A simplified analytical method for estimating the productivity of a horizontal well producing at constant rate or constant pressure

In this work, we present an analytical method for estimating the productivity of an infinite-conductivity horizontal well in a closed, box-shaped reservoir producing at either a constant rate or a constant pressure. It is based on approximate analytical solutions for the 2D inflow performance of an infinite-conductivity fracture in a rectangular drainage area and the near-well pressure drop for flow to a circular well in a vertical cross-section of the reservoir. The method can accommodate reservoirs with arbitrary horizontal and vertical aspect ratios, off-center wells, permeability anisotropy and skin factors. Being simple and straightforward, the method can be readily implemented in a standard spreadsheet program. Well productivities for depletion at constant rate are always higher than at constant pressure. The difference can be as much as 22% for a fully penetrating well in a thin, isotropic reservoir.