An evaluation of Jacob's Method for the interpretation of pumping tests in heterogeneous formations

Abstract

Most pumping tests are interpreted using the classical Theis assumption of large‐scale homogeneity with various corrections to account for early time behavior of drawdown curves. When drawdowns are plotted versus log time, late time data often delineate a straight line, which is consistent with Jacob's approximation of Theis' solution but may seem surprising in view of the heterogeneity of natural media. The aim of our work is to show that Jacob's method leads to a good approximation of the effective transmissivity of heterogeneous media when constrained to late time data. A review of several multiwell pumping tests demonstrates that when drawdown curves from each observation well are interpreted separately, they produce very similar transmissivity T estimates. However, the corresponding estimates for storativity span a broad range. This behavior is verified numerically for several models of formation heterogeneity. A very significant finding of the numerical investigation is that T values estimated using simulated drawdown from individual observation wells are all very close to the effective T value for parallel flow. This was observed even in nonmultiGaussian T fields, where high T zones are well connected and where the effective T is larger than the geometric average of point values. This implies that Jacob's method can be used for estimating effective T values in many, if not most, formations.