Lattice-Boltzmann studies of fluid flow in porous media with realistic rock geometries

Abstract

We present results of lattice-Boltzmann simulations to calculate flow in realistic porous media. Two examples are given for lattice-Boltzmann simulations in two- and three-dimensional (2D and 3D) rock samples. First, we show lattice-Boltzmann simulation results of the flow in quasi-two-dimensional micromodels. The third dimension was taken into account using an effective viscous drag force. In this case, we consider a 2D micromodel of Berea sandstone. We calculate the flow field and permeability of the micromodel and find excellent agreement with Microparticle Image Velocimetry (μ-PIV) experiments. Then, we use a particle tracking algorithm to calculate the dispersion of tracer particles in the Berea geometry, using the lattice-Boltzmann flow field. Second, we use lattice-Boltzmann simulations to calculate the flow in Bentheimer sandstone. The data set used in this study was obtained using X-ray microtomography (XMT). First, we consider a single phase flow. We systematically study the effect of system size and validate Darcy’s law from the linear dependence of the flux on the body force exerted. We observe that the values of the permeability measurements as a function of porosity tend to concentrate in a narrower region of the porosity, as the system size of the computational sub-sample increases. Finally, we compute relative permeabilities for binary immiscible fluids in the XMT rock sample.