Unified lattice Boltzmann method for flow in multiscale porous media

In this paper, we develop a unified lattice Boltzmann method for flow in multiscale porous media. This model not only can simulate flow in porous systems of various length scales but also can simulate flow in porous systems where multiple length scales coexist. Simulations of unidirectional steady flow through homogeneous and heterogeneous porous media both recover Darcy's law when the effects of inertial forces and Brinkman correction may be negligible. Direct use of this model on the usual computational nodes, with zero resistance on void spaces and infinite resistance on solid walls, gives results that agree well with analytical solutions. Simulations performed on a fractured porous system show that the method presented here gives very good overall permeability values for the whole fractured system. A series of simulations is performed on a simplified fractured system. The results indicate that, when the ratio of the permeability of the rock matrix to the fracture permeability calculated by the cubic law is less than 10(-4), the effects of the rock matrix flow are negligible, and the discrete-fracture models that ignore such flow are plausible. When the ratio is larger than 10(-4), the matrix flow has significant effects on the fractured system, and the assumption that the matrix is impermeable does not hold. Therefore, the use of the cubic law to calculate the fracture permeability may cause a significant error. It is also indicated that the larger the ratio of the width of the porous matrix to that of the fracture, the more significant is the error caused by using the cubic law.