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.

Direct characterization of solute transport in unsaturated porous media using fast X-ray synchrotron microtomography

“…None of the commonly used theories, including the mobile–immobile model (MIM) ( 22 ), the multirate mass transfer (MRMT) ( 23 ), and continuous time random walk ( 24 ) models include two-phase flow formulations in their theoretical developments. To date, the capability of such models to match the experimental data using inverse modeling has been tested, but the physical consistency of such models is still open to be evaluated ( 25 , 26 ).…”

Two‐Phase Fluid Flow Properties of Rough Fractures With Heterogeneous Wettability: Analysis With Lattice Boltzmann Simulations

“…The range of the variance, which describes the correlation of the field, is shown to increase from A to C ( Figure 6). Recently, An et al (2020) showed that for porous media applications the correlation length of the pore size distribution should be 1/20th of the minimum sample dimension to guarantee an REV. While we do not attempt to define an REV of a single fracture here, we want to ensure to that our simulations are not sensitive to different realizations of the wetting patterns.…”

Transition From Viscous Fingering to Capillary Fingering: Application of GPU‐Based Fully Implicit Dynamic Pore Network Modeling

“…We provide a brief explanation of the key concepts of dynamic two‐phase pore network modeling here. The first step in pore network modeling is to extract or generate the pore network morphology (An, Hasan, et al, 2020; Raeini et al, 2017). The topology of the network can be extracted using different methods among which the medial axis‐based method is a robust one (Joekar Niasar et al, 2009).…”

“…The direct pore‐scale simulation methods are computationally too demanding compared to the pore network models. This challenge becomes prohibitive if the simulation of multiphase flow is aimed at the REV scale of a porous medium (An, Hasan et al, 2020; Shams et al, 2018). Moreover, none of these models has been able to achieve a superior predictive capability compared to others (Zhao et al, 2019), and in some cases pore network modeling has been successful in predicting pore‐scale phenomena (Joekar Niasar et al, 2009; Oostrom et al, 2016).…”