Unsteady-state Fluid Flow: Analysis and Applications to Petroleum Reservoir Behavior
Regular price
161.000 KD
inc. VAT
Couldn't load pickup availability
Table of contents
- Cover
- Copyright Pageiv
- Contentsvii
- Prefacev
- Part I: Reservoir Characteristics1
- CHAPTER 1. PETROLEUM RESERVES AND THEIR ESTIMATION3
- 1.1 Characterization by Unsteady-State Behavior4
- 1.2 Origins of Petroleum5
- 1.3 Techniques for Estimating Reserves13
- 1.4 Reservoirs and Geologic Provinces16
- CHAPTER 2. PRESSURE/PRODUCTION BEHAVIOR PATTERNS25
- 2.1 Liquids versus Gases25
- 2.2 Maintenance of Production27
- 2.3 Reservoir Pressures28
- 2.4 Reserves and Depletion Times30
- CHAPTER 3. PRESSURE/PRODUCTION DECLINE CORRELATIONS41
- 3.1 Reservoir P-V-T Behavior41
- 3.2 Geometric Production Decline44
- 3.3 Production-Time Decline48
- 3.4 Production Loss Ratio49
- 3.5 Pressure Decline67
- Part II: The Representation of Flow Through Porous Media73
- CHAPTER 4. CONCEPTS OF FLOW75
- 4.1 Unsteady-State Flow and Compressibility75
- 4.2 Flow Systems and Dissipative Effects77
- 4.3 Darcy's Law81
- CHAPTER 5. THE CLASSIC DIFFERENTIAL EQUATIONS FOR FLOW THROUGH POROUS MEDIA89
- 5.1 Continuity Equation89
- 5.2 Steady-State Solutions94
- 5.3 Analytic Solutions for Unsteady-State Flow96
- 5.4 Computer Solutions108
- CHAPTER 6. INTEGRAL FORMS FOR DESCRIBING UNSTEADY-STATE FLOW113
- 6.1 Volume and Surface Integrals113
- 6.2 The Depletion Problem118
- 6.3 Permeability Form128
- 6.4 Production Period141
- 6.5 Prediction of Production142
- 6.6 Repressurization146
- CHAPTER 7. TWO-PHASE AND MULTIPHASE FLOW: GAS, OIL, AND WATER155
- 7.1 Concurrent Two-Phase Flow157
- 7.2 Multiphase Flow165
- 7.3 Immiscible and (Partially) Miscible Drives165
- 7.4 Enhanced Oil Recovery166
- Part III: Reduction to Practice171
- CHAPTER 8. STEADY-STATE: PRODUCTIVITY TESTS173
- 8.1 Determination of Producing Radius175
- 8.2 Productivity Index181
- 8.3 Back-Pressure Tests183
- 8.4 Departure from Ideal Behavior187
- CHAPTER 9. AN EVALUATION OF UNSTEADY-STATE SOLUTIONS FOR DRAWDOWN AND TRANSITION193
- 9.1 Summary Statement193
- 9.2 Unsteady-State Solutions for Drawdown198
- 9.3 Experimental Comparisons206
- CHAPTER 10. GASEOUS UNSTEADY-STATE RADIAL FLOW BEHAVIOR FROM THE CALCULATED RESULTS OF BRUCE ET AL.231
- 10.1 Overview231
- 10.2 Detailing and Analysis of the Results of Bruce et al.235
- 10.3 Closed versus Open Systems265
- 10.4 Determination of Reservoir Extent and Permeability267
- 10.5 Back-Pressure Correlation278
- 10.6 Transitional Behavior280
- CHAPTER 11. A CRITIQUE OF BOUNDARY CONDITIONS, DEGREES OF FREEDOM AND DARCY'S LAW287
- 11.1 Problem and Expediencies287
- 11.2 Pressure Gradient at the closed Boundary292
- 11.3 Degrees of Freedom295
- 11.4 Darcy's Law in Radial Flow314
- 11.5 Systems in Chaos318
- 11.6 Steady-State Profiles319
- CHAPTER 12. THE RESULTS OF BRUCE ET AL. IN TERMS OF INTEGRAL FORMS329
- 12.1 Review of the Derived Relationships and Correlations329
- 12.2 Relation to the Results of Bruce et al.334
- CHAPTER 13. THE COMPUTATION OF RESERVES AND PERMEABILITY FROM STABILIZED FLOW-TEST INFORMATION (Back363
- 13.1 Reserves and Permeability Calculations363
- 13.2 Computer Applications373
- Part IV: The use of Steady-State Profiles for Unsteady-State Flow391
- CHAPTER 14. APPROXIMATE SOLUTIONS DURING DRAWDOWN AND LONG-TERM DEPLETION393
- 14.1 Compressible Liquids393
- 14.2 Compressible Gases412
- 14.3 Transition (or Stabilization) between Drawdown and Long-Term Depletion418
- 14.4 Estimation of Reservoir Extent and Reserves419
- CHAPTER 15. REPRESENTATION OF WATER DRIVES421
- 15.1 Infinite Reservoirs (with Drive)421
- 15.2 Finite Reservoirs (with Drive)423
- 15.3 Gaseous Flow and Displacement427
- 15.4 Field Histories428
- CHAPTER 16. PRODUCTION-DECLINE BEHAVIOR431
- 16.1 Effect of Flow up through the Well Tubing431
- 16.2 Decline of Production Rate436
- AFTERWORD443
- GLOSSARY447
- SYMBOLS453
- INDEX463
The ubiquitous examples of unsteady-state fluid flow pertain to the production or depletion of oil and gas reservoirs. After introductory information about petroleum-bearing formations and fields, reservoirs, and geologic codes, empirical methods for correlating and predicting unsteady-state behavior are presented. This is followed by a more theoretical presentation based on the classical partial differential equations for flow through porous media.
Whereas these equations can be simplified for the flow of (compressible) fluids, and idealized solutions exist in terms of Fourier series for linear flow and Bessel functions for radial flow, the flow of compressible gases requires computer solutions, read approximations. An analysis of computer solutions indicates, fortuitously, that the unsteady-state behavior can be reproduced by steady-state density or pressure profiles at successive times. This will demark draw down and the transition to long-term depletion for reservoirs with closed outer boundaries.
As an alternative, unsteady-state flow may be presented in terms of volume and surface integrals, and the methodology is fully developed with examples furnished. Among other things, permeability and reserves can be estimated from well flow tests.
The foregoing leads to an examination of boundary conditions and degrees of freedom and raises arguments that the classical partial differential equations of mathematical physics may not be allowable representations.
For so-called open petroleum reservoirs where say water-drive exists, the simplifications based on successive steady-state profiles provide a useful means of representation, which is detailed in the form of material balances.
Whereas these equations can be simplified for the flow of (compressible) fluids, and idealized solutions exist in terms of Fourier series for linear flow and Bessel functions for radial flow, the flow of compressible gases requires computer solutions, read approximations. An analysis of computer solutions indicates, fortuitously, that the unsteady-state behavior can be reproduced by steady-state density or pressure profiles at successive times. This will demark draw down and the transition to long-term depletion for reservoirs with closed outer boundaries.
As an alternative, unsteady-state flow may be presented in terms of volume and surface integrals, and the methodology is fully developed with examples furnished. Among other things, permeability and reserves can be estimated from well flow tests.
The foregoing leads to an examination of boundary conditions and degrees of freedom and raises arguments that the classical partial differential equations of mathematical physics may not be allowable representations.
For so-called open petroleum reservoirs where say water-drive exists, the simplifications based on successive steady-state profiles provide a useful means of representation, which is detailed in the form of material balances.
Unsteady-State Fluid Flow provides:
• empirical and classical methods for correlating and predicting the unsteady-state behavior of petroleum reservoirs
• analysis of unsteady-state behavior, both in terms of the classical partial differential equations, and in terms of volume and surface integrals
• simplifications based on successive steady-state profiles which permit application to the depletion of both closed reservoirs and open reservoirs, and serves to distinguish drawdown, transition and long-term depletion performance.