Multiscale Modeling of Nonlinear Flow Behavior in Porous Media

Matthew Balhoff
University of Texas at Austin

Pore-scale network modeling is an approximate technique to solve conservation equations in porous media. Recent advancements have allowed network modeling to become a quantitative and predictive tool for flow and transport in porous media, often replacing the need for experiment. Network models have been used to obtain macroscopic properties of permeability as well as relative permeability and capillary pressure for multiphase flow. Here, the work is extended to other nonlinear behavior, particularly non-Newtonian and high velocity (Forchheimer) flow. CFD modeling is first performed at the sub-pore scale to obtain relationships for flow in pore throats and those equations are substituted into the network model which is then solved to obtain a macroscopic relationship. Some important discrepancies are found between the network model and the well-accepted quadratic Forchheimer equation. Homogenization is also used as a tool to understand inertial effects in porous media.
One potential limitation of pore-scale network models is that they are used as stand-alone tools; the influence of surrounding media is not typically included in the boundary conditions. Here, a method using finite element mortars are used to couple pore-scale models with surrounding media in order to obtain more realistic boundary conditions. The approach results in more accurate macroscopic properties such as permeability and capillary pressure curves for multiphase flow. The scheme also allows a framework for substituting pore-level models directly into macro-scale simulators without the need for upscaling. In specific regions of a reservoir (e.g. near wells), the pore-level models can replace fine grids with the goal of producing more accurate results.