 |
Center for Nonlinear Studies |
Three scales are of crucial importance in the simulation of flow and transport in porous media. Most simulations are intended to capture phenomena at the reservoir scale, which may be kilometers in spatial extent and includes geologic carbon questration, contaminant transport in groundwater, and secondary recovery in oil reservoirs. However, material properties such as porosity and permeability vary at a much smaller scale, which may be on the order of centimeters to meters. This scale is not much larger than the smallest scale at which Darcy's equation is valid. Finally, at the pore scale, which may be on the order of microns, flow is governed by the solution of Navier-Stokes equations on a complex geometry of pore space. In this talk, I will argue that it can be necessary to resolve each of these scales in some cases, and that it is neither possible nor necessary to resolve all of these scales in all cases. This motivates the need for hybrid, multi-scale approaches to accurately and hierarchically traverse these scales. I will demonstrate a domain decomposition approach for coupling regions of pore-scale flow and transport with regions of Darcy-scale flow and transport and discuss a multigrid-based approach for upscaling Darcy-scale flow and transport to reservoir-scale simulations. With these approaches, I hope to present a path toward using a single, hybrid approach to simulate flow and transport in geologic media at all relevant scales.
Host: Shiv K. Sambasivan, T-5 665-8075