An approximate model for well productivity in heterogeneous porous media

An approximate analytical model describing the productivity of vertical wel ls in two-dimensional, heterogeneous porous media is presented. The model r epresents well-driven flow in terms of an effective permeability for linear flow coupled with an effective near-well skin. This representation is diff erent from previous descriptions, which represent the problem solely in ter ms of a system-dependent equivalent permeability for radial flow. Extensive comparisons between the model predictions and numerical calculations for s ingle wells and two-well systems in log-normally distributed permeability f ields are presented. These results demonstrate the high degree of accuracy of the approximate model over an extensive parameter range. For the problem s considered, the method is shown to be more accurate than a previous spati al averaging approach. More importantly, the new method provides a basis fo r extending existing semianalytical solutions, applicable to homogeneous or layered systems, to more general heterogeneous systems in three dimensions .