By
E.J. Hoffman, P.O. Box 1352, Laramie, WY 82070, USA
Description
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 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.
