate the level of difficulty of scale management (Jordan et al. 2001; Graham and Collins 2004; Mackay et al. 2005). The scale risk evaluation is categorized in five categories as function of supersaturation scale index, shown in Table 2.3. To successfully treat scale deposition, the selected inhibition technology must be deployed effectively. The level of difficulty of deploying the technology depends on two factors, well accessibility and well completion. In terms of well accessibility, where accessibility from a platform well has the lowest difficulty, and a subsea well head the highest, and secondly in terms of the completion type, see Table 2.4. Wells are easily accessible from a platform, however for subsea development, the accessibility is significantly reduced with the extra well intervention costs, which includes the hiring of intervention vessels or mobile offshore drilling units. The overall intervention difficulty is obtained by multiplying the access value and the completion type. A risk matrix of scale risk against well intervention difficulty is shown in Fig. 2.11, where a number of field cases are shown (Jordan et al. 2001; Mackay et al. 2005). Table 2.3 Associated risk with the supersaturation scale index value

Supersaturation

Scale risk

3–29

1

30–99

2

100–199

3

200–299

4

>300

5

2.2 Life-Cycle Management of Scale Control

27

Table 2.4 Difficult factor as a function of well type, considering well accessibility and completion Access

Completion

Well type

Difficulty factor

Platform

1

Sub-sea, dry tree

1.5

Sub-sea wellhead

3

Cased and perforated, vertical

1

Cased and perforated, highly deviated

1.5

Short interval cased and perforated, gravel pack

1.5

Long interval cased and perforated, gravel pack

2

Short open hole gravel pack, low angle well

2.5

Long open hole gravel pack, high angle well

4

Fig. 2.11 Scale risk matrix for a number of fields

2.2.3 Scale Control Options There are at least four scale control options, which they should be evaluated and selected at the FEED stage on any new development will be reviewed below.

2.2.3.1

Fluid Modification

Injection water and formation brines are likely to be incompatible. Typically, the concentration of sulphate ions in the injection water is high, particularly in seawater, which will react with the cations present in the formation brine resulting in the precipitation of sulphate scales. Injection water can be modified to reduce the sulphate

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ion concentration to lower the saturation index (Hardy et al. 1994; Vu et al. 2000; Graham and Collins 2004; Jordan et al. 2008). A number of fields have proposed the use of sulphate removal plants to tackle the waterflood sulphate problem (Hardy et al. 1994; Davis et al. 1996; Andersen et al. 2000; Vu et al. 2000; McElhiney 2003).

2.2.3.2

Flow Modification

The volume of produce water can be reduced, commonly known as water-shut off treatments, where the most common ones are relative permeability modifiers, RPM (Zaitoun et al. 1999; Vazquez et al. 2007) and gel treatments (Seright and Liang 1994). In addition, it has been proposed the use of smart wells completed with inflow control valves, ICVs (Kavle et al. 2006). Modifying the flow may delay the problem, but it is unlikely that the scale problem will be completely removed, so other scale option may be necessary.

2.2.3.3

Damage Removal

If scale is deposited, there are several techniques to remove the deposits. It may be removed by chemical dissolution, generally known as scale dissolvers. Carbonate scales are dissolved by any acid, where the most common is hydrochloric acid, HCl (Kelland 2014). Iron sulphide scales can be dissolved by HCl and organic acids (NasrEl-Din and Al-Humaidan 2001) and alkaline chelating agents (Jordan et al. 2002). The standard dissolvers of sulphate scales are sodium salts of EDTA. Ethylenediaminetetraacetic acid (Jordan et al. 2002; Kelland 2014), but also greener chelate dissolvers have been proposed (Raymond et al. 2004). If the scale deposits cannot be removed by chemical dissolution, there are number of mechanical techniques such as milling and jet wash in coil tubing (Brown et al. 1991; Enerstvedt and Boge 2001).

2.2.3.4

Scale Prevention Using Chemical Scale Inhibitors

Once, prevention rather than remediation has been adopted as the strategy for scale control. The following aspects must be considered, chemical selection, where scale is forming and deployment method.

Chemical Selection To identify a suitable scale inhibitor chemical a number of laboratory tests are performed, which include scale prevention efficiency tests, compatibility tests, thermal aging tests, static retention tests and finally, dynamic coreflood experiments (Graham et al. 2001a, b; Mackay 2001).

2.2 Life-Cycle Management of Scale Control

29

Static bottle tests are commonly performed to rank the performance of sulphate scales, although it has been reported that this type of test may underestimate the scaling potential compared to flowing or stirred cells (Sutherland and Johnston 2013; Johnston et al. 2014; Yan et al. 2017). In dynamic tube blocking tests, the concentration of chemical inhibitor is gradually decreased until a pressure drop increase is recorded (Dyer and Graham 2002; Kelland 2014), which is commonly used to test the performance of carbonate scale inhibition, since it is challenging to control the pH is bottle test experiments. Compatibility tests are carried out to determine that no precipitation is observed when mixed with formation and injected brines. Although, precipitation may induced formation damage, if it occurs in the right location, i.e. in the formation, may be enhanced retention (Kelland 2014). Thermal aging tests are performed to evaluate the inhibition performance and stability with temperature, especially important for high temperature reservoirs (Guan and Farmer 2010). It consists in comparing the performance of the chemical aged in a static bottle and no aged. Static retention tests consists of a bottle test to evaluate adsorption and precipitation, it consists in evaluating the mass of chemical retained in different amount of crushed rock (Kahrwad et al. 2009; Jarrahian et al. 2019), where it is possible to differentiate between adsorption, typically at low concentrations, and precipitation. Dynamic coreflood, this test is the most important, it consists of flooding the reservoir core at reservoir conditions and post-flush with formation brine, where the scale inhibitor effluent is recorded. Then, a theoretical adsorption isotherm can be derived to estimate expected treatment lifetime (Sorbie et al. 1992). In addition, formation damage can be evaluated monitoring permeability changes.

Where Is Scale Forming? Scale may form deep in the reservoir, predominately sulphate scales due to mixing of incompatible brines, such as formation brine and seawater (Sorbie and Mackay 2000; Mackay et al. 2003b). Downstream from the near-wellbore area, carbonate and sulphate scales may deposit in gravel packs and/or perforations. Once the fluids enter the flow lines, scale may be formed in downhole safety valves (Johnston et al. 2014), and in surface facilities, such as separator and Vortoil deoiling hydrocyclones (Jordan et al. 2006).

Method to Deploy Scale Inhibitors The main methods to deliver scale inhibitor chemicals in the field are continuous injection, squeeze treatment and solid or encapsulated systems. Continuous injection can be carried out topside to protect surface facilities, usually applied at the wellhead, where other chemicals are injected, such as corrosion inhibitors. In addition, continuous injection can be deployed via capillary string

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or via gas lift injection system (Poggesi et al. 2002; Fleming et al. 2007). Continuous injection might be necessary in injector wells, especially if produced water reinjection is performed (Mackay et al. 2003a). Finally, continuous injection at the injectors has been proposed to protect producers (Samuelsen et al. 2009). Squeeze treatment consists of the injection of a scale inhibitor pill in a producer, when the chemical is in contact with the rock surface, it will be retained by precipitation and/or adsorption, and when the well is back in production, it will slowly be released in the production fluids, scale will be inhibited if the produced concentration is above a certain threshold, commonly known as Minimum Inhibitor Concentration (MIC). Squeeze treatment goal is to provide protection for the well downhole, however when the inhibitor is back produced, it will still provide protection to the downhole safety valves, and production flow lines. Although, it might protect topsides facilities, usually they are treated specifically, where a further dose might be required.

References Al-Harbi BG, Graham AJ, Sorbie KS (2019) Iron Sulfide inhibition and interaction with zinc and lead sulfides. SPE Prod Oper 34(03):551–563 Amjad Z, Zuhl RW (2008) An evaluation of silica scale control additives. Nace 08368:1–12 Andersen KI et al (2000) Water management in a closed loop—problems and solutions at brage field. In: SPE European petroleum conference held Appelo CAJ, Postma D (1993) Geochemistry, groundwater and pollution. A.A. Balkema, Rotterdam Arensdorf J et al (2010) Static and dynamic testing of silicate scale inhibitors. In: Society of Petroleum Engineers (SPE 132212), pp 8–10 Atkins PW, De Paula J (2006) Atkins’ physical chemistry. Oxford University Press, Oxford Atkinson G, Howell RD, Raju K (1992) Thermodynamics of “scale” mineral solubilities 4. Experimental measurements of SrSO4 (s) in H2 O and aqueous NaCl from 25 to 250 °C and from 1 to 500 bar. J Chem Eng Data 37(4):464–469. https://doi.org/10.1021/je00008a020 Bader MSH (2006) Sulfate scale problems in oil fields water injection operations. Desalination 201(1–3):100–105. https://doi.org/10.1016/j.desal.2005.09.039 Bai Y, Bai Q (2005) Subsea pipelines and risers. Elsevier Baraka-lokmane S et al (2014) TOTAL’s experience on the development and implementation of a scale management strategy in Central Graben Field. In: SPE international oilfield scale conference and exhibition Barker R, Burkle D, Neville A (2018) A review of iron carbonate (FeCO3 ) formation in the oil and gas industry. Corros Sci 142:312–341. https://doi.org/10.1016/j.corsci.2018.07.021 Barrett T, Anderson G (1988) The solubility of sphalerite and galena in 1–5 m NaCl solutions to 300 °C. Geochim Cosmochim Acta 52(4):813–820. https://doi.org/10.1016/0016-7037(88)903 53-5 Berner RA (1980) Early diagenesis: a theoretical approach. Princeton University Press, Princeton, NJ Brown ADF, Merrett SJ, Putnam JS (1991) Coil-tubing milling/underreaming of barium sulphate scale and scale control in the forties field, pp 79–95. https://doi.org/10.2118/23106-MS Cavallaro AN, Alberdi MI, Galliano GR (2007) Overview of H2S souring cases in Argentina reservoirs: origin and mitigation sceneries. In: SPE Latin American and Caribbean petroleum engineering conference Chan SH (1989) A review on solubility and polymerization of silica. Geothermics 18(1–2):49–56. https://doi.org/10.1016/0375-6505(89)90009-6

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Clark PD, Hyne JB, Tyrer JD (1983) Chemistry of organosulphur compound types occurring in heavy oil sands. 1. High temperature hydrolysis and thermolysis of tetrahydrothiophene in relation to steam stimulation processes. Fuel [Preprint]. https://doi.org/10.1016/0016-2361(83)90170-9 Collins I (2003) Scale management and risk assessment for deepwater developments. World Oil 224(5):62–69 Collins IR, Jordan MM (2001) Occurrence, prediction and prevention of zinc sulfide scale within Gulf coast and North Sea high temperature/high salinity production wells high temperature/high salinity production wells. In: 3th. international symposium on oilfield scale, pp 1–17 Dai Z et al (2016) A thermodynamic model for the solution density and mineral solubility predictions up to 250 °C, 1,500 Bars for Na-K-Mg-Ca-Ba-Sr-Cl-CO3 -HCO3 -SO4 -CO2 aq systems. In: SPE international oilfield scale conference and exhibition, pp 1–12. https://doi.org/10.2118/179 892-MS Davis JA, Hayes KF (1986) Geochemical processes at mineral surfaces. American Chemical Society Davis R, Lomax I, Plummer M (1996) Membranes solve North Sea waterflood sulfate problems. Oil Gas J 1–9 Dyer SJ, Graham GM (2002) The effect of temperature and pressure on oilfield scale formation. J Petrol Sci Eng 35(1–2):95–107. https://doi.org/10.1016/S0920-4105(02)00217-6 Enerstvedt E, Boge H (2001) Scale removal by milling and jetting with coiled tubing. In: SPE/ICoTA coiled tubing roundtable Fannir J et al (2008) Is oilfield souring impacted by minerals and mineralization? In NIF oilfield chemistry symposium 20, pp 1–15 Fleming N et al (2007) Development and implementation of a scale-management strategy for Oseberg Sør. SPE Prod Oper 22(03):307–317. https://doi.org/10.2118/100371-PA Goodwin NJ et al (2012) Qualification procedure for continuous injection of chemicals in the well—method development. In: SPE international conference and exhibition on oilfield scale Graham GM, Collins IR (2004) Assessing scale risks and uncertainties for subsea marginal field developments. In: SPE international symposium on oilfield scale Graham GM, Dyer SJ et al (2001a) Comparative core flooding and field application implications for scale inhibitor downhole squeeze treatments in high temperature (374F) reservoirs. In: SPE international symposium on oilfield chemistry Graham GM, Wattie I et al (2001b) Scale inhibitor selection criteria for downhole (SQUEEZE) application in a chalk reservoir. In: SPE international symposium on oilfield chemistry Graham GM et al (2002) The challenges for scale control in deepwater production systems: chemical inhibition and placement. In: Corrosion Guan H, Farmer P (2010) Evaluation of scale inhibitors suitable for deepwater fields. In: Society of Petroleum Engineers—SPE Asia pacific oil and gas conference and exhibition 2010, APOGCE 2010, 1 (May), pp 106–116. https://doi.org/10.2118/131110-ms Hardy JA, Barthorpe RT, Rhudy JS (1994) Scale control in the South Brae field. SPE Prod Facil 9(2):127–131. https://doi.org/10.2118/25141-PA Hustad BM et al (2012) Downhole chemical injection lines—why do they fail ? Experiences, challenges and application of new test methods (May) 30–31 Hutcheon I (1998) The potential role of pyrite oxidation in corrosion and reservoir souring. J Can Pet Technol 37(1):27–31. https://doi.org/10.2118/96-95 Irmann-Jacobsen TB (2012) Flow assurance—a system perspective. MEK4450 Offshore Technology Course, universitet i Oslo, Matematisk Institutt [Preprint] Jarrahian K et al (2019) Experimental Investigation of the interaction between a phosphate ester scale inhibitor and carbonate rocks for application in squeeze treatments. Energy Fuels 33(5):4089– 4103 Johnston C, Sutherland L, Herrman T (2014) The influence of turbulence (or hydrodynamic effects) on strontium sulphate scale formation and inhibitor performance. In: Society of Petroleum Engineers—SPE international conference and exhibition on oilfield scale 2014, pp 167–176. https:// doi.org/10.2118/169760-ms

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Jordan MM et al (2000) Inhibition of lead and zinc sulphide scale deposits formed during production from high temperature oil and condensate reservoirs. In: SPE Asia Pacific oil & gas conference. https://doi.org/10.2118/64427-ms Jordan MM et al (2001) Life cycle management of scale control within subsea fields and its impact on flow assurance, Gulf of Mexico and the North Sea Basin. In: SPE annual technical conference and exhibition, pp 1971–1986. https://doi.org/10.2118/71557-MS Jordan MM et al (2002) The design and deployment of enhanced scale dissolver/squeeze treatment in subsea horizontal production wells, North Sea Basin. In: SPE international symposium on formation damage. https://doi.org/10.2118/73717-MS Jordan MM, Buckman J, Johnston CJ (2005) Direct monitoring of the performance of scale control programs across the produced water life cycle via suspended solids analysis. In: SPE European formation damage conference Jordan MM, Johnston CJ, Robb M (2006) Evaluation methods for suspended solids and produced water as an aid in determining effectiveness of scale control both downhole and topside. SPE Prod Oper 21(1):7–18. https://doi.org/10.2118/92663-pa Jordan MM, Collins IR, Mackay EJ (2008) Low sulfate seawater injection for barium sulfate scale control: a life-of-field solution to a complex challenge. SPE Prod Oper 23(02):192–209. https:// doi.org/10.2118/98096-PA Kaasa B (1998) Prediction of pH, mineral precipitation and multiphase equilibria during oil recovery. Norges Teknisk-Naturvitenskapelige Universitet (NTNU) Kahrwad M, Sorbie KS, Boak LS (2009) Coupled adsorption/precipitation of scale inhibitors: experimental results and modeling. SPE Prod Oper 24(03):481–491 Kavle V, Elmsallati S, Davies D (2006) Impact of intelligent wells on oilfield scale management. In: SPE Europec/EAGE annual conference and exhibition [Preprint]. https://doi.org/10.2523/100 112-MS Kelland MA (2014) Production chemicals for the oil and gas industry, 2nd edn. CRC Press, Boca Raton, FL Kharaka Y, Gunter W, Aggarwal P (1989) SOLMINEQ. 88: a computer program for geochemical modeling of water-rock interactions Kriel BG (1994) The performance of scale inhibitors in the inhibition of iron carbonate scale. In: SPE international symposium on formation damage control. https://doi.org/10.2118/27390-ms Mackay EJ (2001) SQUEEZE modelling: current best practice and new capabilities. In: SPE international symposium on oilfield scale Mackay EJ, Jordan MM (2005) Impact of brine flow and mixing in the reservoir on scale control risk assessment and subsurface treatment options: case histories. J Energy Res Technol 127(3):201. https://doi.org/10.1115/1.1944029 Mackay EJ et al (2003a) PWRI: scale formation risk assessment and management. In: International symposium on oilfield scale [Preprint]. https://doi.org/10.2118/80385-MS Mackay EJ, Jordan MM, Torabi F (2003b) Predicting brine mixing deep within the reservoir and its impact on scale control in marginal and deepwater developments. SPE Prod Facil 18(3):210–220. https://doi.org/10.2118/85104-PA Mackay E et al (2005) Integrated risk analysis for scale management in deepwater developments. SPE Prod Facil (May) 138–154. https://doi.org/10.2118/87459-PA Mackay E et al (2006) Impact of in-situ sulfate stripping on scale management in the Gyda field. In: SPE international oilfield scale symposium. https://doi.org/10.2118/100516-MS Marsland SD, Dawe RA, Kelsall GH (1989) Inorganic chemical souring of oil reservoirs. In: SPE international symposium on oilfield chemistry [Preprint]. 18480-MS Maxwell S, Spark I (2005) Souring of reservoirs by bacterial activity during seawater waterflooding. In: SPE 93231, SPE international symposium on oilfield chemistry, pp 1–9. https://doi.org/10. 2523/93231-MS McElhiney J (2003) Deepwater project economics demand sulfate removal to ensure scale-free operation. Offshore 1–9

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Nasr-El-Din H, Al-Humaidan A (2001) Iron sulfide scale: formation removal and prevention. In: SPE international symposium on oilfield scale. https://doi.org/10.2523/68315-MS Nielsen AE, Toft JM (1984) Electrolyte crystal growth kinetics. J Cryst Growth 67(2):278–288. https://doi.org/10.1016/0022-0248(84)90188-X Okocha C, Sorbie K (2013) Scale prediction for iron, zinc, and lead sulfides and its relation to scale test design. In: SPE international symposium on oilfield chemistry. https://doi.org/10.2118/164 111-MS Orr W (2003) Changes in sulfur content and isotopic ratios of sulfur during petroleum maturation— study of big horn basin paleozoic oils. AAPG Bull [Preprint]. https://doi.org/10.1306/83d91b9b16c7-11d7-8645000102c1865d Østvold T, Mackay EJ, McCartney RA (2010) Re-development of the Frøy field: selection of the injection water. In: SPE international conference on oilfield scale Parkhurst DL, Appelo CAJ (1999) User’s guide to PHREEQC (version 2). U S Geological Survey water-resources investigations report 99-4259 Patton CC (1974) Oilfield water systems. Campbell Petroleum Series Pinho SP, Macedo EA (2005) Solubility of NaCl, NaBr, and KCl in water, methanol, ethanol, and their mixed solvents. J Chem Eng Data 50(1):29–32. https://doi.org/10.1021/je049922y Pitzer KS, Peiper JC, Busey RH (1984) Thermodynamic properties of aqueous sodium chloride solutions. J Phys Chem Ref Data 13(1):1–102 Poggesi G, Hurtevent C, Buchart D (2002) Multifunctional chemicals for West African deep offshore fields. In: International symposium on oilfield scale, Aberdeen. https://doi.org/10.2118/ 74649-MS Potter II RW, Clynne MA (1978) Solubility of highly soluble salts in aqueous media—Part 1, NaCl, KCl, CaCl2 , Na2 SO4 , and K2 SO4 solubilities to 100 °C. J Res US Geol Surv 6(6):701–705 Potter RW, Babcock RS, Brown DL (1977) New method for determining the solubility of salts in aqueous solutions at elevated temperatures. J Res US Geol Surv 5:3 Raymond B et al (2004) Creating value with green barium sulphate scale dissolvers-development and field deployment on statfjord unit. In: International symposium on oilfield scale (December 2003), pp 1–11 Rimstidt JD, Barnes HL (1980) The kinetics of silica-water reactions. Geochim Cosmochim Acta 44(11):1683–1699. https://doi.org/10.1016/0016-7037(80)90220-3 Samuelsen EH et al (2009) Downhole scale control through continuous injection of scale inhibitor in the water injection—a field case. In: Tekna oilfield chemistry symposium Sawamura S et al (2007) Solubility of sodium chloride in water under high pressure. Fluid Phase Equilib 254(1–2):158–162. https://doi.org/10.1016/J.FLUID.2007.03.003 Sazali RA, Sorbie KS, Boak LS (2015) The effect of pH on silicate scaling. In: SPE European formation damage conference and exhibition Schroeder WC, Gabriel A, Partridge EP (1935) Solubility equilibria of sodium sulfate at temperatures of 150 to 350°. I. Effect of sodium hydroxide and sodium chloride. J Am Chem Soc 57(9):1539–1546. https://doi.org/10.1021/ja01312a010 Seright RS, Liang J (1994) A survey of field applications of gel treatments for water shutoff. In: Proceedings of SPE Latin America/Caribbean petroleum engineering conference, pp 221–231. https://doi.org/10.2523/26991-MS Seto CJ, Beliveau DA (2000) Reservoir souring in the caroline field. In: SPE/CERI gas technology symposium. https://doi.org/10.2118/59778-ms Shuler PJ et al (2000) Modeling of scale deposition in gas wells with very saline produced water. In: NACE—international corrosion conference series. http://www.onepetro.org/mslib/servlet/onepet ropreview?id=NACE-00629 Sorbie KS, Mackay EJ (2000) Mixing of injected, connate and aquifer brines in waterflooding and its relevance to oilfield scaling. J Petrol Sci Eng 27(1–2):85–106. https://doi.org/10.1016/S09204105(00)00050-4 Sorbie KS, Wat RMS, Todd AC (1992) Interpretation and theoretical modeling of scaleinhibitor/tracer corefloods. SPE Prod Eng 7(03):307–312

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Sunde E et al (1993) Field-related mathematical model to predict and reduce reservoir souring. In: SPE international symposium on oilfield chemistry, SPE 25197, pp 449–456. https://doi.org/10. 2118/25197-MS Sutherland L, Johnston C (2013) The influence of turbulence (or hydrodynamic effects) on barium sulphate scale formation and inhibitor performance. In: SPE international symposium on oilfield chemistry Thrasher DR, Vance I (2014) Reservoir souring: mechanisms and prevention. In: Petroleum microbiology. https://doi.org/10.1128/9781555817589.ch7 Unger K (1979) Porous silica. Edited by Elsevier Science. https://books.google.co.uk/books?id= YbCLx3ydMmsC&pg=PA12&lpg=PA12&dq=dissolution+of+silica+hydration+and+dehydr ation&source=bl&ots=dQ2v6TZaex&sig=x-djuWNm2K5k_idBKjC6tAO8HNc&hl=en&sa= X&ved=0ahUKEwjh-Km3gqrXAhUHPRoKHfHBBmwQ6AEINTAC#v=snippet&q=silica& f=fal Vazquez O et al (2007) Sensitivity study on the main factors affecting a polymeric RPM treatment in the near-wellbore region of a mature oil-producing well. In: Proceedings of international symposium on oilfield chemistry [Preprint]. https://doi.org/10.2118/106012-MS Vazquez O, Fursov I, Mackay EJ (2016) Automatic optimization of oilfield scale inhibitor squeeze treatment designs. J Petrol Sci Eng 147:302–307. https://doi.org/10.1016/j.petrol.2016.06.025 Vazquez O, Kaasa B, Johnston C (2019) Optimisation of halite squeeze treatments in offshore gas wells. In: NIF oilfield chemistry symposium Verri G et al (2017) Iron sulfide scale management in high-H2 S and -CO2 carbonate reservoirs. SPE Prod Oper 32(03):305–313. https://doi.org/10.2118/179871-pa Vetter OJG (1975) How barium sulfate is formed: an interpretation. J Petrol Technol 27(12):1515– 1524. https://doi.org/10.2118/4217-PA Vetter OJ, Kandarpa V, Harouaka A (1982) Prediction of scale problems due to injection of incompatible waters. J Petrol Technol 34(02):273–284. https://doi.org/10.2118/7794-PA Vu VK, Hurtevent C, Davis R (2000) Eliminating the need for scale inhibition treatments for Elf exploration Angola’s Girassol field. In: SPE international symposium on oilfield scale Yan F et al (2017) Barite scale formation and inhibition in laminar and turbulent flow: a rotating cylinder approach. J Petrol Sci Eng 149(October 2016):183–192. https://doi.org/10.1016/j.petrol. 2016.10.030 Yuan MD, Todd AC (1991) Prediction of sulfate scaling tendency in oilfield operations. SPE Prod Eng 6(1):63–72. https://doi.org/10.2118/18484-PA Zaitoun A et al (1999) Water shutoff by relative permeability modifiers: lessons from several field applications. In: SPE annual technical conference and exhibition [Preprint]. https://doi.org/10. 2523/56740-MS

Chapter 3

Scale Inhibitors

This is a brief introduction to scale inhibitors; a much deeper and detailed review can be found in the manuscript authored by Cowan and Weintritt. The intention is to provide a brief historical overview of the use of scale inhibitors in oilfield and water applications. Scale deposition has been present for quite some time, 19 centuries ago, the Romans reported calcium carbonate scale deposits in their water canals (Underhill 1969). During the nineteenth century, natural materials such as tannins, starch and lignin were used to prevent scale deposits in the interior of water boilers (Gill 1996). In the 1930s, the “Threshold Treatment” theory was proposed, (Hatch and Rice 1939), to explain the prevention of calcium carbonate precipitation in the presence of few parts per million of polyphophates, between 1 and 5 ppm. This theory states that phosphates prevent the formation scale by keeping the scale crystals in the submicroscopic range by impeding the crystal growth rather than stopping the initial formation of scale crystal nuclei (Featherston et al. 1959). Phosphates molecules attached on the crystal nuclei surface preventing further growth. Although, the benefits were demonstrated to prevent scale in industrial and municipal water systems. The use of solid phosphates was not regularly reported in oilfield applications. Solid phosphates such as sodium hexametaphosphate dissolve rapidly in water, therefore not suitable for oilfield applications, where a slow controlled solubility is necessary to provide protection over a long period of time. In the 1950s, controlled solubility phosphates crystals were developed (Cowan and Weintritt 1976). During the 1960s controlled solubility phosphate were common in the oil industry. Two methods were proposed to treat scale in producing oil and injection wells. On one hand, phosphate particles may be placed at the bottom of the well (Sloat 1963), where long treatments were accomplished by careful selection of particle size and chemical composition in relation to the formation brine composition and reservoir temperature. Another alternative is to place phosphates particles in hydraulic induced fractures, which involves mixing the phosphate solids and the propping agents injected during a fracture treatment (Earlougher and Love 1957). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 O. Vazquez, Modelling Oilfield Scale Squeeze Treatments, SpringerBriefs in Petroleum Geoscience & Engineering, https://doi.org/10.1007/978-3-319-71852-1_3

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There are several problems associated with this kind of treatment. On one hand, deposits on the phosphate solids may results in a reduction of the dissolution rate, and on the other, fracture treatments are expensive, which may be difficult to justify due to the frequency of these treatments. Alternative materials to the inorganic phosphate were found, such as organophosphorous derivatives, polyacrylates and partially hydrolysed polyacrylamides, which showed additional advantages. These materials could be used to treat the formation with slow release of scale inhibitor, which do not require fracturing. Solid type phosphate inhibitors are not always suitable as oilfield scale inhibitors, they cannot be placed in the desired location at a specific time. Hydrolytically stable scale inhibitors are much more desirable than solid inhibitors, such as organic phosphonates. These materials are as effective preventing scale precipitation, but they can be deployed as liquid and are characterised by satisfactory adsorption and desorption properties (Ralston 1969). These liquid inhibitors can be placed in the formation by matrix squeeze, a technique that consists of injecting the liquid inhibitors into the formation below fracture pressure, the inhibitor adsorbs on the rock matrix, and slowly desorbs in the produced water providing protection for long-lasting periods, (Smith et al. 1968; Skyler 1969). The use of derivatives of natural polymers such as starches, gums, alignates, lignins, tanins and humic acid has been well documented, with numerous patents (Cowan and Weintritt 1976). Since the late 1950s, synthetic polymers have been commonly used as scale inhibitors, they vary in chemical nature, physical properties, and performance. The most common polymer scale inhibitor are polyacrylates, polymethacrylates, polyacrylamides and partially hydrolysed polyacrylamides.

3.1 Type of Scale Inhibitors Scale inhibitors are water soluble chemicals that prevent the deposition of inorganic scales, which may block or hinder fluid through pipelines, valves, and pumps. The most important characteristic of a scale inhibitor is the ability of inhibit scale at very low concentrations, normally few ppm, known as threshold scale inhibition (Liu and Nancollas 1975; Breen et al. 1990; van der Leeden and van Rosmalen 1990; Graham et al. 2003). The threshold effect is a consequence that these additives are active at low doses, because of their strong interaction with the crystal surface. The formation of several bonds between the ions in the crystal surface and the additives, it is because it is more energetically favourable than remain in the bulk of the solution. It is generally accepted that relative small inhibitor molecules like phosphonates are likely to be absorbed on the crystal surface growth sites (Weijnen and Van Rosmalen 1986). For larger polyelectrolyte inhibitors preferential adsorption is unlikely due to the loss of entropy. Although, random adsorption may be expected, crystal growth will be retarded by hampering consecutive growth layers and by the diffusion of crystal units towards active growth sites (van der Leeden and van Rosmalen 1990). The adsorption of inhibitor molecules on the crystal surface

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growing leads to the alteration crystal growth, crystal morphology, tendency to agglomerate and nucleation rate (Naono 1967; van der Leeden and van Rosmalen 1990). Classification of the type of inhibitors, regardless of the inhibition mechanism, may be done based on the nature of the scale to be protected, as suggested before (Kelland 2014).

3.1.1 Carbonate and Sulphate Scales The most common oilfield scales are carbonate and sulphate scales, which consists of divalent anions, CO3 2− and SO4 2− respectively, and a divalent metal cation, such as Ca2+ , Ba2+ and Sr2+ . Any inhibitor needs to interact either with the cation or the anion to be effective, regardless of the inhibition mechanism. There are several anionic groups that can interact well with divalent cations such as phosphate ions (–OPO3 H− ), phosphonate ions (–PO3 H− ), phosphinate ions (–PO2 H− ), carboxylate ions (–COO− ) and sulphonate ions (–SO3 − ). The most common scale inhibitors containing these ions, are polyphosphates, phosphate esters, nonpolymer phosphonates, aminophosphonates, polyphosphonates, polycarboxylates, phosphino polymers, polyphosphinates and polysulfonates. A broader classification will be adopted, which is common in the oil industry, phosphonates and polymers.

3.1.1.1

Phosphonates Versus Polymers

Phosphonate scale inhibitors are considered to prevent more efficiently scale precipitation than their polymeric analogues, whereas polymeric species show higher degree of biodegradability (Inches et al. 2006; Jordan et al. 2012). The presence of phosphonate groups is thought to improve scale control performance, in terms of retention and inhibition efficiency (Singleton et al. 2000; Fleming et al. 2004; Shaw 2012). But the presence of phosphonate functionality reduces the biodegradability, which is a main disadvantage. A high content of phosphorous, such as in phosphonate based chemicals, are categorised as “red” chemicals by OSPAR (Jordan et al. 2012). There have been numerous studies in the last couple of decades to identify “green” chemistries, i.e. biodegradable scale inhibitors with low toxicity (Ping et al. 2002; Kohler et al. 2004). Some of the most common scale inhibitors used in the oil industry, are presented below. DETPMP, Fig. 3.1, is possibly the most common use scale inhibitor in the oil industry, it shows great efficiency inhibiting sulphate and carbonate scales. PPCA is the most phosphino polymer used in the oil industry, see Fig. 3.2, it consists of a phosphino group attached to two polyacrylic chains, the presence of phosphorous makes the PPCA monitoring much easier, which can be detected by ICP-MS, inductively coupled plasma mass spectrometry. PVS, see Fig. 3.3, is a stronger acid with a lower pKa value than phosphonic or carboxylic based scale inhibitors, therefore they can operate at lower pH, they are Ca and Mg tolerant and have a high thermal

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3 Scale Inhibitors HO

O P OH

HO

OH

OH

HO

O

HO P

P HO

P

N

N

P O

OH

N

O

O

OH

Fig. 3.1 Chemical molecular structure of DETPMP (DiEthylene Triamine Penta Methylene Phosphonic acid

Fig. 3.2 Chemical molecular structure of PPCA (Polyphosphinocarboxylic acid)

O

HO

OH

O

O

H

P

mOH

n

H

Fig. 3.3 Chemical molecular structure of PVS (PolyVinylSulphonate)

stability (Sorbie and Laing 2004). Polymeric SIs such as PVS and VS-Co, see Fig. 3.4, display good scale inhibition properties, in certain circumstances even better than other inhibitor types, however, they do not exhibit good retention properties (Chilcott et al. 2000; Singleton et al. 2000).

3.1.2 Sulphide Scale Inhibition To prevent the deposition of this type of scale, two approaches have been proposed. On one hand, the use of chelating agents, or on the other the use of scale inhibitors

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39

Fig. 3.4 Chemical moleculecular structure of VS-Co (VinylSulphonate Acrylic Acid Co-Polymer)

H H

m

n O

S OH

HO

O O

(Collins and Jordan 2003). Chelating agents work by forming a stable water-soluble complex with metal ions, which prevents the reaction. Chelation is a stoichiometric reaction between the chelant agent and the metal ion in solution, therefore the amount of necessary chelant to prevent scale precipitation is directly proportional to the metal ion concentration. Other, divalent or trivalent cations in solution may interact with the chelant, resulting in increased dosage of chelant to effectively prevent scale deposition. Two of the most widely used chelating agents are Na4 EDTA (tetrasodium salt of ethylenediaminetetraacetic acid) and Na5DTPA (pentasodium salt of diethylen-etriaminepentaacetic acid). There has been numerous studies investigating the inhibition efficiency of different chemistries (Jordan et al. 2000; Collins and Jordan 2003; Baraka-lokmane et al. 2014; Okocha et al. 2018; Al-Harbi et al. 2019). Although, phosphonate scale inhibitors such as DETMP, were effective at sub-stoichiometric concentrations preventing deposition, it is unclear if the inhibition was due to a reduction of pH, DETPMP being a strong acid, or because of threshold scale inhibition, (Collins and Jordan 2003). Polymeric species provide better performance than phosphonates, which is clearly because of threshold scale inhibition. Even though the threshold inhibitor concentration is significantly higher than for conventional sulphate and carbonate scales, 25–30 ppm for sulphide scales and 2–5 ppm for sulphate/carbonate scales. The use of scale inhibitors appears to be more cost effective than the use of chelating agents, which are not be effective at sub-stoichiometric concentrations (Jordan et al. 2000).

3.1.3 Halite Inhibition Halite precipitation is primarily controlled by dilution, which consists in the injection of fresh water or low-salinity water, either in a batch mode or continuous injection (Wat et al. 2010; Aquilina 2012; Wylde and Slayer 2013), and enhanced with the addition of a precipitation inhibitor (Johnston et al. 2017). The main drawback of this technique, it is the large volumes of water required to dissolve the Halite deposits or to reduce the ion concentration sufficiently, so the formation brine becomes Halite

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undersaturated. The large volumes of water necessary makes this technique unsustainable, due to the logistical limitations (Wylde and Slayer 2013). Moreover, the dilution water may need to be deoxygenated, to prevent corrosion, and compatible with the production brine. The injected water might contain high concentration of ionic species, such as calcium, sulphate and bicarbonate, which might not be compatible with the formation brine, resulting in scale precipitation (Ho et al. 2013, 2014; Lu et al. 2015; Goodwin et al. 2016). It is likely that the source water might need to undergo extensive treatment to prevent corrosion, scale deposition and/or clay swelling. Due to the logistical challenges posed to control Halite precipitation by water dilution, chemical inhibition has been proposed as an alternative approach. A number of halite inhibitors have been validated in laboratory trials and some of them in field trials. Conventional scale inhibitors mentioned before, which are very efficient scale inhibitors will be not be adequate to control Halite precipitation, due to the fact that Halite contains a monovalent cation (Kelland 2014). Polyacrylic acid has been reported to be poor Halite precipitation inhibitor (Zhang et al. 2019). Several Halite inhibitors have been validated in laboratory trials and some of them in field trials, such as carboxylic acid-based inhibitor (Ho et al. 2014), potassium hexacyanoferrate used to inhibit halite in topside equipment (Frigo et al. 2000), multifunctional polymeric species that inhibits carbonate and sulphate scales as well as Halite (Spicka et al. 2012), and nitrilotriacetamide (NTAA) (Wylde and Slayer 2013). A polymeric species with an organic compound as active component, which was bench marked against NTAA has also been proposed (Guan et al. 2008).

3.1.4 Silicate Scale Inhibition There have been numerous studies focused on silicate scaling inhibition by chemical additives. The main approaches include: inhibiting silica polymerization, increasing the silica solubility as it forms, and dispersion of precipitated silica and silicate compounds using polymeric dispersants (Amjad and Zuhl 2008). Cationic-based copolymers have been reported to be efficient materials to inhibit silica polymerization (Amjad and Yorke 1985); similar results were obtained under geothermal conditions using cationic polymers and surfactants (Harrar et al. 1982). These catanionic homo- and co-polymers were excellent polymerization inhibitors, but they were not very efficient as dispersants. A number of organic additives were tested in the lab and in field tests, it was concluded that these additives primarily function as dispersants of colloidal silica particles, which if overdosed could lead to the agglomeration/flocculation (Gallup 2002). Some of them showed promising results controlling scale deposition, although they could not outperform high temperature injection or brine acidification by organic acids. Non-polymeric additives, including phosphonate groups were reported to be ineffective as silica inhibitors, it was suggested that the phosphonate groups do not prevent silica polymerization (Amjad and Zuhl 2009). The authors also investigated

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the inhibition ability of polymeric species containing different functional groups (e.g., carboxylic acid, sulfonic acid) commonly used to inhibit conventional sulphate and carbonate scales, they concluded that they perform as poor silicate inhibitors, due to the fact the carboxylic acid, sulfonic acid, ester, and non-ionic groups present in the polymers exhibit poor interaction with silane groups present in silica. Finally, they reported good performance of two polymeric inhibitors with significant different functional group composition. Finally, the use of boron compounds was proposed, the method consists injecting boric acid or/and its water soluble salts (Dubin 1986). Silica inhibition is thought to be due to the ability of borate to condense with silicate to form borate-silicate complexes which are more soluble than silica (Amjad and Zuhl 2008).

3.2 Chemical Selection Chemical selection is an important aspect to control scale precipitation effectively for downhole/topside and injection applications. The following experimental tests are used to evaluated and ranked inhibitors into order of suitability (Jordan et al. 1996; Graham et al. 2001): 1. 2. 3. 4. 5.

Static and dynamic inhibitor efficiency Static adsorption Static formation damage test Inhibitor/Formation brine compatibility phase envelope Thermal stability

The results from these test leads to a further screening, where generally 1 to 3 candidates are further tested in reservoir conditioning coreflooding, which must be performed to derive a dynamic adsorption isotherm for “Field Squeeze Strategy” (Sorbie and Yuan 1991; Yuan et al. 1993), and to evaluate formation damage (Jordan et al. 1994). The time and expense involved in this type of test is significant more than the pre-screening tests. Due to the relative short time required to complete these tests, many products and conditions can be evaluated at a relatively short time and low cost. An initial screening to select the most appropriate products, then these products will be further assessed in static and dynamic inhibitor efficiency tests, compatibility phase envelope determination and thermal stability (Graham et al. 2001). The results of these tests in conjunction with static adsorption tests is used to select between 1 and 3 scale inhibitors for further reservoir condition coreflooding for well applications (Jordan et al. 1996). For topside treatments, the adsorption tests are not required.

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3.2.1 Static Inhibitor Efficiency Test This type of test is used to evaluate the inhibitor ability to prevent the deposition of sulphate scales. This test consists of mixing formation and injection brine at a certain proportion in a bottle test, resulting in the highest supersaturation index. Then the mixture is pH adjusted and placed in an oven to represent the field application conditions. To determine the inhibition efficiency, scale inhibitor is added at certain concentrations, the concentration of the divalent cation involved in the reaction is monitored, normally determined by ICP. To determine the inhibition efficiency (IE), a measure how effective the scale inhibitor under study is at preventing sulphate scale precipitation, the mathematical expression below is used: ( I.E. = 100

C(t) − Cb (t) Co − Cb (t)

)

where IE is expressed as a percentage, C(t) is the divalent cation concentration at sampling time, t, Co is the original divalent cation concentration at time, and Cb (t) divalent cation concentration in the blank solution (containing no SI) at time, t (Graham et al. 1997; Sorbie et al. 2000). To establish how effective a scale inhibitor is preventing the precipitation of sulphates scales under specific set of experimental test conditions, i.e., temperature, pH and scaling regime, determined by the mixing of incompatible brines, the IE is measured, normally at 2 and 22 h. The test at 2 h assess the ability to inhibit nucleation, and at 22 h the capacity to hinder crystal growth (Sorbie et al. 2000). To determine the threshold concentration, commonly known as to as the “Minimum Inhibitor Concentration” or MIC, the scale inhibitor IE must be above 90% for 2 and 22 h. In certain application variants, the MIC is determined by IE at 2 h.

3.2.2 Dynamic Inhibitor Efficiency Test This test is also known as dynamic tube blocking test, it consists of co-injecting two non-scaling components of the scaling brine through a thin steel tube, where the pressure across the tube is monitored though time, until the tube starts to block. Tube blocking tests were originally developed to study scale inhibitors for boiler, desalination applications and pipes (Sorbie et al. 2000). And it is commonly used for scale inhibitor performance studies in oilfield environments, examining the ability to prevent the adherence and growth in micro-bore coils (Yuan et al. 1997a, b; Yuan 2001; Graham et al. 2002a, b; Bazin et al. 2007).

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43

3.2.3 Static Adsorption Static adsorption tests involve the evaluation of adsorption of scale inhibitor species in crushed rock, where stock solutions of SI are prepared and then a certain amount of crushed rock is added (Jordan et al. 1995). The adsorption level in mg/g of rock, is calculated as follows: Γ=

V · (Co − Cads ) m

where Co (ppm) is the initial concentration of the stock solution, V (L) volume of the bulk solution, Cads ( ppm) is solution concentration after adsorption, m(g) is the mass of crushed rock and Γ(mg/g) adsorption level. The core material used in this kind of test are disaggregated normally below 600 µm. Crushing or disaggregating of rock or mineral sample results in a higher surface energy, consequently potentially more reactive. Therefore, the level of adsorption in static beaker test may be higher than those observed in consolidated material, such as a coreflood. This type of bulk adsorption tests is not as time consuming as coreflooding, which are significantly more expensive, and therefore an wide range of sensitivities of inhibit adsorption can be examined (Jordan et al. 1995).

3.2.4 Static Formation Damage Test Static formation damage tests were conducted in solvent-cleaned chips of reservoir rock were reported before (Graham et al. 2001). They proposed the use of SEM (Scanning Electron Microscope) to examine the surface of the core chip before and after treatment to determine potential formation damage induced by the scale inhibitors. Complemented by EDAX (Energy Dispersive X-Ray Analysis) technique to identify the elemental composition of the precipitated material on surface of the core chips.

3.2.5 Inhibitor/Formation Brine Compatibility Phase Envelope Compatibility of scale inhibitor with seawater, and Phase diagrams of inhibitor and calcium complex at different pHs were reported before (Sorbie et al. 1993). They reported that the concentration of DETPMP in seawater compatibility, i.e., there is precipitation, depends on the water pH. The phase diagrams showed the higher the pH, temperature and calcium concentration, precipitation is induced at lower inhibitor concentration. Phase diagrams for PPCA resulted in similar behaviour (Farooqui 2015).

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3 Scale Inhibitors

3.2.6 Thermal Stability Thermal stability assessment is important where the reservoir temperature is in excess of 130 °C (Jordan et al. 1996). At this temperature, some inhibitors might show a significant reduction in inhibition efficiency. Thermal degradation may also result in shorter squeeze lifetime in polymeric scale inhibitors, which may be reduced in molecular weight, due to hydrolysis at elevated temperature in low pH and high TDS (Total Dissolved Solids). Low molecular weight species may show low level of retention (Graham and Sorbie 1995), and lower inhibition efficiency (Farooqui et al. 2015).

3.2.7 Mechanisms of Scale Inhibition Threshold scale inhibitors prevent scale precipitation by delaying or preventing the mineral crystal nucleation or/and crystal growth (Mpelwa and Tang 2019). They intervene in one or more steps of scale deposition, which include aggregation, nucleation, and crystal growth. Phosphonate and polymeric species inhibit scale generally by different mechanism. Polymeric species, commonly, are very effective at short residence times, becoming less effective with time. On the other hand, phosphonates species, are normally not as effective at short residence times. However, they are effective for longer residence times. It may be concluded that both phosphonate and polymeric species operate through both mechanisms (Sorbie et al. 2000; Graham et al. 2003). Polymeric species, particularly PPCA, mainly operates through a nucleation inhibition mechanism at short residence times. Once crystallization occurs, it is still very effective very effective at retarding crystal growth in shorter residence times, its effectiveness is reduced with time as it is consumed by adsorption on the crystal lattice. However, scale precipitation occurs, despite inhibitor adsorption, as it does not completely block the growth sites. Phosphonate species mechanistically operate in a similar manner. However, they predominately operate by blocking crystal growth, they are less effective at controlling initial nucleation. Once nucleation, they are very effective at preventing further crystal growth by adsorbing very effectively at active growth sites (Graham et al. 2003).

3.2.8 Relevance to Test Methodology The two main testing methods commonly used to measure scale inhibition efficiency are bulk inhibition efficiency tests and dynamic tube blocking tests. Bulk tests, commonly known as “beaker tests” or “bottle tests”, this type of testing involves the monitoring of ions in solution, which is essentially a “static” test. Dynamic tests

3.3 Factors Controlling Scale Inhibitor Effectiveness

45

involve the monitoring of the pressure drop across a thin steel tube over time, when two non-scaling solutions of scaling brine are mixed at the inlet of this tube, this test is commonly known as flowing test, which historically was used to identify scale inhibitors for boiler, pipe and salination applications. Both tests may be used to evaluate sulphate scale inhibition efficiency. However, static tests are not recommended to perform carbonate inhibition efficiency, unless high-pressure vessels are used to keep CO2 in solution. The back pressure present in tube blocking test keeps CO2 in solution. The efficiency evaluation using each test may be quite different, tube blocking test may indicate that polymeric species our perform phosphonate species, and at the same time static tests suggest that the performance of phosphonate is better than polymeric species. The mechanism of scale inhibition is an important aspect to be considered to evaluate the results from the efficiency tests. Phosphonate species are known to block crystal growth, whereas polymeric operate as nucleation inhibitors. The residence time is another important aspect to consider, static tests can be used to analyse both mechanisms, nucleation short residence time ( Pi . Q j = Ej · i=1 E i ] [ Σ N δ1i Q T − i=2 E 1 i ΣN 1 + δ1 j , production where Pw < Pi , there is a change of Q j = Ej · i=1 E i

sign. Fig. 5.4 Partitioning of total flow in a multi-layer system (Vazquez et al. 2009)

References

81

References Buckley SE, Leverett MC (1942) Mechanism of Fluid Displacement in Sands. Trans AIME 146(01):107–116. https://doi.org/10.2118/942107-g Dake LP (1998) Fundamentals of reservoir engineering. Elsevier Hong SA, Shuler PJ (1988) Mathematical model for the scale-inhibitor squeeze process. SPE Prod Eng 3(4):597–607. https://doi.org/10.2118/16263-pa Lake LW (1989) Enhanced oil recovery. Prentice-Hall Inc. Myhr EAM et al (2001) Preservation of produced water samples for better scale management and extended squeeze lives. In: Tekna oil field chemistry symposium. Pope GA (1980) Application of fractional flow theory to enhanced oil recovery. Soc Pet Eng AIME J 20(3):191–205. https://doi.org/10.2118/7660-pa Sorbie KS (1991) Polymer improved oil recovery, 1st edn. Blackie, Glasgow Sorbie KS, Johnson PAV et al (1989) Non equilibrium effects in the adsorption of polyacrylamide onto sandstone. In Situ 13(3):121–163 Sorbie KS, Wat RMS, Todd AC (1992) Interpretation and theoretical modeling of scaleinhibitor/tracer corefloods. SPE Prod Eng 7(03):307–312 Vazquez O, Mackay EJ, Sorbie KS (2012) A two-phase near-wellbore simulator to model nonaqueous scale inhibitor squeeze treatments. J Petrol Sci Eng 82–83:90–99. https://doi.org/10. 1016/j.petrol.2011.12.030 Vazquez O, Mackay EJ, Sorbie KS (2009) Modelling the placement of scale squeeze treatments in heterogeneous formations with pressurised layers. In SPE European formation damage conference Wang LK, Hung Y-T, Shammas NK (2006) Advanced physicochemical treatment processes. Human Press. https://doi.org/10.1007/978-1-59745-029-4

Chapter 6

Life Cycle of a Field Squeeze Treatment

Once it has been established that scale formation may pose a problem, and the type of scale that will need to be treated against is determined, the selection of an appropriate inhibitor can take place, and the life cycle of squeeze treatment design, shown in Fig. 6.1, may begin. It is regarded as a cycle, since during the producing period the well will need to be treated several times, i.e., the well is under scale deposition risk while producing. A treatment designing process may be at any stage. If the well has not been treated before, usually the first step is the best-in-class study, where the most suitable chemical is identified, more details can be found in Chap. 3. Once, a chemical, or in occasions more than one, has been selected, the next step is to perform a reservoir coreflood experiment. The objective of this experiment is to evaluate the retention level of the selected chemicals and evaluate the performance of the chemical in terms of the treatment lifetime, which is determined at the point when the return concentration, after retention, drops below the value of the MIC (Minimum Inhibitor Concentration). This experiment is used to derive a dynamic adsorption isotherm, commonly known as coreflood isotherm derivation, more details can be found in Chap. 5. Once this adsorption isotherm is derived, an initial primary design optimisation might be performed. At this stage, when the well has not been treated before, or when a new chemical is going to be deployed, the isotherm derived from the coreflood is the most representative estimate of the retention of the chemical. When, the well has been treated for the first time, and a return concentration profile is collected, the coreflood isotherm is adjusted, this stage is known as field isotherm derivation. Generally, a field isotherm predicts with significant accuracy subsequent treatments (Mackay and Jordan 2003; Vazquez et al. 2012, 2013a, b), which is suitable to perform a field design optimisation (Vazquez et al. 2016; Azari et al. 2021, 2022). Since wells will need to be treated again during the well lifetime, the isotherm matching process should be repeated to validate the predictions and adjust the isotherm, if necessary, after each treatment.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 O. Vazquez, Modelling Oilfield Scale Squeeze Treatments, SpringerBriefs in Petroleum Geoscience & Engineering, https://doi.org/10.1007/978-3-319-71852-1_6

83

84

6 Life Cycle of a Field Squeeze Treatment

Best in Class Study

Coreflood Isotherm Derivation

Field Design Optimisation

Primary Design Optimisation

Field Isotherm Derivation

Field SI Return Fig. 6.1 Squeeze treatment design lifecycle

Commonly, a new chemical might be deployed during the lifecycle of the well, due to change of service contracts, well conditions, or environmental concerns implying the use of greener chemistries. In these circumstances, the best-in-class step should be performed, and the squeeze treatment cycle is restarted.

6.1 From Coreflood to Field Design Once a chemical has been selected, including various criteria, such as compatibility tests, the effectiveness in preventing scale precipitation, and the retention of the inhibitor in the rock medium without causing formation damage. To evaluate the retention, usually a coreflood experiment is performed using one or two of the most promising chemicals, where the differential pressures before and after the inhibitor flood are monitored to identify formation damage, represented as an increase in differential pressure, which is interpreted as a reduction of permeability. The other main criterion for selecting a chemical is how long the effluent concentration remains above the MIC.

6.1 From Coreflood to Field Design

85

6.1.1 Derivation of Inhibitor-Rock Adsorption Isotherm The effluent concentrations are used to derive an adsorption isotherm that describes the inhibitor-rock interaction, that relates the solution concentration and the mass of inhibitor adsorbed per unit of volume of rock, see Fig. 6.2, which describes how well the inhibitor will adhere to the rock surface. Once the isotherm has been derived, it can be validated against the coreflood concentration effluent profile, as shown in Fig. 6.3. If the simulated effluent concentrations are in close agreement with the measured values, then the isotherm is accurate (Fig. 6.4). Successful squeeze treatments, resulting in long treatment lifetime, are associated with inhibitors that can propagate deep in the formation, and returns slowly over an extended period. These characteristics are identifiable as properties of the isotherm. As shown before in Chap. 5, the speed in which a certain concentration returns to the well is given by the expression below: VC =

Vfluid 1+

(1−φ) ∂Γ φ ∂C

where VC represents the velocity at which concentration C returns to the well, Vfluid is is the gradient of the isotherm at concentrathe fluid velocity, φ the porosity, and ∂Γ ∂C tion C. A steep gradient reflects a low velocity, therefore a steep gradient at concentrations close to MIC, will result inhibitor at concentrations close to MIC taking a long time to return to the well, which is a desirable characteristic of scale inhibitors.

Fig. 6.2 Derived adsorption isotherm

86

6 Life Cycle of a Field Squeeze Treatment

Fig. 6.3 Validation of the derived adsorption isotherm

Fig. 6.4 Sensitivity study results

Once the inhibitor retention properties have been evaluated, it is possible to design the squeeze treatment, which as mentioned before, commonly consist of the following stages: preflush, main treatment, overflush and shut in. Since the chemical typically is bullheaded in the producing well. It is important to ascertain where the chemical will be placed. If the chemical is not placed in the vulnerable section of the well

6.2 Pseudo-adsorption Isotherm Matching

87

or formation, chemical or mechanical diversion might be necessary. Scale inhibitor placement is an important step in the process designing a squeeze treatment, which is covered in the Sect. 6.3.1. Although scale inhibitor placement is an important aspect, even if the chemical slug is placed in exactly where it is needed, squeeze treatment modelling and the subsequent inhibitor return, is of paramount importance improving the success of the treatment. Modelling may be used to identify where the inhibitor will enter the formation, but also it may be used to evaluate the importance of other treatment parameters, such as chemical selection, chemical injected concentration and volume of injected of brine (main treatment and overflush), which will affect the success of the treatment. Field experience is unvaluable, however, modelling can demonstrate the impact of these parameters have on the treatment lifetime, hence contributing towards the process of identifying the optimum squeeze treatment design.

6.1.2 Squeeze Treatment Sensitivity Calculations Once a well under scale deposition risk has been identified, and the selection of an appropriate chemical including coreflooding experiments to assess retention levels have been completed. The process to design a field treatment may begin, where may start with sensitivity calculations including the inhibitor concentration and volume and the overflush volume, parameters under the engineer’s control. A sensitivity study results are shown below, based on a single layer offshore well with a high rate of water production, 6,000 bbl/day, 20 ft production interval thickness and 23% porosity. The scale inhibitor retention is described by an adsorption isotherm derived from coreflooding experiment, shown in Fig. 6.2. The sensitivity study results seem to suggest that the overflush is the most sensitive parameter, followed by the main treatment volume, and finally the scale inhibitor concentration, see Fig. 6.3. These conclusions are in line with previous studies (Hong and Shuler 1988; Mackay and Jordan 2003). Table 6.1 shows the results of the sensitivity calculations designs, where a preliminary optimum treatment design may be identified, considering the operational costs, compatibility with other chemicals, and minimising the volume of deferred oil produced, shown in Table 6.2. Although this methodology has been used in the past with great success, recent advances in automatic squeeze treatment optimisation will be shown in Chap. 8.

6.2 Pseudo-adsorption Isotherm Matching The derived adsorption isotherm used to identify the primary optimum squeeze treatment; generally, does not perfectly match the first field-return concentration profile for a particular scale inhibitor and for a specific reservoir formation (Sorbie et al. 1992; Yuan et al. 1994). The first squeeze treatment match using the coreflood derived

88

6 Life Cycle of a Field Squeeze Treatment

Table 6.1 Formation and seawater compositions [SI] (ppm) Main treatment (bbls) Overflush (bbls) Squeeze lifetime (days) Base case

150,000

1140

2340

182

Treatment 1

150,000

855

2340

162

Treatment 2

150,000

997.5

2340

167

Treatment 3

150,000

1282.5

2340

186

Treatment 4

150,000

1425

2340

202

Treatment 5

112,500

1140

2340

163

Treatment 6

131,250

1140

2340

169

Treatment 7

150,000

1140

2340

184

Treatment 8

168,750

1140

2340

192

Treatment 9

187,500

1140

2340

157

Treatment 10 150,000

1140

1755

165

Treatment 11 150,000

1140

2047.5

169

Treatment 12 150,000

1140

2632.5

189

Treatment 13 150,000

1140

2925

203

Table 6.2 Squeeze treatment design

Stage

Volume SI concentration Pump rate (bpm) (ppm)

Main treatment 1,425

150,000

4

Overflush

2340

0

4

Shut in

12 h

1140

2925

isotherm, is shown in Fig. 6.5. Although the coreflooding experiment is representative of the well to be treated, it cannot represent fully the conditions of the well, below there are some of the possible reasons (Mackay and Jordan 2003): • • • • • •

Variations in lithology in the formation Assumptions about inhibitor placement Variations in actual production rates and flow profiles Changes in brine chemistry of the produced fluid Differences between coreflood and near-wellbore flow rates and temperatures Errors in analysis because of high-total-dissolved-salts brines

At this stage, it is necessary to re-derive an isotherm based on the first treatment inhibitor return concentration profile, where the isotherm is tuned to match the concentration profile. The methodology consists in finding an empirical form of an adsorption isotherm that fits the well return concentration profile. The empirical form does not incorporate any information about the retention mechanism, namely adsorption and/or precipitation. However, there are numerous examples in the literature where reasonable matches were obtained with this methodology (Durham 1983;

6.2 Pseudo-adsorption Isotherm Matching

89

Fig. 6.5 First squeeze treatment match using the derived isotherm

Hong and Shuler 1988; Sorbie et al. 1992; Mackay and Jordan 2003; Selle et al. 2003; Vazquez et al. 2013a, b). If the adsorption process is at equilibrium, i.e., an instantaneous process, a model to quantify the adsorption level is sufficient, such as a Freundlich isotherm of the form, Γ = kC n , where k and n are constants. If the adsorption process is not at equilibrium, i.e., it is a time-dependent process, it is necessary to define the rate to equilibrium, which may be described by the equation below: ( ) ∂Γ = r · Γeq (C) − Γ ∂t where r describes the kinetic rate, Γeq is the equilibrium adsorption level at a given mobile concentration, C, and Γ is the actual adsorption. The derivation of the new pseudo-adsorption isotherm may be performed by trial and error varying numerical parameters until a reasonable match can be achieved, however, this can be time consuming. Below, a method to find a matching isotherm automatically is presented.

6.2.1 Proposed Method The problem may be posed as an optimisation exercise, where a misfit function needs to be minimised. There are plenty of alternatives to search for the optimum solution, such as data-mining techniques, machine learning and optimization techniques. A machine-learning approach will normally use an algorithm to learn and then produce

90

6 Life Cycle of a Field Squeeze Treatment

a predictive model. Among the optimization techniques, there is a clear distinction between deterministic and approximate search. A deterministic search assumes that the objective or misfit function can be evaluated; this information is used to establish the search direction in a deterministic way at every stage of the algorithm. Examples of deterministic search include the bisection method, the steepest-descent or gradient method, and Newton–Raphson (Spall 2003). Some methods have been proposed showing promising results, but somehow unsatisfactory (Vazquez et al. 2009, 2010). Deterministic search techniques, which ultimately may provide the global optimum solution, may not be the most suitable for complex real-case problems. Deterministic searches might result in a high computational price to find the global optimum solution. In addition, they are not always applicable when the functional relationship between the input variables and the misfit function is unclear, i.e., the surface or fitness landscape is jagged, or in certain problems, it may even be discontinuous. Therefore, approximate search techniques, which could present a reasonable and good solution are better suited (Onwubolu and Babu 2004). Moreover, deterministic searches might not be easy to implement for certain problems, whereas approximate searches are much easier to implement, and much more flexible. On the other hand, approximate search techniques are the best-suited for the problem at hand, because of their flexibility to deal with possible “rugged” misfit landscape and noisy data. Approximate search techniques or stochastic optimization methods are classified in two general categories: local search and population based. Local search techniques explore the neighbours of the current candidate locally until a new candidate becomes the current candidate, and then its neighbours are explored until a certain stopping condition is reached. The stochastic hill climber is one of the simplest and most popular search methods. One of the major drawbacks of this simple algorithm is that it can easily get trapped in one of the possible local minima. Population-based search methods differs from the local-search method in that the current candidate or solution is replaced by a collection or population of potential solutions. The current population, which includes the current solutions, is used to generate a new population, using strategies by means of mutation and recombination operations. The strategy also indicates which members, potential solutions, to maintain in the new population, where others will be replaced. A population-based search method is described in the following steps: 1. Start with a population, S, and evaluate 2. Generate a new population S' from S by mutation and recombination operations 3. Evaluate S' , and replace some members of S with S' by following some preconceived strategy 4. Go to the preceding second step until stopping criterion is reached (e.g., convergence or maximum number of iterations) Evolutionary algorithms fall in this population-based search category. One example of this type of algorithm is the genetic algorithm (GA), which has its basis in natural genetics operations, such as inheritance, mutation, selection, and

6.2 Pseudo-adsorption Isotherm Matching

91

crossover (Goldberg and Deb 1991). A second example is particle-swarm optimization (PSO). This technique was inspired by the social behaviour of a flock of birds; it basically moves candidate solutions, called particles, in the search space based on particle fitness and a simple formula (Kennedy and Eberhart 1995). A third example is differential evolution, DE. This algorithm creates new candidate solutions that combine a target vector, calculated by a simple formula of vector crossover and vector mutation, with existing ones and then keeping the candidate solution with the lowest misfit value (Storn and Price 1995). These techniques have been used in petroleum-reservoir history matching, which aims to find petrophysical and geological properties that can reproduce the reservoir history, such as Genetic Algorithm (Erbas and Christie 2007), PSO (Mohamed et al. 2010), and DE (Hajizadeh et al. 2009). The complexity of the problem has been previously reported, due to the nature of the functional relationship between the input variables and the misfit function (Vazquez et al. 2013a, b). Although describing the misfit landscape is difficult, previous studies by contour maps for specific cases reported significant complexity (Vazquez et al. 2010). It is likely that it will be at least “rugged” since the misfit function depends on the outcome of a computer simulation. In addition, it is almost inevitable to observe undesired noise in the scale inhibitor return-concentration profiles, due to error analysis and challenging and/or changing conditions in the well. The scale inhibitor concentration is monitored in the producing well by taking regular samples. The samples are sealed in plastic bottles and send to the laboratory to be analysed by specialized equipment. There are several possible sources of error, such as samples being compromised and/or laboratory analysis, which involves a certain manipulation of the samples that may lead to further inaccuracies. In addition, the use of specialized equipment and techniques to detect the scale inhibitor in the samples may contribute further to undesired noise, due to unavoidable intrinsic error. Finally, the sample analysis is considerably sensitive to the presence of hydrocarbons in the water samples, high salinity, and contamination by drilling fluids (Thompson et al. 2008). Hill-climbing algorithm, a local stochastic search algorithm has been proposed to for automatic isotherm derivation (Vazquez et al. 2013a, b). It is a robust and fast algorithm, which is capable of coping with complex misfit landscapes and noisy data (Knowles et al. 2009). Although the results were good, PSO seems to better suited for this problem, which has been applied in the optimisation and squeeze treatments (Vazquez et al. 2016), and to evaluate the uncertainty of pseudo-adsorption isotherm history matching (Vazquez et al. 2020).

6.2.1.1

Particle Swarm Optimisation (PSO)

The PSO algorithm is inspired by the flight of flocks of birds, PSO is a set of agents, particles, which is described by a simple law of motion, where each particle motion is updated iteratively to maintain the balance between exploration and exploitation in search of local minima (Vazquez et al. 2013a, b). The velocity of each particle is

92

6 Life Cycle of a Field Squeeze Treatment

updated based on the best solution the particle has seen, pbest , and the best solution across the whole population, gbest (Eberhart and Shi 1998). The general form of PSO is described by the equations below. Showing how the success of a particle in minimizing the objective functions is driven by its own success and the success of its neighbours. Each particle location, xi , is updated by the velocity vector, vi , in each generation. A fully connected topology was applied to the population structure, where each particle location depends on all other particles from the same generation, as shown in Fig. 6.6. This topology can provide the most powerful relationships across a generation. xi (t) = xi (t − 1) + vi (t) ( ) vi (t) = W ·v i (t − 1) + C1 ·r 1 · xpbesti − xi (t) + C2· r2 · (xleader − xi (t)) where: xi (t): The position of particle i at time step t vi (t): The velocity vector of particle i showing the direction of move at time step t W : Inertia weight controls the impact of the history of velocities on the current velocity of the particle r1 and r2 : Random values between [0, 1] C1 : Cognitive learning factor that represents the attraction of a particle toward its own success C2 : Social learning factor that represents the attraction of a particle toward the success of its neighbours Fig. 6.6 Fully connected neighborhood topology, each circle represents a particle

6.2 Pseudo-adsorption Isotherm Matching

93

xpbesti : Personal best position of a given particle that has provided the greatest success xleader : Position of the best particle of the entire swarm.

6.2.1.2

Fitness Function

The return profile shows two characteristic features, an early peak and a long tail, which may be considered as two distinctive objectives. Although, they might be conflicting objectives and some of the Pareto approaches might be applied (Reyessierra and Coello 2006), the match of the tail must prevail. The main purpose of finding a match is to make accurate predictions of the squeeze lifetime for subsequent treatments, which is determined when the return concentration drops below a certain threshold concentration, known as MIC (Minimum Inhibitor Concentration). Compromising the match to the tail for the early peak might imply the worsening of the quality of the solutions to provide accurate predictions. The fitness of the particles is determined by the misfit, which is evaluated using the L1 norm base 10, shown in the equation below. Misfit =

N ∑ |log(Oi ) − log(Si )| i=0

The formulation of the misfit function, depending on the sampling frequency and timing, might weight down the tail of the profile more than the early peak. Usually, approximately the first 30% of the samples correspond to the early peak and 70% the tail. This is a desirable feature, since as mentioned before, in the misfit evaluation the tail of the profile should be more weighted. It is recommended to reduce the sampling frequency as much as possible during the first 24–72 h of production, specifically approximately a third of the samples taking during production (Vazquez et al. 2020). There are a number of examples reported in the literature, where reasonable predictions were obtained by matching the tail of the profile (Mackay and Jordan 2003; Selle et al. 2003; Jordan 2009).

6.2.1.3

Parameter Space

Every field return profile might be described by a pseudo-adsorption isotherm, which can be described by a Freundlich form, defined by two numerical constants k and n. The adsorption process might be at equilibrium conditions, which leads to a 2dimensional optimization problem, in which the pair (k, n) defines the parameter space. On the other hand, if the adsorption process is not at equilibrium, the parameter space becomes 3-dimensional, defined by the trio (k, n, r), where r describes the kinetic adsorption rate.

94

6 Life Cycle of a Field Squeeze Treatment

To constraint the parameter space, the pair (k, n) of the Freundlich isotherm form, can be estimated by linear regression, by fitting the return concentration profile to the empirical form shown in the equation below, where K and S are constants, C is the inhibitor return concentration and V represents the produced water volume (Durham 1983; Hong and Shuler 1988). The equation does not incorporate any information about the retention mechanism; however, it suggests that the return concentration approximates linearity in log–log scale. logC = logK + S logV The k and n values can be estimated from the expressions below, where φ is the porosity, Vp is the volume of reservoir pore space penetrated by the inhibitor front when the overflush is complete, and Cinj is the injected inhibitor concentration. To provide a reasonable exploratory space, the parameter space limits is set to ±50% of the values determined, assuming equilibrium adsorption the pair (k, n). In occasions, a satisfactory match can only be obtained adding the kinetic parameter, where the parameter is described by the trio (k, n, r). S=

1 n−1

Cinj (1 − φ) n−1 kCinj K=( 1 ; α = nNad ; Nad = ) n−1 φ αVp

6.2.1.4

Derivation of the New Pseudo-isotherm

To constraint the parameter space, the n value is estimated by linear regression, see Fig. 6.7, adding ±50% variation, the estimated value is 0.28. Although the same procedure could be applied to estimate the value of k, a wider range was considered to provide a more exploratory capacity. In occasions, a satisfactory match can only be obtained adding the kinetic parameter, where the parameter is described by the trio (k, n, r). The parameter space considered in this case is shown in Table 6.3. The kinetic rate range is thought to be representative. The isotherm match is described by the trio (1785.3, 0.19, 0.67) as shown in Fig. 6.8.

6.3 Estimating Placement Once the chemical retention capability has been evaluated, either by coreflood experiment or from field experience. The squeeze treatment designing process may be started. Most commonly, the chemical slug will be bull-headed into the formation, thus it is imperative to ascertain where the chemical will be placed, commonly known

6.3 Estimating Placement

95

Fig. 6.7 Linear regression to match the tail of the concentration profile

Table 6.3 Isotherm matching parameter space

S = -1.291 K = 8.739

Stage

k

Upper Lower

n

r

2,000

0.42

1

100

0.14

0.01

Fig. 6.8 Squeeze treatment match using the re-derived isotherm

96

6 Life Cycle of a Field Squeeze Treatment

as placement. If the chemical is not placed in the vulnerable section of the well, the treatment will not be successful. Resulting in the apparent protection against scale, i.e., analysed inhibitor return concentration is above the MIC; but evidence of scale deposition, such as loss of productivity, unexpected reduction of scaling ion concentrations, and/or evidence of suspended solids after filtering produced water samples are observed (Jordan et al. 2006). Such a scenario may occur, for example, in a long horizontal well under sulphate scaling risk, if seawater breaks through at the toe of the well, scale will be deposited at the toe, which can be challenging to reach by the chemical slug due to frictional losses along the well, or in wells with over pressurized sections, where it may not be possible to overcome the pressure differential due to restrictions in the injection rate, such as to prevent the creation of hydraulic fractures. Inhibitor placement may accurately be determined by production logging; however, this implies expense and risks. Logging requires the well to be shut-in for some time, resulting in oil deferment and extra operational costs, which may become a prohibitively expensive operation. In wells drilled and completed in a single homogeneous layer formation, the squeeze lifetime is determined by the physical interaction of SI and the rock formation. However, wells are frequently drilled and completed in several sections, characterized by permeability, porosity, and height (completion interval). Each section might at a different pressure, thus scale inhibitor placement will be a function of the injection rate and the pressures (Mackay and Jordan 2003; Vazquez et al. 2009), which is described below.

6.3.1 Analytical Expression for the Partitioning of Flow Analytical expressions to calculate flows and relative penetrations of injected fluid in both linear and radial heterogeneous formations with no-crossflow, assuming that all the layers were at the same pressure have been proposed before (Seright 1988, 1991a, b; Liang et al. 1993). Other investigators studied the flow patterns in layered formations (Root and Skiba 1965; Zapata and Lake 1981) and communicating layered formations, where crossflow is present (Sorbie et al. 1989; Sorbie and Seright 1992; Mackay and Sorbie 2000; Mackay et al. 2000). A mathematical model was implemented to calculate the single-phase flow partitioning in layered formations, based on the permeability height product of each layer (Zhang and Sorbie 1997). Then, it was expanded to a more general expression to calculate the partitioning of flow in two phases in radial layered systems with no communication between layers, where each layer may be at a different pressure (Vazquez et al. 2009). Assuming that each layer is at a different pressure, Pl , and that the pressure is maintained at its boundary during flowing conditions, as shown in Fig. 6.9. Then the pressure drop in any layer can be calculated as function of the pressure drop in the first layer, ΔP, and the pressure difference between the first layer and the others, δ1l = Pl − P1 .

6.3 Estimating Placement

97

Fig. 6.9 Partitioning of total flow in a multi-layer system

ΔP 1 = Pw − P1 = ΔP ΔP 2 = Pw − P2 = Pw − (P1 + δ12 ) = ΔP − δ12 .. . ΔP N = Pw − PN = Pw − (P1 + δ1N ) = ΔP − δ1N Using Darcy’s Law in radial coordinates 1 ΔP i = Ei · Qi , where Ei = · 2π · hi Q1 = Q2 =

{rMax rw

Ki ·

(

1 krw μw

+

kro μo

)·

dr i = 1, . . . , N r

1 · ΔP E1

1 · [ΔP − δ12 ] E2 .. .

QN =

1 · [ΔP − δ1N ] EN

Assuming that the volume is conserved, i.e.,

∑N i=1

Qi = Qt , after substituting:

∑ N N ∑ ∑ Qt + Ni=2 1 δ1i Qt = ΔP · − → ΔP = ∑N 1 Ei Ei i=1 i=2 i=1 Ei

δ1i Ei

98

6 Life Cycle of a Field Squeeze Treatment

Below two expressions to calculate the partitioning of flow for injection and production stages are shown. Note that there is a change of sign, as the pressure in the well (is lower than the pressure in the reservoir, Pw < Pi , and thus ΔP j = ) Pj − Pw = P1 + δ1j −P w = ΔP + δ1j . [ ∑ Qt + Ni=2 1 Qj = · ∑N 1 Ej i=1

δ1i Ei

Ei

[ ∑ Qt − Ni=2 1 Qj = · ∑N 1 Ej i=1

δ1i Ei

] − δ1i where δ11 = 0 for injection stages ] + δ1i where δ11 = 0 for production stages

Ei

6.3.2 Squeeze Treatment/Tracer Programme Designs As mentioned before, wells with varying reservoir quality and/or significant crossflow due to pressure differentials, adequate placement might not be possible. In these circumstances, flow diverters might be used to improve the chemical placement (Jordan et al. 1999; Jordan 2009). In scenarios where production logging is not feasible, due to high intervention costs and operational risks. An alternative to running production-logging tools (PLTs), is to add a tracer package during squeeze treatments to evaluate placement. The applicability of this technique was demonstrated in the Norne field, located in the southern part of the Norwegian Sea, approximately 85 km north of the Heidrun field and 200 km offshore Norway (Vazquez et al. 2018b). KCl brine was injected, where potassium was monitored during the early production stage, potassium was selected as a tracer due to the high contrast with the background concentration of formation brine. 50 m3 of KCl at 10% was pumped into the formation, followed by a period when the well was shut-in to allow the KCl pill to crossflow between the layers as a significant pressure differential existed. Then the well was set back in production, where the rate was increased stepwise, and water sample collected and analysed during the first 2,000 m3 of fluid was produced. Based on simulation results, 1,200 m3 /d, followed by 6,000 m3 /d production rates were recommended, where a clear change of the slope was observed. In the field, a flow rate of 1737.9 m3 /d for 467.4 m3 followed by 6015 m3 /d for 902.2 m3 was implemented. A change of slope of the potassium return concentration was observed after 0.4 days of production as predicted by the simulation study. The layer flow rate distribution was further tuned by matching the tracer observed and simulated data. The results suggested that the scale inhibitor will preferentially be placed in low pressure sections close to the toe. A technique to include a tracer package as part of a squeeze treatment in challenging wells has been proposed before. The tracer slug should be injected as part of the overflush stage, otherwise the tracer will be transported deep in the reservoir and highly diluted, where the desired change of slope will not be easily identifiable. In

References

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terms of well operations, this technique does not require any significant differences with a conventional squeeze treatment. The only main difference is the sampling frequency when the well is back in production. Further details on how to optimise and design this kind of treatments has been reported before (Vazquez et al. 2018a). Although natural tracers have been used in the past to evaluate inter-well communication between injectors and producers (Huseby et al. 2005, 2010; Vazquez et al. 2015), and estimate scale inhibitor placement (Jordan et al. 1999; Vazquez et al. 2014), artificial chemical tracers are commonly used for a variety of applications in the oil industry (Zemel 1995; Huseby et al. 2010; Serres-Piole et al. 2012). There is a great variety, among them fluorinated benzoic acids (FBAs) that were developed in 1990s and are commonly used for hydrothermal, geothermal and oilfield applications (Pritchett et al. 2003; Meza et al. 2007; Seccombe et al. 2010), are recommended. They are highly soluble in water, characterised by high thermal stability (250–300 °C), low presence in formation brines and low level of detectability as low as ppb (parts per billion by HPLC/UV (High-performance Liquid Chromatography) methods (Adams et al. 1992, 2004). These characteristics make FBAs very desirable for field applications, and particularly for squeeze treatment/tracer program. In terms of logistics, FBA are perfect suited, as only few kilograms will be necessary to obtain few ppm, well above the detection level. Further details on the design of this combined treatments have been reported before (Vazquez et al. 2018a).

References Adams MC et al (1992) Thermal stabilities of aromatic acids as geothermal tracers. Geothermics 21(3):323–339. https://doi.org/10.1016/0375-6505(92)90085-N Adams MC et al (2004) Alcohols as two-phase tracers. In: Proceedings 29th workshop on geothermal reservoir engineering, Stanford University [Preprint] Azari V et al (2021) Full-field optimization of offshore squeeze campaigns in total Gulf of Guinea fields. SPE Prod Oper (March):1–15. https://doi.org/10.2118/204384-pa. Azari V, Vazquez O, Mackay E et al (2022) Gradient descent algorithm to optimize the offshore scale squeeze treatments. J Petrol Sci Eng 208:1–12. https://doi.org/10.1016/j.petrol.2021.109469 Durham DK (1983) Equations for prediction of scale inhibitor return after squeeze treatment. In: SPE California regional meeting [Preprint]. https://doi.org/10.2523/11708-ms Eberhart RC, Shi Y (1998) Comparison between genetic algorithms and particle swarm optimization. In: International conference on evolutionary programming. Springer, pp 611–616 Erbas D, Christie MA (2007) Effect of sampling strategies on prediction uncertainty estimation. In: SPE Reservoir simulation symposium Goldberg DE, Deb K (1991) A comparative analysis of selection schemes used in genetic algorithms. Found Genet Algorithms 1:69–93. https://doi.org/10.1.1.101.9494 Hajizadeh Y, Christie MA, Demyanov V (2009) Application of differential evolution as a new method for automatic history matching. In: SPE Kuwait international petroleum conference and exhibition Hong SA, Shuler PJ (1988) Mathematical model for the scale-inhibitor squeeze process. SPE Prod Eng 3(4):597–607. https://doi.org/10.2118/16263-pa Huseby O et al (2005) Use of natural geochemical tracers to improve reservoir simulation models. J Petrol Sci Eng 48(3–4):241–253. https://doi.org/10.1016/j.petrol.2005.06.002

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Huseby O et al (2010) Natural and conventional tracers for improving reservoir models using the EnKF approach. SPE J 15(4):1–15. https://doi.org/10.2118/121190-PA Jordan M (2009) The modelling, application, and monitoring of scale squeeze treatments in heterogeneous reservoirs, North Sea. In: Proceedings of SPE international symposium on oilfield chemistry [Preprint]. https://doi.org/10.2118/121142-MS Jordan MM, Edgerton M, Mackay EJ (1999) Application of computer simulation techniques and solid divertor to improve inhibitor squeeze treatments in horizontal wells. In: Proceedings—SPE international symposium on oilfield chemistry, vol 3, no 1, pp 133–148. https://doi.org/10.2523/ 50713-ms Jordan MM, Johnston CJ, Robb M (2006) Evaluation methods for suspended solids and produced water as an aid in determining effectiveness of scale control both downhole and topside. SPE Prod Oper 21(1):7–18. https://doi.org/10.2118/92663-pa Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE International conference on neural networks—conference proceedings Knowles J, Corne D, Reynolds A (2009) Noisy multiobjective optimization on a budget of 250 evaluations. In: Proceedings of the 5th international conference on evolutionary multi-criterion optimization Liang J-T, Lee RL, Seright RS (1993) Gel placement in production wells with water-coning problems. SPE Prod Facil 8(3):243–272. https://doi.org/10.2118/20211-PA Mackay E, Jordan MM (2003) Squeeze modelling: treatment design and case histories. In: SPE European formation damage conference. Society of Petroleum Engineers Mackay EJ, Sorbie KS (2000) Brine mixing in waterflooded reservoirs and the implications for scale prevention. In: International symposium on oilfield scale [Preprint]. https://doi.org/10.2118/601 93-MS Mackay EJ et al (2000) Modeling scale-inhibitor treatments in horizontal wells: application to the alba field. SPE Prod Facil 15(02):107–114. https://doi.org/10.2118/63013-PA Meza E et al (2007) Optimization of tracer test design—practical applications. In: International oil conference and exhibition Mohamed L, Christie M, Demyanov V (2010) Comparison of stochastic sampling algorithms for uncertainty quantification. SPE J 15(1):31–38. https://doi.org/10.2118/119139-PA Onwubolu GC, Babu BV (2004) New optimization techniques in engineering. Springer, Heidelberg Pritchett J et al (2003) Field application of a new in-depth waterflood conformance improvement tool. In: SPE International improved oil recovery conference in Asia Pacific [Preprint]. https:// doi.org/10.2118/84897-MS Reyes-sierra M, Coello CAC (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res 2(3):287–308 Root PJ, Skiba FF (1965) Crossflow effects during an idealized displacement process in a stratified reservoir. Soc Petrol Eng J 5(03):229–238. https://doi.org/10.2118/958-pa Seccombe J et al (2010) Demonstration of low-salinity EOR at interwell scale, Endicott Field, Alaska. In: SPE Improved oil recovery symposium, 2008. https://doi.org/10.2118/129692-MS Selle OM et al (2003) A way beyond scale inhibitors—extending scale inhibitor squeeze life through bridging. In: SPE International symposium on oilfield scale Seright RS (1988) Placement of gels to modify injection profiles. In: SPE Enhanced oil recovery symposium, pp 4–6. https://doi.org/10.2118/17332-MS Seright RS (1991a) Effect of rheology on gel placement. SPE Reserv Eng 6(2):212–218. https:// doi.org/10.2118/18502-PA Seright RS (1991b) Impact of dispersion on gel placement for profile control. SPE Reserv Eng 6(3):343–352. https://doi.org/10.2118/20127-PA Serres-Piole C et al (2012) Water tracers in oilfield applications: guidelines. J Petrol Sci Eng 98–99:22–39. https://doi.org/10.1016/j.petrol.2012.08.009 Sorbie KS, Seright RS (1992) Gel placement in heterogeneous systems with crossflow. In: SPElDOE Symposium on enhanced oil recovery. https://doi.org/10.2523/24192-ms

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Sorbie KS, Wat RMS et al (1989) Miscible displacements in heterogeneous core systems: tomographic confirmation of flow mechanisms. In: Society of petroleum engineers of AIME. https:// doi.org/10.2523/18493-ms Sorbie KS, Wat RMS, Todd AC (1992) Interpretation and theoretical modeling of scaleinhibitor/tracer corefloods. SPE Prod Eng 7(03):307–312 Spall JC (2003) Introduction to stochastic search and optimization: estimation, simulation, and control. Wiley-Interscience, New York Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. J Glob Optim 23(1): 1–12. ftp://ftp.icsi.berkeley.edu/pub/ techreports/1995/tr-95-012.pdf Thompson A, Kotlar HK, Gangstad A (2008) Oilfield data/return analysis: a comparison of scale inhibitor return concentrations obtained with a novel analytical method and current commercial techniques. In: SPE International oilfield scale conference Vazquez O, Mackay E, Sorbie K (2009) Towards automation of the history matching process for scale inhibitor squeeze modelling. In: 20th NIF oilfield chemistry symposium, pp 22–25 Vazquez O, Aboobaker A, Stephen K (2010) Developments in the automation of the history matching process for scale inhibitor squeeze modelling. In: 21th NIF oilfield chemistry symposium, pp 14–17 Vazquez O, Mackay EJ, Sorbie KS (2012) A two-phase near-wellbore simulator to model nonaqueous scale inhibitor squeeze treatments. J Petrol Sci Eng 82–83:90–99. https://doi.org/10. 1016/j.petrol.2011.12.030 Vazquez O et al (2013a) Automatic isotherm derivation from field data for oilfield scale-inhibitor squeeze treatments. SPE J 18(03):563–574. https://doi.org/10.2118/154954-PA Vazquez O, Mccartney R, Mackay EJ (2013b) Produced-water-chemistry history matching using a 1d reactive injector/producer reservoir model. SPE Prod Oper 28(04):369–375. https://doi.org/ 10.2118/164113-PA Vazquez O, Mackay E et al (2014) Use of tracers to evaluate and optimize scale-squeeze-treatment design in the Norne Field. SPE Prod Oper 29(01):5–13. https://doi.org/10.2118/164114-PA Vazquez O et al (2015) Produced-water-chemistry history matching in the Janice field. SPE Reserv Eval Eng 18(4) Vazquez O, Fursov I, Mackay EJ (2016) Automatic optimization of oilfield scale inhibitor squeeze treatment designs. J Petrol Sci Eng 147:302–307. https://doi.org/10.1016/j.petrol.2016.06.025 Vazquez O, Giannakouras I, Mackay EJ (2018a) Simulation of squeeze treatment/tracer programme designs. In: SPE International oilfield scale conference and exhibition, pp 20–21 Vazquez O et al (2018b) Scale inhibitor squeeze placement modelling in a North Sea Reservoir with injection gas breakthrough. In: NIF Oilfield chemistry symposium. https://doi.org/10.1017/ CBO9781107415324.004 Vazquez O et al (2020) Uncertainty quantification of pseudo-adsorption isotherm history matching. In: Society of petroleum engineers—SPE international oilfield scale conference and exhibition, OSS 2020 Yuan MD et al (1994) Phosphonate scale inhibitor adsorption on outcrop and reservoir rock substrates the “static” and “dynamic” adsorption isotherms’. In: Fifth symposium on chemistry in the oil industry Zapata VJ, Lake LW (1981) A theoretical analysis of viscous crossflow. In: SPE Annual fall technical conference and exhibition Zemel B (1995) Tracers in the oil field. Elsevier Zhang HR, Sorbie KS (1997) Scale inhibitor squeeze treatments. Heriot-Watt University, Department of Petroleum Engineering

Chapter 7

Reservoir Scale Management

Scale precipitation is perceived as production issue since the greatest impact of solid deposits is encountered in the production well and surface facilities. However, reservoir processes have a very important impact on scale precipitation. The brines contained in reservoirs are in chemical equilibrium between them and with the formation. When fields are produced, this equilibrium is disturbed by changes in pressure and temperature, and because of the injection of other brines with a different composition than the formation brine, or by the injection of gases such as CO2 . Waterflooding is one of the most common methods of oil recovery, which involves the injection of water for pressure support, in offshore reservoirs, mainly seawater. When the brine, rich in sulphate ions, is injected into the reservoir it may mix with formation brine, rich in cation ions, resulting in the precipitation of sulphate scales. Another technique to improve recovery is the injection of CO2 , considered as carbon storage and utilisation. Once CO2 is injected, it partitions in the aqueous phase, reducing the pH of the formation brine, leading to the dissolution of carbonate minerals, which may disrupt the chemical equilibrium, resulting in the precipitation of carbonate scales.

7.1 Reservoir-Simulation Process for Inorganic Scale Management Reservoir simulation is a very important tool in terms of scale management, it enables the assessment of reservoir processes to identify the extent of the scaling problem, evaluate fluid modification techniques, such as sulphate removal of the injected brine, the impact of in-situ ion stripping, and finally, assisting in the optimisation of inhibition techniques, such as squeeze treatments.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 O. Vazquez, Modelling Oilfield Scale Squeeze Treatments, SpringerBriefs in Petroleum Geoscience & Engineering, https://doi.org/10.1007/978-3-319-71852-1_7

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7.1.1 Reservoir Scale Deposition As mentioned before the main types of scale are sulphates and carbonates. Sulphate scale precipitates when incompatible brines mix, such as injected seawater and formation brine. Carbonates precipitate due to a pressure drop, where CO2 evolves increasing the pH, but they can also occur when CO2 is injected to enhance oil recovery. In both scenarios, scaling risk in the producers will depend on the processes occurring in the reservoir, as the injected fluids are transported through the reservoir, where the chemical equilibrium is disrupted.

7.1.1.1

Injected and Formation Brine Mixing

Evaluating the mixing of injected seawater, rich in sulphate ions, and formation brine, rich is cations, is imperative to identify the conditions leading to scale precipitation, but also predicting the conditions at producing wells, (Mackay et al. 2005). Particularly, identifying seawater breakthrough in productions wells, and predicting the co-production of injected seawater and formation brine, aquifer and connate water, and example is shown Fig. 7.1, to estimate the scaling risk, described by supersaturation, shown Fig. 7.2. These predictions can be used to estimate the severity of the scale problem, and thus, for how long the producers will need to be treated, and the volume of inhibitor that will be required. In addition, well-by-well analysis of predicted seawater/formation brine production profiles are used to identify if zones under scaling risk are protected by the correct placement of inhibitor by bull-heading treatments. This simulation technique has been implemented in several experimental and modelling studies to estimate the reduction of the severity of sulphate scales deposition, where desulphated seawater was injected (Mackay et al. 2005; Al Kalbani et al. 2021). LSSW (Low Sulphate Seawater) has been implemented in fields under waterflooding to control sulphate scaling, such as Tiffany (Al-Riyami et al. 2008), South Brae (McElhlney et al. 2006), North Sea, Girasol, Angola (Vu et al. 2000), Marlim Leste, Campos Basin, Brazil (Boak et al. 2005).

7.1.1.2

Reservoir Ion Stripping

Geochemical reactions between the injected seawater and the formation brine may result in the significant reduction cation concentration in the produced water, involved in the precipitation of sulphate scales. Consequently, impacting the severity of the scaling risk, and therefore the scale inhibition strategy might need to be revised. The inhibitor MIC, Minimum Inhibitor Concentration, required to inhibit scale deposition, will be lower, as a result the inhibition strategy, either continuous injection or squeeze treatments, will need to be revised, where concentration and volumes could be reduced, lowering operational and logistical expenditure. The impact of the

7.1 Reservoir-Simulation Process for Inorganic Scale Management

Fig. 7.1 Connate, aquifer and seawater fraction, and water production rate

Fig. 7.2 Barium and Strontium Sulphate supersaturation versus seawater fraction

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relaxation of the injection of Low-Sulphate Seawater has been presented before (Al Kalbani et al. 2021), where the supersaturation of barium sulphate was calculated considering multiple scenarios switching from LSSW and FSSW (Full -Sulphate Seawater) to determine the optimal relaxation strategy.

7.1.1.3

CO2 -WAG

Reservoir simulation has been applied to determine the optimal operational controls in a Water alternating Gas flood to maximise economic return and minimise the risk of scale deposition. CO2 -WAG in Carbonate reservoir may be challenging due to the intrinsic heterogeneity and geochemical reactivity. A compositional reservoir model was built to simulate a reactive 3-phase miscible flow in porous media to optimise the CO2 -WAG strategy production in a Brazilian pre-salt carbonate reservoir, and then estimate the calcium carbonate scaling tendency for the scenarios of interest and design scale management strategies, particularly a long-term squeeze treatment campaign to minimize costs (Rodrigues et al. 2020).

7.1.1.4

Inhibitor Placement

Well-by-well analysis of the predicted seawater-production and injection profiles along the wellbore is performed to determine if the correct placement of scale inhibitor by bullhead treatments (squeeze treatments) is achieved, reaching the zones under risk of scale deposition. Although, this technique has been predominately applied for sulphate scales, it could potentially be applied for carbonate scales. Figure 7.3 shows an example of the calculated seawater fraction, oil and water production profiles, and the injection profile at several pumping rates, and crossflow. These data are then used to build a near wellbore model to design squeeze treatments, identifying the concentration and volumes required to achieve protection for a typical squeeze life of approximately 1 year. From the example in Fig. 7.3, it is desirable to pump at relatively high rates to achieve good placement, particularly in zones where seawater is breaking through. In this case, seawater breaks through at the toe of the well. By controlling the pump rate alone, it may be possible to avoid the need to use chemical or mechanical diversion to achieve adequate placement.

7.2 Estimation of Scale Deposition Through Reservoir History Matching This technique builds on the methodology described in Sect. 7.1, and the integrated risk analysis of scale management proposed during the front-end-engineering design (FEED) (Mackay et al. 2005), where the produced water chemistry is used to track the

7.2 Estimation of Scale Deposition Through Reservoir History Matching

107

Fig. 7.3 Flow profiles

seawater mixing front in a reservoir-matching framework, to estimate the deposition of sulphate scales, (Vazquez et al. 2014). During the FEED stage of field development, production data is not available, therefore reservoir processes are estimated from a history-matched model. Reservoir history matching implies the calibrating of a simulation model to match the observed data. The calibration is naturally nonunique, therefore a great effort has been made to estimate the level of uncertainty, because using a single model, matching reasonably well all measurements, may not have the necessary predictive capability to make engineering decisions. A possible approach to tackle this issue is to generate an ensemble of history-matched models to quantify the level of uncertainty. However, more rigorously, probability densities should be considered, i.e., prior probability of the model, and the posterior probability conditioned to the observed data, where the final goal is to generate models which follow the posterior probability, (Fursov 2015), which is the full solution of an inverse problem, (Oliver et al. 2008). Generally, a Bayesian approach is adopted to quantify uncertainty, prior information about the reservoir expressed as probability of input parameters of the model, information on how to determine prior probabilities may come from several sources, such as analog outcrop data or previous experience, (Mohamed et al. 2010). Then the Bayes rule is applied to establish a link between the posterior probability, p(m|Obs), with the prior probability p(m) and the likelihood, model error, p(Obs|m). p(m|Obs) =

p(Obs|m) · p(m) p(Obs)

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The technique adopted to estimate the scale deposition was the neighbourhoodalgorithm/Bayes (NAB) method, a proven technique that can be used in conjunction with a variety of other optimization algorithms (Demyanov et al. 2020).

7.2.1 Produced Water Chemistry Produced Water Chemistry. PWC, is the composition of the produced water with time, the composition analysis consists in the determination of the concentration among other ones of the following ions, Cl– , Mg2+ , Ca2+ , Ba2+ , Sr2+ and SO42− . This type of analysis is common to detect if scale deposition occurs down the wellbore. In addition, there are several numerical methods to estimate the seawater fraction in the produced brine, such as tracking conservative ions (Braden and McLelland 1993), reacting ions (Ishkov et al. 2009) and by multivariate analysis (Scheck and Ross 2008). The ion tracking method was adopted, based on principles of mixing of formation brine and seawater, assuming that there will be no precipitation when the waters are mixed. Therefore, if seawater and formation brine mix, the concentration of nonreacting ions are linearly proportional to the percent seawater. Cl− concentration is used to calculate the seawater fraction, based on the linear interpolation between the Cl− concentration in seawater and formation brine, with the following endpoints 19,700 and 116,950 mg/l, see Fig. 7.4. Fig. 7.4 Seawater fraction as function of Cl− ion

7.2 Estimation of Scale Deposition Through Reservoir History Matching

109

Fig. 7.5 Water cut and seawater fraction History matching, original model, left, and adding PWC, right

7.2.2 Produced Water Chemistry (PWC) History Matching Methodology There have been several attempts to include PWC to improve reservoir models, using natural tracers to estimate the connectivity between seawater injectors and producers (Huseby et al. 2005, 2008, 2010). A similar methodology, considering the seawater fraction as an extra constraint, calculated as a function of Cl− concentration, considering the following assumptions and limitations to improve the history matching in the Janice field (Vazquez et al. 2014): . Aquifer and connate water saturation are assumed to have same composition everywhere in the reservoir. . No chemical reactions, Cl− is assumed to be a conservative ion. . Injected water is 100% North Sea water with constant composition. The original reservoir model was modified, to include tracers to predict the seawater fraction and then compare the estimated seawater fraction from the Cl− concentration. The results were compared with an updated history matched model including PWC, i.e., tracers to track the seawater fraction, and the original history matched model, see Fig. 7.5. Adding the PWC as an extra constraint improved the conventional history matching in terms of oil and water production rates, shown as water cut match, and produced seawater fraction.

7.2.3 Seawater Mixing Front Uncertainty Maps Including PWC as an extra constraint not only improves the reservoir history matching, see Sect. 7.2.2, but also it provides a methodology to estimate the seawater and formation brine mixing front. Including PWC in the history matching exercise

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within a Bayesian framework, provides a methodology to predict the uncertainty of the formation brine and the injected seawater mixing zone within the reservoir formation, presented as scale deposition probability maps, which can be used to predict the risk of scale deposition spatially and temporally. Therefore, wells having higher probability of scale deposition can be promptly identified and treated with the correct scale treatment strategy. Figure 7.6 shows the Bayesian confidence interval in time and space of the seawater mixing front at one year after the last historical datum for a new producer. These maps estimate the connectivity between the seawater injector and a new planned producer, the results suggest that seawater is likely to breakthrough in the mid completion sections of the new producer. This is information is of great value for squeeze treatments, particularly about placement of scale inhibitor, bearing in mind that the new producer is a long horizontal well.

Fig. 7.6 P10-P50-P90 seawater mixing front one year after the historical data

7.3 Non-aqueous vs Aqueous Overflush Scale Inhibitor Squeeze Treatment …

111

7.3 Non-aqueous vs Aqueous Overflush Scale Inhibitor Squeeze Treatment in an Oilfield Offshore Norway Squeeze treatments consists in the injection of scale inhibitor chemical in a producer to prevent scale deposition. Commonly, it consists in the following stages: preflush, main treatment, overflush and shut in. Preflush is deployed to condition the formation, the chemical slug is injected in the main treatment. The overflush stage is deployed to displace the chemical slug deeper into the formation, exposing the chemical to a greater surface area of rock to achieve a higher level of retention. Generally, the overflush is deployed as an aqueous phase; however, it is not always feasible to inject large volumes of water in wells prone to water formation damage, hydrate formation, and/or limitations with gas lift. Water is denser than hydrocarbons, and therefore more difficult to lift. In these circumstances, a non-aqueous overflush, generally marine diesel, may be preferable. Non-conventional squeeze treatments, referring to treatments where the overflush is split into aqueous and non-aqueous stages, where typically marine diesel is injected as non-aqueous fluid, have been deployed in the field. A series of scale inhibitor squeeze treatments were deployed in Campos Basin, Brazil, where a marine-diesel overflush in deep-water subsea fields to reduce the risk of productivity damage in low water cut wells was deployed (Bogaert et al. 2007). Injecting OSi package (oil soluble scale inhibitors), which consisted of an amphiphile package with a water-based scale inhibitor and an AFD (additive free diesel) overflush has been deployed in the Galley Reservoir in the North Sea were reported (Jenvey et al. 2000). A scale squeeze treatment strategy for the Heidrun field, where alternatively slugs of seawater and diesel in the overflush stage were deployed was reported (Wat et al. 2001; Vazquez et al. 2011). A comparison of the squeeze treatment lifetime achieved by conventional and non-conventional designs has been described before (Vazquez et al. 2016), the methodology employed will be described below.

7.3.1 Near Wellbore Squeeze Simulation Splitting the overflush into aqueous and non-aqueous stages might not be as effective as purely an aqueous overflush, as the propagation of the scale inhibitor may not be as effective. However, this may be counterbalanced by injecting small volume of water, to achieve comparable squeeze treatment lifetime, reducing the risk of formation damage, and well clean-up as less water will need to be produced. In addition, it will ease any lift issues when the well is back in production. To build the near wellbore model, the full reservoir simulation must be modified, as shown before, to produce the following data: . Seawater fraction, watercut and water rate per well versus production time, see Fig. 7.7 . Injection and production profiles per well versus completion, see Fig. 7.8

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Fig. 7.7 Connate, aquifer and seawater fraction, watercut and water production rate

Fig. 7.8 Flow profiles along completion length

7.3 Non-aqueous vs Aqueous Overflush Scale Inhibitor Squeeze Treatment …

113

. Water/oil production rates over time for each well Figure 7.7 shows connate water, aquifer water, seawater, water cut and water rate versus production time, which encapsulates the main factors necessary to determine when a scale inhibition treatment will need to be deployed. Typically, at seawater breakthrough, which is considered when the seawater fraction is above 5%. Water production and water-cut is included in the graph to evaluate the flow of the different waters present in the reservoir. The volume of water produced may be used to evaluate the amount of mass of mineral which may be deposited, and thus evaluate the risk of scale deposition. Bull-heading the treatment at 5 bpm might be sufficient to achieve a good placement, protecting the heel and the midsections of the well, where seawater is predicted to breakthrough, see Fig. 7.8. Although 5 bpm may be adequate, it is recommended to inject at 7 bpm to achieve full protection of the well completion, including the toe. Once the injection and production profile for the time of the treatment and the layering have been identified, the next step is to build a near wellbore model. The layering consists in identify geological units with a similar permeability, based on a permeability log, each layer is determined by porosity, permeability and height. Finally, to perform two phase flow simulations the predicted water cut by the reservoir model needs to be matched. To match the well watercut, it is necessary to determine the layer water saturation at the time of the treatment, which can be calculated from the fractional flow equation, as shown below, where capillary pressure is assumed to be negligible. A methodology where the layer water saturation is varied honouring the permeability-height product of each layer until a match is obtained, shown in Fig. 7.9., has been reported before (Vazquez et al. 2012).

Fig. 7.9 Watercut match for treatment lifetime

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Table 7.1 Squeeze treatment designs Option 1

Option 2

Option 3

Option 4

Configuration

WWDD

WWDD

WDDD

DDDD

Date first squeeze

31/01/2018

31/01/2018

31/01/2018

31/01/2018

Time to reach MIC = 5 (days)

186

209

206

181

Total treatment volume

267

267

267

267

Main slug volume (%)

50

60

60

50

Overflush volume (%)

50

40

40

50

Water volume (bbls)

133.5

160.2

80.1

0

Diesel volume (bbls)

133.5

106.8

186.9

267.0

fw =

1 1+

µw ·kr o µo ·kr w

7.3.2 Sensitivity on Splitting the Overflush Once the near wellbore model is built, the design of squeeze treatment may begin, the objective was to squeeze twice a year with a maximum downtime of two days, the MIC was considered to be 5 ppm. After identifying an optimum squeeze treatment design, a sensisity study on splitting the overflush was undertaken, the overflush was divided if four stages of equal volume, either water (W) or marine diesel (D). Table 7.1 shows treatments meeting the target squeze lifetime of 180 days at 5 ppm MIC. Option 2 shows the largest squeeze lifetime, 209 days, where the main treatment is increased by 20% with the extra associated cost of the additional scale inhibitor and the extra injected volume from 133 to 160 bbls, approximately 20% more water, compared to option 1. Options 3 minimizes the amount of injecting water in the treatment design, providing a squeeze lifetime well above the target, injecting 50% less water than option 2.

References Al M et al (2021) Impact of relaxation of low-sulfate seawater parameters on scaling risk. SPE Prod Oper 36(3):760–779. https://doi.org/10.2118/200695-PA Al-Riyami M et al (2008) When will low sulphate seawater no longer be required on the Tiffany field? In: SPE international symposium on formation damage control. https://doi.org/10.2118/ 112537-ms Boak LS et al (2005) What level of sulfate reduction is required to eliminate the need for scaleinhibitor squeezing? In: SPE seventh international symposium on oilfield scale 2005: pushing the boundaries of scale control, proceedings, pp 195–209. https://doi.org/10.2118/95089-ms

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Bogaert P, Berredo MC et al (2007) Scale inhibitor squeeze treatments deployed from an FPSO in deepwater, subsea fields in the Campos Basin. SPE Prod Oper 22(4):451–471. https://doi.org/10. 2118/102503-pa Braden JC, McLelland WG (1993) Produced water chemistry points to damage mechanisms associated with seawater injection. In: SPE western regional meeting. https://doi.org/10.2118/260 45-MS Demyanov V, Subbey S, Christie M (2020) Uncertainty assessment in PUNQ-S3—neighbourhood algorithm framework for geostatistical modelling. In: European conference on the mathematics of oil recovery Fursov I (2015) Quantitative application of 4D seismic data for updating thin-reservoir models. Heriot Watt University Huseby O et al (2005) Use of natural geochemical tracers to improve reservoir simulation models. J Petrol Sci Eng 48(3–4):241–253. https://doi.org/10.1016/j.petrol.2005.06.002 Huseby O et al (2008) Improved understanding of reservoir fluid dynamics in the North Sea Snorre field by combining tracers, 4D seismic, and production data. SPE Reservoir Eval Eng 11(4):15–17. https://doi.org/10.2118/105288-MS Huseby O et al (2010) Natural and conventional tracers for improving reservoir models using the EnKF approach. SPE J 15(4):1–15. https://doi.org/10.2118/121190-PA Ishkov O, Mackay E, Sorbie K (2009) Reacting ions method to identify injected water fraction in produced brine. In: SPE international symposium on oilfield chemistry, pp 20–22 Jenvey NJ et al (2000) The application of oil soluble scale inhibitors into the Texaco galley reservoir. A comparison with traditional squeeze techniques to avoid problems associated with wettability modification in low water-cut wells. In: SPE international oilfield scale conference. https://doi. org/10.2118/60197-ms Mackay E et al (2005) Integrated risk analysis for scale management in deepwater developments. SPE Prod Facil, 138–154. https://doi.org/10.2118/87459-PA McElhlney JE, Tomson MB, Kan AT (2006) Design of low-sulfate seawater injection based upon kinetic limits. In: SPE international oilfield scale symposium, pp 154–164. https://doi.org/10. 2523/100480-ms Mohamed L, Christie M, Demyanov V (2010) Comparison of stochastic sampling algorithms for uncertainty quantification. SPE J 15(1):31–38. https://doi.org/10.2118/119139-PA Oliver DS, Reynolds AC, Liu N (2008) Inverse theory for petroleum reservoir characterization and history matching. https://doi.org/10.1017/CBO9780511535642 Rodrigues H et al (2020) Economic optimization and calcite scale management of CO2 -EOR in carbonate reservoirs. In: Society of petroleum engineers—SPE international oilfield scale conference and exhibition, OSS 2020 [Preprint]. https://doi.org/10.2118/200678-ms Scheck M, Ross G (2008) Improvement of scale management using analytical and statistical tools. In: SPE international oilfield scale conference. https://doi.org/10.2118/114103-MS Vazquez O et al (2011) Modeling a series of nonaqueous field-scale inhibitor squeeze treatments in the Heidrun field. SPE Prod Oper 26(1):98–110. https://doi.org/10.2118/131496-PA Vazquez O, Fursov I, Mackay EJ (2016) Automatic optimization of oilfield scale inhibitor squeeze treatment designs. J Petrol Sci Eng 147:302–307. https://doi.org/10.1016/j.petrol.2016.06.025 Vazquez O, Mackay EJ, Sorbie KS (2012) A two-phase near-wellbore simulator to model nonaqueous scale inhibitor squeeze treatments. J Petrol Sci Eng 82–83:90–99. https://doi.org/10. 1016/j.petrol.2011.12.030 Vazquez O, Young C et al (2014) Estimating scale deposition through reservoir history matching in the Janice field. SPE Prod Oper 29(01):21–28 Vu VK, Hurtevent C, Davis R (2000) Eliminating the need for scale inhibition treatments for Elf exploration Angola’s Girassol field. In: SPE international symposium on oilfield scale Wat R et al (2001) Scale inhibitor squeeze treatment strategy on Heidrun. In: SPE European formation damage conference

Chapter 8

Optimisation of Oilfield Scale Inhibitor Squeeze Treatments

Optimization consists of maximizing or minimizing an objective function: the value of the objective function is determined by several input parameters. This process may be attempted by varying the parameters by hand until a desired match is obtained; however, this approach might be extremely time consuming, onerous and error prone. There have been several sensitivity studies, (Hong and Shuler 1988; Mackay and Jordan 2003a, b; Vazquez et al. 2016), the information provided by this type of analysis provide valuable information to optimise squeeze treatments. Typically, this type of analysis has been performed manually. The process can be automated by using an optimization algorithm, which will be able to explore a much wider search space. There are a great variety of optimization algorithms or techniques, typically classified as deterministic and stochastic. Deterministic optimization is the classical type of optimization algorithms used in engineering. They are typically based on the computation of the gradient to establish the search direction to find the optimal solution. These types of algorithms generally require a small number of evaluations to reach the solution, (Francisco et al. 2005), however they are not always applicable particularly if the functional relationship between input variables and misfit is not clear, i.e., the objective function might not be differentiable or even discontinuous. Examples of deterministic search algorithms are the bisection method, Newton Raphson, and the steepest descent or gradient method, (Spall 2003). Stochastic search algorithms can be classified between local search and population search. The hill climber algorithm, a well- known local search algorithm, has been successfully used for the automatic adsorption isotherm matching, (Vazquez et al. 2013). However, the population search algorithm has been extensively used in automatic reservoir history matching, due to its flexibility to accommodate complex real-life problems. Some of the most popular population based algorithms are the Genetic Algorithm, (Goldberg 1989), Differential Evolution, (Storn and Price 1995) and Particle Swarm Optimization (PSO), (Kennedy and Eberhart 1995).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 O. Vazquez, Modelling Oilfield Scale Squeeze Treatments, SpringerBriefs in Petroleum Geoscience & Engineering, https://doi.org/10.1007/978-3-319-71852-1_8

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A squeeze treatment is described by several parameters, i.e., the main treatment volume, inhibitor injected concentration and overflush volume are commonly the most varied operationally. Potentially, the shut-in and preflush stages could also be optimised, however they are not normally included. The shut-in stage is typically determined by secondary factors, such as the time necessary to put the well on production. And it is not yet fully understood how a mutual solvent preflush may enhanced chemical retention. The goal of the squeeze optimisation is to achieve the longest treatment lifetime at the lowest possible cost, however operational constraints need to be considered, which may limit the flexibility in terms of the treatment design, particularly determining the inhibitor concentration, total volume of water injected and well down time.

8.1 Operational Constraints Squeeze treatment designs are generally constrained by logistics and/or reservoir conditions. They can be addressed in the modelling process to identify suitable and feasible squeeze designs, i.e., optimizing the squeeze treatment designs, subject to the operational constraints. Generally, operational constraints may be described as the volume of neat chemical volume, the injection concentration and the total volume of water injected.

8.1.1 SI Neat Volume In offshore scenarios, inhibitor is usually stored and transported in tanks to the field. Chemical tanks are placed on deck if the treatment can be deployed from the platform. Due to space limitation, there might be a limitation on the number on tanks that may be placed on deck at a given time. Therefore, there might be a limitation on the volume of chemical available. For subsea wells, the treatment might be deployed from DSV (Diving Support Vessel), where the volume of chemical is constraint by the storage capacity of the vessel, (Vazquez et al. 2019).

8.1.2 SI Injection Concentration Chemical pumps are commonly used to add neat inhibitor into the main water injection line to provide the specified injection scale inhibitor concentration. Typically, the main water injection line is set the maximum feasible injection rate, usually just below to prevent any hydraulic fracturing. The mixing ratio, to adjust the injection concentration, is regulated by the chemical pump, the higher the rate the higher the

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concentration. Usually, the chemical pump is much smaller than the main injection pump, therefore there might a limitation on the maximum injection concentration. On the other hand, incompatibility with the formation brine, resulting in undesired precipitation of scale inhibitor and divalent ions, which may lead to near-wellbore formation damage, may constraint the maximum injection concentration. This is particularly relevant for wells treated for the first time, or when new chemistry is deployed in a treated well, (Mackay and Jordan 2003a, b).

8.1.3 Total Injected Water Volume The total injected water volume is considered as an operational constraint in two aspects. On one hand, if the formation is water sensitive and/or the well has lifting constraints, the volume of water injected should be minimised. On the other hand, in certain offshore scenarios, such as subsea developments, where the available injection time may be restricted by operational constraints. In addition, restrictions on the pumping rate, usually below fracture pressure or limited by the pump capacity, may limit the available total injected water volume. Finally, a prolonged injection time, results in longer down-time, with the subsequent deferred oil production, which should be also considered as part of the economic impact of the treatment. The total injected volume, VT , is defined as the sum of the main treatment, VMT , plus the overflush volume, VOF , i.e., VT = VMT + VOF .

8.2 Single-Well Squeeze Design Optimization Squeeze treatment design optimisation does not necessarily mean to identify the treatment resulting in the longest treatment lifetime, i.e., protecting the highest possible of produced water volume, but to identify the design that achieves the target squeeze lifetime considering treatment chemical costs, water injected volume and operational deployment costs. These considerations will be very different on whether the squeeze treatment is to be performed onshore or offshore, either from a platform or by diving-support vessel (DSV), which can be divided in terms of treatment lifetime criticality, operation costs and chemical costs in three different scenarios platform, DSV or onshore. In terms of squeeze optimization, two scenarios should be considered, in one hand when there is no flexibility concerning the squeeze lifetime, i.e., fixed squeeze lifetime and global, and on the other where there is some degree of flexibility.

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8.2.1 Squeeze Lifetime Criticality/Reliability In a platform well, since the well is relatively easy for intervention, the objective is to minimize well downtime to achieve a reasonable squeeze lifetime. If the treatment is to be delivered by DSV, a specific squeeze lifetime might be necessary, wells treated by DSVs are normally part of a campaign, and therefore the target is to achieve a squeeze lifetime long enough to reach the next agreed campaign date. Campaigns in the North Sea are generally performed in the summer months, between April and September, due to weather constraints. A DSV might be mobilized during winter months, however, it is not recommended due to weather constraints, which might delay the well intervention. Therefore, in the North Sea the recommended squeeze treatment lifetime is a year. Finally, in onshore wells, the squeeze lifetime should be optimal, not critical, as well access significantly easier than offshore development.

8.2.2 Operational Costs If the treatment is deployed from a platform, operational costs are not as expensive as if the treatment were to be delivered by DSV, resulting in low scope for potential savings. A treatment deployed by DSV is significant much more operationally demanding, so there is potentially a great scope for costs savings. Finally, in an onshore scenario, due to the operational flexibility there is great potential for significant savings.

8.2.3 Chemical Costs The chemical costs are small percentage of the operational costs in a DSV treatment, therefore not a very important factor. However, in a platform well, chemical cost might be a significant contribution to the total costs. Finally, in an onshore development the chemical cost is critical, where potential savings might be achievable, due to the flexibility of the treatment deployment, in terms of chemical volume, injection time and volume of water injected.

8.2.4 Squeeze Optimization with Fixed Target Lifetime This is relevant for offshore treatments, such as treatments part of campaign, deployed by DSV in the North Sea, where operations are commonly scheduled in the summer period, and squeeze treatment are designed to achieve a specific target squeeze lifetime. In these cases, the treatment must protect the well for the next 12 or 24 months

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(Jordan et al. 2020). A methodology presented before, (Azari et al. 2022a, b), where the Gradient Descent (GD) algorithm is applied to produce “Iso-Lifetime Curve”, which identifies al the squeeze designs that achieving the target treatment lifetime, is presented below.

8.2.4.1

Optimum Inhibitor Concentration Identification

Studies performed before on scale inhibitor concentration concluded that the lifetime treatment increases with chemical concentration, when fixing the total amount of chemical and the total injected volume, i.e., at the same chemical and operational costs, (Azari et al. 2020). Given the main treatment volume, VMT , the overflush volume, VOF , and the SI injection concentration, the neat volume of inhibitor, VSI , and the total injected water volume, VT , can be calculated using equations below: VSI = VMT × SI Concentration in the Main Slug VT = VMT + VOF Increasing the chemical concentration, the main treatment volume, VMT , decreases to keep the neat volume of inhibitor, VSI , constant and consequently the overflush volume proportionally increases, to honour the total injected water volume, VT . In other words, when a more concentrated inhibitor slug is injected, the inhibitor slug can penetrate deeper into the formation, due to larger overflush volume, resulting in higher inhibitor retention, and ultimately leading to a longer squeeze lifetime, Fig. 8.1 shows atypical response of squeeze lifetime as function of scale inhibitor concentration, where there is clear change of slope, the optimum concentration can be identified, (Azari et al. 2022a, b). Fig. 8.1 Scale inhibitor concentration optimisation

122

8.2.4.2

8 Optimisation of Oilfield Scale Inhibitor Squeeze Treatments

Iso-Lifetime Curve

The treatment lifetime increases continuously and smoothly as a function of the main treatment volume, inhibitor concentration and overflush volume, (Mackay and Jordan 2003a, b). Thus, the GD algorithm was applied, since it is faster and more object orientated, and it is thought to be more suitable for squeeze optimization with a fixed target lifetime. For a given main treatment volume, the overflush volume is iteratively changed according to equation below until the design achieves the target lifetime. Using this procedure, the overflush volume is updated at each iteration, starting from an initial value, in the opposite direction of the gradient of the lifetime function. The goal of optimization is to minimize the misfit function, which calculates the absolute relative error between the target lifetime and the predicted lifetime at each iteration. OF i − OF i−1 ( i) ( ) Lifetime OF − Lifetime OF i−1 )) ( ( × Target Lifetime − Lifetime OF i

OF i+1 = OF i+1 +

MIsfit =

| ( )| |Target; Lifetime − Lifetime OF i | Target Lifetime

Figure 8.2 shows the “Iso-Lifetime” curves for a fixed target treatment lifetime for chemical concentration of 5, 10, 15 and 20%, which in combination with the scale inhibitor concentration optimization and considering any concerns about formation damage at higher concentrations, an optimum design can be identified. In addition, Fig. 8.3 shows the cost per barrel of treated water that may be used to optimize the total cost of the operation. These two graphs encapsulate all possible designs for a given target squeeze lifetime, which provides unvaluable assistance to the engineer responsible of designing the next treatment. Combining the results shown in these graphs, it is possible to identify the optimum design in terms of cost and considerations related to the chemical concentration, volume of water injected and operational treatment costs.

8.2.5 Global Squeeze Treatment Optimization There are scenarios, where the required treatment lifetime might be flexible such as in platform wells with easy access, and in onshore wells. The optimum treatment design is usually the one with the longest lifetime, but it might not be the most cost effective or/and nor the most efficient. As mentioned before, the following objectives should be considered: • Squeeze lifetime • Total operational costs

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123

Fig. 8.2 Squeeze treatment “Iso-Lifetime” curves with fixed target lifetime for inhibitor concentrations of 5 to 20%

Fig. 8.3 Cost per barrel of treated barrel of water “Iso-Lifetime” curves with fixed target lifetime for inhibitor concentrations of 5 to 20%

• Treatment Chemical costs • Total Injected water volume Unlike the treatment optimization with fixed target lifetime, it seems reasonable to use a stochastic algorithm, since it is a real-life problem, where the surface of fitness landscape is likely to be jagged, (Onwubolu and Babu 2013). Among the numerous stochastic algorithms, Particle Swarm Optimization, PSO, is a popular

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algorithm from the category of population-based search algorithms which works by simulating the social behaviour of bird flock or fish school seeking food, (Kennedy and Eberhart 1995). The equations below show the general form of the PSO algorithm, showing how the success of a particle in minimizing the objective functions is governed by its own success and the success of its neighbours. Each particle xi comprises a distinct combination of the optimization variables, which is improved by the velocity vector vi through the generations. Where xi (t) holds the position of particle i at time step t; vi (t) is the velocity vector of particle i, showing the direction of movement at time step t; W is the inertia weight which controls the impact of the history of velocities on the current velocity of the particle; r1 and r2 are random values between [0,1]; C1 is the cognitive learning factor that represents the attraction of a particle towards its own success; C2 is the social learning factor that represents the attraction of a particle toward the success of its neighbours; xpbesti is the personal best position of a given particle that has provided the greatest success and finally, xleader holds the position of the best particle of the entire swarm. xi (t) = xi (t − 1) + vi (t) ( ) vi (t) = W vi (t − 1) + C1 r1 xpbesti − xi (t) + C2 r2 (xleader − xi (t)) The fitness of each particle is calculated using the conventional L1 norm, resulting in the normalised difference between the target and the suggested squeeze lifetime, as shown in Sect. 8.2.4.2. The closer the suggested design is to the target treatment lifetime the fitter the design, particle, will be.

8.2.5.1

Multi-objective Optimization

The most effective parameter in squeeze designs is the overflush volume, coupled with the main treatment volume, (Mackay and Jordan 2003a, b; Vazquez et al. 2009a, b, c); however, other engineering considerations must be also considered, such as the impact of lifting all the water injected and deferred oil production. Therefore, it seems that not only one objective, squeeze lifetime, should be considered, but three objectives: the operational cost, the total injected water, and the squeeze lifetime. Therefore, the problem becomes a multi-objective optimization, where there might not be a single design that optimizes each objective. In this case, the objectives are said to be in conflict, thus there exists several Pareto optimal solutions, or squeeze designs. A solution is part of the Pareto front if it is not dominated by any other design. A solution v strictly dominates w, if vi ≤ wi r for every objective i, and at least one inequality is strict. Although, in the optimization exercise assumes one objective, i.e., squeeze lifetime, since priority is to identify a design that achieves the required target lifetime; however, since other objectives need to be considered, the Pareto front of the suggested designs is calculated, to identify the most effective design, in terms

8.2 Single-Well Squeeze Design Optimization

125

of the operations management criteria. The pareto front considering the treatment lifetime versus total chemical volume injected is shown in Fig. 8.4, treatment lifetime versus total chemical volume injected, Fig. 8.5, and treatment lifetime versus total cost, Fig. 8.6, which provides a general overview of squeeze treatment design. The methodology may be used to identify the most efficient designs, and the limits in terms of cost, chemical volume, and injected water volume.

Fig. 8.4 Pareto front considering treatment lifetime versus volume of scale inhibitor

Fig. 8.5 Pareto front considering treatment lifetime versus total injected water volume

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Fig. 8.6 Pareto front considering treatment lifetime versus total cost

8.3 Multi-well Squeeze Design Optimization In this section, the focus will be on the optimization of treatments design for multiple wells that considers the scenario where several wells are treated simultaneously, which will be termed “squeeze campaign”. The wells included in a campaign will be treated in a single trip of a supply vessel; based on the storage capacity of the vessel, the optimum squeeze campaign design is identified, which maximises the squeeze lifetime for all the wells. The storage capacity of the supply vessel used to transport the chemical is limited, thus the available amount of inhibitor onboard should be optimally distributed among the wells. Provided that the treatment lifetime in each well achieves the target treatment lifetime, i.e., the next campaign, but also minimizing the total campaign injection volume. Minimizing the total injected volume, the main treatment and the overflush volume for all wells, minimizes the total campaign injection time, and therefore the total deferred oil volume of the whole field. A hybrid optimization methodology to optimize the squeeze campaign design, proposed before, (Azari et al. 2021), will briefly described. The first step consists on the identification of the optimum inhibitor concentration, methodology shown in Sect. 8.2.4.1, then the Gradient Descent algorithm was applied to derive the squeeze iso-lifetime curve for each well, as discussed before in Sect. 8.2.4.2. Once the isolifetime curves related to all the wells are calculated, any combination of treatment designs may be nominated as the campaign design, since would result in treating all wells for the target treatment lifetime. However, it is not necessarily the optimum design for the campaign.

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127

8.3.1 Gradient Descent Algorithm GD algorithm is used to identify the iso-lifetime curves for the target lifetime that are used as proxy models to predict the lifetime for the whole possible range of squeeze designs. To estimate the overflush volume required for a given main treatment volume in each well linear interpolation was applied, resulting in no further need to perform extra simulations, to reduce the computational time. The search space in this optimization problem is based on the iso-lifetime curve related to each well, which is bounded by the minimum possible main treatment volume (the first point of the iso-lifetime curve with the largest required overflush volume) and a maximum main treatment volume, which results in the target lifetime without any overflush.

8.3.2 Multi-objective Optimization Algorithm (MOPSO) As discussed before, to optimize the squeeze campaign, two objectives should be considered, namely the neat volume of inhibitor, VSI , and the total injected water volume, VT . To minimise the cost of the squeeze campaign, both should be minimized, however, the are in conflict with respect to each other, i.e., it is not possible to minimize both objectives simultaneously. Therefore, an optimum “trade-off” solution should be identified, which are part of the Pareto optimal designs. The general formulation of the PSO algorithm was described in 8.2.5. A fully connected topology was applied for the population structure, in which the particles are compared with all other particles from the same generation as the neighbours. This topology can provide the most powerful relationships across the population. The multi-objective version of the PSO algorithm known as MOPSO was applied, it uses leader selection based on the Pareto dominance technique, (Reyes-sierra and Coello 2006). The leader selection procedure in this approach is to select the particle leaders from those designs non-dominated with respect to the swarm, considering VSI and VT as the objectives. The set of non-dominated designs is updated in every generation, the number may vary generation by generation. Then, the leader, xleader for each member of the swarm in the next generation is randomly selected from the current set of non-dominated designs. The particle’s best position, xpbest is also randomly selected from the set of non-dominated positions of the same particle through the generations.

8.3.3 Field Case Below a squeeze campaign was optimised in an offshore field in in the Gulf of Guinea, operated by Total Company reported before, (Azari et al. 2021). The campaign target lifetime of the field was set to be a year (365 days), during which all wells must remain

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Table 8.1 Wells’ properties Wells

Thickness (m)

Porosity

Injection rate (m3 /min)

Rate (m3 /day)

Well-1

13.99

0.2

0.635

200

Well-2

31.11

0.16

0.635

430

Well-3

6.1

0.2

0.635

520

Well-4

3.8

0.27

0.635

600

Well-5

16.5

0.21

0.635

130

Well-6

54.21

0.065

0.635

100

Well-7

36.4

0.2

0.635

80

Well-8

17.8

0.11

0.635

80

Table 8.2 Wells’ squeeze treatment designs achieving 365 days lifetime Wells

MT (m3 )

Inhibitor concentration (%)

OF (m3 )

Shut-in (h)

Well-1

51

15

141

12

Well-2

117

15

207

12

Well-3

149

15

352

12

Well-4

165

15

656

12

Well-5

36

15

79

12

Well-6

21

15

15

12

Well-7

27

15

27

12

Well-8

19

15

23

12

protected until the next campaign. The MIC for all wells was considered to be 10 ppm, and the optimum concentration was identified to be 150,000 ppm. Finally, Table 8.1 presents the wells’ properties in addition to the water production rates. The optimisation was set to identify the squeeze campaign design resulting in the minimum total cost. The identified optimum design requires using a vessel with a storage capacity of at least of 88 m3 to transport the neat inhibitor volume, a total of 2,086 m3 of water should be injected distributed between the main treatment and overflush volume, wells’ designs shown in Table 8.2. The injection operation will take a total of 54 h.

8.4 Squeeze Treatment Lifetime Prediction Uncertainty Quantification After squeezing the well with scale inhibitor, field samples are normally collected from the produced brine to monitor the squeeze treatment lifetime, resulting in

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129

a return concentration profile. This profile is typically used to derive a “fieldrepresentative” isotherm by history matching the return data. This field isotherm is then used to predict the lifetime and to optimize the subsequent treatments in the well. However, isotherm history matching is an inverse problem, and its solution is non-unique, there might be multiple history matched isotherms, (Vazquez et al. 2013). Hence, multiple isotherms may be identified that satisfy the data-match criteria reasonably well, causing prediction uncertainty for the next squeeze treatments. Ignoring this feature and selecting just one single isotherm out of a whole range of the plausible solutions may result in a poor-quality lifetime prediction based on the model. Therefore, the uncertainty of lifetime prediction is estimated using the P10/P50/P90 percentiles and then the iso-lifetime curves related to each percentile is derived to help evaluating the optimum range of squeeze design for the subsequent treatments.

8.4.1 Isotherm Matching Non-uniqueness To demonstrate the non-uniqueness nature of the problem a synthetic and a field case will be presented below, a comprehensive study has been reported before, (Azari et al. 2022a, b). To represent the field conditions more closely, randomly generated synthetic noise was added to the return concentration profile. In practice, the noise may come from the errors in sampling/analysing or from the reservoir heterogeneity. Then, a sensitivity study was conducted to show the degree of uncertainty in the lifetime prediction for a variety range of squeeze designs, using several isotherms matching the return profile. Figure 8.6 shows the synthetic case with added noise, and three reasonable matches with different isotherms, clearly demonstrating the nonuniqueness nature of the problem. Figure 8.7 shows a sensitivity study using the three isotherms in comparison with the original isotherm. The results clearly show that considering just one of the possible matches might lead to significant inaccuracies in terms of predicting the treatment lifetime. Therefore, selecting just one single isotherm out of a whole range of the plausible solutions, which match reasonably well the return profile, may result in a poor-quality lifetime prediction. A methodology to evaluate squeeze treatment lifetime prediction uncertainty quantification will be shown below for a field case.

8.4.2 Uncertainty Quantification Uncertainty Quantification is generally regarded as the evaluation of uncertainty when mathematical/computer models are used to make predictions related to realworld processes. Some of these uncertainties stem from the errors in constructing the model or when numerical methods are used to approximate solutions to complex calculations (modelling errors), and some are also referred to the errors of measuring

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Fig. 8.7 Matching the return profile with three best isotherms, synthetic case with added noise

the data (measurement errors). However, the model uncertainty is frequently encountered by adopting the knowledge that reflects our best understanding of the reality up to date. The inhibitor retention during injection and its release during the production could be regarded as the most uncertain part of the squeeze treatment simulation since they are only partially or indirectly observed. The retention/release behaviour of the inhibitor is described by the retention isotherm, which may be identify as the best to fit the field return concentration profile. This is a key element to predict the treatment lifetime. As shown in the section before, there might multiple isotherms satisfying the data-match criteria equally well, thus leading to prediction uncertainty for the next squeeze treatments. Solving this inverse problem in Bayesian formulation, incorporating the prior information, and the likelihood involving the return concentration profile, it is possible to quantify the posterior distribution, and therefore calculate the uncertainty range, commonly known as P90/P50/P10, based on the Randomized Maximum Likelihood (RML) approach, details have been reported before, (Vazquez et al. 2020). This methodology has been applied before to design a filed treatment, (Tambach et al. 2022), it consists in calculating the cumulative density function, CDF, of the predicted squeeze lifetime of the next treatment, shown in Fig. 8.8. Then the corresponding isotherms of P10/P50/P90 treatment lifetime prediction percentiles are identified. And finally, the iso-lifetime curves for the P10, P50 and P90 isotherms are calculated. Squeeze treatment prediction uncertainty is included in the treatment design stage by considering the iso-lifetime curves for the P10, P50 and P90 isotherms. Figure 8.9 shows the iso-lifetime curves, for a fixed target lifetime of 1.1 million barrels of treated water at 12 ppm MIC, which should be treated as a safe envelope in terms of squeeze treatment lifetime prediction. The recommended treatment design should be one in the area between the P10, P50 and P90 iso-lifetime curves (Fig. 8.10).

8.4 Squeeze Treatment Lifetime Prediction Uncertainty Quantification

131

Fig. 8.8 Sensitivity study results using the matched isotherms, synthetic case with added noise

Fig. 8.9 Squeeze treatment lifetime prediction cumulative density function

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8 Optimisation of Oilfield Scale Inhibitor Squeeze Treatments

Fig. 8.10 Uncertainty range of iso-lifetime curves for target of 1.1 MMbbl and MIC = 12 ppm

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