Summary: Efficient forward modeling for DNAPL site evaluation and remediation
Todd Arbogast & Steven Bryant
Center for Subsurface Modeling, Texas Institute for Computational and Applied Mathematics, C0200,
The University of Texas at Austin, Austin, Texas 78712, USA.
ABSTRACT: Although the general characteristics of DNAPL flow and transport in the subsurface are reason-
ably 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 uncer-
tainty, yet capable of handling large numbers of grid elements, so that more accurate (small scale) determi-
nations 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.