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Abstract

A numerical method based on the calculus of variations is proposed for the solution of the problem of computing the behavior of single-phase linear or radiial gas flow. The method is shown to allow consideration of the effect of linear or radially-varying reservoir rock properties.

This paper discusses both the method of solution and the computer program which results from its application. Examples are presented which demonstrate the relevance and usefulness of the program, as well as the small computer cost program, as well as the small computer cost required for solution to a particular problem. problem

Introduction

The application of computer simulation to reservoir engineering has grown very rapidly in the past few years. This growth has paralleled the increased activity in research on numerical methods for approximating the solution of partial differential equations. Until partial differential equations. Until quite recently most of the development in numerical methods centered on the use of finite difference methods, but in the last three or four years quite a large portion of the theoretical work in portion of the theoretical work in numerical analysis has shifted to the study of variational methods and this paper is devoted to the treatment of the paper is devoted to the treatment of the single-phase flow of a gas in a radially symmetric reservoir. The specific objectives of this research are as follows:

  1. The development of a one-dimensional, radial, one-flowing phase, unsteady-state, heterogenous gas well simulator based on variational methods.

  2. The simulator should allow the properties of formation net pay, properties of formation net pay, permeability, and porosity to vary as a permeability, and porosity to vary as a function of distance from the well. Jump discontinuities should be allowed to occur in these data.

  3. The effect of water and rock compressibility and of varying gas viscosity, gravity and Z-Factor should be included.

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