Dimp-Hydro Solver for Direct Numerical Simulation of Fluid Microflows within Pore Space of Core Samples

Abstract

The paper is devoted to a description of the DiMP-Hydro software package being developed at the Keldysh Institute of Applied Mathematics (Russian Academy of Sciences). It is intended to simulate microflows of single- and two-phase viscous compressible fluids with different rheology in spatial voxel domains. Such geometric models are relevant due to the development and widespread use of computer microtomography methods. One of the main areas of the application of this software package is the simulation of microflows within pore spaces of core (rock) samples. The simulation results can be used to determine the macroscopic properties of core samples (for instance, absolute permeability) and features of displacement processes at the micro level, which is one of main tasks of digital rock technology. The used mathematical models, numerical algorithms, and the software package are described. To describe the fluid dynamics, the regularized Navier–Stokes (for single-phase flows) and Navier–Stokes–Cahn–Hillard equations (for two-phase flows) are used. The regularization is based on the quasi-hydrodynamic approach, which is physically justified and makes it possible to use explicit stable numerical algorithms that are relatively simple to implement. The software package is parallel and focused on the use of high-performance computing systems. The results of the use of DiMP-Hydro to simulate microflows of fluid (including two-phase fluid) and gas (including moderately rarefied gas) in the pore space of core samples are presented.