Simulation of Non-Darcy Porous Media Flow According to the Barree and Conway Model

Abstract

Non-Darcy porous media flow has been traditionally handled using the Forchheimer equation. However, recent experimental studies have shown that the Forchheimer model is unable to fit laboratory results at high flow rates. On the other hand, the non-Darcy flow model, proposed by Barree and Conway, is capable of describing the entire range of relationships between flow rate and potential gradient from low- to high-flow rates through proppant packs. In this paper, we present a numerical model by incorporating the Barree and Conway model into a general-purpose reservoir simulator for modeling single-phase and multiphase non-Darcy flow in porous and fractured media. The numerical formulation is based on the TOUGH2 methodology, i.e., spatial integral-finite-difference discretization, leading to an unstructured grid, followed by time discretization carried out with a backward, first-order, finite-difference method. The final discrete nonlinear equations are handled fully implicitly by Newton iteration. In the numerical approach, flow through fractured rock is handled using a general multi-continuum approach, applicable to both continuum and discrete fracture conceptual models. In an effort for model validation, we use analytical solutions to verify our numerical model results for both single-phase and multiphase non-Darcy flow. In addition, the numerical model is applied for well testing analysis of transient non-Darcy flow toward a well.