Analytical Evaluation of Well Productivity Index and Dietz Shape Factor for Double-Periodic Multi-well Reservoir Systems

Abstract

This work is devoted to the modeling of oil fields development with a multi-well systems located in a homogeneous closed reservoir of constant thickness and working under pseudo-steady state conditions. For these purposes, a closed reservoir is represented as an element of unbounded doubly-periodic array of multi-well clusters, and the inflow conditions in multi-well systems are described by the Weierstrass elliptic functions. This approach allows us: • to find the pressure distribution and the field of fluid velocities for any wells location in the reservoir; • to calculate the productivity index (PI) and the Dietz's shape factor (C_A) for any wells location in the reservoir; • to establish the optimal wells location in the reservoir, maximizing the multi-well productivity index (MPI) of the reservoir.