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.

[1] Spontaneous, counter-current imbibition (SI) is a key mechanism in many multiphase flow processes, such as cleanup of nonaqueous phase liquids (NAPLs), bioremediation, or CO 2 storage. For interpreting and upscaling laboratory SI data, and modeling and prediction purposes, scaling groups are an essential tool. The question of how to formulate a general scaling group has been debated for over 90 years. Here we propose the first scaling group that incorporates the influence of all parameters on SI that are present in the two-phase Darcy model. The group is derived rigorously from the only known exact analytical solution for spontaneous imbibition by relating the cumulative water phase imbibed to the normalized pore volume. We show the validity of the group by applying it to 42 published SI studies for water-oil and water-air experiments, for a wide range of viscosity ratios, different materials, different initial water saturations, and different length-scales. In all cases, water was the wetting phase. Our group serves as a ''master equation'' whose generality allows the rigorous prediction of the validity of a large number of specialized scaling groups proposed during the last 90 years. Furthermore, our results give strong evidence that the Darcy model is suitable for describing SI, and that including dynamic effects in capillary pressure is not necessary for counter-current SI, contrary to what has been hypothesized. Two key applications of the group are discussed: First, the group can serve as the long sought after general transfer rate for imbibition used in dual-porosity models. Second, it is the so far missing proportionality constant in imbibition-germination models for plant seeds.Citation: Schmid, K. S., and S. Geiger (2012), Universal scaling of spontaneous imbibition for water-wet systems, Water Resour. Res., 48, W03507,

The permeability of the Earth's crust commonly varies over many orders of magnitude. Flow velocity can range over several orders of magnitude in structures of interest that vary in scale from centimeters to kilometers. To accurately and efficiently model multiphase flow in geologic media, we introduce a fully conservative node-centered finite volume method coupled with a Galerkin finite element method on an unstructured triangular grid with a complementary finite volume subgrid. The effectiveness of this approach is demonstrated by comparison with traditional solution methods and by multiphase flow simulations for heterogeneous permeability fields including complex geometries that produce transport parameters and lengths scales varying over four orders of magnitude.

[1] The dynamic behavior of magmatic hydrothermal systems entails coupled and nonlinear multiphase flow, heat and solute transport, and deformation in highly heterogeneous media. Thus, quantitative analysis of these systems depends mainly on numerical solution of coupled partial differential equations and complementary equations of state (EOS). The past 2 decades have seen steady growth of computational power and the development of numerical models that have eliminated or minimized the need for various simplifying assumptions. Considerable heuristic insight has been gained from process-oriented numerical modeling. Recent modeling efforts employing relatively complete EOS and accurate transport calculations have revealed dynamic behavior that was damped by linearized, less accurate models, including fluid property control of hydrothermal plume temperatures and three-dimensional geometries. Other recent modeling results have further elucidated the controlling role of permeability structure and revealed the potential for significant hydrothermally driven deformation. Key areas for future research include incorporation of accurate EOS for the complete H 2 O-NaCl-CO 2 system, more realistic treatment of material heterogeneity in space and time, realistic description of large-scale relative permeability behavior, and intercode benchmarking comparisons. PURPOSE AND SCOPE[2] This review emphasizes the application of numerical modeling to understand and quantify processes in magmatic hydrothermal systems. We assess the state of knowledge and describe advances that have emerged in the 2 decades since a similar review by Lowell [1991]. Though our ability to rigorously describe key hydrothermal processes is still imperfect, there have been substantial advances since Lowell's [1991] review. These advances owe mainly to the steady growth of computational power and the concomitant development of numerical models that have gradually minimized various simplifying assumptions. They include incorporation of more accurate equations of state (EOS) for the fluid system, an increased ability to represent geometric complexity and heterogeneity, and faster and more accurate computational schemes. These advances have revealed dynamic behaviors that were entirely obscured in previous generations of models.[3] For purposes of this paper we define "magmatic hydrothermal systems" as aqueous fluid systems that are influenced by magma bodies in the upper crust. We particularly emphasize multiphase, multicomponent phenomena, which can have both quantitative and qualitative effects on the behavior of hydrothermal systems [Lu and Kieffer, 2009]. Multiphase (liquid-vapor) hydrothermal phenomena of interest include phase separation at scales ranging from centimeters to kilometers, with concomitant geochemical effects; novel modes of heat transport such as boiling plumes and countercurrent liquid-vapor flow ("heat pipes") [Hayba and Ingebritsen, 1997]; profound retardation of pressure transmission [Grant and Sorey, 1979]; and boiling-related minera...

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