Advances in Computer-Aided Well Test Interpretation

Abstract

Summary Several different computer methods combine to constitute a computer-aided well-test interpretation. This paper compares some of the different approaches currently in use. Future directions are discussed, as are deconvolution, pressure derivatives, model recognition, nonlinear regression, and confidence intervals. Introduction Despite the feeling expressed several times over the past 40 years that well-test analysis had reached its peak development, an examination of recent advances shows continuous expansion in capability, with future improvement likely. The expansion in interpretation capability over the past decade arose mainly from the development of computer-aided techniques, which, although introduced 20 years ago, have come into use only recently. The broad application of computer-aided interpretation originated with the improvement of the methodologies and continued with the expansion in computer access and capability that accompanied the explosive development of the microcomputer industry. This paper focuses on the different pieces of the methodology that combine to constitute a computer-aided interpretation and attempts to compare some of the approaches currently used. Future directions of the approach are also discussed. The separate areas discussed are deconvolution, pressure derivatives, model recognition, nonlinear regression, and confidence intervals. Background During the 1970's and 1980's, mathematical and numerical techniques provided new well-test solutions for a wide variety of reservoir configurations, such as fractures, layered reservoirs, and multiple porosities. The complexity of these models and the large number of parameters that they contain limited their analysis by traditional graphical methods. Of the two main types of graphical analyses, straight-line methods (such as Horner plots) can provide estimates of, at most, two unknowns (from the slope and intercept of the line). Type-curve methods can usually provide only three parameters--one from each of the two axes and one from a curve from the family of curves used. In the process of seeking a method to match more unknowns, work began on the use of nonlinear regression. Earlougher and Kersch's 1972 paper was key in this area. That and later work showed that nonlinear regression could not only match reservoir models with more than a few parameters, but also provide several significant advantages over graphical matching. One important advantage was the illustration of the use of confidence intervals, another was the application of nonlinear regression to reservoir responses that resulted from complex (variable-rate) impulses. Matching complex models and complex impulses made up the challenge in and motivation for computer-aided analysis.