A computational framework for well production simulation: Coupling steady state Darcy flow and channel flow by SGBEM–FEM

Abstract

In this paper, a computationally efficient framework capable of modeling well production simulation with general shaped fractures embedded in three dimensional porous matrix is presented. The flow in the matrix is modeled by classical theory of Darcy flow, whereas flow in hydraulic fractures is treated as channel flow. Governing equations of the Darcy flow are formulated in terms of weakly singular, weak-form boundary integral equations, whereas those of channel flow are cast in a weak form using Galerkin method of weighted residuals. We develop a special tip element to capture the dominant O(1r) asymptotic field of Darcy flow near the crack tip in porous media. We elaborate a unified transformation technique to overcome the difficulty with singular and nearly singular integrals. The numerical implementation is comprehensively verified through decoupled Darcy flow equation, decoupled channel flow equation and coupled equations, respectively. We show three steady state examples, which are sequential circular cracks case, sequential long cracks case and petal cracks case, to demonstrate the capability of the proposed framework.