Lattice-Boltzmann simulations are employed to determine the mean settling velocity and pair distribution function for spheres settling in a liquid. The Reynolds number based on the terminal velocity ranges from 1 to 20, the solid-to-fluid density ratio is p / f = 2.0, and the solid volume fraction is varied from 0.005 to 0.40. At volume fractions larger than about 0.05, the ratio of the mean settling velocity to the terminal velocity u * can be fit by a power-law expression u * = k͑1 − ͒ n , where k and n are functions of the Reynolds number based on the terminal velocity. The constant k is typically about 0.86-0.92 and u * deviates from the power-law behavior in dilute suspensions. The extent of this deviation increases with increasing Reynolds number. We show that the hindered settling velocity follows a power law when the particle microstructure is similar to that in a hard-sphere suspension. The deviation from the power-law behavior can be correlated with an anisotropic microstructure resulting from wake interactions among the spheres. This microstructure, which occurs in dilute suspensions and is most pronounced at the higher Reynolds numbers explored in our study, consists of a decreased pair distribution function for pairs with vertical separation vectors and a peak in the pair distribution function for horizontal separations corresponding to about two particle diameters.

Numerous studies indicate that the pressure/volume/temperature (PVT) phase behavior of fluids in large pores (designated "unconfined" space) deviates from phase behavior in nanopores (designated "confined" space). The deviation in confined space has been attributed to the increase in capillary force, electrostatic interactions, van der Waals forces, and fluid structural changes.In this paper, conventional vapor/liquid equilibrium (VLE) calculations are modified to account for the capillary pressure and the critical-pressure and -temperature shifts in nanopores. The modified VLE is used to study the phase behavior of reservoir fluids in unconventional reservoirs. The multiple-mixing-cell (MMC) algorithm and the modified VLE procedure were used to determine the minimal miscibility pressure (MMP) of a synthetic oil and Bakken oil with carbon dioxide (CO 2 ) and mixtures of CO 2 and methane gas.We show that the bubblepoint pressure, gas/oil interfacial tension (IFT), and MMP are decreased with confinement (nanopores), whereas the upper dewpoint pressure increases and the lower dewpoint pressure decreases.

Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) generation of porous media samples, (2) computation of permeability via fluid dynamics simulations, (3) training of convolutional neural networks (CNN) with simulated data, and (4) validations against simulations. Comparison of machine learning results and the ground truths suggests excellent predictive performance across a wide range of porosities and pore geometries, especially for those with dilated pores. Owning to such heterogeneity, the permeability cannot be estimated using the conventional Kozeny-Carman approach. Computational time was reduced by several orders of magnitude compared to fluid dynamic simulations. We found that, by including physical parameters that are known to affect permeability into the neural network, the physics-informed CNN generated better results than regular CNN, however improvements vary with implemented heterogeneity.Computation of pore-scale transport properties from pore-scale images is an important aspect of image-based pore-scale studies. Such computations are generally performed in two ways, i.e., direct simulation approach and simplified network approach. In the first approach, the microscopic transport equations are solved directly on the geometry shown by the porescale images to obtain averaged properties such as permeability, relative permeability, or dispersion coefficient. Both single and multiphase flows can be accounted for, and both reactive and non-reactive transport equations can be solved. This direct approach is generally considered to be more accurate, but the computational cost is very high. For processes such as multiphase flows and reactive transport with slow kinetics, it is nearly impossible to solve the governing equations in a medium of even a moderate size. Therefore, the second alternative approach is to first abstract the porous medium as a discrete network. By applying simplified flow and transport laws on the network, the computational cost to obtain averaged properties can be effectively lowered [11].Some transport properties of porous media such as permeability are solely functions of pore geometry. Therefore, it should be possible to predict them using a neural network approach, which is to develop a surrogate model that directly maps a pore geometry to physical properties. Such a task resembles that in image classification [12,13], where a model takes an image as input and give the classification label as output by recognizing the object in the image, e.g., cars, animals, or even subtypes thereof (i.e., car make or animal breed). Once constructed, such surrogate models can potentially enable fast prediction of physical properties of porous media without performing direct simulations or network calculations. The recent studies of chemical imaging of rocks also involve surrogate models. For example, Hao et al.[14] generated a molecula...

Transport properties of a suspension of solid particles in a viscous gas are studied. The dissipation in such systems arises from two sources: inelasticity in particle collisions and viscous dissipation due to the effect of the gas phase on the particles. Here we consider a simplified case in which the mean relative velocity between the gas and solid phases is taken to be zero, such that "thermal drag" is the only remaining gas-solid interaction. Unlike the previous, more general, treatment of the drag force [Garzó et al., J. Fluid Mech. 712, 129 (2012)]JFLSA70022-112010.1017/jfm.2012.404, here we take into account contributions to the (scaled) transport coefficients η^{*} (shear viscosity), κ^{*} (thermal conductivity), and μ^{*} (Dufour-like coefficient) coming from the temperature dependence of the (dimensionless) friction coefficient γ^{*} characterizing the amplitude of the drag force. At moderate densities, the thermal drag model (which is based on the Enskog kinetic equation) is solved by means of the Chapman-Enskog method and the Navier-Stokes transport coefficients are determined in terms of the coefficient of restitution, the solid volume fraction, and the friction coefficient. The results indicate that the effect of the gas phase on η^{*} and μ^{*} is non-negligible (especially in the case of relatively dilute systems) while the form of κ^{*} is the same as the one obtained in the dry granular limit. Finally, as an application of these results, a linear stability analysis of the hydrodynamic equations is carried out to analyze the conditions for stability of the homogeneous cooling state. A comparison with direct numerical simulations shows a good agreement for conditions of practical interest.

Lattice-Boltzmann simulations of low-Reynolds-number fluid flow in bidisperse fixed beds and suspensions with particle-particle relative motions have been performed. The particles are spherical and are intimately mixed. The total volume fraction of the suspension was varied between 0.1 and 0.4, the volume fraction ratio / 1 // 2 from 1:1 to 1:6, and the particle size ratio d 1 /d 2 from 1:1.5 to 1:4. A drag law with improved accuracy has been established for bidisperse fixed beds. For suspensions with particleparticle relative motions, the hydrodynamic particle-particle drag representing the momentum transfer between particle species through hydrodynamic interaction is found to be an important contribution to the net fluid-particle drag. It has a logarithmic dependence on the lubrication cutoff distance and can be fit as the harmonic mean of the drag forces in bidisperse fixed beds. The proposed drag laws for bidisperse fixed beds and suspensions are generalized to polydisperse suspensions with three or more particle species.

The objective of this study was to create a microfluidic model of complex porous media for studying single and multiphase flows. Most experimental porous media models consist of periodic geometries that lend themselves to comparison with well-developed theoretical predictions. However, many real porous media such as geological formations and biological tissues contain a degree of randomness and complexity at certain length scales that is not adequately represented in periodic geometries. To design an experimental tool to study these complex geometries, we created microfluidic models of random homogeneous and heterogeneous networks based on Voronoi tessellations. These networks consisted of approximately 600 grains separated by a highly connected network of channels with an overall porosity of 0.11-0.20. We found that introducing heterogeneities in the form of large cavities within the network changed the permeability in a way that cannot be predicted by the classical porosity-permeability relationship known as the Kozeny equation. The values of permeability found in experiments were in excellent agreement with those calculated from three-dimensional lattice Boltzmann simulations. In two-phase flow experiments of oil displacement with water we found that the wettability of channel walls determined the pattern of water invasion, while the network topology determined the residual oil saturation. The presence of cavities increased the microscopic sweeping efficiency in water-oil displacement. These results suggest that complex network topologies lead to fluid flow behavior that is difficult to predict based solely on porosity. The novelty of this approach is a unique geometry generation algorithm coupled with microfabrication techniques to produce pore scale models of stochastic homogeneous and heterogeneous porous media. The ability to perform and visualize multiphase flow experiments within these geometries will be useful in measuring the mechanism(s) of displacement within micro- and nanoscale pores.

The pore sizes of shale and other unconventional plays are of the order of tens of nanometers. Based on the fundamental theory of thermodynamics, several studies have indicated that, in such small pores, phase behavior is affected by the capillary pressure and surface forces and is different from that characterized in PVT cells. No experimental evidence of this phenomenon, however, has been presented in the literature. In this study, we apply nanofluidic devices to visualize phase changes of pure alkane and an alkane mixture under nanoconfinement as a means to approach oil/gas phase behaviors in nanoporous rocks. Pure alkane starts vaporizing in the micro-channels first, and then the meniscus flashes into the nanochannels immediately after the complete vaporization of the liquid in the micro-channels. The vaporization of the ternary hydrocarbon mixture, however, is very different from pure alkane. Although the liquid starts to vaporize in the microchannels first, as expected, the meniscus cannot propagate into the nano-channels in a comparable time scale as the pure alkane. The reason is that the liberation of lighter components from the liquid phase to the gas phase in the micro-channels increases the apparent molecular weight of the liquid in the nano-channels, suppressing the bubble point of the remaining fluid. A modified flash calculation procedure that uses the sizes of micro-channels and nano-channels as the characteristic lengths and assumed contact angle can reproduce the vaporization propagation sequence in the experimental observations. Experiments and modeling presented in this paper provide the proof of the concept and promote the understanding of phase behavior in nanoporous unconventional reservoirs.

Using oil-wet polydimethylsiloxane (PDMS) microfluidic porous media analogs, we studied the effect of pore geometry and interfacial tension on water-oil displacement efficiency driven by a constant pressure gradient. This situation is relevant to the drainage of oil from a bypassed oil-wet zone during water flooding in a heterogeneous formation. The porosity and permeability of analogs are 0.19 and 0.133–0.268 × 10−12 m2, respectively; each analog is 30 mm in length and 3 mm in width, with the longer dimension aligned with the flow direction. The pore geometries include three random networks based on Voronoi diagrams and eight periodic networks of triangles, squares, diamonds, and hexagons. We found that among random networks both pore width distribution and vugs (large cavities) decreased the displacement efficiency, among the periodic networks the displacement efficiency decreased with increasing coordination number, and the random network with uniform microfluidic channel width was similar to the hexagon network in the displacement efficiency. When vugs were present, displacement was controlled by the sequence of vug-filling and the structure of inter-vug texture was less relevant. Surfactant (0.5 wt. % ethoxylated alcohol) increased the displacement efficiency in all geometries by increasing the capillary number and suppressing the capillary instability.