NEI-N0--1119 NO9905156 Kjell Erik Wennberg Particle retention in porous media Applications to water injectivity decline r. €)< X DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. Particle Retention in Porous Media: Applications to Water Injectivity Decline by Kjell Erik Wennberg A dissertation for the partial fulfillment of requirements for the degree of doktor ingenidr. Department of Petroleum Engineering and Applied Geophysics The Norwegian University of Science and Technology Trondheim, February 1998 i vtuuiu iuvv iv cApivaa my arnvcic giauiuuc iu my principal supervisor, nr. uie ror- saeter, professor at the Department of Petroleum Engineering and Applied Geophysics, NTNU, and my two technical advisors, Dr. Alex Hansen, professor at the Physics De­ partments at NTNU and Dr. Mukul M. Sharma, professor at the Department of Petro ­ leum and Geosystems Engineering at the University of Texas at Austin. Dedication To my dear wife May Helen and my three lovely children Miriam, Daniel and Sondre for their love, support and understanding throughout this study Acknowledgments I would like to express my sincere gratitude to my principal supervisor, Dr. Ole Tor- saeter, professor at the Department of Petroleum Engineering and Applied Geophysics, NTNU, and my two technical advisors, Dr. Alex Hansen, professor at the Physics De­ partments at NTNU and Dr. Mukul M. Sharma, professor at the Department of Petro ­ leum and Geosystems Engineering at the University of Texas at Austin. With their different backgrounds and research interests, they all gave invaluable contributions during my study. I have had many long and encouraging discussions with each of them. The results obtained in developing the WID simulator for water injectivity decline were accomplished when Dr. Sharma hosted me one year in his research group and gave me access to previous results obtained at UT. The significance of the multidi­ mensional nature of particle deposition in porous media was emphasized by Dr. Hansen who willingly shared his encyclopedia! knowledge in modem physics with me. And with his broad knowledge in Petroleum engineering, Dr. Torsaeter gave inputs all along and helped me to tie everything together in this document. Also, I want to thank my colleagues at IKU Petroleum Research, especially my section manager Erling Fjaer and our project secretary, Reidun Knutsen, for continued support throughout the study. I thank IKU for giving me the opportunity to fulfill this study. Finally, I am grateful to the Norwegian Research Council for the scholarships they provided for my study and the additional expenses related to me and my family staying one year in Austin, Tx. The stay greatly benefited both my scientific work and the per­ sonal development for myself and my family. Abstract The problem of migration and deposition of colloidal particles within porous media is studied theoretically and by computer simulations. Special emphasis is put on the pre­ diction of injectivity decline in water injection wells due to inherent particles in the in­ jection water. The study of particle deposition within porous media requires - among other things — a correct prediction of the deposition rate or filtration coefficient. A thorough review of the modeling approaches used in the past are combined with new ideas in order to arrive at an improved model for the prediction of the filtration coefficient. Also, a new way of determining the transition time, i.e. the time where the dominant deposition mechanism changes from internal deposition (deep filtration) to external cake formation is proposed. From this fundamental theory, equations for water injectivity decline pre­ dictions are given. Based on the theoretical model, a computer program named WID for water injec­ tivity decline predictions was developed. The simulator has a very friendly graphical user interface and runs on a PC under Windows-95. As input parameters, the simulator needs water quality and formation properties as well as injection rate/pressure and com ­ pletion information. Given these input parameters, WID is able to predict decline in vertical and horizontal injection wells with openhole, perforated and fractured comple ­ tions. WID has been tested against field data from different parts of the world. In some cases it matches the field data excellent and in most cases the match is fair. However, a poor match in a few cases indicates that more mechanisms can be responsible for injec­ tivity decline than those presently accounted for by the simulator. The second part of the study is devoted to a theoretical investigation of the multi­ dimensional nature of particle deposition in porous media. A velocity dependent form of the filtration coefficient is proposed. Based on this model, a 2-d numerical code is im­ plemented. It is shown that the permeability decline in a 2-d porous sample is a function of the velocity dependence in the filtration coefficient. In particular, it is shown that under certains conditions, low permeability bands orthogonal to the macroscopic direc­ - IV - tion of flow (localization) will form. For other conditions, high-permeability bands (wormholes) parallel to the direction of flow will form. Attempts to quantify wormhole and band formation are made. Table of Contents 1. Introduction 1 1.1 Objectives of Study 2 2. Literature Review 5 2.1 Particle Mobilization and Retention in Porous Media 5 2.1.1 Types of Particles 5 2.1.2 Overview of Retention Mechanisms. 5 2.1.3 Mobilization and Retention Forces 7 2.2 Formation Damage due to Various Operations 7 2.2.1 Formation Damage due to Drilling Operations 7 2.2.2 Formation Damage due to Completion Operations 8 2.2.3 Formation Damage During Production 9 2.2.4 Formation Damage during Water Injection 10 2.3 Continuum Models for Flow of Particle Suspensions in Porous Media 10 2.3.1 The Convection-Diffusion Equation 10 2.3.2 Approximations to the Convection Diffusion Equation 12 2.4 Water Injectivity Decline Models 13 2.4.1 Iwasaki's Model 13 2.4.2 The Barkman and Davidson Model 14 2.4.3 Eylander's Model 17 2.4.4 The Van Velzen Model 17 2.4.5 The Pang and Sharma Model 18 2.4.6 The IFP Models 19 2.5 General Formation Damage Models 20 2.5.1 The Parallel Pathway Model 20 2.5.2 Other Continuum Models 21 2.5.3 Network Models 21 2.6 Permeability Models 23 2.6.1 Darcy's law 23 2.6.2 Permeability Correlations 23 2.6.3 Experimental Relations 24 2.6.4 Kozeny-Carman Equation 24 2.6.5 Rumpf and Gupte's Equation 26 2.7 Permeability Reduction Models 27 2.7.1 Overview 27 2.7.2 Reduction Models based on the Rumpf and Gupte Equation 28 2.7.3 Reduction Models based on the Kozeny-Carman Equation 28 2.7.4 Other Models 30 3. The Filtration Coefficient and The Transition Time 31 3.1 Solutions for Non-changing Filtration Coefficient 31 3.2 Solutions for Variable Filtration Coefficient 33 3.3 Determination of the Initial Filtration Coefficient 35 3.3.1 Experimental Determination of X q 35 3.3.2 Effect of Fluid Velocity, u. 36 3.3.3 Effect of Injected Particle Size, d p. 39 - vi - 3.3.4 Effect of Formation Grain Size, d g . 40 3.3.5 Effect of Porosity, <|>. 40 3.3.6 Effect of Ion Concentration. 40 3.3.7 Determining Xo from Computer Simulations. 40 3.4 Variation of Filtration Coefficient with Specific Deposit 43 3.5 Simplified Approach for Water Injection Projects 45 3.5.1 The Transition Time 45 3.6 Parameter Estimation from Experimental Data 48 3.6.1 Summary 50 4. Effect of Completion Geometry on Water Injection Well Performance 51 4.1 How Resistance and IPR 51 4.2 How Resistance for Various Well Completions 52 4.3 How Resistance in Linear Geometry (e.g. Cores) 52 4.4 How Resistance in an Openhole Well 53 4.5 How Resistance Calculation for Fractured Wells 54 4.5.1 Raymond and Binder's Method 54 4.5.2 Muskat's Solution for an Infinite-Conductivity Fracture 56 4.5.3 Prats' Method 59 4.5.4 Comparison between the Solutions by R&B and Muskat 59 4.6 Plugging of Fractured Injection Wells 60 4.6.1 Internal Filtration 60 4.6.2 External Filtration 62 4.7 How Resistance around Perforations - Ellipsoidal Geometry 63 4.8 Decline in Horizontal Injection Wells 66 4.9 Layered Reservoirs 69 4.9.1 Unconnected Layers 69 4.9.2 Connected Layers 69 5. Development and Testing of a Simulator for Water Injectivity Decline 73 5.1 Introduction 73 5.2 Development of the Simulator - WID 73 5.2.1 Model Features and Limitations 73 5.2.2 Method of Solution 74 5.3 Comparison of WID with Core Hood Experiments by Todd et al. 77 5.3.1 Alundum Cores 78 5.3.2 Lochaline Sandstone Cores 79 5.3.3 North Sea Cores 81 6. Testing of WID against Field Data 83 6.1 Injectivity Decline in Water Injection Wells: An Offshore Gulf of Mexico Case Study 83 6.1.1 Water Injection Project History 83 6.1.2 Water Quality 85 6.1.3 Results 86 6.1.4 Discussion 90 6.1.5 Summary of Gulf of Mexico Case Study 91 6.2 Application of the WID Simulator to an Offshore Injection Well outside West-Africa with relevant Core How Tests. 101 - vii - 6.2.1 Field history 101 6.2.2 Analysis and treatment of the Injection Water 101 6.2.3 Core Flood tests 102 6.2.4 The TK-M1 Injection Well 108 6.3 Analysis of an Injection Well in the North Sea 111 7.