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Lanfranchi, E., S.A. Consultores C.S.C.

Abstract

A rather comprehensive theory has been developed to describe fluid flow phenomena in porous media. This theory, under the constraints porous media. This theory, under the constraints of appropriate simplifying assumptions, ultimately leads to expressions which enable the petroleum engineer to characterize reservoir behaviour. In this context, one frequently treats some form of the diffusivity equation in conjunction with data obtained from well tests to arrive at specific reservoir parameters. For example, so-called pressure transient analysis can be used to arrive pressure transient analysis can be used to arrive at estimates of the formation thickness-permeability product, the storage capacity, the average reservoir pressure, etc. For liquid flow, the technique involves reducing the diffusivity equation to a form where pressure becomes the independent variable. This requires the assumptions that the liquid is both, ideal and slightly compressible.

In this work it has been developed an alternative approach which does not depend upon the assumptions cited above. An additional intent is to investigate the effects of these suppositions on computed pressure distributions in a one-dimensional system.

Introduction

The mathematical description of fluid flow through porous media has been known for a long time porous media has been known for a long time However, in the past most solutions to reservoir problems were limited to simple cases where the problems were limited to simple cases where the applications did not involve much computation. The development of computers and new numerical techniques), have made it possible to treat the more difficult problems of petroleum engineering.

In 1934, Hurst and Muskat introduced mathematical equations describing flow of a single-phase slightly-compressible fluid through a homogeneous porous medium. They presented several solutions for some relatively simple cases. The first effort to apply these equations to buildup pressure analysis for incommpressible fluid flow was made by Muskat. The advance in methods and computers allowed the study of more complicated situations, but in all of them, it is implicitly assumed that the liquid phases in a reservoir are ideal and that they furthermore are slightly compressible. when a large amount of gas is dissolved in a crude under reservoir conditions, the departure from ideality and slight compressibility may be substantial. The present work was undertaken to evaluate the effects of these assumptions and develop an alternative approach which does not rely upon them. To this end, we confine our attention to a comparison of computed pressure distributions in a one-dimensional system.

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