Unravelling Effects of the Pore-Size Correlation Length on the Two-Phase Flow and Solute Transport Properties: GPU-based Pore-Network Modeling

Abstract

Continuum-scale models for two-phase flow and transport in porous media are based on the empirical constitutive relations that highly depend on the porous medium heterogeneity at multiple scales including the microscale pore-size correlation length. The pore-size correlation length determines the representative elementary volume and controls the immiscible two-phase invasion pattern and fluids occupancy. The fluids occupancy controls not only the shape of relative permeability curves but also the transport zonation under two-phase flow conditions, which results in the non-Fickian transport. This study aims to quantify the signature of the pore-size correlation length on two-phase flow and solute transport properties such as the capillary pressure- and relative permeability-saturation, dispersivity, stagnant saturation, and mass transfer rate. Given the capability of pore-scale models in capturing the pore morphology and detailed physics of flow and transport, a novel graphics processing unit (GPU)-based pore-network model has been developed. This GPU-based model allows us to simulate flow and transport in networks with multimillions pores, equivalent to the centimeter length scale. The impact of the pore-size correlation length on all aforementioned properties was studied and quantified. Moreover, by classification of the pore space to flowing and stagnant regions, a simple semianalytical relation for the mass transfer between the flowing and stagnant regions was derived, which showed a very good agreement with pore-network simulation results. Results indicate that the characterization of the topology of the stagnant regions as a function of pore-size correlation length is essential for a better estimation of the two-phase flow and solute transport properties.