Hybrid lattice gas simulations of flow through porous media

Jeffrey Lynn Becklehimer


This study introduces a suite of models designed to investigate transport phenomena in simulated porous media such as rigid or quenched sediment and clay-like deformable environments. This is achieved by using a variety of techniques that are borrowed from the field of statistical physics. These techniques include percolation, lattice gas, and cellular automata. A percolation-based model is used to study a porous medium by using rods and chains of various shapes and sizes to model the porous media formed by sediments. This is further extended to model clay-like deformable media by interacting heavy sediment particles. An interacting lattice gas computer simulation model based on the Metropolis algorithm is used to study the transport properties of fluid particles and permeability of a porous sediment. Finally, a hybrid lattice gas model is introduced by combining the Metropolis Monte Carlo method with a direct simulation which involves the collision rules as in cellular automata. This model is then used to study shock propagation in a fluid filled porous medium. This study is then extended to study shock propagation through in a fluid filled elastic porous medium. Several interesting and new results were obtained. These results show that for rigid chain percolation the percolation threshold shows a dependence on the chain length of $p\sb{c}\sim L\sbsp{c}{-1/2}$ and the jamming coverage decreases with the chain length as $L\sbsp{c}{-1/3}.$ For the random SAW-like chains the percolation threshold decays with the chain length as $L\sbsp{c}{-0.01}$ and the jamming coverage as $L\sbsp{c}{-1/3}.$ The fluid flow model shows that permeability depends nonmonotonically on the concentration of the fluid. For some fluids at a fixed porosity, the permeability increases on increasing the bias until a certain value $B\sb{c}$ above which it decreases. Also, it was found that a shock propagates in a drift-like fashion when in a rigid porous medium when the porosity is high; low porosity damps out the shock front very quickly. For a shock propagating in a clay-like porous medium an unusually super-fast power-law behavior is observed for the RMS displacements of the fluid and clay particles.