Variable Flow Well Test Analysis by a Computer Assisted Matching Procedure
Authors: Tsang Chin Fu , Narasimhan T.N. , Witherspoon P.A. 
Published: December 2007

Abstract
The technique of type-curve matching by eye judgement continues to be an extremely powerful tool in modern well test analysis. In practice, the method is restricted to cases involving steady flow rates and to include not more than three curve fitting parameters. In order to extend the type-curve method to more general problems of interest in the fields of petroleum problems of interest in the fields of petroleum engineering and hydrogeology, a computer aided curve matching procedure is proposed, which employs a multiparameter least square minimization procedure. Using this technique, the type-curve procedure. Using this technique, the type-curve method has been extended to problems involving arbitrarily varying flow rates in the presence of a boundary, well-bore storage and steady state skin. The proposed method has been verified against four hypothetical problems with known analytic solutions and has been applied to actual drawdown data collected from four geothermal well tests. The proposed method can easily be expanded to include such other type-curve situations as leaky multiple-aquifer systems, wells with horizontal or vertical fractures and wells with partial penetration. It is believed that this partial penetration. It is believed that this method is a very useful addition to the existing repertoire of well test analysis techniques.

Introduction
The technique of type-curve matching is extensively employed by petroleum engineers and hydrogeologists for analyzing well test data. Although this technique is extremely useful, it has a few inherent drawbacks. For example, the process of matching curves by eye judgement is process of matching curves by eye judgement is subject to individual bias. Moreover, most of the type-curves used in the literature relate to constant flow rate and when it is desired to include such additional features as well-bore storage, skin effects or boundaries, the result is the generation of too many families of type-curves, rendering the process of curve matching to be extremely cumbersome. To avoid some of these difficulties the method of ratios has been suggested by some. However, the ratio method uses only two or three data points for interpretation and as such is sensitive to the errors inherent in the data points chosen for interpretation. Under these circumstances, it is of great practical interest to develop computer assisted practical interest to develop computer assisted techniques of curve-fitting which will not only minimize the variabilities of personal judgements in the analysis but also extend the curve- matching technique to sufficiently general situations usually neglected while developing type-curves for eye-judgment applications. The purpose of this paper is to present a computer assisted curve-matching technique which permits the analysis of data from well tests with arbitrarily varying discharge, with or without effects of well-bore storage and skin. In addition, the method can also take into consideration the presence of a boundary (barrier or leaky), using the classical concept of the image well. Alternatively, the image well could be replaced by a second real well, enabling one to consider a production-production or production-injection doublet. The method is quite production-injection doublet. The method is quite powerful and can be extended to cases involving powerful and can be extended to cases involving leaky cap-rocks or the presence of fractures close to the well-bore.