Multiple-wells system productivity equations in a rectangular reservoir

Several oil reservoirs in Kuwait and Saudi Arabia are operating under active water drive maintaining their reservoir pressure close to its initial and above bubble-point pressure. For such reservoirs, productivity equations based on the steady-state condition are highly required. This work presents new analytical equations to obtain steady-state productivity for a multiple-wells system in homogeneous, anisotropic rectangular reservoirs with different lateral boundaries. Five cases of different lateral boundaries are defined and studied in this paper. The equations are derived by taking fully penetrating vertical wells as uniform line sinks, and solving a square matrix of dimension n, where n is the number of wells. The derived equations relate the production rate vector to the pressure drawdown vector. They provide fast analytical tools to evaluate the performance of multiple-wells system, which are located arbitrarily in an anisotropic rectangular reservoir. It is concluded that for a given multiple-wells system, as the number of constant pressure boundaries increases, the total productivity index increases. Also, in a given rectangular reservoir, if the wells are located symmetrically with respect to the same type of lateral boundary, then their productivity indices are equal.