The source-type solution in the problem of unsteady filtration in a medium with random nonuniformity

Abstract

The fundamental problems of the theory of filtration in media with random nonuniformities were formulated in [1] and methods of solution were indicated. Primary attention was devoted to the steadystate filtration processes. In the following we solve one of the most important unsteady problems and indicate the connection of the result obtained with the widely used methods of determining strata parameters from the curves of the pressure variation in nonflowing wells. We note that the interpretation of the results of such measurements is usually carried out with the aid of the solution of the corresponding problem for a homogeneous stratum or for a stratum whose nonuniformity has a regular nature (for example, [2]), which definitely limits the possibilities of the method. At the same time it is obvious that the solution of these problems for irregular media and particularly the determination of their effective characteristics requires the use of statistical methods of computation.

It is also not difficult to see that the results obtained below may be used for the solution of the corresponding problems of heat conduction, diffusion, etc.