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At the high water cut stage, the residual oil in a reservoir becomes complex and dispersed. Moreover, it is challenging to achieve good predictions of the movement of oil and water in a reservoir according to the macroscopic models based on the statistic parameters of this scenario. However, pore-scale simulation technology based on directly tracking the interaction among different phases can make an accurate prediction of the fluid distribution in the pore space, which is highly important in the improvement of the recovery rate. In this work, pore-scale simulation methods, including the pore network model, lattice Boltzmann method, Navier–Stokes equation-based interface tracking methods, and smoothed particle hydrodynamics, and relevant technologies are summarized. The principles, advantages, and disadvantages, as well as the degree of difficulty in the implementation are analyzed and compared. Problems in the current simulation technologies, micro sub-models, and applications in physicochemical percolation are also discussed. Finally, potential developments and prospects in this field are summarized.

A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another “equivalent” sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics. [ABSTRACT FROM AUTHOR]

Summary The Lattice Boltzmann (LB) method is an established prominent model for simulating water flow at pore scale in saturated porous media. However, its application in unsaturated soil is less satisfactory because of the difficulties associated with most two-phase LB models in simulating immiscible fluids, such as water and air, which have contrasting densities and viscosities. While progress has been made in developing LB models for fluids with high density ratio, they are still prone to numerical instability and cannot accurately describe the interfacial friction on water–air interface in unsaturated media. Considering that one important application of the LB model in porous materials is to calculate their hydraulic properties when flow is at steady state, we develop a simple LB model to simulate steady water flow at pore scale in unsaturated soils. The method consists of two steps. The first one is to determine water distribution within the soil structure using a morphological model; once the water distribution is known, its interfaces with air are fixed. The second step is to use a single-phase LB model to simulate water flow by treating the water–air interfaces as free-flow boundaries where the shear resistance of air to water flow is assumed to be negligible. We propose a method to solve such free-flow boundaries, and validate the model against analytical solutions of flows of water film over non-slip walls in both two and three dimensions. We then apply the model to calculate water retention and hydraulic properties of a medium acquired using X-ray computed tomography at resolution of 6 μm. The model is quasi-static, similar to the porous network model, but is an improvement as it directly simulates water flow in the pore geometries acquired by tomography without making any further simplifications. [ABSTRACT FROM AUTHOR]

The enormous growth in computational capabilities of recent years has made Navier-Stokes-based simulation of flow and transport in natural porous media possible. Because of the complex multiscale nature of porous media, however, full Navier-Stokes representation of the physics everywhere in the domain is not always feasible. Here, we employ, a filtering-or micro-continuum-approach to model the smallest length scales. The Darcy-Brinkman-Stokes (DBS) equation offers an appealing framework for this hybrid modeling. A general modeling framework based on the DBS equation is proposed. The approach is then used to bridge the gap between scales for several challenging problems, including flow in fractured media, pore-scale simulation with immersed boundary conditions, modeling of dissolution phenomena, and thermal evolution of oil shale. [ABSTRACT FROM AUTHOR]

There is growing interest in using advanced imaging techniques to describe the complex pore-space of natural rocks at resolutions that allow for quantitative assessment of the flow and transport behaviors in these complex media. Here, we focus on representations of the complex pore-space obtained from X-ray microtomography and the subsequent use of such 'pore-scale' representations to characterize the overall porosity and permeability of the rock sample. Specifically, we analyze the impact of sub-resolution porosity on the macroscopic (Darcy scale) flow properties of the rock. The pore structure of a rock sample is obtained using high-resolution X-ray microtomography $$(3.16^3\,{\upmu } \hbox {m}^{3}/\hbox {voxel})$$ . Image analysis of the Berea sandstone sample indicates that about 2 % of the connected porosity lies below the resolution of the instrument. We employ a Darcy-Brinkman approach, in which a Darcy model is used for the sub-resolution porosity, and the Stokes equation is used to describe the flow in the fully resolved pore-space. We compare the Darcy-Brinkman numerical simulations with core flooding experiments, and we show that proper interpretation of the sub-resolution porosity can be essential in characterizing the overall permeability of natural porous media. [ABSTRACT FROM AUTHOR]

The unique properties of ceramic foams make them well suited to a range of applications in science and engineering such as heat transfer, reaction catalysis, flow stabilization, and filtration. Consequently, a detailed understanding of the transport properties (i.e. permeability, pressure drop) of these foams is essential. This paper presents the results of both numerical and experimental investigations of the morphology and pressure drop in 10 ppi (pores per inch), 20 ppi and 30 ppi ceramic foam specimens with porosity in the range of 75–79%. The numerical simulations were carried out using a GPU implementation of the three-dimensional, multiple-relaxation-time lattice Boltzmann method (MRT-LBM) on geometries of up to 360 million nodes in size. The experiments were undertaken using a water channel. Foam morphology (porosity and specific surface area) was studied on post-processed, computed tomography (CT) images, and the sensitivity of these results to CT image thresholding was also investigated. Comparison of the numerical and experimental data for pressure drop exhibited very good agreement. Additionally, the results of this study were verified against other researchers׳ data and correlations, with varying outcomes. [ABSTRACT FROM AUTHOR]

[Display omitted] • 3D model of reactive transport process in the CID cell is established based on LBM. • Microstructures of porous electrodes are reconstructed using improved QSGS method. • Ion transport behavior under the constant current is revealed from the pore-scale level. • Effects of current density, porosity and particle size on transport processes are investigated. Cation intercalation desalination (CID) has gained great popularity in the field of water desalination because of its excellent desalination performance. Due to lack of understanding of the relationship between electrode microstructures and reactive adsorption processes in CIDs, the further development of high-performance CID electrodes has been hindered. To this end, the influences of electrode microstructures on the desalination performance of CID cells were investigated from the pore-scale level in this work. The three-dimensional microstructures of porous electrodes are first reconstructed by an improved random generation method. Based on the reconstructed porous electrodes, the flow, mass transfer and intercalation reaction processes under the constant current are simulated using the lattice Boltzmann method. The effects of applied current density, porosity and size of active particles on the change of liquid-phase sodium concentration and Na-intercalated degree in the solid phase are evaluated. The simulation results show that increasing the current density can accelerate the ion intercalation and desalination rates. During the desalination, the ion concentration is unevenly distributed in the pores of porous electrodes, and the intercalation degrees are different along the electrode thickness direction and in the particle radial direction. The increase of porosity can alleviate the concentration polarization of liquid-phase sodium ion and reduce the difference of particle intercalation degree between the front- and back-sides of the electrode. In addition, the increase of porosity can accelerate the desalination process, but cannot improve the total salt removal. Reducing particle size can shorten the time for particles to reach the sodium-rich state, but it can aggravate the polarization of sodium ion concentration in the liquid phase at both ends of the electrode. This work reveals the ion intercalation behavior in the CID and its relationship with the electrode microstructures, and may provide useful information for the design and research of CID. [ABSTRACT FROM AUTHOR]

• Effect of hydrate saturation, morphology and particle size on HBS permeability. • Analysis of pore-scale flow behavior at pore throat on HBS permeability. • Abrupt permeability reduction identified at S H = 33.9% for pore-filling HBS. • A new model proposed for HBS permeability calculation considering tortuosity. • HBS permeability comparison between uniform and non-uniform settings. The distribution pattern of CH 4 hydrate in hydrate-bearing sediments (HBS) significantly impacts the permeability, which is one of the critical flow properties controlling the fluid production in the exploitation of natural gas hydrate (NGH) reservoirs. Thus, it warrants investigation on the key influencing factors, i.e., (a) hydrate saturation; (b) hydrate distribution patterns; (c) sediment particle size on the associated permeability of HBS especially at pore-scale. In this study, a series of two-dimensional geometric models were constructed that best represent the commonly-observed hydrate distribution patterns. The pore-scale flow behavior of the resulting models was simulated through computational fluid dynamics. The simulation results suggest that the reduction of permeability is dependent on the distribution pattern of hydrate. The permeability of grain-coating HBS decreases by a maximum of five orders of magnitude at S H = 0.3. Additionally, increasing S H results in new pore throats and induces clogging in fluid flow that controls permeability reduction. A strong log-log linear relationship was identified between sediment particle size and the simulated permeability. A modified empirical model for the estimation of HBS permeability was proposed considering both tortuosity and effective porosity. Moreover, a heterogeneous sediment particle distribution model was constructed for the first time that accurately described the particle size distribution of a hydrate-bearing core sample recovered from Japan Nankai Trough. Compared to the homogeneous model, a heterogeneous model results in a more substantial reduction of permeability with S H and better represents the permeability of the HBS core sample. The finding of this study can be significant in understanding the pore-scale flow behavior in HBS and are meaningful for the design of safe and effective production methods in the exploitation of NGH reservoirs. [Display omitted] [ABSTRACT FROM AUTHOR]

X-ray microtomography is routinely used to image the three-dimensional pore space of sedimentary rocks. Flow and transport properties can then be simulated directly in such images. Advective transport in porous media is frequently simulated using streamlines. We present a novel streamline tracing algorithm based on a substantial development of the most widely used method (the Pollock algorithm) employed for macroscale (Darcy) flow, making it consistent with solutions of the Navier-Stokes equation with no flow at solid boundaries. We use this new algorithm to calculate breakthrough curves and time-of-flight distributions for advection-dominated transport in two three-dimensional images of sedimentary rocks containing up to $$10^9$$ voxels: a sandstone and a carbonate. We show that our approach provides a more accurate description of flow, particularly when only a few image voxels span each pore. Therefore, it is better suited to capture anomalous (non-Fickian) transport behaviour than the standard Pollock method. [ABSTRACT FROM AUTHOR]

The selection of an appropriate membrane for a particular application is a complex and expensive process. Computational modeling can significantly aid membrane researchers and manufacturers in this process. The membrane morphology is highly influential on its efficiency within several applications, but is often overlooked in simulation. Two such applications which are very important in the provision of clean water are forward osmosis and filtration using functionalized micro/ultra/nano-filtration membranes. Herein, we investigate the effect of the membrane morphology in these two applications. First we present results of the separation process using resolved finger- and sponge-like support layers. Second, we represent the functionalization of a typical microfiltration membrane using absorptive pore walls, and illustrate the effect of different microstructures on the reactive process. Such numerical modeling will aid manufacturers in optimizing operating conditions and designing efficient membranes. [ABSTRACT FROM AUTHOR]

A new capillary model is proposed to simulate fluid flow through tight formations considering electrokinetic coupling effects at the pore scale. The capillary is constructed by using trigonometric functions to mimic pore and throat structures of porous media. The coupled Navier–Stokes equation, Poisson equation and Planck–Nernst equation are solved simultaneously using finite element method to obtain the velocity profile, the distribution of electric potential and the concentration of ions in the model. The numerical results are then compared with that of the model which does not consider the electrokinetic coupling effects. The results show that the electric charges on the capillary wall can strongly affect the distribution of pressure, especially at the locations of throats, and we also give our explanation to account for this new observation. Besides, the coupling of electrical potential field and flow field can increase the resistance of fluid flow through the capillary and therefore decrease the total flow rate. Finally, we investigate the relationship between flow rate and pressure gradient under different conditions considering the electrokinetic coupling effects, and the result shows that this relationship remains linear. Therefore, our simulation result suggests that the nonlinear relationship between flow rate and pressure gradient observed in tight formations cannot be explained by electrokinetic coupling effect. [ABSTRACT FROM AUTHOR]

A lattice Boltzmann color-fluid model, which was recently proposed by Liu et al. (2012) based on a concept of continuum surface force, is improved to simulate immiscible two-phase flows in porous media. The new improvements allow the model to account for different kinematic viscosities of both fluids and to model fluid–solid interactions. The capability and accuracy of this model is first validated by two benchmark tests: a layered two-phase flow with a variable viscosity ratio, and a dynamic capillary intrusion. This model is then used to simulate liquid CO 2 (LCO 2 ) displacing water in a dual-permeability pore network. The extent and behavior of LCO 2 preferential flow (i.e., fingering) is found to depend on the capillary number ( Ca ), and three different displacement patterns observed in previous micromodel experiments are reproduced. The predicted variation of LCO 2 saturation with Ca , as well as variation of specific interfacial length with LCO 2 saturation, are both in reasonable agreement with the experimental observations. To understand the effect of heterogeneity on pore-scale displacement, we also simulate LCO 2 displacing water in a randomly heterogeneous pore network, which has the same size and porosity as the simulated dual-permeability pore network. In comparison to the dual-permeability case, the transition from capillary fingering to viscous fingering occurs at a higher Ca , and LCO 2 saturation is higher at low Ca but lower at high Ca . In either pore network, the LCO 2 –water specific interfacial length is found to obey a power-law dependence on LCO 2 saturation. [ABSTRACT FROM AUTHOR]

Abstract: Pore-scale simulations of transport phenomena in foam based catalytic converters are highly desirable due to their intrinsic accuracy in describing the involved physics. Unfortunately, such computations are prohibitively time consuming and costly. Here we combine a detailed pore-scale characterization with a volume average description of an open-cell foam based catalytic converter. The resulting volume averaged model is accurate and more than three orders of magnitude more efficient in terms of computational time, compared to direct pore scale simulations. This makes simulations of the related complex phenomena tractable, providing a highly flexible and powerful tool for parametric studies of open-cell foams. The volume-averaged model is validated with a pore-scale simulation of a full-scale catalytic converter used for automotive exhaust gas treatment. Fast chemistry is assumed and the heat released by the chemical reaction in combination with conjugate heat transfer is considered. We show that the conversion to pressure drop trade-off improves with increasing foam porosity and the heat release of the reaction significantly affects the pressure drop across the reactor. The simulations show non-uniform surface temperatures which are attributed to the non-unity Lewis number of the mass transfer limiting species. The model predictions agree well with experimental measurements of pressure drop and Sherwood number in open-cell foams. [Copyright &y& Elsevier]

Highlights: [•] In this work pore-scale CFD simulations of several porous media were performed. [•] Colloidal particle deposition due to Brownian motions and steric interception were analyzed. [•] Several models representing porous media with different characteristics were considered. [•] Results highlight strong deviations from the extended Levich law for many-collector systems. [•] Results also show deviations due to the irregular shape of the collectors. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann method is a popular tool for pore-scale simulation of flow. This is likely due to the ease of including complex geometries such as porous media and representing multiphase and multifluid flows. Many advancements, including multiple relaxation times, increased isotropy, and others have improved the accuracy and physical fidelity of the method. Additionally, the lattice Bolzmann method is computationally very efficient, thanks to the explicit nature of the algorithm and relatively large amount of local work. The combination of many algorithmic options and efficiency means that a software framework enabling the usage and comparison of these advancements on computers from laptops to large clusters has much to offer. In this paper, we introduce Taxila LBM, an open-source software framework for lattice Boltzmann simulations. We discuss the design of the framework and lay out the features available, including both methods in the literature and a few new enhancements which generalize methods to complex geometries. We discuss the trade-off of accuracy and performance in various methods, noting how the Taxila LBM makes it easy to perform these comparisons for real problems. And finally, we demonstrate a few common applications in pore-scale simulation, including the characterization of permeability of a Berea sandstone and analysis of multifluid flow in heterogenous micromodels. [ABSTRACT FROM AUTHOR]

Highlights: [•] Development of a model for the microbial conversion of hydrogen in UHS. [•] Gas flow is simulated on the pore scale using Stokes’ equations. [•] Multispecies microbial activity within biofilms is accounted for with a separate model. [•] The two models are coupled via boundary conditions. [•] A sample simulation shows the biofilm growth process within films of residual water. [Copyright &y& Elsevier]

• This study examines the impact of pore structure parameters on thermal conductivity. • With a pore-scale thermal simulations employing virtually generated pore structures. • Total porosity and matrix conductivity are dominant parameters for low conductivity. • With gas conductivity and radiative properties as potentially secondarily important. • While average pore size and pore size distribution do not play a significant role. This study examines the interacting influence of different pore structure parameters on the thermal conductivity of porous building blocks with pores of micrometer and nanometer magnitudes. A first exploratory study varies the pore structure parameters over a wide spectrum, and reveals that total porosity and matrix conductivity are most dominant. A second selective study applies high total porosities and low matrix conductivities to assess the secondary parameters. But this study confirms the dominant character of total porosity and matrix conductivity, with substantial secondary influences of gas conductivity and radiative properties. In all investigations, the average pore size and the pore size distribution appears as (far) less important. [ABSTRACT FROM AUTHOR]

• Multiphase pore-scale modelling of the hydrate dissociation is investigated. • Effects of the water saturation and Péclet number on the hydrate dissociation are revealed. • The mass-transfer-limitation and heat-transfer-limitation on hydrate dissociation are quantified. • Regime diagram of the hydrate dissociation are mapped. • Empirical models of the permeability and specific surface area are obtained. Methane hydrate is a promising energy resource, but the hydrate development still faces technical difficulties due to the complicated multiple physicochemical and thermal processes during the multiphase hydrate dissociation in the sediment. In this study, a pore-scale numerical model based on the lattice Boltzmann method was proposed to simulate methane hydrate dissociation considering multiphase flow, heat and species transport, heterogeneous reaction and hydrate structure evolution. The single-phase hydrate dissociation was firstly simulated to identify the convection and diffusion transport-limited regimes according to the Péclet number. Effects of the connate water saturation and the Péclet number on the multiphase hydrate dissociation were then investigated to understand the varying dissociation dynamics and dissociation mechanisms. The competitive mass-transfer-limitation and heat-transfer-limitation were quantified to elucidate the interplay between multiphase mass transport and heat transport on the hydrate recovery efficiency. The regime diagram of the methane hydrate dissociation was mapped to exhibit five dissociation regimes according to the connate water saturation and the Péclet number. Empirical correction of the permeability and the specific surface area was obtained to improve the REV (Representative Element Volume)-scaled modeling accuracy of the volume-averaged transport and geometric properties with three typical dissociation patterns. The insights from the pore-scale multiphase dissociation studies can enlighten the accurate REV-scaled simulation with the addressed non-negligible physics. [ABSTRACT FROM AUTHOR]

Pore-scale heat and fluid flow simulation through reconstructed porous media is presented with the aim of investigating the physics of heat flux splitting at the boundary of porous media. As such, the effects of the solid to fluid thermal conductivity ratio, porosity, pore-scale Reynolds number, Prandtl number and heat conduction within the solid matrix are investigated. The results of the present study for heat transfer coefficient and pressure drop are compared with available experimental data and good agreement was observed. The validated results are then used to investigate the validity of the existing volume-averaged models. It was observed that while results based on the volume-averaged models are reasonably close to current predictions for $$\varepsilon \le 0.7$$, the discrepancy between the two becomes notable for higher porosities. While existing models rely exclusively on porosity and thermal conductivity ratio, our newly proposed correlations show the effects of Reynolds number on the heat split mechanism for high porosities. On the other hand, the Prandtl number, at least for the range of parameters studies here, is found to be less influential on the boundary heat split mechanism. [ABSTRACT FROM AUTHOR]

Convective drying of disordered glass bead packings has been investigated both experimentally and numerically. X-ray microtomography (XMT) and image analysis techniques have been used to determine the three-dimensional spatial distribution of the liquid and solid phases at the pore scale within the wet particle aggregates. The evolution of the liquid distribution in the aggregate has been tracked during the drying process. Particle center coordinates and radii have been extracted from the X-ray images using binarization and segmentation techniques. Based on this geometric data for a real aggregate, a pore network approximation of the pore space has been generated from a Voronoi tessellation about particle centers by designating Voronoi edges as interconnected cylindrical pores with radii computed from the distance between neighboring particles. This three-dimensional irregular pore network takes into account both the geometrical and topological characteristics (pore size distribution and connectivity) of the actual pore space. Drying simulations have been carried out for the pore networks obtained from the XMT and results are presented as phase distributions and moisture profiles. The simulated liquid phase distributions are in qualitative agreement with the experimental result, which indicates that pore network models are suited to describe the drying of dense particle aggregates at the pore scale. [ABSTRACT FROM PUBLISHER]

Abstract: We report finite-element simulations of gas–liquid two-phase flows through a model porous medium made of corrugated tubes. By resolving the pore-scale fluid dynamics and interfacial morphology, we compute the relative permeability of the porous medium by averaging over a pore-size-distribution of a real porous medium. A constant pressure gradient is applied on both fluids to simulate a pressure-driven creeping flow, and a diffuse-interface model is used to compute the interfacial evolution and the contact line motion. We observe a number of flow regimes in the micro-pores, depending on the pore size, imposed pressure gradient, and other geometric and physical parameters. The flow rates vary nonlinearly with the pressure gradient, and the extended Darcy’s law does not hold in general. The interaction between the two phases, known as viscous coupling, is a prominent feature of the process. As a result, the relative permeability depends not only on saturation, but also on the capillary number, viscosity ratio, wettability of the solid wall, pore geometry, and the initial configuration. The effects of these factors are explored systematically and compared with previous studies. [Copyright &y& Elsevier]

Abstract: Laminar steady forced convection through an array of disconnected conducting cylindrical fins is simulated by implementing a pore-scale numerical simulation. Effects of fin array porosity, fin arrangements, pore-scale Reynolds number, and the solid to fluid thermal conductivity ratio, on the heat flux bifurcation at the uniformly heated wall are investigated. The results show that decreasing the Reynolds number or increasing the solid to fluid thermal conductivity ratio monotonically increases the solid to fluid wall heat flux ratio. It is also observed that solid to fluid heat flux ratio increases with increasing the porosity. The obtained results have been compared to available models in the literature. While in some cases the results are close, errors associated with available models are analyzed and accurate correlations for heat flux bifurcation are proposed. [Copyright &y& Elsevier]

Abstract: Capillary pressures in a carbon paper gas diffusion layer (GDL) having hydrophilic and hydrophobic pores of a polymer electrolyte membrane fuel cell (PEMFC) are investigated by both lattice Boltzmann simulations and experimental measurements. The simulated and measured capillary pressures as a function of water saturation for water drainage and imbibition processes in the GDL are presented and compared. It is shown that the pore-scale simulated drainage and imbibition capillary pressure curves are in good agreement with that obtained by experiment, both indicating the coexistence of hydrophilic and hydrophobic properties in the polytetrafluoroethylene (PTFE) treated carbon paper GDLs. The fitted capillary pressure curves, obtained from this paper, can provide more accurate predictions of the capillary pressure in carbon paper GDLs with non-uniform porosity and wettability than the standard Leverett–Udell relationship which was obtained for soil with more uniform porosity and wettability. [Copyright &y& Elsevier]

There have been conjectures that a spatial average could result in a volume-average concentration which is no longer continuous at sharp interfaces between different materials. However, convincing experimental evidence showing the existence of such a discontinuity is not available because of the difficulty associated with measuring solute concentration in the void space within a porous medium. In this paper we used pore-scale simulations to explore the change in macroscopic concentration when solute moves from one material into another. Water flow through the void space was assumed to be laminar, and solute transport consisted of molecular diffusion and advection; both were simulated using the lattice Boltzmann equation methods. To accurately represent the fluid-solid interface, the multiple-relaxation-time lattice Boltzmann equation method was used to simulate fluid flow. We first simulated solute transport in a 3D column with one half packed with fine glass beads and the other half with coarse glass beads. The simulated solute concentration and solute flux at pore scale were then spatially averaged to produce volume-average and flux-average concentration profiles, respectively, in attempts to understand if solute accumulates at the media interface when moving from one medium into another. The results revealed that, when solute migrated from the coarse medium into the fine medium, it did accumulate at the media interface; we also found mass accumulation at the reservoir-column interface. Such accumulations made solute take more time to break through the column when flowing from the coarse medium to the fine medium than from the fine medium to the coarse medium. We also simulated solute movement in an idealized 2D column packed with different rectangular solids and with high porosity; the results indicated that, although the dispersive properties of the two media differed considerably, there was no mass accumulation and the macroscopic concentration was found to be continuous at the media interface. These simulated results suggest that a sharp change in material properties with moderate porosity will likely lead to a mass accumulation, but knowing the transport properties of the two materials alone is not sufficient to determine if a mass accumulation could develop. What causes mass accumulations appears to be some microstructures in the vicinity of the interface, which cannot be accounted for by the macroscopic transport parameters of each of the two media. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the possibility of using nominally second-order-accurate techniques for resolving flow about solid boundaries as a means of improving accuracy and reducing grid resolution requirements in pore-scale simulations. An LBGK method is used to calculate flow in several geometries of increasing complexity, using a first-order accurate and two nominally second-order-accurate methods for no-slip boundaries. The geometries include uniform flow past an isolated sphere, quadratic flow past a sphere near a wall, flow through a BCC array of spheres, and through a randomly packed bed of spheres. The packed bed flows are also used to compare hydrodynamic dispersion results. The results confirm second-order-accurate behavior where Navier–Stokes flows are clearly developed. However 3D pore-scale simulations involve a trade-off between resolution of the flow and the number of pore spaces, and there is a resolution threshold, below which certain flow features, such as recirculation, are not resolved. We conjecture that most simulations will tend to operate near this threshold because of the competing demands for resolution and statistical accuracy. We consider local flow features and the velocity distribution, in addition to hydraulic permeability and drag, to provide a fuller understanding of accuracy near this threshold. [Copyright &y& Elsevier]

• CNNs and downsamling techniques are implemented for upscaling. • Two-phase flow and petrophysical properties are upscaled for a low-resolution model. • Upscaled properties shows a good agreement with the high-resolution properties. In digital rock physics, finding the trade-off between image resolution and field of view and, at the same time, maintaining the accuracy of flow prediction in a low-resolution large-scale model is a challenging task. Multiphase flow characteristics are strongly dependent on image resolution. Therefore, the upscaling process based on pore-scale simulations is crucial for predicting low-resolution model properties regarding the referred trade-off. This study has disclosed an upscaling method taking advantage of convolutional neural networks (CNNs) and downsampling techniques. The method has been applied to a set of multi-scale images taken from Fontainebleau sandstone. High-resolution images are downsampled and then labelled with their properties to train CNNs. Trained CNNs are then used to predict the upscaled properties of low-resolution samples. The predicted upscaled properties by CNNs are assigned to computational grids of the reconstructed low-resolution model in a continuum-scale simulator. By performing multiphase flow simulations of the mentioned model and various assigned properties, the resultant dynamic behaviours from low-resolution and CNN upscaled properties are compared with the dynamic behaviour of the high-resolution case. Results showed a satisfying match between the dynamic behaviour of the upscaled model through CNNs and high-resolution properties with a significant reduction of computational cost and time. [ABSTRACT FROM AUTHOR]

Pore structure has a significant effect on transport phenomena inside porous media. This effect can be considered in simulations by using suitable transport coefficients. Some correlations are reported in the literature, which can be applied for simple pore geometries. In the present study, a pore-scale simulation approach is presented to determine mass diffusion coefficient considering molecular and Knudsen diffusion in a fibrous porous medium as a complex porous geometry. The methodology is employed for species in catalytic combustion of Methane inside a fibrous porous structure. The effect of Solid Volume Fraction (SVF), fibers orientation, and diameter are discussed in different temperatures. It is found that SVF plays the dominant role in mass diffusion, specifically above 600K. Mass diffusion coefficients obtained in the present study and flow permeability, conduction and radiation heat transfer coefficients from the previous study are used to simulate methane combustion inside the fibrous structure on the macro scale. An experimental setup is developed for validation. The results indicated that the simulation could well predict the temperature distribution, also 6.4% error in estimating the Methane conversion rate was observed. Due to the low Peclet number, the concentration of CH 4 and O 2 decreased unexpectedly before entering the catalytic zone. [Display omitted] • Experimental and numerical study of catalytic combustion in fibrous porous media. • Determination of mass diffusion coefficients inside a complex porous media. • Pore-scale simulation considering molecular and Knudsen diffusion in porous media. • Effect of geometric parameters on the mass diffusion coefficient. • Reaction rate obtained by incorporating transport phenomena coefficients. [ABSTRACT FROM AUTHOR]

• Aggregates taken from the longest experiments in the world were scanned using X-ray CT. • Transport ability of each aggregate was calculated from pore-scale simulations. • Soil organic carbon and bulk diffusion coefficient of the aggregates are positively correlated. • Bulk diffusion coefficient of the aggregates tends to plateau as soil organic carbon increases. A key finding in soil carbon studies over the past decade is that soil organic carbon (SOC) stabilization is not controlled by its molecular complexity or adsorption to clay, but by its physicochemical protection including occlusion in aggregates and sorption-precipitation with organo-mineral associations. The organo-mineral complexes and the adsorbed SOC can be dissolved microbially under anoxic conditions, which is an important pathway in carbon cycle but has been overlooked by most carbon models. As organo-mineral associations are reported to form in aerobic conditions and can be lost under anaerobic conditions, there should be a positive correlation between SOC and ability of the aggregates to transport dissolved oxygen. We develop a simulation model to test this using soil structural data from two long-term experiments which naturally created a SOC gradient: One is a winter wheat experiment established in 1843 to compare the effects of different fertilizations on the yield of winter wheat and the other one is a ley-arable experiment established in 1948 to investigate the consequence of cropping system changes for ecological yield. Aggregates from different treatments on the two experiments were scanned using X-ray Computed Tomography to simulate oxygen transport using a pore-scale model. We compared porosity and diffusion coefficient of all aggregates and linked them to SOC measured from the two experiments. The agronomic practice changes which occurred 67 or 172 years ago substantially reshaped the intra-aggregate structure (<2 mm), and the accrual of SOC is positively correlated with diffusion coefficient of the aggregates to transport oxygen. However, the diffusion coefficient increases with SOC asymptotically, plateauing when SOC exceeds a threshold value. We also found the diffusion coefficient of the aggregates in chemically fertilized soils trended with their porosity approximately in the same way, deviating from those for other non-cropped treatments or fertilized with farmyard manure. [ABSTRACT FROM AUTHOR]

• We compared tortuosities of 30 soil samples calculated by three methods. • Correlations between tortuosities calculated by different methods are weak. • Tortuosity for fluid flow is the highest and geometrical tortuosity is the least. • Porosity and geometrical tortuosity cannot be used to estimated soil transport parameters. Tortuosity is a parameter characterising the complexity of pore geometry in porous media for fluids and solutes to move through. It is loosely defined and has been calculated by different methods based on either the pore geometry or a special transport process. While it has been known that tortuosities calculated from different methods vary, it remains obscure if there is a one-to-one relationship between them, especially for soils which are not randomly structured but self-organised by a myriad of interactive biotic and abiotic processes. We studied this based on X-ray images of 30 soil aggregates taken from fields which have been under different land managements for more than 70 years and thus have contrasting structures. The tortuosity of every soil sample was calculated using three methods: viscous fluid flow, solute diffusion, and geometric structure of the pores, with the former two calculated from pore-scale simulations. The results showed that although the tortuosities calculated by all methods are correlated, their correlation is weak and there is no one-to-one relationship between them. On average, the tortuosity calculated from fluid flow is the highest and the geometrical tortuosity is the least, with that calculated from solute diffusion in between. The tortuosity calculated from all three methods decreases as porosity increases, but the coefficient of determination is low. We also found that the bulk diffusion coefficient cannot be predicted using geometrical tortuosity and porosity of the soils from the formulae suggested in the literature. These findings reveal that tortuosity is a process-dependent parameter rather than an intrinsic soil property, and that tortuosity calculated from different methods cannot be used interchangeably to estimate soil transport parameters. [ABSTRACT FROM AUTHOR]

• The interplay between wettability alteration and domain geometry in impacting pore-scale two-phase flow in porous media is investigated. • A wettability alteration algorithm is developed and utilized to track spatial and temporal variation in the wettability state. • The effect of wettability alteration on the oil phase fractional flow enhancement is more pronounced at comparable saturations of the two phases. • The extent of oil ganglia remobilization and coalescence events due to wettability alteration are observed to be correlated with domain heterogeneity, capillary number, and phase saturation. • The pore-scale displacement mechanisms are controlled by the local wettability state and pore topology, but the overall flow pathways are dictated by the interactions between the displacement mechanisms. • The developed algorithm provides an efficient framework to track wettability alteration, update the wettability state, and detect trapped ganglia. The objective of this paper is to investigate the interplay between wettability alteration and domain geometry in influencing the pore-scale displacement and trapping mechanisms of two-phase flow in porous media. A new wettability alteration algorithm is introduced to quantify and track the spatial and temporal variability of the wettability state of every pore. Simulations in an initially oil-wet domain are conducted using the lattice Boltzmann model while utilizing the wettability alteration algorithm to capture the new wettability states. The simulations are then resumed under the new generated wettability states to investigate the coupled impacts of wettability alteration and domain topology on the resulting pore-scale displacement behavior. We observe varying degrees of improvements in the oil phase fractional flow as the wettability state is varied towards water-wet conditions influenced by the domain geometry, capillary number, and phase saturation. Significant heterogeneity, increased surface roughness, and the prevalence of narrower pore spaces in the rock sample in comparison to the spherepack increase the percentage of trapped oil ganglia. As a result, wettability alteration results in varying degrees of oil remobilization events, followed by coalescence with the main flow path, especially at higher capillary numbers. Moreover, oil phase fractional flow at higher oil saturation becomes influenced primarily by the increased phase connectivity, and improvements due to wettability alteration become less significant. Similar displacement mechanisms are observed in both domains, controlled primarily by the wettability distribution and the local pore geometry. However, the resulting flow pathways, which dictate the overall flow behavior, are controlled by the frequency of various displacement mechanisms and are a function of the domain geometry. The observations in this study highlight the complex interactions between wettability heterogeneity and pore geometry in influencing pore-scale two-phase flow. The wettability alteration algorithm introduced can be used to optimize pore-scale displacement processes by providing a framework to track the locations and the relative degree of wettability alteration, enable automatic wettability alteration, and detect trapped ganglia without the need for post-processing. [ABSTRACT FROM AUTHOR]

Pore-scale studies of premixed gas combustion in a packed bed is conducted to study the flow and thermal non-equilibrium phenomenon in packed bed. The 3D random packed bed is generated using the EDEM software and solid surface radiation is computed using Discrete Ordinates (DO) model. The simulations are carried out using a commercial software package based on the finite volume method. It is shown that the local variation of species mass fraction, reaction rate et al. in pores near the flame front is significant, the radiation heat flux is transferred layer-by-layer. Cold flow simulation without reaction reveals that flow non-equilibrium is one of the essential characteristics of packing bed and increase in flow velocity leads to intensify non-equilibrium phenomenon. The distributions for content of axial velocity and gas temperature are wave-like shape in the burner and vary with time. [ABSTRACT FROM AUTHOR]

Abstract: Modelling adsorptive solute transport in soils needs a number of parameters to describe its reaction kinetics and the values of these parameters are usually determined from batch and displacement experiments. Some experimental results reveal that when describing the adsorption as first-order kinetics, its associated reaction rates are not constants but vary with pore water velocity. Explanation of this varies but an independent verification of each explanation is difficult because simultaneously measuring the spatiotemporal distributions of dissolved and adsorbed solutes in soils is formidable. Pore-scale modelling could play an important role to address this gap and has received increased attention over the past few years. This paper investigated the transport of adsorptive solute in a simple porous medium using pore-scale modelling. Fluid flow through the void space of the medium was assumed to be laminar and in saturated condition, and solute transport consisted of advection and molecular diffusion; the sorption and desorption occurring at the fluid–solid interface were modelled as linear first-order kinetics. Based on the simulated spatiotemporal distribution of dissolved and adsorbed solutes at pore scale, volumetric-average reaction kinetics at macroscopic scale and its associated reactive parameters were measured. Both homogeneous adsorption where the reaction rates at microscopic scale are constant, and heterogeneous adsorption where the reaction rates vary from site to site, were investigated. The results indicate that, in contrast to previously thought, the macroscopic reaction rates directly measured from the pore-scale simulations do not change with pore velocity under both homogeneous and heterogeneous adsorptions. In particular, we found that for the homogeneous adsorption, the macroscopic adsorption remains first-order kinetic and can be described by constant reaction rates, regardless of flow rate; whilst for the heterogeneous adsorption, the macroscopic adsorption kinetics continues not to be affected by flow rate but is no longer first-order kinetics that can be described by constant reaction rates. We discuss how these findings could help explain some contrary literature reports over the dependence of reaction rates on pore water velocity. [Copyright &y& Elsevier]

Abstract: The lattice Boltzmann (LB) method has been used to simulate, at the pore scale, the flow of non-Newtonian fluids through complex random porous media in both two and three dimensions. We focus our work on power-law fluids with index n <1 (shear-thinning), though the method is sufficiently general to include other stress–shear rate relationships. Simulated results of flux versus driving force show excellent agreement with established theory, provided sufficient lattice resolution is used. In this respect we explore and quantify the relationship between lattice resolution and simulation accuracy as a function of n. [Copyright &y& Elsevier]

• Insight into pore scale processes of low-velocity filtration combustion is provided. • Estimation expression for root mean of average gas temperature is proposed. • Non-equilibrium exists in the full bed for filtration combustion. • Flow and thermal non-equilibrium in the bed is accelerated with mixture velocity. • The computational time increases 225 time by the 3D pore scale model. 3D pore-scale simulations of the flow and thermal non-equilibrium for low-velocity filtration combustion are numerically performed in randomly packed bed of 2282 pellets with a diameter of 5.6 mm. A 1D volume-averaged simulation is also conducted for comparison. The root-mean-square (RMS) of variables is used to quantitatively study the non-equilibrium characteristics. Results show that the 1D model underpredicts the flame thickness. Predictions by the 3D pore-scale model show that the flow and thermal non-equilibrium exist in the entirely packed bed for all the conditions investigated, but the extent of flow and thermal non-equilibrium in the packed bed varies with time and operating condition. An estimation expression for the root mean of the average gas temperature is proposed using the mixture gradient and the ratio between the average axial velocity and its value of RMS. With increasing mixture inlet velocity, the extent of the flow and thermal non-equilibrium increases, demonstrating that the spatially inhomogeneous variation of the mixture velocity and gas temperature in the packed bed is accelerated with mixture velocity at the inlet. It is observed that the computational time of the 3D pore-scale model is higher by a factor of 225 compared with the 1D volume-averaged model. [ABSTRACT FROM AUTHOR]

During the last years the thin-layered radial porous burners are of growing interest, primarily due to low pressure loss, advanced flame stability and high radiant output. The aim of this study is to investigate the flame stabilization phenomena in radial flow burner using a pore-scale approach with direct simulation of the realistic three-dimensional porous structure and interstitial flow with thermal interaction between the fluid and solid phases including surface radiation. The stabilization mechanisms are investigated with focus on the detailed inner flame structure and its aerodynamical and thermal interaction with the porous shell. The results demonstrate that three characteristic combustion regimes can be distinguished, namely, the internal, submerged and surface-stabilized flames that form depending on the mixture composition and the flow rate. The general principles governing change of regimes are discussed. A key factor of the internal flame stabilization within the burner cavity is a kinematic balance between flow and burning velocity. When the reaction zone submerges the porous shell, the heat recuperation becomes an important factor of flame stabilization. In the surface-stabilized regime, the large velocity gradients lead to the highly stretched and curved flames that aerodynamically anchor at the external surface of the shell analogously with the perforated plates and bluff bodies but have wrinkled shape due to the nonuniformity of the flow field within irregular porous structure. A characteristic diagram of regime change is proposed. It is discussed that for porous burners with size of structural elements of the same magnitude as shell thickness, application of the quasi-homogeneous assumption is restricted in contrast to the pore-scale simulation approach that considers as a prospective technique for studying combustion phenomena. [ABSTRACT FROM AUTHOR]

Combustion and gasification of pulverized char often occur under zone II conditions, in which the rate of conversion depends on both heterogeneous reaction and gas transport within the particle's porous structure. The morphology of porous char has a strong influence on intra-particle diffusion, and thus, on the overall conversion rate. Because pulverized coal and biomass char particles are often irregularly shaped and contain pores and voids which can approach the size of the particles themselves, conventional models based on spherical symmetry and coarse-grained, upscaled, effective continuum conservation equations are not applicable or appropriate. A recent 3-D, pore-resolving CFD simulation approach based on real char particle geometries obtained from X-ray micro-computed tomography (micro-CT) obviates the need to upscale over large heterogeneities and to make oversimplifying geometric assumptions. The micro-CT-based pore-resolving approach is employed here to study zone II combustion for fifty pulverized, porous coal char particles produced at a high heating rate. The large pores often present in char particles enhance reactant transport throughout the particles, even within the micro- and meso-porous carbon surrounding the large pores. This is particularly the case for network-type particle structures, due to the prominence of channels that extend from the particle surface. Because reactor-scale codes often employ one-dimensional models to calculate the reaction rates of tracked particles, pore-resolving simulations are used to assess the accuracy of existing effectiveness factor models for real char. Cenospherical particles can be reasonably modeled using an effectiveness factor solution for hollow spheres, but the behavior of more complex network morphologies is not well-predicted by any of the effectiveness factor models examined. [ABSTRACT FROM AUTHOR]

• Properties of metal foams are sensitive to not only porosity but also topology. • Thermal conductivities of commercial stochastic foams are almost isotropic. • Architected foams have 103% higher thermal conductivity than stochastic foams. • Architected foams are stiffer and absorb 265% more energy than stochastic foams. This study conducted pore-scale simulations to estimate the stagnant thermal conductivity and mechanical performance of stochastic metal foams and architected metal foams. The stagnant thermal conductivity of 5-, 10-, 20- and 40-ppi commercial aluminum foams were estimated to be 6.74, 6.49, 5.97, and 7.16 W/m/K, respectively. Thermal conductivity depended mainly on porosity and was not a strong function of pore size. The pore-scale models simulated thermal conductivities of 40-ppi Al foam along three orthogonal directions are 7.16, 7.92, and 7.56 W/m/K, respectively, indicating a strong isotropic nature. Compared with stochastic foams, the architected foam with a triply periodic minimal surface showed 103% higher thermal conductivity, 488% higher stiffness, and 265% more energy absorption capability. The findings reported here not only provide a fundamental understanding of the interplay between performance and architecture but also open a new avenue to create multifunctional foams. [ABSTRACT FROM AUTHOR]

Geological carbon sequestration is one of the key effective technologies proposed to reduce the atmospheric CO 2 , which is essential to achieve the net zero-emission target. Injection of supercritical CO 2 in saline aquifers can trigger geochemical reactions, which would lead to a change of pore morphology, porosity and permeability of the rock. Reservoir models – as the key tools to simulate and predict the behaviour of a saline aquifer – employ reaction rates that are obtained from the batch experiments. Here, there is a critical discrepancy in the physical scales of a grid cell in a reservoir model and the physical scale of a batch experiment. To address this shortcoming, pore-scale models are utilized to upscale the geochemical reactions in the CO 2 –brine–rock system. We have developed a pore-scale volumetric lattice-Boltzmann model coupled with the geochemical simulator, PhreeqcRM, to investigate the pore-scale reactive transport in carbonate rocks. The model was successfully validated against two sets of pore-scale experiments. Finally, the evolution of porosity and permeability with time was studied under various flow rates, pressures and temperatures of the injected CO 2 -dissolved brine. Results show that with increase of flow rate, dissolution occurs more homogeneously in the rock, while at low injection rates, dissolution is larger closer to the injection boundary. As a result, for a given porosity, the permeability increase at higher injection rates is much more compared to small injection rates. Upscaled reaction rates initially increase with time until they reach a plateau reaction rates but still are smaller than the batch reaction rates. Finally, the implication of the results for the time scale of dissolution to impede the caprock integrity was explored. • A robust pore-scale model has been developed to simulate calcite dissolution due to CO 2 injection. • The pore-scale simulations using volumetric lattice Boltzmann method have been validated against μ -CT experiments. • Hydrodynamic and thermodynamic conditions control the upscaled reaction rates. • Batch reaction rates overestimate the flow-based porous media reaction rates. [ABSTRACT FROM AUTHOR]

Quantitative modelling of the rheology of non-Newtonian fluids requires significant empirical input due to very complex behaviour of the bulk fluid as a result of particle-scale physics of fluids. The existing rheology models are mainly limited to certain fluid dynamics conditions such as shear rate, shear stress, etc. Adopting Doolittle's free volume theory approach, we have proposed an empirical equation to describe the relative free volume-dependent viscosity, the shear stress-dependent viscosity, the shear rate-dependent viscosity, and the dimensionless Péclet number-dependent relative viscosity of shear thickening fluids. The proposed formulae predict all rheologically different behaving Newtonian, intermediate shear thinning, shear thickening and extreme shear thinning regimes of shear-thickening fluids. The proposed formulae have been validated against the experimental rheological data of various shear thickening fluids over a range of pH, volume fraction, electrolyte concentration, temperature, and magnetic field. The results suggest that the predicted threshold material parameters of shear thickening fluids help to quantitatively evaluate the effect of varying physico-chemical conditions on the rheology of shear thickening fluids. We simulated the flow of a shear thickening fluid, modelled using proposed shear rate-dependent equation, in a 2D staggered porous medium. We observed bimodal distribution of pore-scale shear rate, shear viscosity and velocity in a porous medium. Unlabelled Image • An empirical viscosity function for shear thickening fluids (STF), • Equation's material parameters help to correlate an effect of physicochemical conditions on the rheology of STF, • Pore-scale single-phase shear thickening fluid flow simulation using the finite volume method, • Bi -model distribution of shear rate and shear viscosity in the 2D porous medium. [ABSTRACT FROM AUTHOR]

A need for a reduction in energy intensity and greenhouse gas emissions of bitumen and heavy oil recovery processes has led to the invention of several methods where mass-transfer-based recovery processes in terms of cold or heated solvent injection are used to reduce bitumen viscosity rather than steam injection. Despite the extensive numerical and experimental investigations, the field results are not always aligned to what is predicted unless several history matches are done. These discrepancies can be explained by investigating the mechanisms involved in mass transfer and corresponding viscosity reduction at the pore level. A two-phase multicomponent pore-scale simulator is developed to be used for realistic porous media simulation. The simulator developed predicts the chamber front velocity and chamber propagation in agreement with 2D experimental data in the literature. The simulator is specifically used for vapor extraction (VAPEX) modelling in a 2D porous medium. It was found that the solvent cannot reach its equilibrium value everywhere in the oleic phase confirming the non-equilibrium phase behavior in VAPEX. The equilibrium assumption is found to be invalid for VAPEX processes even at a small scale. The model developed can be used for further investigation of mass transfer-based processes in porous media. [ABSTRACT FROM AUTHOR]

Miscible and near-miscible flooding are used to improve the performance of carbon-dioxide-enhanced oil recovery in heterogeneous porous media. However, knowledge of the effects of heterogeneous pore structure on CO2/oil flow behavior under these two flooding conditions is insufficient. In this study, we construct pore-scale CO2/oil flooding models for various flooding methods and comparatively analyze CO2/oil flow behavior and oil recovery efficiency in heterogeneous porous media. The simulation results indicate that compared to immiscible flooding, near-miscible flooding can increase the CO2 sweep area to some extent, but it is still inefficient to displace oil in small pore throats. For miscible flooding, although CO2 still preferentially displaces oil through big throats, it may subsequently invade small pore throats. In order to substantially increase oil recovery efficiency, miscible flooding is the priority choice; however, the increase of CO2 diffusivity has little effect on oil recovery enhancement. For immiscible and near-miscible flooding, CO2 injection velocity needs to be optimized. High CO2 injection velocity can speed up the oil recovery process while maintaining equivalent oil recovery efficiency for immiscible flooding, and low CO2 injection velocity may be beneficial to further enhancing oil recovery efficiency under near-miscible conditions. [ABSTRACT FROM AUTHOR]