Fikri J. Kuchuk, T. S. Ramakrishnan and Mustafa Onur
390 pgs.; Softcover
ISBN: 978-1-61399-843-4
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Delivering a comprehensive exploration of modeling through hardware, advanced formation testing, and new interpretation techniques, Wireline Formation Testing will appeal to engineers looking for a deeper understanding of the potential insights and limitations of these important computations and analytics. Since improving reservoir characterization is paramount to computing reliable predictors and uncertainties in reservoir performance, the advanced techniques presented here will help with meeting that goal. Wireline Formation Testing is the must-have resource for engineers who wish to evaluate reservoirs simultaneously with the scope of the testing results, as well as for engineering students seeking understanding of this primary source of wireline formation pressure data collection.

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Fikri J. Kuchuk, emeritus geoscientist fellow, retired from Schlumberger after 35 years as fellow and chief reservoir engineer in the USA, France, and the Middle East. He holds 45 years of experience in reservoir char-acterization and engineering, particularly in pressure transient formation and well testing. From 1988 to 1994,Kuchuk was a consulting professor in the petroleum engineering department of Stanford University, where he taught Advanced Well Testing. Kuchuk is a distinguished and honorary member of the Society of Petroleum Engineers, from which he has received the following: 1994 Reservoir Engineering Award, 2000 Formation Evaluation Award, and 2001 Regional Service Award. In 2010, he received an honorary membership to SPE. Kuchuk is also a member of the Society for Industrial and Applied Mathematics, the Russian Academy of Natural Sciences, and the American National Academy of Engineering. He is a two-time recipient of the Henri G. Doll award.

T. S. Ramakrishnan is a senior science adviser in Schlumberger-Doll Research. He holds a BTech from IIT Delhi, and a PhD from IIT Chicago, both in chemical engineering. In addition to developing some of the theories behind high pH flooding, he has published in the areas of injection and formation testing, array induction logging,and downhole relative permeability, among others. He is a distinguished member of SPE (2003) and was the recipient of the SPE Formation Evaluation award (2009). He is also a distinguished alumnus of IIT Delhi and received the Charles W. Pierce distinguished alumni award from IIT Chicago. His undergraduate thesis received the national P. C. Ray award. He holds 67 awarded U.S. patents.

Mustafa Onur is McMann chair professor of the McDougall School of Petroleum Engineering and director of Tulsa University Petroleum Reservoir Exploitation Projects (TUPREP) at the University of Tulsa. His current research is on the application of inverse problem theory, mathematical optimization, and data science to problems of relevance in optimal reservoir management and development, assisted history matching and uncertainty quantification for oil, gas, and geothermal reservoirs. Onur is the recipient of the 2010 International SPE Formation Evaluation Award and the 2018 International Reservoir Description and Dynamics Award and has been an SPE Distinguished Member since 2014.

Preface . . . vii
About the Authors . . . ix
Acknowledgments . . . x
Introduction . . . xi

Chapter 1 Formation Testing Hardware and Pressure Gauge Metrology
. . . 1
Chapter 1 describes WFT hardware. Demarcated by flow geometry, WFT may be classified as either a dual packer or a probe tool or both. The dual packer or packer module contains two inflatable packer components set against the borehole wall to hydraulically isolate the volume between them (interval) from the rest of the wellbore. The probe module consists of a probe in tubular-shape coaxial with a packer element and is set against the borehole wall to hydraulically isolate it from the rest of the wellbore while communicating to the formation. The packer’s radius is smaller than the wellbore radius and is shaped to be almost flush with the curved wellbore. Probe geometry is also available in a casedhole version, in which the casing and the cement are drilled to establish flow communication between the tool and the formation and the hole plugged post-testing. Pressure gauge metrology and measurement errors are common to all these tools.

Chapter 2 Reservoir Geology
. . . 21
Chapter 2 outlines reservoir geology to the extent needed for improvising models for formation testers. The chapter covers structural, stratigraphic, and other traps. It introduces aquifers, carbonates and their porosity evolution, and naturally fractured reservoirs.

Chapter 3 Porous Media and Rock and Fluid Properties
. . . 35
Chapter 3 presents the basics of porous media and rock and fluid properties. It covers pore size, porous media classification, representative elementary volume, macroscopic equations, heterogeneous media, distribution of reservoir fluids, connate and residual saturations, wettability, capillary pressure, hydrocarbon phase behavior, and properties of the reservoir fluids.

Chapter 4 Single-Phase Fluid Flow Through Porous Media
. . . 59
Chapter 4 presents single-phase fluid flow through porous media, Darcy’s law, and permeability. It covers pressure diffusion with and without gravity in nondeformable media and introduces deformable media. Modification of Darcy’s law, Klingenberg, and other nonlinear effects are given. Macroscopic and continuity equations for pressure diffusion in ideal porous media are also covered, along with some standard coordinate systems.

Chapter 5 Fundamentals of Multiphase Flow through Porous Media
. . . 79
Chapter 5 presents the fundamentals of two-phase flow and extensions to Darcy’s law. It covers relative permeability and capillary pressure and governing equations for two-phase flow in nondeformable porous media. It also presents an example for estimating multiphase fluid properties, such as relative permeabilities, using array induction logs including enhancement with pressure and water-cut measurements from a packer-probe wireline formation tester.

Chapter 6 Mathematical Preliminaries and Boundary and Initial Conditions for Pressure Diffusion in Formation Testing
. . . 91
Boundary and initial conditions are introduced in Chapter 6. These include prescribed pressure (Dirichlet), prescribed flux (Neumann), Robin, and mixed boundary conditions. By mixed, we mean that Dirichlet or Neumann conditions may apply to subsets of a coordinate surface. Additional material on skin and storage are also given. Components necessary to develop generalized impulse responses, including multilayer formations, are also presented.

Chapter 7 Steady-State and Transient Solutions of Pressure Diffusion for Probe Tool Configurations
. . . 111
Differential equations with boundary and initial conditions applicable to formation testing for several sink and observation probes are given in Chapter 7. Probe geometries include circular, rectangular, elliptical, ring, and guarded coaxial. Transient and steady-state solutions for mixed boundary value problems are stated here. For complicated probe geometries, acceptable and computationally efficient solutions are given. Efficient computable solutions are essential for nonlinear parameter estimation—a topic addressed in Chapter 10.

Chapter 8 Steady-State and Transient Solutions of Pressure Diffusion for Packer-Probe Tool Configurations
. . . 135
Chapter 8 presents differential equations with boundary and initial conditions and their analytical solutions dual-packer and slotted-packer modules with observations probes in vertical, horizontal, and deviated wells.

Chapter 9 Convolution and Deconvolution
. . . 165
Pressure-rate and pressure-pressure convolution and deconvolution techniques are in Chapter 9. Solving convolution integrals is known to be an ill-posed problem and presents challenges in system identification. This chapter introduces some techniques to reconstruct stable and physically acceptable solutions. Several examples are given for both pressure-rate and pressure-pressure deconvolution.

Chapter 10 Nonlinear Parameter Estimation
. . . 193
Most of the nonlinear regression algorithms presented in the well-test literature are based on minimizing a simple sum of squares. Chapter 10 presents the maximum-likelihood-based evaluation (MLE). The MLE treats observations as random variables with specified probability distributions and is more appropriate for statistical inference. Procedures using MLE are illustrated using several synthetic and field WFT pressure and rate data sets.

Chapter 11 Pressure Profiles and Gradients
. . . 209
Chapter 11 introduces pretests, examines pressure profiles and gradients with uncertainties and validation, and presents illustrative examples. Fluid contact determination from pressure profiles is also given in this chapter.

Chapter 12 Data Preparation and Processing and Geological Model Building
. . . 239
Geological model building for interpretation of WFT pressure and rate data, quality assurance, and data processing are given in Chapter 12.

Chapter 13 Interpretation Methodology
. . . 253
A unified framework for interpreting WFT pressure and rate data from multiprobe and packer-probe modules is in Chapter 13. Model recognition and building, flow-regime identification, parameter estimation, and validation and consistency of results are discussed. Formation testing hardware and gauge selection for test design are introduced in this chapter.

Chapter 14 Mobility Estimation and Conventional Flow Regime Analysis
. . . 265
Chapter 14 presents techniques for obtaining formation mobility (permeability/viscosity) from pretest draw analyses for drawdown and buildup tests, along with examples.

Chapter 15 Pressure Transient Test Interpretation Examples
. . . 281
Chapter 15 is devoted to the application of the interpretation methodology given in Chapters 13 and 14 for interpretation of many field and synthetic examples. A key aspect is the radius of investigation in formation testing.

Chapter 16 Radius of Investigation
. . . 325
In particular, likelihood estimators of formation anomalies are given in Chapter 16.

Chapter 17 Fluid Sampling
. . . 347
Chapter 17 discusses downhole-sampling-formation fluid. This chapter covers flowline resistivity, optical fluid analyzer, and in situ measurements of downhole viscosity, density, and refractive index, along with mixture models for these properties.

Chapter 18 Stress Testing
. . . 365
Chapter 18 presents stress testing with a field example.

Appendix A
. . . 377
A.1 Dirac Delta and Associated Functions . . . 377
A.2 Laplace Transform . . . 378
A.3 Fourier Transform. . . 379
A.4 Fourier Sine and Cosine Transforms . . . 380
A.5 Convolution Integral . . . 380
A.6 Bessel Functions . . . 380
A.6.1 Bessel Functions of the First Kind . . . 381
A.6.2 Bessel Functions of the Second Kind, Yn.z/ . . . 381
A.6.3 Modified Bessel Functions of the First Kind . . . 381
A.6.4 Modified Bessel Functions of the Second Kind, Kn.z/ . . . 381
A.7 Error and Related Function . . . 382
A.8 Exponential Integral . . . 383
A.9 Sine Integral . . . 383
A.10 Gamma Function . . . 383
A.11 Struve Function . . . 384
A.12 Integral Representation . . . 384
A.13 Generalized Hypergeometric Function . . . 384
A.14 Integral Representation (Askey and Olde Daalhuis 2020) . . . 384
Appendix B: Abbreviations . . . 387
Appendix C: SI base units . . . 389
Appendix D: Unit Conversions . . . 391
Index. . . 393

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