An Approximate Model for Well Productivity in Heterogeneous Porous Media

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