Simulation time: 11 seconds
Ewing, Robert P. and Brian Berkowitz, A generalized growth model for simulating initial migration of dense non-aqueous phase liquids. Water Resour. Res. 34:611-622, 1998, and
Ewing, Robert P. and Brian Berkowitz. Stochastic pore-scale growth models of DNAPL migration in porous media. Advances in Water Resources (special issue on pore-scale modeling) 24:309-323, 2001.
The generalized growth model involves two modifications to "normal", gravity-influenced invasion percolation. First, we introduced randomness into the selection of the next site to invade. Normal invasion percolation is purely deterministic once the medium is defined, but we add a stochastic step to the selection of the next invadable site. This translates into a form of viscosity, and by varying the amount of randomness, we effectively vary the Capillary number. Next, we introduced the concept of the finger (clearly an element in many DNAPL flow regimes), and performed stochastic selection of fingers as well as sites. This bi-scale stochastic invasion (BSI) model proved capable of producing the full range of behaviors seen in laboratory and field studies of DNAPL migration: single fingers, multiple parallel fingers, merging and splitting, thick and thin fingers, and stable fronts.
Some 2D example simulations are shown below. These were performed on an anisotropic loamy sand with a DNAPL having a density of 1.4 g/cm3. The DNAPL is injected in the middle 20% of the medium, and changes color from blue to red over time. This color change allows you to reconstruct the invasion sequence. Each grid point represents a 1 cm square, so the problem domain is 2.57 m square. More recent runs have used up to 7,000,000 points in 3D. Each simulation is shown with the actual simulation time used on a 486-66.
Simulation time: 11 seconds
Simulation
time: 24 seconds
Simulation
time: 49 seconds
