Modeling of subgrid effects in coarse-scale simulations of transport in heterogeneous porous media

A methodology for incorporating subgrid effects in coarse-scale numerical m odels of flow in heterogeneous porous media is presented. The method procee ds by upscaling the deterministic fine-grid permeability description and th en solving the pressure equation over the coarse grid to obtain coarse-scal e velocities. The coarse-grid saturation equation is formed through a volum e average of the fine-scale equations and includes terms involving both the average and fluctuating components of the velocity field. The terms involv ing the fluctuating components are subgrid effects that appear as length- a nd time-dependent dispersivities. A simplified model for the coarse-scale d ispersivity, in terms of these subgrid velocity fluctuations, is proposed, and a numerical scheme based on this model is implemented. Results using th e new method are presented for a variety of two-dimensional heterogeneous s ystems characterized by moderate permeability correlation length in the dom inant (horizontal) flow direction and small correlation length in the verti cal direction. The new method is shown to provide much more accurate result s than comparable coarse-grid models that do not contain the subgrid treatm ent. Extensions of the overall methodology to handle more general systems a re discussed.