Analysis of the semianalytical method for matching aquifer influence functions using an analytical model

Abstract

For a heterogeneous aquifer of unknown size and shape, ics. Aquifer Influence Functions (AIF) can be used to model the aquifer pressure behavior from field production and pressure data. Two methods have been used in the past to accomplish this, namely Linear Programming (LP) and the Semianalytical technique. The latter is based on the analytical solution form of a heterogeneous aquifer of any size and shape. The approximating AIF is a continuous function, which is a truncated series of the exact analytical solution. This Semianalytical function is fitted to field data by the use of nonlinear least squares fitting. It has the advantages over the LP method that it is much faster, uses less computer space, and does not require evenly spaced production periods. For the cases in which the OGIP is unknown, a technique was proposed in the past in which the term Relative Error is defined. Several values of OGIP are assumed, and the one that yields the minimum Relative Error is the actual or optimum value of OGIP. Because of the nonlinear nature of the optimization procedure, when the Semianalytical technique is used along with the Relative Error technique, it tends to be caught in the so-called local minima, which lead to the determination of spurious values of the AIF and the optimum OGIP. Both the LP and the Semianalytical techniques have been validated using field data. However, when the latter is used, weird variations of the Relative Error function, and unrealistically low values of the optimum OGIP are observed. A simple analytical model is used in this project. It allows the generation of synthetic data. The objective is to use those as input data to the Semianalytical and Relative Error techniques and determine their effectiveness to determine the AIF and the optimum OGIP which are known in advance. A modification is proposed in the current research to prevent the nonlinear regression from getting caught in the local minima. After this goal is attained, typical features in the normalized Relative Error and allows the determination of the drive mechanism and the OGIP even in gas reservoirs whose histories are so brief that the use of the p/Z technique becomes prohibitive.