American Institute of Mining, Metallurgical and Petroleum Engineers Inc.

Abstract

Description of flow near wells is difficult when modeling steady-state flow in an oil reservoir. A technique is presented which avoids this difficulty by describing pressure and velocity in part numerically and in part analytically.

Introduction

Numerous mathematical models have been developed to predict water-flood recovery. Often a steady-state or semisteady-state model will yield adequate predictions. The method described predictions. The method described herein is the basis of an improved steady-state reservoir model.

A frequent numerical approach is to represent the reservoir by a grid network and to determine the steady-state pressure distribution by relaxation. pressure distribution by relaxation. The principle weakness of this method is that a rectangular grid is poorly suited to represent the pressure distribution around wells. Flow near wells is radially symmetrical and rapidly changing. Flow in a grid network is assumed to occur only along grid lines. Figure 1 depicts the difficulty of representing flow near a source by a grid network. For this reason most numerical models require a large number of grid points to adequately describe flow.

The method presented here utilizes pressure distribution and flow pressure distribution and flow velocities which are in part analytical. In essence, the point sources and sink are subtracted from the original flow problem, leaving a modified flow problem, leaving a modified flow problem with distributed sources and sinks. problem with distributed sources and sinks. The modified flow problem can then be solved numerically with less difficulty than the original flow problem.

DEVELOPMENT

The mathematical analog to steady state flow in a reservoir is based on Darcy's Law and the conservation equation. If the three-dimensional physical system is reduced to a two-physical system is reduced to a two-dimensional model, and if other simplifying assumptions are made, flow in a reservoir can be related to the solution of the following equations.

This content is only available via PDF.