Abstract

In this investigation, a new method was developed for analysis of variable-rate drawdown tests of low-permeability gas reservoirs. Rate variation, usually declining during the test, is considered as a continuous function of time, contrasted with most other multiple-rate solutions which superpose the effects of representative rates corresponding to discrete time steps.

A computer program was developed to perform a non-linear least squares determination of the coefficients in the equation which uniquely describes the rate-time profile recorded during the test. A mathematical model was formulated in terms of the Volterra linear integral equation. The unique pressure response as a function of time, corresponding to what the authors' term a constant rate, may be determined from this model. A companion computer program was written to provide a numerical solution of the model, including values for effective gas permeability and skin. After obtaining from the model appropriate pressure response f(tk) as a function of time, conventional (semilog) analytical procedures may be used.

Several field cases are presented which illustrate the good match achieved between predicted pressure history and that recorded at wells pressure history and that recorded at wells producing from a low-permeability gas reservoir. producing from a low-permeability gas reservoir. In the case of an unfractured reservoir, a good history match was achieved without further assessment of permeability and skin data. Wells subjected to hydraulic stimulation exhibited the enfluence of the vertical fracture system during the drawdown test resulting in optimistic values for permeability and skin. In such cases, a good history match was achieved by correcting permeability using the methods proposed by Russell and Truitt.

Introduction

Methods for analyzing flowing well behavior to obtain estimates of the physical parameters of the reservoir require as a fundamental condition that flow rate be held constant. This is an unreasonable requirement applied to low-permeability gas reservoirs where rates often vary (decline) uncontrollably during a single-point drawdown test. Several descriptions appear in the literature for conducting and analyzing variable-rate tests, usually entailing application of the principle of superposition in time.

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