A Cellular Automaton Model for Flow in a Heterogeneous Reservoir

Abstract

A 2-dimensional cellular automaton model is developed to simulate Darcy's flow in complex, heterogeneous porous media. 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 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 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 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 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 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. Introduction Flow in porous media is generally described by Darcy's law, which linearly relates fluid velocity to pressure gradient. Although the governing equations are linear in reservoir simulation, we have not fully resolved difficulties associated with multiscale phenomena, complicated permeability distribution in a reservoir, and nonlinear functional dependencies description of a reservoir includes large uncertainties due to the difficulty of field measurements at the reservoir conditions. Thus, they are often described by a statistical method rather than by a deterministic one.

Simulation Study of Fluid Flow and Estimation of a Heterogeneous Porous Media Properties Using Lattice Gas Automata Method

“…Zanetti (1989), defined a lattice-gas automata as a particle of gas that occupy the site of a regular lattice and can hop from the lattice sites to the nearest neighbors. Lee et al (1993), used the lattice gas automata method for hydrodynamic calculations. The lattice gas automata method employs interactions of discrete fluids on a regular lattice analogous to microscopic molecular dynamics.…”

Modeling Miscible Injection in Fractured Porous Media using Non-classical Simulation Approaches (Russian)

“…Приведем несколько примеров использования неклассического моделирования: (1) Случайное блуждание (Random walk, RW) (Araktingi and Orr 1990), (2) отслеживание частиц (particle tracking) (Jha et al 2009), (3) перколяционные теории (classical and invasion percolation) (Meakin et al 1999), (4) наращивание, контролируемое диффузией (diffusion limited aggregation, DLA) (Lenormand 1989), решение уравнения Больцмана на решетке (lattice Bolztmann method, LBM) (Rothman and Zaleski 1994;Hatiboglu and Babadagli 2007), и клеточный автомат (cellular automata) (Lee and Chung 1993). Приведем несколько примеров использования неклассического моделирования: (1) Случайное блуждание (Random walk, RW) (Araktingi and Orr 1990), (2) отслеживание частиц (particle tracking) (Jha et al 2009), (3) перколяционные теории (classical and invasion percolation) (Meakin et al 1999), (4) наращивание, контролируемое диффузией (diffusion limited aggregation, DLA) (Lenormand 1989), решение уравнения Больцмана на решетке (lattice Bolztmann method, LBM) (Rothman and Zaleski 1994;Hatiboglu and Babadagli 2007), и клеточный автомат (cellular automata) (Lee and Chung 1993).…”