Unsteady-state Fluid Flow

1st Edition

Analysis and Applications to Petroleum Reservoir Behavior

Authors: E.J. Hoffman
Hardcover ISBN: 9780444501844
eBook ISBN: 9780080543451
Imprint: Elsevier Science
Published Date: 2nd July 1999
Page Count: 473
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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.

Unsteady-State Fluid Flow provides:
• empirical and classical methods for correlating and predicting the unsteady-state behavior of petroleum reservoirs
• analysis

Table of Contents

Part I. Reservoir Characteristics.
  1. Petroleum Reserves and their Estimation. Characterization by unsteady-state behavior. Origins of petroleum. Techniques for estimating reserves. Reservoirs and geologic provinces.

  2. Pressure/Production Behavior Patterns. Liquids versus gases. Maintenance of production. Reservoir pressures. Reserves and depletion times.

  3. Pressure/Production Decline Correlations. Reservoir P-V-T behavior. Geometric production decline. Production-time decline. Production loss ratio. Pressure decline.

Part II. The Representation of Flow Through Porous Media.
  1. Concepts of Flow. Unsteady-state flow and compressibility. Flow systems and dissipative effects. Darcy's Law.

  2. The Classic Differential Equations for Flow Through Porous Media. Continuity equation. Steady-state solutions. Analytic solutions for unsteady-state flow. Computer solutions.

  3. Integral Forms for Describing Unsteady-State Flow. Volume and surface integrals. The depletion problem. Permeability form. Production period. Prediction of production. Repressurization.

  4. Two-Phase and Multiphase Flow: Gas, Oil, and Water. Concurrent two-phase flow. Multiphase flow. Immiscible and (partially) miscible drives. Enhanced oil recovery.

Part III. Reduction to Practice.
  1. Steady-State: Productivity Tests. Determination of producing radius. Productiv


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© Elsevier Science 1999
Elsevier Science
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About the Author

E.J. Hoffman

Affiliations and Expertise

P.O. Box 1352, Laramie, WY 82070, USA