HR: 1340h
AN: H23G-1694    [Abstracts]
TI: A Stochastically Based Method for Multiphase Flow Modeling in Heterogeneous Media - Experimental Observations and Model Design
AU: * Dean, D W
EM: deandw@gmail.com
AF: Colorado School Of Mines, 1600 Illinois St, Golden, CO 80401, United States
AU: Illangasekare, T H
EM: tissa@mines.edu
AF: Colorado School Of Mines, 1600 Illinois St, Golden, CO 80401, United States
AU: Russell, T F
AF: University Of Colorado - DHSC, 1250 14th St, Suite 600 PO Box 173364 Campus Box 170, Denver, CO 80217, United States
AU: Barnhart, K S
EM: kbarnhar@mines.edu
AF: Colorado School Of Mines, 1600 Illinois St, Golden, CO 80401, United States
AB: The results of two collaborative studies of multiphase flow that involve new modeling and experimentation are summarized. The goal was to explore new modeling approaches to explain observations of NAPL behavior in heterogeneous soils. In the modeling component, the ideas involving stochastic differential equations (SDE) used previously to model single-phase flow are extended to two phase flow. This approach results in a nonlinear SDE describing the position of the non-wetting phase fluid particle. The control of non-wetting phase particles across an interface is made using a jump term which derives from the Ito formula for cadlag semimartingales and is based on capillary diffusivity and the pressure-saturation curves of the sands forming the interface. The experiments were conducted in two-dimensional test tanks. The focus was to characterize the test material, develop experimental methods and conduct spill simulations in test tanks. The tanks were packed to represent different configurations of heterogeneity. The packing produced interfaces between different combinations of test sands, which allowed for the investigation of critical flow, fingering and pooling phenomena that occur at the transition zones of the heterogeneity field. The test soils that were used in the packing were accurately characterized using a new method based on Time Domain Reflectometry to obtain the constitutive relations needed in flow modeling. An X-ray photon attenuation method was used to determine porosity and saturations. This automated X-ray system was installed on a movable gantry that allowed for the continuous tracking of the NAPL saturations during migration and after entrapment. Three original ideas in our SDE model of multiphase flow are described which contribute to the relationship between the mathematical theory and the physical theory. The first idea is the inclusion of the jump term to model the capillary end effect. The second is what we call "anisotropic dispersion", where both the mathematical theory and the physical theory contribute to each other. In the case of the physics, the physical experiments clearly demonstrated the anomalous dispersion of the NAPL along the interface between two different sands, which dictated to the mathematical theory that a modification to the traditional diffusion model was needed. The mathematical theory, on the other hand, responded with the Girsanov-Meyer change of measure, which added a scaled dispersion term to the drift component of the SDE, allowing the model to simulate the anomalous dispersion effect. Finally, the third idea that we implemented was based on an approach that takes the flow to be controlled by pore-scale processes. Again, the modification to the macro-scale model was driven by the experimental observations, which many times showed the NAPL plume finding unexpected channels and exhibiting other types of instabilities commonly called "fingering".
DE: 1828 Groundwater hydraulics
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1847 Modeling
DE: 1869 Stochastic hydrology
SC: Hydrology [H]
MN: 2007 Fall Meeting