Green's Functions for Solving Unsteady Fluid Flow Problems in Naturally Fractured Reservoirs with Arbitrary Fracture Connectivity: Part II—Applications

Abstract

ABSTRACT A general theory of Green's functions for solving unsteady fluid flow problems in naturally fractured reservoirs was presented in Part I of this paper. The governing equations for the fracture and pore system pressures are two linear parabolic partial differential equations which are coupled by a pressure-history dependent interporosity fluid transfer term. This model allows for the connectivity and permeability of both the fracture and pore systems over macroscopic distances and incorporates an improved unsteady interporosity flow model that is valid for general fracture configurations. In this paper, we present a simple technique for deriving the Green's functions and source solutions required to solve unsteady flow problems by the theory developed in Part I. The technique is based on the solution of the eigenvalue problem for the Laplace operator and can be applied to solve a class of problems in which the boundary conditions for the fracture and pore system pressures are uncoupled and have the same functional form. Tables of Green's functions and source functions are presented for layered and rectangular reservoir configurations in bounded and unbounded domains.