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Pore-network models have become a critical tool in the study of fluid flow in geo-energy researches over the last few decades, and the accuracy of pore-network modeling results highly depends on the extraction of pore networks. Traditional methods of pore-network extraction are based on pixels and require images with high quality. Here, a pixel-free method called the flashlight search medial axis algorithm is proposed for pore-network extraction in a continuous space. The search domain in a two-dimensional space is a line, whereas a surface domain is searched in a three-dimensional scenario. Thus, the algorithm follows the dimensionality reduction idea; the medial axis can be identified using only a few points instead of calculating every point in the void space. In this way, computational complexity of this method is greatly reduced compared to that of traditional pixel-based extraction methods, thus enabling large-scale pore-network extraction. Based on cases featuring two- and three-dimensional porous media, the algorithm performs well regardless of the topological structure of the pore network or the positions of the pore and throat centers. This algorithm can also be used to examine both closed-boundary and open-boundary cases. Finally, this algorithm can identify the medial axis accurately, which is of great significance in the study of geo-energy. [ABSTRACT FROM AUTHOR]

Coupled free-flow–porous medium systems are of great importance in various natural and industrial applications. Modeling of such systems is always challenging, especially when droplets form at the interface between the two domains. We propose a new concept to take droplet formation, growth and detachment at the interface into account. In this concept, we use pore-network modeling to describe the porous medium and the Navier–Stokes equations for the free-flow domain. New coupling conditions are developed which include droplet interactions with the free flow and the porous medium. Impacts of using different descriptions of the forces acting on the triple contact line and contact angle hysteresis on the predicted onset of the droplet detachment are examined. In addition, we compare the new approach with another model built using ANSYS Fluent based on the volume of fluid method. The results show that the new model is able to describe the droplet formation, growth and then detachment by the free flow. The proposed model provides a base for further developments to handle formation of multiple droplets at the interface between a free flow and a porous medium as well as to include the evaporation in future works. [ABSTRACT FROM AUTHOR]

The pore network is an approximate representation of the void space of porous materials, such as rocks and soil, via pores (corresponding to large cavities) and throats (narrow constrictions). During extraction of networks from real void space, ambiguous definitions or determinations of pores and throats may cause significant errors in the prediction of single/multi‐phase transport properties. Meanwhile, the pore‐throat segmentation needs to exclude non‐physical parameters as much as possible. In this work, we propose a pore‐throat segmentation method based on local hydraulic resistance equivalence between the real void space and the simplified pore‐throat geometry. Each pore‐throat interface is carefully determined at the position where the simplified tubes preserve the local hydraulic resistance of the real space best. This local segmentation method ensures equivalency between extracted pore network and real pore space without any empirical or non‐physical parameters. After validations of accuracy and reliability by benchmarks, this method is applied to real porous materials including spherical pack, sand pack, sandstone, limestone, and carbonate. The single/two‐phase transport properties predicted by the new method agree well with the experimental data and the direct simulation results. The proposed method improves the accuracy of pore network model (PNM) predictions significantly with a slight increase in computational cost. This local pore‐throat segmentation method may enhance the capability of PNM for more complicated applications. Key Points: A pore‐throat segmentation method is proposed based on local hydraulic resistance equivalenceThe reliability and accuracy are validated via various benchmark casesThe proposed method accurately predicts single/two‐phase transport properties [ABSTRACT FROM AUTHOR]

Fluid flow through layered materials with different wetting behavior is observed in a wide range of applications in biological, environmental and technical systems. Therefore, it is necessary to understand the occuring transport mechanisms of the fluids at the interface between the layered constituents. Of special interest is the water transport in polymer electrolyte membrane fuel cells. Here, it is necessary to understand the transport mechanisms of water throughout the cell constituents especially on the cathode side, where the excess water has to be removed. This is crucial to choose optimal operating conditions and improve the overall cell performance. Pore-scale modeling of gas diffusion layers (GDLs) and gas distributor has been established as a favorable technique to investigate the ongoing processes. Investigating the interface between the hydrophobic porous GDL and the hydrophilic gas distributor, a particular challenge is the combination and interaction of the different material structures and wetting properties at the interface and its influence on the flow. In this paper, a modeling approach is presented which captures the influence of a hydrophilic domain on the flow in a hydrophobic porous domain at the interface between the two domains. A pore-network model is used as the basis of the developed concept which is extended to allow the modeling of mixed-wet interactions at the interface. The functionality of the model is demonstrated using basic example configurations with one and several interface pores and it is applied to a realistic GDL representation in contact with a channel-land structured gas distributor. [ABSTRACT FROM AUTHOR]

For improved operating conditions of a polymer electrolyte membrane (PEM) fuel cell, a sophisticated water management is crucial. Therefore, it is necessary to understand the transport mechanisms of water throughout the cell constituents especially on the cathode side, where the excess water has to be removed. Pore-scale modeling of diffusion layers and gas distributor has been established as a favorable technique to investigate the ongoing processes. Investigating the interface between the cathode layers, a particular challenge is the combination and interaction of the multi-phase flow in the porous material of the gas diffusion layer (GDL) with the free flow in the gas distributor channels. The formation, growth and detachment of water droplets on the hydrophobic, porous surface of the GDL have a major influence on the mass, momentum and energy exchange between the layers. A dynamic pore-network model is used to describe the flow through the porous GDL on the pore-scale. To capture the droplet occurrence and its influence on the flow, this dynamic two-phase pore-network model is extended to capture droplet formation and growth at the surface of the GDL as well as droplet detachment due to the gas flow in the gas distributor channels. In this article, the developed model is applied to single- and multi-tube systems to investigate the general drop behavior. These rather simple test-cases are compared to experimental and numerical data available in the literature. Finally, the model is applied to a GDL unit cell to analyze the interaction between two-phase flow through the GDL and drop formation at the interface between GDL and gas distributor channel. [ABSTRACT FROM AUTHOR]

Water management remains a critical issue for polymer electrolyte fuel cell performance and durability, especially at lower temperatures and with ultrathin electrodes. To understand and explain experimental observations better, water transport in gas diffusion layers (GDLs) with macroscopically heterogeneous morphologies was simulated using a novel coupling of continuum and pore-network models. X-ray computed tomography was used to extract GDL material parameters for use in the pore-network model. The simulations were conducted to explain experimental observations associated with stacking of anode GDLs, where stacking of the anode GDLs increased the limiting current density. Through imaging, it is shown that the stacked anode GDL exhibited an interfacial region of high porosity. The coupled model shows that this morphology allowed more efficient water movement through the anode and higher temperatures at the cathode compared to the single GDL case. As a result, the cathode exhibited less flooding and hence better low temperature performance with the stacked anode GDL.

• A simple and highly actionable method to design electrode's pore structure. • Flow field and combination of large and small pores are considered simultaneously. • The power density was increased by 2.4 times compared to that with the pristine felt. • For VRFB, perforate under the rib near the outlet channel is optimal. To further enhance the efficiency of redox flow batteries, there is a vital need to decouple the conflict between specific surface area and hydraulic permeability in porous electrodes. In this work, we propose a facile and highly productive method to devise porous electrode's pore structure in conjunction with the flow field topology based on the infrared laser perforation to reconcile the combination of large and small pores. We find experimentally that the method of perforation under the center of the rib yields a significant improvement on the overall performance, with an increase in the maximum power density by approximately 2.4 times compared to that without the perforation. We also devise a pore-network model, by using which we explore the effects of large pores formed by the laser perforation on the distributions with respect to the local velocity, active species concentration and reaction rate, as well as the effects of the perforation location and diverse operating conditions on flow cell's overall performance. The results show that under the general operating conditions of the VRFB, we recommend to produce large pores in the region under the rib close to the outlet channel to enable substantial performance gains. [ABSTRACT FROM AUTHOR]

Numerical experiments were conducted to investigate the influence of pore-level microstructure on the drying performance of porous media using pore network (P-N) models. The drying simulation based on the invasion-percolation (I-P) algorithm included the film effect, however the interaction with the outside flow-field was simplified using a constant-concentration vapor-diffusion layer. Three groups of experiments with progressive relationships are designed starting from some general rules learned from previous research, such as: (1) increasing the opening area; (2) making the big-throats penetrate into the inside of a pore network to form good transportation routes. Group 1 compared 7 one-side open 60 × 60 planar P-N microstructures with the same liquid volume, different opening area and different transportation routes; Group 2 compared 4 one-side open 20 × 200 planar P-N microstructures with the same liquid volume, different opening area, different transportation routes, and different cross-sectional throat shape; Group 3 compared 4 four-sides open 120 × 30 planar P-N microstructures with the same liquid volume, the same opening area, but different transportation routes. All experiments demonstrated that large opening area and good transportation route are all beneficial to the quick-drying performance. However, the strength of different mechanisms influencing the drying performance changes with the pore network itself and the environmental conditions, including the P-N size, P-N aspect ratio, cross-sectional shape of throats, and environmental humidity. Accordingly, the optimum microstructure of quick-drying porous media changes with all these conditions. The final optimal design for a quick-drying microstructure can only be achieved by getting back to the fundamental pore-level dynamics which takes all the influencing mechanisms into account. [ABSTRACT FROM AUTHOR]

The article discusses the concepts of upscaling, the representative volume element (RVE) of the geological environment in relation to porosity from the point of view of the theory of structured continuum. The manifestation of the large-scale effect of porosity in terrigenous and carbonate reservoirs has been studied. The analysis of domestic and foreign methods of core sampling was carried out using the example of the Schlumberger company to study the porosity and permeability of the core in petrophysical laboratories and calculate the RVE of rock samples according to the porosity values ​​determined by analyzing the pore-network model, liquid saturation, nuclear magnetic resonance and X-ray computed tomography, as well as the gas-volumetric method. The features and reasons for the manifestation of the large-scale effect of porosity in heterogeneous carbonate reservoirs have been studied. Methods for quantitative assessment of the anisotropy of rocks in the study of heterogeneity of rocks are considered. The necessity of taking into account the scale effect of porosity in the analysis of the correlation dependence “core - geophysical well logging”, established from the porosity data for both terrigenous and carbonate sections. The feasibility of using a core with a diameter of 60–100 mm and standard-size samples is considered when comparing laboratory values ​​of porosity and porosity values ​​determined from logging data. A study of direct and indirect petrophysical methods for determining the porosity of core samples was carried out when solving the same problems to identify the minimum representative volume of a core sample. It has been established that direct methods are the most effective in terms of time and financial costs for the prompt calculation of porosity coefficients for specimens with a diameter and height of 30–100 mm. The analysis of the porosity data ultimately made it possible to study the manifestation of the scale effect of porosity with a change in the sample size. A detailed analysis of published works will allow in the future to develop our own effective sampling technique for determining the RVE of the core interval as applied to porosity.

Geological storage of CO2 in deep saline aquifers mitigates atmospheric emissions. In situ storage is facilitated by several trapping mechanisms including residual trapping, which plays a major role in the containment of CO2. Understanding the underlying mechanisms of residual trapping is crucial for planning storage projects. Of special interest is the relationship between the initial and residual CO2 saturations—the so‐called IR curve, needed for predictive macroscopic‐scale simulations. This study aims to improve the understanding of residual trapping in sandstone from the Heletz site, where extensive field experiments have been performed, by using 3D‐image analysis on core sample CT‐data. This was done to gain knowledge on physical properties (such as radius, coordination number, aspect ratio, shape factor of pores, and pore connectivity) of importance to residual CO2 trapping. Pore‐network flow modeling on a network representation, with the extracted pore‐space topology, was employed to estimate the IR curve. The core sample exhibited pores with a large range of coordination numbers, a mean aspect ratio of 1.4, and shape factors mostly corresponding to triangular cross‐sections. The estimated IR curve was monotonic, fitting an Aissaoui‐type trapping model, displaying a lower sensitivity to the advancing contact angle than previously thought, and indicating a good ability to residually trap CO2. This study provides the first report of values for the three above mentioned properties for Heletz sandstone, and the first estimate of an IR curve for CO2/brine in Heletz sandstone based on pore‐network modeling on a network with a topology retrieved from a core‐sample CT‐scan. © 2021 Society of Chemical Industry and John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a dual network model to simulate coupled single-phase flow and energy transport in porous media including conditions under which local thermal equilibrium cannot be assumed. The models target applications such as the simulation of catalytic reactors, micro-fluidic experiments, or micro-cooling devices. The new technique is based on a recently developed algorithm that extracts both the pore space and the solid grain matrix of a porous medium from CT images into an interconnected network representation. We simulate coupled heat and mass transfer in these networks simultaneously, allowing naturally to model scenarios with heterogeneous temperature distributions in both void space and solid matrix. The model is compared with 3D conjugate heat transfer simulations for both conduction- and convection-dominated scenarios. It is shown to reproduce effective thermal conductivities over a wide range of fluid to solid thermal conductivity ratios with a single parameter set. Morevoer, it captures local thermal nonequilibrium effects in a micro-cooling device scenario. [ABSTRACT FROM AUTHOR]

This paper analyzes a pore-network simulation to model isothermal drying in single-porosity and dual-porosity porous media after employing the invasion-percolation algorithm and the effect of liquid film. Utilizing a novel logistic equation to relate the inside and outside variables of the pore-network, the fully coupled implicit method is employed to solve the vapor transport problems in the pore-network and in the adjoining external flow field. A parametric study is conducted on the drying of a single-porosity square network placed next to a slit flow. Higher hydraulic diameter of the throats leads to higher drying rates and longer constant drying rate periods. The drying time increases and the drying rate decreases as the throat cross-section changes from a triangle to a square to a hexagon to a circle due to the weakening of the film effect. Increasing the external air humidity from 30% to 70% leads to a large decrease in the drying rates and the consequent increase in the overall drying times. Increasing the external flow velocity through Peclet number has little effect on the drying rates and times. Increasing the contact angle makes it harder for the corner films to materialize, which in turn decreases the constant drying rate period. Increase in the surface tension leads to an increase in the spread of the corner film which results in longer constant drying rate periods. Later the drying simulations of a dual-porosity domain using 100 x 100 networks are carried out in a uniform air flow after keeping either the large pores or the small pores side open. The former leads to faster drying characterized by a previously observed bi-linear drying curve, and complete emptying of the outer large pores before the inner small pores. The latter witnesses the phenomenon of capillary pumping leading to a premature emptying of the inner larger pores. The case of all side open is also studied. Changing the throat cross-section from circle to square leads to a much faster drying due to the appearance of the film. Introduction of microstructural irregularity in the network by randomly changing the throat diameter and coordination number of pores does not affect the drying rate and drying time significantly. [ABSTRACT FROM AUTHOR]

This paper analyzes a pore-network simulation to model isothermal drying in single-porosity and dual-porosity porous media after employing the invasion-percolation algorithm and the effect of liquid film. Utilizing a novel logistic equation to relate the inside and outside variables of the pore-network, the fully coupled implicit method is employed to solve the vapor transport problems in the pore-network and in the adjoining external flow field. A parametric study is conducted on the drying of a single-porosity square network placed next to a slit flow. Higher hydraulic diameter of the throats leads to higher drying rates and longer constant drying rate periods. The drying time increases and the drying rate decreases as the throat cross-section changes from a triangle to a square to a hexagon to a circle due to the weakening of the film effect. Increasing the external air humidity from 30% to 70% leads to a large decrease in the drying rates and the consequent increase in the overall drying times. Increasing the external flow velocity through Péclet number has little effect on the drying rates and times. Increasing the contact angle makes it harder for the corner films to materialize, which in turn decreases the constant drying rate period. Increase in the surface tension leads to an increase in the spread of the corner film which results in longer constant drying rate periods. Later the drying simulations of a dual-porosity domain using 100 × 100 networks are carried out in a uniform air flow after keeping either the large pores or the small pores side open. The former leads to faster drying characterized by a previously observed bi-linear drying curve, and complete emptying of the outer large pores before the inner small pores. The latter witnesses the phenomenon of capillary pumping leading to a premature emptying of the inner larger pores. The case of all side open is also studied. Changing the throat cross-section from circle to square leads to a much faster drying due to the appearance of the film. Introduction of microstructural irregularity in the network by randomly changing the throat diameter and coordination number of pores does not affect the drying rate and drying time significantly. [ABSTRACT FROM AUTHOR]

We study how grain shapes impact multiphase flow in porous media in the quasi‐static regime using an extended pore‐network model. The algorithm allows the explicit determination of different types of pore‐scale instabilities and tracks the interface motion during the fluid‐fluid displacement process. It also includes the volume capacitance model, such that both the evolution of capillary pressure signal and sizes of Haines jumps can be captured. Further, it considers the pinning of menisci at sharp edges of grains, through which the distribution of effective contact angles can be obtained. Simulations are carried out across a wide range of wetting conditions for different particle shapes. Our results show that the effective contact angle distribution during displacement widens as the grain becomes more angular, which consequently modifies the macroscopic fluid invasion morphology. By analyzing various characteristic metrics during displacement, including capillary pressure signal, Haines jump size distribution, and fractal dimension, our results highlight the profound influence of particle shape on the multiphase flow. Key Points: A novel pore‐network model algorithm is developed to probe the effect of grain shape on multiphase displacement in porous mediaSystematic simulations are conducted using the proposed algorithm across a wide range of wetting conditions and particle shapesThrough analyzing various metrics during displacement, the results highlight the profound influence of particle shape on multiphase flow [ABSTRACT FROM AUTHOR]

Colloid transport and retention in porous media is a common phenomenon in both nature and industry. However, many questions remain on how to obtain colloid transport and retention parameters. Previous work usually assumed constant transport parameters in a medium under a given physicochemical condition. In this study, pore‐network modeling is employed to upscale colloid transport and retention from the pore‐scale to the macro‐scale. The pore‐scale transport parameters including the collection efficiency (η), the sticking efficiency (α), and the fraction of the solid‐water interface that contributes to the colloid attachment (Sf) are obtained using numerical simulation and probability analysis for each pore throat. The influence of roughness and charge heterogeneity on the distribution of pore‐scale parameters is discussed. Breakthrough curves and the retention profiles under different roughness and charge heterogeneity conditions are also analyzed. Results show that pore‐scale parameters η, α, and Sf have various distributions in porous media that may not be accurately described using single‐valued effective parameters. The value of η decreases with velocity and exhibits a wide distribution under low‐velocity conditions. The parameter α tends to decrease with the colloid size and the pore water velocity and increased with the charge heterogeneity fraction. Nanoscale roughness alters α in a non‐monotonic fashion but tends to increase for lower roughness fractions and zeta potential. Microscopic roughness increases values of α for colloids that would otherwise be susceptible to hydrodynamic removal. Breakthrough curves and retention profiles show that more retention occurs for smaller particles, which reflects the influence of blocking. Key Points: Pore‐network modeling is employed to upscale colloid transport and retention from the pore‐scale to the macro‐scaleThe nanoscale roughness, charge heterogeneity, and microscopic roughness have an obvious impact on colloid transport and retentionPore‐scale parameters for different pore throats in the porous media have various distribution [ABSTRACT FROM AUTHOR]

Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier–Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow model taking into account pore-scale slip at the local interfaces between free flow and the pores. We consider two-dimensional and three-dimensional setups and show that our proposed slip condition can significantly increase the coupled model's accuracy: compared to fully resolved equidimensional numerical reference solutions, the normalized errors for velocity are reduced by a factor of more than five, depending on the flow configuration. A pore-scale slip parameter β pore required by the slip condition was determined numerically in a preprocessing step. We found a linear scaling behavior of β pore with the size of the interface pore body for three-dimensional and two-dimensional domains. The slip condition can thus be applied without incurring any run-time cost. In the last section of this work, we used the coupled model to recalculate a microfluidic experiment where we additionally exploited the flat structure of the micromodel which permits the use of a quasi-3D free-flow model. The extended coupled model is accurate and efficient. [ABSTRACT FROM AUTHOR]

One attractive aspect of CO2 sequestration in shale formations is the preferential adsorption of CO2 compared to methane, which may provide enhanced methane production as well as sequestration of carbon dioxide. In this work, a comprehensive theoretical model of CO2 migration at the pore scale is developed to study CO2 migration properties in organic-rich shale formations. The proposed model takes into account dynamic competitive adsorption between CO2 and CH4, slip-flow effects due to the nanometer range of pore sizes, and pore-size changes due to adsorption. Because of the high pressure and temperature, the injected CO2 is in supercritical phase. Pore bodies in the shale matrix are irregular in shape, with roughness along pore wall. The structure of pore body affects the amount of surface areas and associated number of adsorption sites, and hence, a shape factor is proposed in this work to consider the irregularity of pore structure in shale matrix. The sorption of CO2 leads to an apparent retardation of the migration of CO2, which is quantified in this work. The developed pore-network model is extended to consider the impacts of different spatial distributions of the organic materials within the shale matrix. [ABSTRACT FROM AUTHOR]

A reliable and practical method of hygric property characterisation is a major determinant in properly analysing hygric performance of built constructions. The current empirical approach, however, yields data that are still incomplete, not fully representative, and not entirely reliable. In this study, hygric properties are therefore determined directly from pore structure information by applying stationary unsaturated pore-scale physics to model moisture storage and transport. The pore space is captured by visualisation techniques and further extracted into a discrete network of variably shaped pore bodies interconnected by pore throats. In this network, corner and surface adsorption and capillary condensation are simulated to define the moisture storage. Air entrapment is furthermore considered to determine the capillary moisture content. The resulting spatial moisture distribution in the pore network allows moisture to flow, in wet elements in the liquid phase and in dry elements in the vapour phase. The adsorbed corner and surface films moreover enable additional liquid flow. These various simultaneous flows aggregately define the transport property. A comparison to measured data validates the presented hygric property model. [ABSTRACT FROM AUTHOR]

During geological storage in deep saline aquifers, immobilization of CO2 in reservoir rock determines both storage safety and capacity. Assessment of the sensitivity of residual trapping to different parameters (interfacial tension and contact angles) and the storage conditions affecting these is therefore of great importance. One aspect of concern is the presence of co‐contaminants such as SO2 in the injected gas. Using experimentally measured values of interfacial tensions and contact angles, we apply pore‐network modelling (which accounts for pore‐scale mechanisms such as snap‐off, cooperative pore body filling and piston‐type displacement) to a generic sandstone network to quantify the impact of SO2 co‐injection on residual CO2 trapping, and its relative importance as compared to the influences of thermodynamic conditions and salinity. We show that the presence of small amounts of SO2 in the injected CO2 has a notable positive effect on the amount of CO2 becoming residually trapped (∼3% increase at 1 wt% SO2). However, this effect is small compared to that of the brine salinity (∼20% decrease in residually trapped CO2 over the salinity range 0.2 to 5 M NaCl). Still, co‐injection of SO2 could potentially favour the residual trapping of CO2 in reservoir rocks, especially at storage sites with inclined aquifers where the CO2 is set to migrate hydro‐dynamically over long distances. The salinity of the resident brine is of primary importance during storage site selection. Furthermore, sensitivity analysis shows that the advancing contact angle strongly impacts residual CO2 trapping. © 2018 Society of Chemical Industry and John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Liquid penetration into thin porous media such as paper is often simulated using continuum-scale single-phase Darcy’s law. The underlying assumption was that a sharp invasion front percolates through the layer. To explore this ambiguous assumption and to understand the controlling pore-scale mechanisms, we have developed a dynamic pore-network model to simulate imbibition of a wetting phase from a droplet into a paper coating layer. The realistic pore structures are obtained using the FIB-SEM imaging of the coating material with a minimum resolution of 3.5 nm. Pore network was extracted from FIB-SEM images using Avizo software. Data of extracted pore network are used for statistically generating pore network. Droplet sizes are chosen in the range of those applicable in inkjet printing. Our simulations show no sharp invasion front exists and there is the presence of residual non-wetting phase. In addition, penetration of different sizes of droplets of different material properties into the pore network with different pore body and pore throat sizes are performed. We have found an approximately linear decrease in droplet volume with time. This contradicts the expected t-behavior in vertical imbibition that is obtained using macroscopic single-phase Darcy’s law. With increase in flow rate, transition of imbibition invasion front from percolation-like pattern to a more sharper one with less trapping of non-wetting phase is also reported. Our simulations suggest that the single-phase Darcy’s law does not adequately describe liquid penetration into materials such as paper coating layer. Instead Richards equation would be a better choice. [ABSTRACT FROM AUTHOR]

This paper examines the role of momentum transfer across fluid-fluid interfaces in two-phase flow. A volume-of-fluid finite-volume numerical method is used to solve the Navier-Stokes equations for two-phase flow at the micro-scale. The model is applied to investigate viscous coupling effects as a function of the viscosity ratio, the wetting phase saturation and the wettability, for different fluid configurations in simple pore geometries. It is shown that viscous coupling effects can be significant for certain pore geometries such as oil layers sandwiched between water in the corner of mixed wettability capillaries. A simple parametric model is then presented to estimate general mobility terms as a function of geometric properties and viscosity ratio. Finally, the model is validated by comparison with the mobilities computed using direct numerical simulation. [ABSTRACT FROM AUTHOR]

To reduce emissions of the greenhouse gas CO 2 to the atmosphere, sequestration in deep saline aquifers is a viable strategy. Residual trapping is a key containment process important to the success of CO 2 storage operations. While residual trapping affects CO 2 migration over large scales, it is inherently a pore-scale process. Pore-network models (PNMs), capturing such processes, are useful for our understanding of residual trapping, and for upscaling trapping parameters for larger scale models. A PNM for simulation of quasi-static two-phase flow; CO 2 intrusion (drainage) followed by water flooding (imbibition) was developed. It accounts for pore-scale displacement mechanisms, and was used to investigate residual CO 2 trapping. The sensitivity of the residual CO 2 saturation to several parameters was studied, to validate a trapping behavior in agreement with earlier studies. Then the PNM was calibrated to core sample data and used to simulate drainage-imbibition scenarios with different turning point saturations. From these the initial-residual saturation curves of CO 2 in Heletz sandstone were estimated, essential for future macroscopic-scale simulations. Further, the occurrence of different pore-scale mechanisms were quantified and the size distribution of the residual clusters was shown to exhibit a bimodal appearance. The findings improve the understanding of residual trapping in Heletz sandstone. [ABSTRACT FROM AUTHOR]

Abstract: Gas bubbles can be naturally generated or intentionally introduced in sediments. Gas bubble migration and trapping affect the rate of gas emission into the atmosphere or modify the sediment properties such as hydraulic and mechanical properties. In this study, the migration and trapping of gas bubbles are simulated using the pore‐network model extracted from the 3D X‐ray image of in situ sediment. Two types of bubble size distribution (mono‐sized and distributed‐sized cases) are used in the simulation. The spatial and statistical bubble size distribution, residual gas saturation, and hydraulic conductivity reduction due to the bubble trapping are investigated. The results show that the bubble size distribution becomes wider during the gas bubble migration due to bubble coalescence for both mono‐sized and distributed‐sized cases. And the trapped bubble fraction and the residual gas saturation increase as the bubble size increases. The hydraulic conductivity is reduced as a result of the gas bubble trapping. The reduction in hydraulic conductivity is apparently observed as bubble size and the number of nucleation points increase. [ABSTRACT FROM AUTHOR]

In this paper, the influence of micro-fractures on the flow of tight reservoirs is studied on the microscopic scale. Three-dimensional digital cores of fractured tight sandstone with varying fracture apertures, lengths, and dip angles are constructed using computed tomography (CT) scans. Pore-network models are built using the three-dimensional digital cores to simulate the flow in tight oil reservoirs. The effects of the micro-fracture aperture, length and dip angle on the pore-throat structure, single-phase flow, and two-phase flow for fracture surfaces with/without roughness are studied. The study demonstrates different influences of micro-fracture characteristics on the flow, and the fracture aperture has the most critical effect. Meanwhile, the roughness of the micro-fracture makes a difference in addition to the three factors of micro-fractures. This paper provides a theoretical basis for the effective development of tight sandstone reservoirs.

Electrical transport properties of saturated porous media, such as soils, rocks and fractured networks, typically composed of a non-conductive solid matrix and a conductive brine in the pore space, have numerous applications in reservoir engineering and petrophysics. One of the widely used electrical conductivity models is the empirical Archie's law that has a practical application in well-log interpretation of reservoir rocks. The Archie equation does not take into account the contributions of clay minerals, isolated porosity, heterogeneity in grains and pores and their distributions, as well as anisotropy. In the literature, either some modifications were presented to apply Archie's law to tight and clay-rich reservoirs or more modern models were developed to describe electrical conductivity in such reservoirs. In the former, a number of empirically derived parameters were proposed, which typically vary from one reservoir to another. In the latter, theoretical improvements by including detailed characteristics of pore space morphology led to developing more complex electrical conductivity models. Such models enabled us to address the electrical properties in a wider range of potential reservoir rocks through theoretical parameters related to key reservoir-defining petrophysical properties. This paper presents a review of the electrical conductivity models developed using fractal, percolation and effective medium theories. Key results obtained by comparing experiential and theoretical models with experiments/simulations, as well as advantages and drawbacks of each model are analyzed. Approaches to obtaining more reasonable electrical conductivity models are discussed. Experiments suggest more complex relationships between electrical conductivity and porosity than experiential models, particularly in low-porosity formations. However, the available theoretical models combined with simulations do provide insight to how microscale physics affects macroscale electrical conductivity in porous media. [ABSTRACT FROM AUTHOR]

Viscous coupling during simultaneous flow of different fluid phases has a significant impact on their flow through porous media. In this work, a new multiscale strategy is proposed for multiphase flow in porous media. We use the lattice Boltzmann method (LBM) to simulate two-phase flow at pore scale and obtain empirical terms for the viscous coupling inside individual pores. The empirical coupling terms are then used in a pore-network model to efficiently simulate two-phase flow through porous media at core scale. It is shown that including viscous coupling leads to better predictions of relative permeability. [ABSTRACT FROM AUTHOR]

The engineering of microbially induced calcium carbonate precipitation (MICP) has attracted much attention in a number of applications, such as sealing of CO2 leakage pathways, soil stabilization, and subsurface remediation of radionuclides and toxic metals. The goal of this work is to gain insight into pore-scale processes of MICP and scale dependence of biogeochemical reaction rates. This will help us develop efficient field-scale MICP models. In this work, we have developed a comprehensive pore-network model for MICP, with geochemical speciation calculated by the open-source PHREEQC module. A numerical pseudo-3-D micromodel as the computational domain was generated by a novel pore-network generation method. We modeled a three-stage process in the engineering of MICP including the growth of biofilm, the injection of calcium-rich medium, and the precipitation of calcium carbonate. A number of test cases were conducted to illustrate how calcite precipitation was influenced by different operating conditions. In addition, we studied the possibility of reducing the computational effort by simplifying geochemical calculations. Finally, the effect of mass transfer limitation of possible carbonate ions in a pore element on calcite precipitation was explored. [ABSTRACT FROM AUTHOR]

We developed a new method for predicting accurately the imbibition oil/water relative permeabilities for carbonates using pore network modelling. The proposed method uses Hamiltonian dynamics for the stochastic inversion of the pore-network model parameters, which are conditioned only to the capillary pressure. We applied our method to three carbonate rock samples of different rock types. Carbonate rock samples are particularly challenging because of their wettability and the various orders of variation in the pore-size distribution. We found that micro- and submicron-porosity had larger advancing contact angles than larger pore sizes. This better explains the gentle curvature of the imbibition water relative permeability, compared with the customary assumed mixed-wet large wettability model. Our results showed that, when inferring wettability for pore-network models, the oil residual saturation, minimum and maximum capillary pressure during drainage and imbibition were particularly important. Additionally, we showed that the average contact angles and the contact angles measured outside porous media cannot sufficiently characterise the wettability in pore-network models. This work is important because it provides guidelines for interpreting more complicated pore-network models. [ABSTRACT FROM AUTHOR]

Background and Aims: Although maize roots have been extensively studied, there is limited information on the effect of root exudates on the hydraulic properties of maize rhizosphere. Recent experiments suggested that the mucilaginous fraction of root exudates may cause water repellency of the rhizosphere. Our objectives were: 1) to investigate whether maize rhizosphere turns hydrophobic after drying and subsequent rewetting; 2) to test whether maize mucilage is hydrophobic; and 3) to find a quantitative relation between rhizosphere rewetting, particle size, soil matric potential and mucilage concentration. Methods: Maize plants were grown in aluminum containers filled with a sandy soil. When the plants were 3-weeks-old, the soil was let dry and then it was irrigated. The soil water content during irrigation was imaged using neutron radiography. In a parallel experiment, ten maize plants were grown in sandy soil for 5 weeks. Mucilage was collected from young brace roots growing above the soil. Mucilage was placed on glass slides and let dry. The contact angle was measured with the sessile drop method for varying mucilage concentration. Additionally, capillary rise experiments were performed in soils of varying particle size mixed with maize mucilage. We then used a pore-network model in which mucilage was randomly distributed in a cubic lattice. The general idea was that rewetting of a pore is impeded when the concentration of mucilage on the pore surface (g cm) is higher than a given threshold value. The threshold value depended on soil matric potential, pore radius and contract angle. Then, we randomly distributed mucilage in the pore network and we calculated the percolation of water across a cubic lattice for varying soil particle size, mucilage concentration and matric potential. Results: Our results showed that: 1) the rhizosphere of maize stayed temporarily dry after irrigation; 2) mucilage became water repellent after drying. Mucilage contact angle increased with mucilage surface concentration (gram of dry mucilage per surface area); 3) Water could easily cross the rhizosphere when the mucilage concentration was below a given threshold. In contrast, above a critical mucilage concentration water could not flow through the rhizosphere. The critical mucilage concentration decreased with increasing particle size and decreasing matric potential. Conclusions: These results show the importance of mucilage exudation for the water fluxes across the root-soil interface. Our percolation model predicts at what mucilage concentration the rhizosphere turns hydrophobic depending on soil texture and matric potential. Further studies are needed to extend these results to varying soil conditions and to upscale them to the entire root system. [ABSTRACT FROM AUTHOR]

The problem of isothermal (slow) drying of a porous medium in the form of a square bluff body resting on a flat surface while being exposed to turbulent air flow is investigated in this paper. The porous medium is represented by a pore-network model consisting of a network of volume-less nodes connected to each other via narrow throats. As the air flows past the water-saturated network, the water evaporates in the network and the evaporated water vapors diffuse through the air inside the network to advect away in the outside domain. In the history of such simulations coupling the 'outside-inside' processes during drying, this paper investigates, for the first time, the effect of turbulent flow on drying of a porous medium after coupling the outside-the-network flow and transport with the inside-the-network drying and liquid redistribution. Also, a commercial software package is used for the first time to obtain the outside flow. The water redistribution inside the network is predicted by the invasion-percolation algorithm after assuming the dominance of capillary forces over viscous and gravity forces. The outside velocity field is first obtained using the $$k\hbox {-}\varepsilon $$ model in ANSYS Fluent package. Then, the velocity field is used in a finite-volume-based code in order to solve for mass transfer outside the network using the regular convective-diffusive species transport equation. The drying mechanism and vapor transport inside the pore network is coupled with the outside mass-transfer simulation by considering a flux-balancing condition at the top surface of the network. After achieving grid independence and demonstrating the suitability of the no-slip boundary condition for the network top, the effects of the outside-flow Reynolds number and different turbulent flow models on several global drying parameters such as evaporation or drying rate, cumulative drying time, and top-surface saturation were studied. The resistance to vapor transport within the network was observed to dominate the enhanced vapor transport outside the network through the use of turbulent flow. Though the effect of variations in the network throat-size distribution upon saturation distribution within the network was found to be significant, its effect on the drying rate evolution was minimal. The concentration boundary layer thickness, which is employed to set the mass-transfer boundary condition in pore-network simulations and has been hitherto taken as constant in the literature, was found to change not only with position on the network top, but was also found to decline with time due to the drying of the network top. [ABSTRACT FROM AUTHOR]

Plant roots exude a significant fraction of the carbon assimilated via photosynthesis into the soil. The mucilaginous fraction of root exudates affects the hydraulic properties of the soil near the roots, the so called rhizosphere, in a remarkable and dynamic way. After drying, mucilage becomes hydrophobic and limits the rewetting of the rhizosphere. Here, we aim to find a quantitative relation between rhizosphere rewetting, particle size, soil matric potential and mucilage concentration. We used a pore-network model in which mucilage was randomly distributed in a cubic lattice. The general idea was that the mucilage concentration per solid soil surface increases the contact angle between the liquid and solid phases consequently limiting the rewetting of pores covered with dry mucilage. We used the Young–Laplace equation to calculate the mucilage concentration at which pores are not wettable for varying particle sizes and matric potentials. Then, we simulated the percolation of water across a cubic lattice. Our simulations predicted that above a critical mucilage concentration water could not flow through the porous medium. The critical mucilage concentration decreased with increasing particle size and decreasing matric potential. The model was compared with experiments of capillary rise in soils of different particle size and mucilage concentration. The experiments confirmed the percolation behaviour of the rhizosphere rewetting. Mucilage turned hydrophobic at concentrations above 0.1 mg/cm 2 . The critical mucilage concentration at matric potential of −2.5 hPa was ca. 1% [g/g] for fine sand and 0.1 % [g/g] for coarse sand. Our conceptual model is a first step towards a better understanding of the water dynamics in the rhizosphere during rewetting and it can be used to predict in what soil textures rhizosphere water repellency becomes a critical issue for root water uptake. [ABSTRACT FROM AUTHOR]

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based on the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables ( e.g. , permeability, solute breakthrough curves) and microscopic variables ( e.g. , local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods. [ABSTRACT FROM AUTHOR]

We construct a three-dimensional pore-network model with mixed wettability to study the two-phase flow mechanisms in dry gas producing shales. Previous pore-scale modeling studies on shale have been focused on single-phase gas flow through the nano-pores. However, at most field sites, the majority of the injected fracking fluid does not return to the surface during the flow-back period. It is believed that a large portion of the fracking fluid imbibes into the shale matrix during the fracking process, and thus two-phase flow occurs. In addition, while the inorganic shale matrix is generally water-wet, the organic material embedded within the matrix is hydrophobic. As such, the system displays spatial heterogeneity of wettability. Other important physics are also coupled in the model. Pressure-dependent gas sorption effects are included in the organic pores, with pore size reduction accounted for in those pores. Compressibility and slip flow effects of the gas phase are included throughout the pore-network, with the latter underscoring the fact that the sizes of the nano-pores are comparable to the mean free path of the methane molecule. The coupled effects of these various physical processes are studied to determine the importance of each effect. Continuum-scale properties are computed, including relative permeability curves, as a function of fraction and structure of organic regions and type and magnitude of boundary conditions. [ABSTRACT FROM AUTHOR]

Three novel iterative methodologies for coupling continuum and pore-network models (PNM) applied to polymer-electrolyte fuel cells (PEFCs) are presented. The modeling framework developed in this work merges the advantages of a continuum model, such as computational time, ease of implementation, and complicated physics, with those of relatively novel PNMs, such as discrete information on water-front location and distribution. The outputs generated by the PNM are fed into the continuum model to compute electrochemical reaction rates and associated heat and mass fluxes. Out of three presented coupling methodologies, the most effective coupling is identified to be where locally-resolved effective diffusivity, thermal conductivity, and liquid permeability are computed with the PNM and fed into the continuum model and the fluxes from continuum model fed back into the PNM in an iterative scheme until solution convergence is reached. The described method is computationally efficient with stable convergence of less than five iterations. The proposed algorithms can be applied to multiple computational platforms and PEFC and related model architectures. [ABSTRACT FROM AUTHOR]

Heat and mass transfer with liquid–vapour phase change in a representative unit cell of a capillary evaporator is studied using a mixed pore network model. The model combines the computation of temperature and pressure fields in vapour and liquid pores according to mean field approaches with pore scale invasion rules depending on the capillary pressure thresholds associated with each local constriction between two pores. The metallic body through which heat is transferred to the porous wick is also taken into account in the simulations. After comparisons with a visualisation experiment, numerical simulations performed in three dimensional pore networks lead to the identification of three main regimes depending on the applied heat load. Compared with previous works using the so-called vapour pocket assumption, the 3D simulations reveal a regime where the phase distribution within the wick is fundamentally different. This regime is characterised by the coexistence of both the liquid and vapour phases underneath the casing within the wick. This regime is shown to correspond to the best evaporator performance. [ABSTRACT FROM AUTHOR]

• A neural-network model is trained to predict collector contact efficiency of each pore throat (η t). • Influence of pore structure of porous media is described by pore network models, where the η t occurs as a distribution. • Upscaled values of the deposition rate coefficient are provided by PNMs and compared with the prediction of colloid filtration theory. • High velocity region of flow field neglected in colloid filtration theory leads to the difference in the prediction of deposition rate coefficient. Conventional colloid filtration theory (CFT) uses the single collector contact efficiency (η) to describe the mass transfer of colloids to a collector surface. However, this approach neglects the full complexity of the pore structure and flow field of real porous media. In this study, the porous medium geometry, flow field, and colloid mass transfer are quantified using a pore-network model (PNM). A database of pore scale η is established by finite-element method to train a Neural-network model (NNM). The reasonable prediction of η indicates the potential of using the developed NNMs as an alternative to correlation equations, which can free the users from repeated numerical simulation. In contrast to the prediction by conventional CFT, the value of η in the PNM occurs as a distribution, which is dependent upon the geometry parameters of the PNM. The mean value of η increases with the standard deviation of pore radius and decreases with the curvature number, but the dependency on coordination number is more complex. Upscaled values of the deposition rate coefficient (k d) corresponding to the distribution of η are calculated by the breakthrough curves by PNMs. The prediction of k d by PNM is then compared with that by CFT. Results show that k d predicted by PNM shows more significant response to velocity change, and less remarkable response to colloid density change than k d predicted by CFT. The comparison between the flow velocity distribution between PNM and CFT shows that the high-velocity region of the flow field in the porous media has been neglected in CFT, which can lead to insufficient consideration of convection. The results of this work imply that it is necessary to consider the influence of the complex pore structure of porous media on the collection of colloids. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the influence of relaxing the local thermal and chemical equilibrium assumptions in multiphase, multicomponent flow in porous media is studied. In order to do so, balance equations allowing for the coupled description of thermal and chemical non-equilibrium are developed. The example application presented is taken from the field of evaporation from porous media. Necessary input parameters are obtained from an extended quasi-static three-dimensional pore-network model. These relations are put into a macro-scale model and simulations not employing local thermal and chemical equilibrium assumptions are conducted. The influence of the rate of heat and mass transfer on evaporation rates is shown and convergence of the model demonstrated. [Copyright &y& Elsevier]

We present an interface tracking algorithm that incorporates essential pore-scale invasion mechanisms for simulating multiphase flow in porous media in capillary dominated regime. The algorithm allows the capture of the actual shape of porous medium with complex geometrical features, including both convex and concave particles or irregular channels. It also incorporates the sharp edge pinning effect such that pinning of menisci at corners can be naturally taken into account. We firstly conduct simulations under imbibition and drainage conditions in a single junction micro-model and in disordered porous media for validation. It is shown that the invasion mechanisms at pore scale are accurately captured, and the macroscopic invasion morphology in porous media are reproduced. A series of simulations for fluid displacement processes are carried out across a wide range of intrinsic contact angles in a two-dimensional representation of a Berea sandstone. The transition between stable displacement and capillary fingering is characterized using displacement efficiency, fractal dimension, and fluid–fluid interfacial length. This work deepens the understanding of fluid–fluid displacement processes in porous media. Furthermore, the presented interface tracking algorithm offers a highly efficient tool for further exploration of effects of wettability, geometry, and topology on multiphase flow in realistic porous materials. • We present an efficient numerical method for multiphase flow in porous media. • The algorithm is validated by comparing the results with the literature. • Systematic multiphase flow simulations are conducted in realistic porous media. • The transition between stable displacement and capillary fingering is characterized. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a fluorescein solution is injected into the gas diffusion layer (GDL) of a PEM fuel cell to simulate water flow through the porous medium under flooding conditions. The effect of the GDL hydrophobic treatment is studied by analyzing the images obtained from fluorescence microscopy. The intensity of images is correlated to the liquid water content in the medium. As a result, three distinguishable patterns are recognized between the treated and untreated GDL samples. These patterns include: (1) initial invasion, (2) progression and (3) pore filling. Based on the flow characteristics, a pore-network model is developed and applied to unique network geometry with different hydrophobic fractions to study the effect of hydrophobicity on the flow configuration. It is shown that the model predicts the flow configurations which are qualitatively in agreement with the experimental observation. The model is then used to obtain saturation for samples with different hydrophobic fractions. The trend is in agreement with the results reported in the past. [Copyright &y& Elsevier]

Abstract: A novel method to simulate drying from a pore-network model is presented. Due to the evaporative mass-flux going out from the network as well as the outside airflow, a vapor mole-concentration boundary layer forms around the network. Concentration Boundary Layer Thickness (CBLT) and consequently the mass transfer coefficient are usually assumed constant in the literature. However, CBLT varies during drying owing to the changes in the outgoing mass flux from the network. To investigate the variation in CBLT and its dependence on convective effects due to the airflow, a numerical code based on the finite volume method has been developed to simulate drying characteristics of a pore-network. Laminar, steady state and two-dimensional Navier–Stokes equations as well as the vapor mole-concentration equation with both the convective and diffusive terms are discretized and solved according to the SIMPLE algorithm. A 20×20 two-dimensional pore-network after including cylindrical throats with circular cross sections is considered to model slow (isothermal) evaporation. Due to the geometry of throats and the network size, the effects of liquid film, viscous and gravitational forces are not considered. Therefore the capillary effect remains the dominant force for liquid transport inside the pore network. The drying algorithm applied inside the pore-network is the same as the one proposed by Metzger et al. (2007) [14], and it is verified that the convective effects are negligible within the gas phase inside the network. The effect of air flow over the exposed surface of the network causes a sudden decrease in evaporation rate from the pore-network after a short time period. This confirms the existence of the first drying period, as addressed in previous publications (e.g. Metzger et al. [14]). Also, a unique CBLT that grows along the length of the pore-network has been obtained. It is shown that the thickness of the concentration boundary layer decreases with time everywhere along the top surface of the network; therefore the assumption of constant CBLT that is used in the literature is merely a rough estimate. The present model provides a more accurate analysis of the isothermal evaporation from the porous structures exposed to laminar external air flow. [Copyright &y& Elsevier]