A distributed parallel direct simulator for pore-scale two-phase flow on digital rock images using a finite difference implementation of the phase-field method - Alpak, Faruk Omer; Samardžić, Alexander; Frank, Florian (Journal of Petroleum Science and Engineering, 2018)
The phase-field method is a versatile and robust technique for modeling interfacial motion in multiphase flows in pore-scale media. The method provides an effective way to account for surface effects by use of diffuse interfaces. The resulting model significantly simplifies the numerical implementation of mass transport and momentum balance solvers for simulating two-phase flow with a large number of moving interfaces. The interfaces can be generated, transported or destroyed based on a thermodynamic Helmholtz free-energy minimization framework underpinning the governing equations. The phase-field method accurately conserves mass and is relatively straightforward to implement in conjunction with contact angle models that account for wettability on rock surfaces. The underlying free-energy minimization framework leads to the advective Cahn-Hilliard equation and modified Navier-Stokes equations that describe the phase-field model. We have implemented a particular variant of the phase-field method (PFM) into the computational core of a pore-scale multiphase flow simulator, namely PMFS-PFM, for the numerical simulations of incompressible flows of two immiscible fluid phases. The implementation was discussed in a previous paper for rectangular prism-shaped fully-connected domains, e.g., for simulating two-phase flow in a 2D slit or a 3D duct (Alpak et al., 2016). In this paper, we discuss the recent developments on PMFS-PFM. The main components of the new work are (I) implementation of support for inactive cells in PMFS-PFM by extending the original finite-volume method-based discretizations of the underlying partial differential equations (PDEs) in order to solve realistic 3D pore-scale flow problems on rock volumes stemming from imaging, and (II) enhancing the performance of the simulator through implementation of modern sparse linear solvers and distributed parallel computing. It has been shown that the simulations performed on complex pore-scale domains are consistent with the physics of the immiscible two-phase displacement. The parallel scalability of the code is reasonably well varying between 50% and 86% on the investigated test cases of varying complexity. Results indicate that the more disconnected the pore-scale domains, the lower the parallel efficiency. It has been noted that there is a possibility of improving the parallel efficiency by exploring various grid subdivisions.<br
Keywords: phase-field method; pore-scale two-phase flow; digital rock; finite difference method (FDM); computational fluid dynamics (CFD)