Darcy flow in porous media: Cellular automata simulations

Abstract

This contribution presents two cellular automata for the computation of 2-D, incompressible, one- and two-phase Darcy flow. The one-phase automaton is based on a Navier-Stokes automaton (Frisch, et al.). Darcy characteristics are brought in with the help of so-called scatter cells. The convergence is speeded up by a kind of multi-grid technique. The two-phase automaton is based on diffusion-limited aggregation (DLA). In this automaton ‘voids’ are released at a production well, they make their way to an injection well and then leave the system. The motion of the voids, which is controlled by the mobility of the fluids and by a stochastic parameter, stirs the fluids and determines the flow.

The results obtained so far suggest that work on more realistic situations is particularly promising along the lines of the DLA automaton.