Simulation of the oil and gas flow toward a well — A stability analysis

A radial semi-implicit model of two-phase (oil–gas) flow toward a well is developed by creatively modifying the IMPES black-oil model. Traditional black-oil models consider the well as a source term in the differential equations with the hypothesis of single-phase flow, whereas this model considers well production conditions as boundary conditions that take into account two-phase flow. Two production conditions are applied: constant total (oil and gas) flow rate and constant oil flow rate. Numerical instabilities generated by IMPES are analysed. The maximum time increment to maintain stability is obtained. For the constant total flow rate, that maximum decreases until a minimum, and then increases with production time. For the constant oil flow rate, that maximum diminishes as production time increases. These stability restrictions, including the boundary conditions, are new. This model, with the known oil flow rate condition, is adequate to be included in an inverse algorithm of well test interpretation.