The Use of a Semianalytical Method for Matching Aquifer Influence Functions

Abstract

ABSTRACT Aquifer performance can be modelled with an aquifer influence function (AIF). For a heterogeneous aquifer of unknown size and shape, the AIF can be calculated from field production and pressure data. The most successful method for doing this has used linear programming (LP) to compute the AIF. The current research introduces an alternate method to LP in an effort to improve computer storage and speed. The new technique 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 analytical solution. This "semi-analytical function" is fit to field data by the use of nonlinear least squares fitting, using the Levenberg-Marquardt method. The advantages of this method, over the LP method, are that the new method (1) uses less computer storage, (2) is much faster, (3) does not require evenly spaced production periods, and (4) is more robust in use with actual field data. The results of the new method are striking. Results show that the new method runs as much as 3,218 times as fast as LP and only uses a fraction of the computer storage. The previous implementation of the LP methods was limited to about 70 months of production history on a microcomputer, whereas the new method is virtually unlimited on the amount of production data it can handle.