Development and application of the multiwell productivity index (MPI)
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In this article we generalize the concept of the pseudosteady-state productivity index for the case of multiple wells producing from or injecting into a closed rectangular reservoir of constant thickness. The work complements the analytical study by Rodrguez and Cinco-Ley1 for systems produced at constant flowing pressures. Wells are represented by fully penetrating vertical line sources located arbitrarily in a homogeneous and isotropic reservoir. The multiwell productivity index (MPI) is a square matrix of dimension n, where n is the number of wells. The MPI provides a simple, reasonably accurate and fast analytical tool to evaluate well performance without dividing the cluster into single-well drainage areas. The MPI approach is used to obtain approximate analytical solutions for constant (but possibly different) wellbore flowing pressures, and to visualize the resulting pressure field. In addition, the skin factor trace technique is introduced as a tool to monitor a cluster of wells. The MPI technique is illustrated using a synthetic example taken from Ref. 2, as well as two field cases.
