Efficient forward modeling for DNAPL site evaluation and remediation

Although the general characteristics of DNAPL flow and transport in the subsurface are reasonably well understood, it is often difficult and expensive to pinpoint sources of DNAPL contamination. Inversion techniques to improve site characterization rely on a forward model of multiphase flow. Ideally the forward model would be very fast, so that many realizations can be carried out in order to quantify and reduce uncertainty, yet capable of handling large numbers of grid elements, so that more accurate (small scale) determinations of soil properties and DNAPL content can be made. To meet these conflicting requirements of speed and detail in the forward modeling of contamination events, we present a subgrid-scale numerical technique for upscaling multiphase flow. Upscaling is achieved by explicitly decomposing the differential system into a coarse-grid-scale operator coupled to a subgrid-scale operator. The subgrid-scale operator is approximated as an operator localized in space to a coarse-grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid-scale problems independently of the coarse-grid approximation. The coarse-grid problem is modified to take into account the subgrid-scale solution and solved as a large linear system of equations. Finally, the coarse scale solution is corrected on the subgrid-scale, providing a fine-grid scale representation of the solution. In this approach, no explicit macroscopic coefficients nor pseudo-functions result. The method is easily seen to be optimally convergent in the case of a single linear parabolic equation. The method is fast, robust, and achieves good results.