Simulation of Two Phase Flow in Reservoir Rocks Using a Lattice Boltzmann Method

Abstract We present results from simulations of two-phase flow directly on digitized rock microstructure images of porous media using a lattice Boltzmann method. The implemented method is done on a D3Q19 lattice with fluid-fluid and fluid-solid interaction rules to handle interfacial tension and wetting properties. We demonstrate that the model accurately reproduces capillary and wetting effects in pores with non-circular shape. The model is applied to study viscous coupling effects for two-phase cocurrent annular flow in circular tubes. Simulated relative permeabilities for this case agree with analytical predictions and show that the non-wetting phase relative permeability might greatly exceed unity when the wetting phase is less viscous than the non-wetting phase. Two-phase lattice Boltzmann simulations are performed on microstructure images derived from X-ray microtomography and process based reconstructions of Bentheimer sandstone. By imposing a flow regulator to control the capillary number of the flow, the lattice Boltzmann model can closely mimic typical experimental setups, such as centrifuge capillary pressure and un-steady and steady-state relative permeability measurements. Computed drainage capillary pressure curves are found to be in excellent agreement with experimental data. Simulated steady-state relative permeabilities at typical capillary numbers in the vicinity of 10−5 are in fair agreement with measured data. The simulations accurately reproduce the wetting phase relative permeability, but tend to under-predict the non-wetting phase relative permeability at high wetting phase saturations. For higher capillary numbers, we correctly observe increased relative permeability for the non-wetting phase due to mobilization and flow of trapped fluid. It is concluded that the lattice Boltzmann model is a powerful and promising tool for deriving physically meaningful constitutive relations directly from rock microstructure images.