Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quantitative comparisons between different pore-scale models, and between these models and experimental data, are lacking. Here, we perform an objective comparison of a variety of state-of-the-art pore-scale models, including lattice Boltzmann, stochastic rotation dynamics, volume-of-fluid, level-set, phase-field, and pore-network models. As the basis for this comparison, we use a dataset from recent microfluidic experiments with precisely controlled pore geometry and wettability conditions, which offers an unprecedented benchmarking opportunity. We compare the results of the 14 participating teams both qualitatively and quantitatively using several standard metrics, such as fractal dimension, finger width, and displacement efficiency. We find that no single method excels across all conditions and that thin films and corner flow present substantial modeling and computational challenges.

A closure relation for capillary pressure plays an important role in the formulation of both traditional and evolving models of two‐fluid‐phase flow in porous medium systems. We review the traditional approaches to define capillary pressure, to describe it mathematically, to determine parameters for this relation, and to constrain the domain of applicability of this relation. In contrast to the traditional approach, we provide a rigorous, multiscale definition of capillary pressure, define the state domain of interest in practice, summarize computational and experimental approaches to investigate the system state, and apply the methods for two‐fluid states in a model ink bottle system, the classical Finney pack of spheres, and a synthetic sphere pack system. The results of these applications show that a state equation exists that describes capillary pressure without hysteresis. This state equation parameterizes a function that describes the nonwetting phase volume fraction in terms of the capillary pressure, the interfacial area, and the specific Euler characteristic of the nonwetting phase. Furthermore, this state equation applies over the complete range of conditions encountered in practice, and it applies under both equilibrium and dynamic conditions. This state equation involving capillary pressure forms an important foundation for the development of the next generation of macroscale two‐fluid‐phase flow models in porous medium systems.

In electrochemical processes such as electrodialysis or redox flow batteries, where ion exchange membranes (IEMs) play a critical role in process performance, energy losses can be reduced by minimizing the permeability of IEMs to water and salt. In pure, homogeneous polymer membranes, water permeability is known to be controlled by the size of the free volume elements. However, there is very limited evidence concerning the extent to which this theory applies to practical, commercial IEMs, which frequently have more complex structures. We recently reported water and salt transport characteristics (i.e., permeability, partition, and diffusion coefficients) of 20 commercial IEMs, and demonstrated that water and salt transport were governed primarily by the microstructure of the membrane rather than the polymer chemistry. To further investigate the factors that determine water and salt transport in commercial IEMs, in this study we adopted a statistical approach informed by free volume theory and other literature to examine relationships between transport characteristics and water uptake (i.e., swelling) in addition to fixed charge concentration, ion exchange capacity (IEC), Manning parameter, and contact angle. Our analysis shows that water uptake had the strongest correlation with water and salt transport in commercial IEMs, which is consistent with the predictions of free volume theory for homogeneous polymers; however, the relationship observed between water uptake and permeability in commercial membranes was not as straightforward as that reported in the literature for homogeneous polymers. Membrane charge (IEC) was also correlated with permeability and diffusion coefficients, but to a more limited extent than water uptake, while the Manning parameter and contact angle did not appear to be correlated to any transport properties. Furthermore, there are indications that microstructural differences among membranes may significantly affect permeability. Therefore, further study of IEM microstructure, e.g., phase separation, is an important strategy for advancing the development of commercial IEMs.

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Traditional models of two-fluid flow through porous media at the macroscale have existed for nearly a century. These phenomenological models are not firmly connected to the microscale; thermodynamic constraints are not enforced; empirical closure relations are well known to be hysteretic; fluid pressures are typically assumed to be in a local equilibrium state with fluid saturations; and important quantities such as interfacial and curvilinear geometric extents, tensions, and curvatures, known to be important from microscale studies, do not explicitly appear in traditional macroscale models. Despite these shortcomings, the traditional model for two-fluid flow in porous media has been extensively studied to develop efficient numerical approximation methods, experimental and surrogate measure parameterization approaches, and convenient pre- and post-processing environments; and they have been applied in a large number of applications from a variety of fields. The thermodynamically constrained averaging theory (TCAT) was developed to overcome the limitations associated with traditional approaches, and we consider here issues associated with the closure of this new generation of models. It has been shown that a hysteretic-free state equation exists based upon integral geometry that relates changes in volume fractions, capillary pressure, interfacial areas, and the Euler characteristic. We show an analysis of how this state equation can be parameterized with a relatively small amount of data. We also formulate a state equation for resistance coefficients that we show to be hysteretic free, unlike traditional relative permeability models. Lastly, we comment on the open issues remaining for this new generation of models.