A pore-scale numerical framework for solute transport and dispersion in porous media

Abstract

Pore-scale modeling plays a crucial role in understanding and upscaling solute transport behavior in porous media. Direct simulation offers the highest fidelity in resolving pore-scale fluid flow and mass transfer, nevertheless, with unacceptable computational costs for practical applications. Pore network models (PNM), on the other hand, provide an efficient alternative but with reduced accuracy in representing transport dynamics. In this study, we propose a new framework of pore network models that ensures both accuracy and efficiency, which reproduces the pore-scale shear dispersion effect by utilizing the pore-scale shear dispersion coefficient to calculate the diffusive mass exchange rate between network elements. The coefficient is determined based on the extension of Taylor-Aris theory that expands the classical Taylor-Aris theory to encompass the pre-asymptotic regime. Additionally, the framework adopts a physically representative pore network, where the conduit length and volume of network elements are determined based on local resistance equivalence. After verifying its accuracy and reliability, we conduct a series of numerical cases on tube networks, sphere packs, and sand packs. The breakthrough curves and concentration profiles obtained from our new model show good agreement with direct simulation results and experimental data, while the simulation outcomes of the models that rely on the molecular diffusion coefficient or Taylor dispersion coefficient for local mass exchange may exhibit significant errors. We finally demonstrate that the significance of pore-scale shear dispersion on solute transport weakens for tube networks with increasing degrees of geometrical disorder. The proposed model provides an accurate and efficient numerical framework for the study of solute transport and dispersion in porous media.