Comprehensive comparison of pore-scale models for multiphase flow in porous media.

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.

Drying in a microfluidic chip: experiments and simulations.

We present an experimental micro-model of drying porous media, based on microfluidic cells made of arrays of pillars on a regular grid, and complement these experiments with a matching two-dimensional pore-network model of drying. Disorder, or small-scale heterogeneity, was introduced into the cells by randomly varying the radii of the pillars. The microfluidic chips were filled with a volatile oil and then dried horizontally, such that gravitational effects were excluded. The experimental and simulated drying rates and patterns were then compared in detail, for various levels of disorder. The geometrical features were reproduced well, although the model under-predicted the formation of trapped clusters of drying fluid. Reproducing drying rates proved to be more challenging, but improved if the additional trapped clusters were added to the model. The methods reported can be adapted to a wide range of multi-phase flow problems, and allow for the rapid development of high-precision micro-models containing tens of thousands of individual elements.

Dispersive transport and symmetry of the dispersion tensor in porous media.

The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010)TPMEEI0169-391310.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor D_{ij} satisfies the flow-reversal symmetry D_{ij}(+q)=D_{ji}(-q) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.

Effects of Pore-Scale Disorder on Fluid Displacement in Partially-Wettable Porous Media.

We present a systematic, quantitative assessment of the impact of pore size disorder and its interplay with flow rates and wettability on immiscible displacement of a viscous fluid. Pore-scale simulations and micromodel experiments show that reducing disorder increases the displacement efficiency and compactness, minimizing the fluid-fluid interfacial area, through (i) trapping at low rates and (ii) viscous fingering at high rates. Increasing the wetting angle suppresses both trapping and fingering, hence reducing the sensitivity of the displacement to the underlying disorder. A modified capillary number Ca* that includes the impact of disorder λ on viscous forces (through pore connectivity) is direct related to λ, in par with previous works. Our findings bear important consequences on sweep efficiency and fluid mixing and reactions, which are key in applications such as microfluidics to carbon geosequestration, energy recovery, and soil aeration and remediation.

Wettability Stabilizes Fluid Invasion into Porous Media via Nonlocal, Cooperative Pore Filling.

We study the impact of the wetting properties on the immiscible displacement of a viscous fluid in disordered porous media. We present a novel pore-scale model that captures wettability and dynamic effects, including the spatiotemporal nonlocality associated with interface readjustments. Our simulations show that increasing the wettability of the invading fluid (the contact angle) promotes cooperative pore filling that stabilizes the invasion and that this effect is suppressed as the flow rate increases, due to viscous instabilities. We use scaling analysis to derive two dimensionless numbers that predict the mode of displacement. By elucidating the underlying mechanisms, we explain classical yet intriguing experimental observations. These insights could be used to improve technologies such as hydraulic fracturing, CO2 geosequestration, and microfluidics.

Capillary fracturing in granular media.

We study the displacement of immiscible fluids in deformable, noncohesive granular media. Experimentally, we inject air into a thin bed of water-saturated glass beads and observe the invasion morphology. The control parameters are the injection rate, the bead size, and the confining stress. We identify three invasion regimes: capillary fingering, viscous fingering, and "capillary fracturing," where capillary forces overcome frictional resistance and induce the opening of conduits. We derive two dimensionless numbers that govern the transition among the different regimes: a modified capillary number and a fracturing number. The experiments and analysis predict the emergence of fracturing in fine-grained media under low confining stress, a phenomenon that likely plays a fundamental role in many natural processes such as primary oil migration, methane venting from lake sediments, and the formation of desiccation cracks.

Crossover from fingering to fracturing in deformable disordered media.

We investigate the displacement of one fluid by another in a deformable medium with pore-scale disorder. We develop a model that captures the dynamic pressure redistribution at the invasion front and the feedback between fluid invasion and microstructure rearrangement. Our results suggest how to collapse the transition between invasion percolation and viscous fingering in the presence of quenched disorder. We predict the emergence of a fracturing pattern for sufficiently deformable media, in agreement with observations of drainage in granular material. We identify a dimensionless number that appears to govern the crossover from fingering to fracturing.

Quantifying ground water inputs along the Lower Jordan River.

The flow rate of the Lower Jordan River has changed dramatically during the second half of the 20th century. The diversion of its major natural sources reduced its flow rate and led to drying events during the drought years of 2000 and 2001. Under these conditions of low flow rates, the potential influence of external sources on the river discharge and chemical composition became significant. Our measurements show that the concentrations of chloride, calcium, and sodium in the river water decrease along the first 20-km section, while sulfate and magnesium concentrations increase. These variations were addressed by a recent geochemical study, suggesting that ground water inflow plays a major role. To further examine the role of ground water, we applied mass-balance calculations, using detailed flow rate measurements, water samplings, and chemical analyses along the northern (upstream) part of the river. Our flow-rate measurements showed that the river base-flow during 2000 and 2001 was 500 to 1100 L s(-1), which is about 40 times lower than the historical flow rates. Our measurements and calculations indicate that ground water input was 20 to 80% of the river water flow, and 20 to 50% of its solute mass flow. This study independently identifies the composition of possible end-members. These end-members contain high sulfate concentration and have similar chemical characteristics as were found in agricultural drains and in the "saline" Yarmouk River. Future regional development plans that include the river flow rate and chemistry should consider the interactions between the river and its shallow ground water system.

Sources and transformations of nitrogen compounds along the Lower Jordan River.

The Lower Jordan River is located in the semiarid area of the Jordan Valley, along the border between Israel and Jordan. The implementation of the water sections of the peace treaty between Israel and Jordan and the countries' commitment to improve the ecological sustainability of the river system require a better understanding of the riverine environment. This paper investigates the sources and transformations of nitrogen compounds in the Lower Jordan River by applying a combination of physical, chemical, isotopic, and mathematical techniques. The source waters of the Lower Jordan River contain sewage, which contributes high ammonium loads to the river. Ammonium concentrations decrease from 20 to 0-5 mg N L(-1) along the first 20 km of the Lower Jordan River, while nitrate concentrations increase from nearly zero to 10-15 mg N L(-1), and delta(15)N (NO(3)) values increase from less than 5 per thousand to 15-20 per thousand. Our data analysis indicates that intensive nitrification occurs along the river, between 5 and 12 km from the Sea of Galilee, while further downstream nitrate concentration increases mostly due to an external subsurface water source that enters the river.