 
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 subgridscale numerical technique
for upscaling multiphase flow. Upscaling is achieved by explicitly decomposing the differential system into
a coarsegridscale operator coupled to a subgridscale operator. The subgridscale operator is approximated
as an operator localized in space to a coarsegrid element. An influence function (numerical Greens function)
technique allows us to solve these subgridscale problems independently of the coarsegrid approximation. The
coarsegrid problem is modified to take into account the subgridscale solution and solved as a large linear
system of equations. Finally, the coarse scale solution is corrected on the subgridscale, providing a finegrid
scale representation of the solution. In this approach, no explicit macroscopic coefficients nor pseudofunctions
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.
