Numerical simulation of a one-phase steady flow towards a multistage fractured horizontal well

Abstract

This paper presents a 3D mathematical model and its numerical implementation for a one-phase flow around a multistage fractured horizontal well with transverse fractures. The flows in the reservoir and in the fractures are governed by the Darcy’s law and were simulated separately. The problem was approximated by the finite volume method. The obtained systems of linear equations for the reservoir and the fractures were solved simultaneously, which allowed us to avoid the use of iterative process for solution adjustment both in the fractures and the reservoir. We investigated various techniques and proposed an optimal variant for solving ill-conditioned systems of linear equations appearing due to the grid approximation of the continuous mathematical flow model. We also studied how the fractures and well parameters affect the well productivity.