A Cellular Automaton Model for Flow in a Heterogeneous Reservoir

Abstract

ABSTRACT This paper reports on the development of a 2-dimensional cellular automaton (CA) model to simulate fluid flow in porous media. In CA, simple rules of particle interactions at a lattice are used to simulate complex flow phenomena. Since the numerical operations involved are largely bit manipulation, CA can be potentially more efficient in memory usage than conventional methods, such as finite difference or finite element methods. While other research on the use of CA to model porous media flow primarily focuses on Stokes flow at the pore level, with the intent of understanding flow at the core scale, this work concentrates on modeling Darcy flow in large heterogeneous fields. Permeability variations and anisotropy are modeled by a distribution of "soft scatterers" and "directional scatterers". Collision of incoming particles with scatterers is a stochastic process. Anisotropy is modeled via a preferred direction of collision between the directional scatterers and incoming particles The CA model is verified through the study of single-phase flow in porous media. Simulation results obtained from this CA model show that particle flow rates are linearly proportional to pressure gradient (pressure is modeled through particle density in CA), and permeability is linearly correlated with scatterer density over a certain domain. Therefore, the CA model can be used to predict Darcy-like flow. It is shown that heterogeneity is modeled properly by varying the density of scatterers. In addition to the single fluid model, a model with two fluids with identical physical properties has also been developed to study dispersion characteristics of a CA model. In the numerical simulation results, the transverse diffusivity converges to the theoretical constant, but the longitudinal diffusivity increases with time. Finally, extension of the current model to a more general case (i.e., three-dimensional, multiphase flow) is also discussed.