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Well Test Analysis for Multilayered Reservoirs with Formation Crossflow

Book Description

Well Test Analysis for Multilayered Reservoirs with Formation Crossflow introduces the fundamentals of well test analysis of a multilayered reservoir with formation crossflow. The effects of reservoir parameters on wellbore pressure and flow rate are examined, as is a proper method that has been established to analyze well test data that leads to better determinations on the reservoir parameters for each layer of the reservoir.

Focusing on multilayer models for data analysis, this reference explains the reasons for the existence of single-phase crossflow in multilayer reservoirs, exploring methods to establish them and presenting practical applications to utilize and implement for today’s more complex reservoirs.

Aiding in better well testing operations and models, this book is a one-stop solution for today’s reservoir and production engineer, helping them understand every layer of their reservoir.

  • Includes real-world examples of well testing through multilayered reservoirs, whether with crossflow or with formation crossflow
  • Provides strong guidance and criteria of research on reservoir dynamic performance, such as physical models and mathematical models
  • Includes a new unsteady crossflow model for vertical interference testing in low-permeability zones
  • Describes interpretation methods for different cases in multilayer reservoirs, including a new model called semipermeable walls for stratified reservoirs, drawdown test procedures and layer-by-layer test procedures that are useful for shales between layers

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. About the Author
  6. Acknowledgment
  7. Introduction
  8. Chapter 1: Semipermeable Wall Model of a Multilayer Reservoir with Crossflow
    1. Abstract
    2. 1.1 Introduction
    3. 1.2 Semipermeable Wall Model and Fundamental Differential Equations—Oil Reservoir
    4. 1.3 Semipermeable Wall Model and Fundamental Differential Equations—Gas Reservoir
    5. 1.4 Crossflow Behavior for Incompressible Flow
    6. 1.5 Summary
  9. Chapter 2: Single-Phase Fluid Flow in a Two-Layer Reservoir with Significant Crossflow
    1. Abstract
    2. 2.1 Introduction
    3. 2.2 Pressure Drawdown and Buildup Behavior When Both Layers Are Completed at a Single Well
    4. 2.3 Crossflow Behavior in a Partially Perforated Two-Layer Reservoir
    5. 2.4 Maximum Effective Hole Mathematical Model and Analytical Solution for a Two-Layer Reservoir
  10. Chapter 3: Pressure Transients and Crossflow Caused by Diffusivities in Multilayer Reservoirs
    1. Abstract
    2. 3.1 Assumption and the Flow Problem
    3. 3.2 Approximate Analytic Solutions
    4. 3.3 Numerical Solutions for Cases with n=3 and n=5
    5. 3.4 Numerical Solutions and Comparison with Theory
    6. 3.5 Analytical Solution of the Three-Layer Reservoir
    7. 3.6 Summary
  11. Chapter 4: Crossflow Behavior and the Determination Reservoir Parameters by Drawdown Tests in Multilayer Reservoirs
    1. Abstract
    2. 4.1 Assumption and Mathematical Expression of the Problem
    3. 4.2 The Unsteady Flow Behavior in Drawdown and Buildup Tests When Partial Layers Produce with Crossflow
    4. 4.3 New Drawdown Test
    5. 4.4 Summary
  12. Chapter 5: Determination of Total Productivity by a Constant Wellbore Pressure Flow Test and the Crossflow Behavior in Multilayer Reservoirs
    1. Abstract
    2. 5.1 Assumption and Approximate Theoretical Solution of the Problem
    3. 5.2 Numerical Results and Comparison with the Approximation Theory
    4. 5.3 Exact Solution of a Two-Layer Reservoir with Crossflow Under a Constant Pressure Condition
    5. 5.4 Summary
  13. Chapter 6: Determination of Individual Layer Properties by Layer-by-Layer Well Tests in Multilayer Reservoirs with Crossflow
    1. Abstract
    2. 6.1 Assumptions and Mathematical Model
    3. 6.2 Approximate Solution of Unsteady Flow in a Three-Layered Reservoir and Its Extension
    4. 6.3 Discussion of Simulation Results
    5. 6.4 Interpretation Theory
    6. 6.5 Summary
  14. Chapter 7: Determination of Parameters for Individual Layers by Transient Well Tests in Multilayer Reservoirs
    1. Abstract
    2. 7.1 Introduction
    3. 7.2 Approximation Solution of Unsteady-Flow and Crossflow Behavior Caused by Skin Factors
    4. 7.3 Determination of Parameters for Individual Layers by a Series of Transient Tests
    5. 7.4 Determination of Semipermeabilities by Steady Rates
    6. 7.5 Summary
  15. Chapter 8: Interpretation Theory for Vertical Interference Testing Across a Low-Permeability Zone
    1. Abstract
    2. 8.1 Introduction
    3. 8.2 Model Description
    4. 8.3 The Interpretation Theory When q(t) is Known
    5. 8.4 The Interpretation Theory When the Well Produces with a Constant Surface Rate
    6. 8.5 The Influence of Different Parameters on Drawdown Curves
    7. 8.6 Summary
  16. Chapter 9: Unsteady Crossflow Model for Leaky Vertical Interference Testing Across a Low-Permeability Zone
    1. Abstract
    2. 9.1 Introduction
    3. 9.2 Model Description
    4. 9.3 Relationships of Different Models
    5. 9.4 Solution of the Problem
    6. 9.5 Interpretation Method of Parameters
    7. 9.6 Comparison of Different Models
    8. 9.7 Summary
  17. Chapter 10: Material Balance Equation of Multilayer Gas Reservoir
    1. Abstract
    2. 10.1 Material Balance of Two-Layer Gas Reservoir
    3. 10.2 Reserve Estimation of a Two-Layer Commingled Gas Well
    4. 10.3 Material Balance Equation of Gas Reservoir with a Supplying Region
    5. 10.4 Summary
  18. Chapter 11: Computer-Aided Well Test Design and Well Test Analysis of Layered Reservoirs
    1. Abstract
    2. 11.1 Introduction
    3. 11.2 Computer Program
    4. 11.3 Examples of Well Test Design
    5. 11.4 Examples of Well Test Analysis
    6. 11.5 Summary
  19. Nomenclature
  20. Appendix A: Analytical Solution for the Stationary Value of f (Chapter 2)
  21. Appendix B: Approximate Solution of the Diffusivity Crossflow Problem in n-Layer Reservoirs (Chapter 3)
  22. Appendix C: Solution of the Crossflow Caused by Different Boundary Pressures (Chapter 4)
  23. Appendix D: Approximate Solution for a Well Producing From All Layers
    1. D.1 Approximate Solution for the Short Time Period
    2. D.2 Approximate Solution for the Long Time Period
  24. Appendix E: Approximate Solution and Its Extension When Each Layer of a Two-Layer Reservoir Produces Independently
    1. E.1 Approximate Solution for the Short Time Period
    2. E.2 Approximate Solution for the Long Time Period
    3. E.3 Buildup Case
    4. E.4 Extension of the Solution for Two-Layer Reservoirs to n-Layer Reservoirs
  25. Appendix F: Case for Variable Bottom-Hole Rate (Chapter 8)
    1. F.1 Case for Unknown Function
    2. F.2 Case for a Known Leakage Rate
    3. F.3 Case for
  26. Appendix G: Case for Constant Wellhead Rate (Chapter 8)
    1. G.1 Case for Unknown Leakage Rate qD2
    2. G.2 Case for Known Function f(tD)
    3. G.3 Case for Leakage Function
    4. G.4 Case for
    5. G.5 Limiting Behavior for Function
  27. Appendix H: Solution of the Problem (Chapter 9)
    1. H.1 When Leakage Function f Is Known
    2. H.2 When Leakage Function
    3. H.3 When Leakage Function f Is Unknown
  28. Appendix I: Limiting Behavior for f=α=αD(pwD1-pwD2) (Chapter 9)
    1. I.1 Early Time Period
    2. I.2 Behavior When t→0 (Short Time Period)→0 (Short Time Period)
    3. I.3 Behavior When t→∞ (Long Time Period)→∞ (Long Time Period)
  29. Appendix J: Commonly Used Units in Different Unit Systems
  30. References
  31. Index