Study of fracture permeability using Lattice Gas Automata

We study the problem of flow permeability of fracture joints using Lattice-Gas Automata simulations. We model the fracture as a rough channel bounded by a self-affine surface. Changing the surface roughness exponent, rough walls having different microstructures are obtained. Different relative roughnesses — defined as the height of the largest surface asperity divided by the mean aperture — are obtained pulling apart the two surfaces that constitute the rough walls of the channel. We calculate the macroscopic variables volume flow rate and pressure difference using microscopic balances. In the low Reynolds number regime the pressure difference and the flow rate are linearly related (the behavior is described by Darcy's law). In this regime, we study the effect of geometry on the permeability. We have found that permeability is independent of the surface roughness exponentH and it is fully determined in terms of the relative roughness and mean aperture of the fracture joint. For larger Reynolds numbers a transition to a regime in which pressure difference and flow rate are not longer linearly related is observed. This transition is observed in a domain of Reynolds numbers for which the behavior in a smooth channel remains linear. We discuss this transition.