From Molecular Dynamics to Lattice Boltzmann: A New Approach for Pore Scale Modelling of Multi-Phase Flow

Absolute permeability tensor and relative permeability curves, which are the two most important properties in prediction of subsurface flow dynamics, are both obtained from lab experiments traditionally. Although the measuring approaches have been widely used and results are largely accepted for many years in most cases, the lab experiments are usually expensive, not robust especially for low and ultra-low permeability core measurements, and can not always be repeated for different fluids or under different flow scenarios. Multi-phase modeling based on geometry information of cores obtained by Micro X-ray Computed Tomography becomes an emerging technology that tries to yield rock properties directly. Among all the methods of pore scale modeling, Lattice Boltzmann Method (LBM) shows an apparent advantage in terms of computational efficiency, readiness for parallel computing, and capability of modeling flow with complex boundary conditions. Several multi-phase LB models have been proposed in the last two decades, with successful implementation in the simulation of actual single component two phase (liquid and vapor) flow problems. But for actual solid-fluid systems, most models suffer from the parameters fitting in order to match the experimental results. In this study, we propose to integrate Molecular Dynamics (MD) simulation with Lattice Boltzmann method to solve this problem. The basic idea is to first construct the molecular model based on the actual components of the rock-fluid system. Then MD simulation is performed to compute the interaction force between the rock and the fluid of different densities. MD simulation results indicate that the composition of the forces is a surface force as a nonlinear function of fluid density. This calculated rock-fluid interaction force, combined with the fluid-fluid force determined from the equation of state (EOS), is then used in LBM modeling. Without parameter fitting or assuming the linear relationship between the rock-fluid interaction force and fluid density, this study presents a new systematic approach for pore-scale modeling of multi-phase flow. We have validated this approach by simulating a two-phase separation process and gas-liquid-solid three-phase contact angle. The success of MD-LBM results in agreement with published EOS solution and experimental results demonstrated a breakthrough in pore-scale, multi-phase flow modeling. Based on an actual X-ray CT image of a reservoir core, we applied our workflow to calculate absolute permeability of the core, vapor-liquid H2O relative permeability and capillary pressure curves. With the application of this workflow to a more realistic model considering actual reservoir rock and fluid parameters, the ultimate goal is to develop an accurate method for prediction of permeability tensor, relative permeability and capillary curves based on 3D CT image of the rock, actual fluid and rock components.