Well Test Analysis of Heterogeneous Reservoirs

Abstract

Abstract The method of Green's functions has been a powerful tool to solve unsteady flow problems in homogeneous reservoirs. This paper extends the application of Green's function method to difFusivity problems in heterogeneous reservoirs. A basic formula is obtained for expressing in terms of Green's functions the general solution to the pressure equation with nonhomo-geneous initial and boundary conditions. Through some practical examples, appropriate methods are suggested to obtain the Green's function, which is more difficult to find in heterogeneous problems than in homogeneous ones. Reciprocity is a basic and useful property which facilitates our understanding of porous media flow problems. With the Green's function method developed, the conditions under which the Principle of Reciprocity holds in heterogeneous formation are studied. The application of the reciprocity principle to interference tests in heterogeneous reservoirs is discussed for practical cases.