A simulation approach including under-resolved scales for multi-component fluid flows in multi-scale porous structures

TL;DR

This work tackles the impracticality of fully resolving multi-scale porous structures in multi-component flows by introducing an under-resolved-scale framework that leverages pre-computed properties $K_0$, $K_r^{\alpha}$, and $P_C(S_w)$ from resolved subdomains. A lattice Boltzmann formulation with regularized multi-component components and volumetric boundary conditions is used to model under-resolved regions, with forces constructed from the local porous-type properties and geometry. The authors validate the approach across a suite of benchmarks—including force balance, multi-type porous media, and imbibition in 1D and 2D geometries—showing accurate reproduction of $K_0$, capillary pressures, and relative permeabilities while achieving large computational savings (up to 200x in some cases). The results demonstrate that multi-scale, library-driven simulations can yield reliable predictions for complex porous systems such as reservoir rocks, enabling practical, high-fidelity analysis at reduced cost.

Abstract

In this study, we develop computational models and methodology for accurate multi-component-flow simulation in under-resolved multi-scale porous structures. It is generally impractical to fully resolve the flow in porous structures with large length-scale difference due to tremendously high computational expense. The flow contributions from under-resolved scales need to be accounted for with proper physics modeling as well as simulation processes. Using pre-computed physical properties such as the absolute permeability, K0, the capillary-pressure-saturation curve, and the relative permeability, Kr, in typically resolved porous structures, local fluid force is conjectured and applied to simulation in the under-resolved regions that are represented by porous media. By doing so, accurate simulation of flow in multi-scale porous structures becomes feasible. In order to check the accuracy and robustness of this method, a set of benchmark test cases are performed for both single-component and multi-component flows in artificially constructed multi-scale porous structures, and simulation results are compared with analytic solutions and/or results with much finer resolution resolving the porous structures. Quantitatively consistent results are obtained with proper input of K0, capillary pressure, and Kr in all tested cases. Specifically, imbibition patterns, entry pressure, residual component patterns, and the absolute and relative permeability are accurately captured with this approach.

Figures (19)

• Figure 1: A cross section pictures of a Carbonate rock. An original scanned picture (left) and a segmented picture with small-scale porous structure marked in grey (right) are shown.
• Figure 2: Steps in the procedure
• Figure 3: A sampled porous structure applied for the multi-scale simulation in Section \ref{['sec:validation']}.
• Figure 4: Simulated absolute permeability vs porosity (left), the capillary pressure vs water saturation $S_w$(center), and the relative permeability vs $S_w$ (right) in the PM of Fig. \ref{['fig:typrock_crosssec']}. Their fitted results are plotted with lines.
• Figure 5: Setups of the the single component fluid flow simulation through various typed porous media.