Transient flow of slightly compressible fluids through double-porosity, double-permeability systems ? A state-of-the-art review

Abstract

The theory of transient flow of slightly compressible fluids through naturally fractured reservoirs based on the double porosity conceptualization is summarized. The main achievements in the theory of fluid flow in leaky aquifer systems which are closely related with the double-porosity, double-permeability problems are also addressed. The main emphasis of this review is the analytical treatment of these problems.

A numerical dual‐porosity model with semianalytical treatment of fracture/matrix flow

“…assuming that it is directly proportional to the difference between P 1 and jim: (7) where a. is a parameter that depends on block shape, and has dimensions of area-l [m-2 ]. The governing equation (6) for jim then takes the form (8) Expressions (7) and (8) for the flux and the matrix pressure are often referred to as the "quasi-steady-state" approximation [Barker, 1985;Chen, 1989]. ThiS terminology can be understood by considering the basic problem in which · the fracture pressure P f , which serves as the boundary condition for the matrix block, increases abruptly at t = 0 -8 -from its initial value Pi to a new value P 0 • In this example, and in much of the following discussion, we assume that the matrix block is a sphere of radius am; extension to other block geometries is discussed in Appendix A.…”

Critique of dual continuum formulations of multicomponent reactive transport in fractured porous media

“…An important unanswered question is how to scale such processes to the macroscale where the continuum formulation is valid. Triple-and multiple-porosity models that have been used to (Closmann, 1975;Abdassah and Ershaghi, 1986;Chen, 1989) may 'be useful in such instances, but are beyond the scope of the present treatment.…”

Numerical dual-porosity model with semianalytical treatment of fracture/matrix flow

“…When a single-phase, slightly compressible fluid flows through a macroscopically-homogeneous fractured medium, the fluid pressure in the fractures is ·governed by the following diffusion equation used in reservoir engineering [Matthews and Russell, 1967]: see Chen, 1989]. (It is not clear that such a length scale will always exist [Long and .…”

“…assuming that it is directly proportional to the difference between P 1 and jim: (7) where a. is a parameter that depends on block shape, and has dimensions of area-l [m-2 ]. The governing equation (6) for jim then takes the form (8) Expressions (7) and (8) for the flux and the matrix pressure are often referred to as the "quasi-steady-state" approximation [Barker, 1985;Chen, 1989]. ThiS terminology can be understood by considering the basic problem in which · the fracture pressure P f , which serves as the boundary condition for the matrix block, increases abruptly at t = 0 from its initial value Pi to a new value P 0…”