Calculation of well productivity in a reservoir simulator (II)

Conventional simulators calculate the well productivity using Peaceman's equation for equivalent block radius and the well block pressure. This is generally acceptable for most vertical and horizontal wells. However, no formulation is available for slanted wells. Even for vertical and horizontal wells in which block aspect ratios are far from unity or where the well completion interval is short or the well is located close to a reservoir boundary or other wells, the existing formulations can give erroneous answers. In our previous paper, a novel method was introduced for calculating very accurately the productivity of wells of any deviation (0-90°) for a homogeneous reservoir. In this paper, we present a more general solution for general well position and applicable to multiple wells and heterogeneous reservoirs. A novel method is presented to convert the heterogeneous model to an anisotropic but uniform permeability model before applying the new analytical technique, in conjunction with a numerical simulator. The analytical model developed for this purpose is coupled with a numerical simulator to produce the necessary parameters needs for simulation of well performance in a conventional simulator. The results will have a wide field application for horizontal, vertical and deviated wells.