Abstract

Two-phase and multi-phase flows in geological formation are central to a wide range of natural and engineered processes, including water infiltration into soil, geologic carbon sequestration, enhanced oil recovery, and geothermal energy extraction.  Petroleum engineers use reservoir simulation models to manage existing petroleum fields and to develop new oil and gas reservoirs, while environmental scientists use subsurface flow and transport models to investigate and compare for example various schemes to inject and store carbon dioxide in subsurface geological formations, such as depleted reservoirs and deep saline aquifers. Darcy-scale multi-phase flow simulation in subsurface reservoirs has routinely used by reservoir engineers over half a century. More recently, digital Rock Physics (DRP) and pore-scale flow simulation have also become a complementary part in reservoir characterization over the past two or three decades as non-destructive methods used to determine absolute/relative permeability, capillarity, effective elastic rock parameters and other porous media properties.  In the recent 20 years, the Navier–Stokes–Cahn–Hilliard (NSCH) system has started to merge as the standard model for the Direct Numerical Simulation (DNS) of incompressible immiscible two-phase flow, with finite volume methods (FVM), finite element methods (FEM), Lattice Boltzmann methods (LBM), and Smoothed Particles Hydrodynamics (SPH) as popular discretization schemes. Since DNS is computationally expensive with complex geometrical pore space, a simplified yet powerful strategy known as the pore network model has been constructed and applied widely for simulating a variety of different physical and chemical processes in porous media, including capillarity effect, phase exchange, non-Newtonian displacement, non-Darcy flow, and reactive transport.

In this talk, we share a few of our recent works in digital rock physics and pore-scale flow simulation.  First, we present our new pixel-free algorithm of pore-network model extraction for pore-scale fluid flow known as the flashlight search medial axis algorithm. Traditional methods of pore-network model extraction are based on pixels; thus, it requires images with high quality and it is slow. Our new algorithm follows the dimensionality reduction idea; the medial axis can be identified using only a few points instead of calculating every point in the void space. In this way, the computational complexity is greatly reduced as compared to that of traditional pixel-based extraction methods, thus enabling large-scale pore-network extraction. Based on cases featuring two- and three-dimensional porous media, the algorithm performs well regardless of the topological structure of the pore network or the positions of the pore and throat centers.  In the second part of this talk, we highlight our new unconditionally stable scheme of Lattice Boltzmann method (LBM).  The proposed LBM scheme is as fast as the commonly-used fully explicit LBM method, and it also preserves local mass conservation and local momentum conservation just like the commonly-used LBM.  Different from the conventional LBM, the new scheme preserves both positivity of the unknown distribution function and energy stability (i.e., satisfies the discrete H-theorem) unconditionally with respect to the mesh size and the time step.  Numerical examples are given to illustrate its strength.  In the third part of this talk, we report a novel SPH-based particle method for pore-scale flow simulations. Even though SPH has been attempted for the application of pore-scale two-phase flow simulation in the literature, structure-preserving (especially unconditionally energy-stable) particle methods for the NSCH equation system have not been constructed nor thoroughly studied yet.  In our work, an efficient and structure-preserving Smoothed Particle Hydrodynamics (SPH) method is proposed and implemented for pore-scale two-phase fluid flow modeled by the NSCH system.  In addition to preserve the conservation of mass, the conservation of linear momentum and the conservation of angular momentum in the discrete solution, our scheme also preserves the conversion between kinetic energy and interfacial energy exactly, and moreover, it is unconditionally energy-stable.  It is more flexible, more powerful and more accurate than conventional, mesh-based simulation methods, in particular for the treatment of convection (in fact, the numerical treatment of linear convection can be made to be exact). In order to enhance efficiency, we decouple the NSCH system to simplify the calculation into a few linear steps while still maintaining unconditional energy stability. Numerical experiments are carried out to confirm that the proposed SPH is indeed unconditionally energy-stable for two-phase flow, as predicted by the theory. The numerical results also demonstrate that our method captures the interface behaviors exceptionally well even with a small number of particles.

Biography

Shuyu Sun is a founding Professor of Earth Science and Engineering at King Abdullah University of Science and Technology (KAUST); he is also jointly affiliated with the Program of Applied Mathematics and Computational Science at KAUST.  He obtained his Ph.D. degree in computational and applied mathematics from The University of Texas at Austin in 2003.  He has published 380+ refereed journal articles, most of them focusing on the modeling, simulation and algorithms of pore media flow and transport.  According to the google scholar (as of May 2024), his h-index is 52 and he has been cited 11100+ times.  Currently he is the president of InterPore (International Society for Porous Media) Saudi Chapter. He is also an editor or an editorial board member for Journal of Computational Physics, Computational Geoscience, Gas Science and Engineering, and the InterPore Journal, four reputable journals in his field.