Accelerated Computation of Relative Permeability by Coupled Morphological and Direct Multiphase Flow Simulation

Abstract

Computation of two-phase flow in porous media with low capillary numbers is challenging due to slow convergence and the presence of spurious currents at the phase interfaces that are greater than the viscous flow. The relative permeability of such systems is a critical parameter for upscaling flow properties but requires steady state flow configurations at low capillary numbers; a computationally slow problem to calculate. By using a morphologically coupled multiphase Lattice Boltzmann Method (LBM), it is observed that phase distributions converge an order of magnitude faster (1,000-50,000 timesteps) than flow fields (250,000-350,000 timesteps) during capillary dominated regimes. The proposed method couples a quasi-static, morphological method with direct LBM simulation that combines the efficiency of morphological calculations with the accuracy of direct simulation. The system fluid distribution is initialised morphologically instead of using simulated forced primary drainage to reduce dynamic simulation time and remove saturation end effects. The approach preconditions the simulation towards steady state conditions and the LBM routine relaxes the phase distributions until phases are stable. The steady state velocity fields are obtained by solving for flow in each stable connected phase distribution with a fast Semi Analytical Laplace solver to overcome spurious currents. A morphological Shell Aggregation method is then applied, condensing the displacing phase as a shell over pre-existing phase distributions and allowed to again reach phase equilibrium. Results obtained from the simulations are consistent with experimental relative permeability curves and phase morphology obtained from Gildehauser sandstone. This method allows rapid computation of phase distributions and relative permeability for capillary dominated flows. Shell Aggregation typically reaches steady state within 50,000-150,000 LBM timesteps opposed to 250,000-350,000 by spinodal decomposition for the tested 500 cubed Bentheimer sandstone and 150 cubed sand pack samples. Solving for flow in each connected phase body after Shell Aggregation LBM reaches steady state is furthermore shown to require down to 1,000-10,000 LBM timesteps at the expense of some interfacial physics.