Pore-to-Core Upscaling of Solute Transport Under Steady-State Two-Phase Flow Conditions Using Dynamic Pore Network Modeling Approach

We present a solute transport model, developed by employing a dynamic pore network modeling approach, to investigate dispersive solute transport behaviors in consolidated porous media. The model is capable of upscaling solute transport processes from pore to core, under two-phase fluid configurations. The governing equations of fluid flow, fluid displacement, and solute transport are solved at the pore level. A heavily parallelized computing scheme is utilized to simulate dynamic fluid displacements and transport processes in a core-scale pore network constructed from micro-computed tomography (micro-CT) images of a Berea sandstone sample. A series of solute transport simulations are conducted under the single-phase condition to validate the model by comparing the computed longitudinal dispersion coefficients against the experimental data over a wide range of Peclet numbers (Pe), i.e., 3×10-2∼3×105\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3 \times 10^{-2}{\sim}3 \times 10^5$$\end{document}. The model is then used to simulate solute transport under two-phase fluid configurations to examine the effects of the non-wetting phase saturation on solute transport behaviors. More specifically, solute transport is studied at different Pe and different water saturations obtained at the end of imbibition processes. We find that in a two-phase system, the longitudinal dispersion coefficient substantially increases with enhanced convective mixing under the transport regime with high Pe but decreases with restricted diffusive mixing at low Pe. In addition, the results indicate a non-monotonic dispersion–saturation relation under the convective transport condition. We illustrate that a strong correlation exists between the extent of dispersive mixing and the heterogeneity of fluid saturation profile across a core-scale network.