HR: 1340h
AN: H13A-0393    [Abstracts]
TI: Stochastic Approach for Modeling of DNAPL Migration in Heterogeneous Aquifers: Model Development and Experimental Data Generation
AU: * Dean, D W
EM: ddean@math.cudenver.edu
AF: University Of Colorado At Denver, Department Of Mathematics 1250 14th Street, Suite 600, Denver, CO 80202 United States
AU: Illangasekare, T H
EM: tissa@mines.edu
AF: Colorado School Of Mines, Center for Experimental Study of Subsurface Environmental Processes Colorado School Of Mines, Golden, CO 80401 United States
AU: Turner, A
EM: aturner@mines.edu
AF: Colorado School Of Mines, Center for Experimental Study of Subsurface Environmental Processes Colorado School Of Mines, Golden, CO 80401 United States
AU: Russell, T F
AF: University Of Colorado At Denver, Department Of Mathematics 1250 14th Street, Suite 600, Denver, CO 80202 United States
AB: Modeling of the complex behavior of DNAPLs in naturally heterogeneous subsurface formations poses many challenges. Even though considerable progress have been made in developing improved numerical schemes to solve the governing partial differential equations, most of these methods still rely on deterministic description of the processes. This research explores the use of stochastic differential equations to model multiphase flow in heterogeneous aquifers, specifically the flow of DNAPLs in saturated soils. The models developed are evaluated using experimental data generated in two-dimensional test systems. A fundamental assumption used in the model formulation is that the movement of a fluid particle in each phase is described by a stochastic process and that the positions of all fluid particles over time are governed by a specific law. It is this law, which we seek to determine. The approach results in a nonlinear stochastic differential equation describing the position of the non-wetting phase fluid particle. The nonlinearity in the stochastic differential equation arises because both the drift and diffusion coefficients depend on the volumetric fraction of the phase, which in turn depends on the position of the fluid particles in the problem domain. The concept of a fluid particle is central to the development of the proposed model. Expressions for both saturation and volumetric fraction are developed using this concept of fluid particle. Darcy's law and the continuity equation are used to derive a Fokker-Planck equation governing flow. The Ito calculus is then applied to derive a stochastic differential equation(SDE) for the non-wetting phase. This SDE has both drift and diffusion terms which depend on the volumetric fraction of the non-wetting phase. Standard stochastic theories based on the Ito calculus and the Wiener process and the equivalent Fokker-Planck PDE's are typically used to model diffusion processes. However, these models, in their usual form, cannot represent barrier effects that occur at the interfaces of the soil layers with different characteristics. For example, in tracking a DNAPL plume, the behavior of the plume at an interface depends on the pressure-saturation relationships of the two soils forming the interface. In the model, the control of the flow of DNAPL particles across an interface is accomplished using a jump term, which derives from the Ito formula. The jump term is based on capillary diffusivity and the pressure-saturation curves of the two soils forming the interface. A series of laboratory spill experiments in two-dimensional test cells were conducted to create a comprehensive database to evaluate the model under development. These experiments utilized five well-characterized test sands that are used to create different heterogeneous packing configurations. The experiments that have been completed used horizontal and dipping capillarity barriers. The propagation of the spill was monitored using an automated X-ray photon attenuation system that accurately measures the DNAPL and water saturations. The computational aspects of the modeling approach, experimental results and preliminary analysis that were conducted to validate the new modeling method are presented.
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1869 Stochastic processes
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting