Calculation of the permeability of porous media using hydrodynamic cellular automata

Abstract

The permeability of two-dimensional porous media is calculated numerically as a function of porosity using the hydrodynamic cellular automata (lattice gas) approach. Results are presented for systems with up to 22 million sites (8192×2688). For randomly distributed solid obstacles whose macroscopic dimensions are much longer than the mean free path of particles in the fluid, the permeabilityκ varies with porositye asκ ∞(e−0.6)/(1−e) fore>0.7. When the solid obstacles are much smaller than the mean free path of particles in the fluid, i.e., when they form a dust of point objects, then such a relationship no longer holds and the permeability is more than an order of magnitude smaller than for the former case. The program used for the simulations is discussed and a listing is presented in the Appendix which achieved a sustained speed of 185 million sites updated per second on a single processor of the Cray-YMP. (On a Sun Sparc Workstation, the same program ran about 100 times slower.)