Pore Network Modeling Approach Research Articles

Insights Into Estimation of Sand Permeability: From Empirical Relations to Microstructure-based Methods

Abstract This study evaluates various methods for estimating soil permeability using microtomography-derived data and compares them to the conventional laboratory approaches. Different methods, including measurement in custom-designed permeameter at micro-CT-compatible scale, empirical equations, simulated sifting, semi-theoretical equations, pore-network modeling, and lattice-Boltzmann simulations, were applied to samples of sandy soils with distinct microstructural properties. The empirical equations showed varied results, highly dependent on the method chosen. The simulated sifting method was able to adequately estimate the granulometric properties of the soil, allowing the use of empirical permeability formulations for substantially small samples. Semi-theoretical equations based on the microstructural properties presented reasonable agreement for some samples. The pore-network modeling approach demonstrated computational efficiency but lacked accuracy. The lattice-Boltzmann method required significant computational resources but did not provide substantially closer alignment with the measured hydraulic properties of some samples. None of the simulations was able to properly determine the permeability of silty and organically contaminated sand. The study highlights the complexity of permeability estimation, emphasizing the need for choosing volumes of interest, resolution of micro-CT scans, and methods that match specific soil characteristics and available computational resources.

Microstructural investigation of concretes with recycled aggregates using X-ray microtomography

Recycled aggregates (RA) derive from reprocessed materials from construction and demolition activities. Although the use of RA has been growing worldwide, material standardization and new mix design protocols still need to be developed to enable its use on larger scales. For this, an investigation of the properties of this material is necessary. The present study used microcomputed tomography (microCT) to observe the material's porous structure in cylindrical concrete samples of reference concrete (RC) with natural aggregates and sustainable concrete (SC) with the addition of RA. Through a computational routine, the images obtained were evaluated qualitatively and quantitatively. The pore volume and shape in concretes with and without recycled aggregates were analyzed and correlated with their respective compressive strengths. Even though the SC samples' resistance was lower than the RC samples, the values found followed the required standards. Porosity, pore volume, and shape were similar for the two kinds of concrete. The Pore Network Modeling (PNM) approach was applied to characterize further the pores' spatial distribution and connectivity. The analysis showed that 98.20 % and 97.26 % of the pores were disconnected for the RC and SC samples, respectively. The results indicate that the addition of RA is not detrimental to the properties of concrete. Further PNM-based analysis can help evaluate both samples' absolute and relative permeability to various fluids.

Pore network modeling approach for simulating soil water retention curve under different stress conditions

The field of unsaturated soil mechanics has recently seen the introduction of pore network models, which attempt to replicate the void structure of porous materials. They are robust physically-based simulation tools and have been used to simulate constitutive relationships like soil water retention curves (SWRC) and unsaturated hydraulic conductivity functions. This work aims to present a pore networkmodeling approach for predicting hysteretic SWRC at various stress states using only grain size distribution and porosity data of the granular soils. The soil sample subjected to given stress conditions is simulated using the Discrete Element Method to obtain a stable packing of spherical particles representing the soil structure. From this packing, an algorithm based on the medial axis is availed to extract a network of pores and throats that describes the geometry and topology of the void structure of the granular soils. Various pore-scale mechanisms like the piston-like advance, corner flow, pore body filling, and snap-off are then used to model fluid displacements at the pore scale to simulate SWRC along the drying and wetting paths. The modeled SWRC under various stress conditions is compared with the measured curves obtained for granular soils from the literature, and the predictions are in good agreement with the experimental results.

Dynamic pore-scale modeling of residual fluid configurations in disordered porous media

Fluid trapping in porous media is important in many subsurface flow processes such as enhanced oil recovery and geological sequestration of carbon dioxide. To achieve optimal performance in such applications, a fundamental understanding of residual trapping mechanisms at the pore scale is necessary. In this work, we present a computational study of fluid trapping behaviors in natural porous media under different flow regimes by employing a dynamic pore-network modeling approach. The model incorporates many advanced features that have not been collectively used in previous dynamic platforms. For instance, it rigorously solves for fluid pressure fields from two-phase mass balance equations in each pore element, incorporates a detailed description of pore-scale fluid displacement dynamics of piston-like advance, snap-off, and pore-body filling, and explicitly accounts for flow through wetting layers forming in corners and rough surfaces of pore spaces. Moreover, we extend the ability of our model by including contact angle hysteresis, which is often neglected in existing dynamic models. A heavily-parallelized implementation of this platform is further advanced to achieve an efficient computational performance. We first conduct primary drainage and imbibition simulations in pore networks representing Bentheimer and Berea sandstones. We show that the predicted two-phase relative permeability curves agree well with their experimental counterparts reported in the literature. Afterwards, the validated model is used to systematically probe fluid trapping behaviors in a core-sized pore network that is constructed from high-resolution micro-computed tomography images of a Berea sandstone core sample. The effects of dynamic flow conditions and fluid properties on core-scale two-phase displacement pattern, residual-fluid configuration, and residual oil saturations are examined in detail. Fluid trapping properties such as maximum and average residual-fluid cluster size and capillary-controlled invasion selectivity at the pore scale are analyzed under both capillaryand viscous-dominated flow regimes.

A novel approach for pore-scale study of fines migration mechanism in porous media

The migration of fine particles in oil reservoir rock is the most important cause of formation damage and permeability impairment. The mechanism of this phenomenon includes fines detachment, mobilization, agglomeration, and re-attachment, which lead to throat clogging and/or blocking. Therefore, accurate modeling of this complex mechanism requires a model with high solver efficiency.In this work, based on the physical features of fines migration in pore throat, the conventional DPM model of ANSYS FLUENT software was initially modified by UDF code. Then, predetermined scenarios of suspension injection into a two dimensional (2D) microchannel were simulated for predicting pressure drop as a function of injected pore volume using the modified DPM model. Next, based on these simulation results, a proxy model using the artificial neural network (ANN) was developed for computational cost reduction of fines migration modeling in the microchannel (pore throat). Secondly, a dual pore scale numerical model by combination of proxy model and pore network modeling approach was developed to predict pressure drop as well as permeability impairment in a network of microchannels (porous media). Moreover, for rapid computation of pressure drop in the network model, a meta-heuristic method of rain optimization algorithm (ROA) has been used. Finally, for model validation, a series of laboratory tests including suspension injections into the glass micromodels were conducted.A comparison of simulation results using both proxy model and dual pore scale model with experimental data shows a good agreement and according to the obtained results, a decrease in the particles mean size, and Reynolds number as well as increase in particles concentration lead to increase in pressure drop and permeability reduction. On the other hand, use of a proxy model based on artificial neural network and a meta-heuristic method of rain optimization algorithm lead to significant computational cost reduction, while the accuracy of fines migration modeling is high enough. Hence, using our modeling approach for fines migration study in porous media as an accurate and fast computational tool can help for a better understanding of this phenomenon, which is very important in the petroleum industry.

Capillary equilibration of trapped ganglia in porous media: A pore-network modeling approach

Ganglia, or bubbles, trapped by capillary forces inside porous materials occur in a wide range of subsurface and manufacturing applications. In geologic CO2 storage, ganglia are desired as they render the injected CO2 hydrodynamically immobile. But they may evolve by dissolution or mass exchange across the brine, called ripening. In fuel cells and electrolyzers, water/oxygen ganglia must be removed to ensure optimal performance of the device. In both applications, the porous microstructure plays a key role in how the geometry/topology of ganglia evolve as they grow/shrink in size. This dependence is poorly understood but important for controlling ganglion dynamics. Pore-scale models are useful tools for probing the physics, but existing ones are either computationally expensive (e.g., CFD) or incapable of accurately simulating ganglia spanning multiple pores (e.g., pore networks). Our main contribution is a new pore-network model (PNM) that removes this barrier. The PNM can simulate the evolution of multi-pore occupying ganglia due to diffusive mass transfer by ripening or an external concentration field. We validate the PNM against published microfluidic experiments, 2D direct numerical simulations, and an analytical solution previously derived by the authors for a 2D homogeneous domain. We then use the PNM to study quasi-static growth-shrinkage cycles of trapped ganglia inside heterogeneous porous media. The findings constitute our second contribution, generalizing previous theoretical results by the authors from 2D homogeneous to 3D-planar heterogeneous microstructures. They include: (1) the interfacial area of a ganglion depends approximately linearly on its volume; (2) if the throat-to-pore aspect ratio is large, growth is percolation-like; but (3) if it is small, a hitherto unreported intermittent growth regime precedes percolation, in which ganglia repeatedly fragment and reconnect. These outcomes have implications for selecting optimal storage sites for CO2 and designing fuel cells and electrolyzers with finetuned porous microstructures.

Peat macropore networks – new insights into episodic and hotspot methane emission

Abstract. Peatlands are important natural sources of atmospheric methane (CH4) emissions. The production and emission of CH4 are strongly influenced by the diffusion of oxygen into the soil and of CH4 from the soil to the atmosphere, respectively. This diffusion, in turn, is controlled by the structure of macropore networks. The characterization of peat pore structure and connectivity through complex network theory approaches can give conceptual insight into how the relationship between the microscale pore space properties and CH4 emissions on a macroscopic scale is shaped. The evolution of the pore space that is connected to the atmosphere can also be conceptualized through a pore network modeling approach. Pore regions isolated from the atmosphere may further develop into anaerobic pockets, which are local hotspots of CH4 production in unsaturated peat. In this study, we extracted interconnecting macropore networks from three-dimensional X-ray micro-computed tomography (µCT) images of peat samples and evaluated local and global connectivity metrics for the networks. We also simulated the water retention characteristics of the peat samples using a pore network modeling approach and compared the simulation results with measured water retention characteristics. The results showed large differences in peat macropore structure and pore network connectivity between vertical soil layers. The macropore space was more connected and the flow paths through the peat matrix were less tortuous near the soil surface than at deeper depths. In addition, macroporosity, structural anisotropy, and average pore throat diameter decreased with depth. Narrower and more winding air-filled diffusion channels may reduce the rate of gas transport as the distance from the peat layer to the soil–air interface increases. The network analysis also suggests that both local and global network connectivity metrics, such as the network average clustering coefficient and closeness centrality, might serve as proxies for assessing the efficiency of gas diffusion in air-filled pore networks. However, the applicability of the network metrics was restricted to the high-porosity near-surface layer. The spatial extent and continuity of the pore network and the spatial distribution of the pores may be reflected in different network metrics in contrasting ways. The hysteresis of peat water content between wetting and drying was found to affect the evolution of the volume of connected air-filled pore space in unsaturated peat. Thus, the formation of anaerobic pockets may occur in a smaller soil volume and methanogenesis may be slower when the peat is wetting compared to in drying conditions. This hysteretic behavior might explain the hotspots and episodic spikes of CH4 emissions, and therefore, it should be taken into account in biogeochemical models.

Characterization of a Geopolymer Foam by X-ray Tomography.

Metakaolin based geopolymer foams were synthesized at room temperature by direct foaming using hydrogen peroxide (H2O2) as a blowing agent and two types of surfactants such as AER5 and CTAB allowing to tune the connection between two adjacent cells. In the field of decontamination process of liquid wastes, the knowledge of the topology of the generated macroporous network is a primary of interest. Due to the complex structure of porous material, 2D conventional techniques as optical or scanning electron microscopy are often not able to provide all the necessary informations. The 3D networks were therefore characterized by X-ray tomography to determine the morphological structure parameters that is useful to manufacture geopolymer material for filtration applications. The porosity, the pore size distribution and constriction between adjacent cells, as well as the connection rates between pores were analyzed by the iMorph program. The results show that the total porosity increases from 26 to 74% when the initial concentration of H2O2 increases, which is in complete agreement with the tomography results. Materials synthetized from CTAB surfactant are poorly connected whereas those generated from AER5 surfactant have a higher mean cell size (at equivalent initial H2O2 concentration) and are fully connected, which will facilitate the transport of fluid through the material. These features have a strong impact on the value of permeability coefficients of the geopolymer foams. Indeed, permeabilities calculated from a Pore Network Modeling (PNM) approach or Kozeny-Carman equation, are ranged in between 10−14 to 10−10 m2 depending on the cell connectivity, the throat size and the total porosity.

Stress-dependent fluid dynamics of shale gas reservoirs: A pore network modeling approach

In this study, the pore network modeling approach is implemented to study the flow behavior of the methane gas in shale reservoirs in the presence of slip flow and gas desorption under different effective stress conditions through the effect on apparent permeability. A single pore and a pore network are constructed using a down-scaled Berea sandstone image. The compressible Stokes is applied with proper boundary conditions to capture slip flow and gas desorption effects. To include the effect of stress, poroelasticity principles are applied to describe the interaction between fluid flow and solid deformation. The model performance is verified against an experimental data taken from the literature. Both models show a negative effect of stress on gas flow when slip flow and desorption mechanisms are activated in the models. In the single pore model, slip has a positive and complementary effect on desorption at a specific stress value when their coupled contributions are summative. However, the results of pore network model show that slip has a destructive effect on desorption contribution specially at low effective stress values. That is, the changes in pore pressure induced by the slip mechanism act to limit the desorption contribution. This is clearly noted with the consideration of stress effects. At high effective stress values, the slip effect is limited due to the increase in pore pressure by compression, hence a closer matching between the permeability enhancement produced by the desorption mechanism alone and the coupled effect of desorption and slip can be noticed. Stress acts to limit the slip flow and also the desorption mechanism as they both are a function of pore pressure, however, as stress increases the contribution of desorption no longer would be reduced by slip flow. This study provides insights into stress role in multiphysics gas flow in shale reservoirs.

Distribution of liquid flow in a pore network during evaporation

The variation of the distribution of the liquid flow in porous media during evaporation is still a puzzle. We resolve it with the pore network modeling approach. The distribution of the evaporation-induced liquid flow in a pore network composed of about 2.5 million pores is determined. The probability density function of the magnitude of the normalized liquid flow rate is obtained. For the low normalized liquid flow rate, the probability density function is power-lawlike. The power-law exponent depends on both the liquid saturation and the location of the moving meniscus in the main liquid cluster. The evaporation-induced liquid flow in the pores in the pore network can be correlated. Whether the liquid flow distributions in various zones in the pore network are similar or not relies significantly on the location of the moving meniscus in the main liquid cluster. The functions depicting the relation between the power-law exponent and the local liquid saturation for the zones adjacent to and away from the open side of the pore network are different. These findings from the pore scale studies provide insights into developing the accurate continuum model for evaporation in porous media.

The influence of layer separation on multilayer mist coalescing filter performance

• Influence of small gaps between layers in a multilayer mist filter “sandwich” confirmed experimentally. • Gap size needed to induce onset of effect studied using pore network modelling. • Important implications for filter performance. • Parametric study to inform future research and design. This work experimentally and numerically examined the influence of micro-sized gaps between layers of filter media on the micro-physics of multilayer porous media commonly used in gas–liquid filter/coalescer applications. It had previously been assumed that if the layers are sufficiently closely packed then they will behave as a monolithic filter with equivalent properties, however no studies have been conducted on the micro-scale interstitial properties of multilayer filters to confirm this. High resolution micro-Computed Tomography ( μ -CT) carried out in this work, determined that even in closely packed “sandwiches” of media, the layers in the filter element behave more like individual filters than a monolithic entity, with each layer having a characteristic liquid saturation profile that repeats throughout the media. To further investigate and understand this phenomenon, simulations using a Dynamic Pore Network Model (DPNM) approach were undertaken to replicate the effect and investigate the influence of layer gap on the onset and magnitude of the effect. The DPNM simulations also revealed the presence of local minima in saturation in the gap, similar to the experiments. Such local reduction in saturation could be interpreted by the concept of capillary bundles. Both experiments and PNM predictions showed that the local minima is more pronounced at the lower velocities. It was also found that the monolith assumption breaks down at a gap thickness of 60 μ m for the micro-glass filter ( d = 4.5 μ m) for the range of parameters considered; however, this was likely larger than the gap width in the experimental cases.

Pore-to-Core Upscaling of Solute Transport Under Steady-State Two-Phase Flow Conditions Using Dynamic Pore Network Modeling Approach

We present a solute transport model, developed by employing a dynamic pore network modeling approach, to investigate dispersive solute transport behaviors in consolidated porous media. The model is capable of upscaling solute transport processes from pore to core, under two-phase fluid configurations. The governing equations of fluid flow, fluid displacement, and solute transport are solved at the pore level. A heavily parallelized computing scheme is utilized to simulate dynamic fluid displacements and transport processes in a core-scale pore network constructed from micro-computed tomography (micro-CT) images of a Berea sandstone sample. A series of solute transport simulations are conducted under the single-phase condition to validate the model by comparing the computed longitudinal dispersion coefficients against the experimental data over a wide range of Peclet numbers (Pe), i.e., $$3 \times 10^{-2}{\sim}3 \times 10^5$$ . The model is then used to simulate solute transport under two-phase fluid configurations to examine the effects of the non-wetting phase saturation on solute transport behaviors. More specifically, solute transport is studied at different Pe and different water saturations obtained at the end of imbibition processes. We find that in a two-phase system, the longitudinal dispersion coefficient substantially increases with enhanced convective mixing under the transport regime with high Pe but decreases with restricted diffusive mixing at low Pe. In addition, the results indicate a non-monotonic dispersion–saturation relation under the convective transport condition. We illustrate that a strong correlation exists between the extent of dispersive mixing and the heterogeneity of fluid saturation profile across a core-scale network.

Pore-network modeling of single-phase reactive transport and dissolution pattern evaluation

A pore-network modeling approach is proposed to understand mineral dissolution regimes during reactive transport, as well as changes in porosity and permeability. The transport problem is implemented with full consideration of the mass balance of the solute in all pore spaces, including pore-bodies and throats. The changes in geometry of the pore network due to calcite dissolution are taken into account based on the rate of the heterogeneous chemical reaction happening at the mineral surface. The networks consider two- and three-dimensional domains with a variety of number of pores. The evolution of network geometry and flow properties are investigated under various flow conditions using representative Péclet and Damköhler numbers to understand the interplay of transport and reaction. A behavior diagram is constructed aiming to identify different regimes and their boundaries. The dissolution patterns identified in this study further the applicability of the pore-network model approach as a tool for understanding of reactive transport and dissolution processes.

The Transport Mechanisms and Dynamics of Shale via Multiscale Multiphysics Pore Network Modeling

Abstract Source rocks such as shale are highly heterogeneous, consisting of organic matter and various inorganic minerals. Microscopic images suggest that microcracks serve as conduits for the gas released from organic nanopores. The permeability of the shale matrix is primarily attributed to stress-sensitive microcracks that are highly influenced by changes in fluid pressure. As the microcracks are depleted, more gas molecules desorb from the organic nanopores; this, in turn, affects the fluid pressure in the microcracks. Linking the local properties of the organic nanopores to the microcracks allows for a better understanding of the coupling between them, which is necessary for improved modeling. In this research, a multiscale pore network modeling approach is presented to describe the organic material and microcrack system and investigate the large-scale features of gas transport in shale. A multiscale pore network model consisting of clusters of organic pore networks and microcracks was built to examine shale gas transport on a microscopic scale. The organic part of the network model consisted of nano-capillaries interconnected at nanopores. The network accounted for the adsorptive–convective–diffusive transport mechanisms recently derived for a single capillary. This organic nanopore network was hydraulically connected to a single microcrack. Then, the mass balance at each node in the new domain was solved, along with the assumed boundary conditions. Using the information at the nodes, the total flowrate and pressure distribution in the system were obtained as a function of time. The results show that the fluid pressure in the microcrack was primarily sensitive to the content of the organic material and its permeability. Then, the microcracks–organic materials interactions are studied and empirically quantified at larger macroscopic scale of gridblocks. This relationship can be investigated in the laboratory and used in theoretical models to predict shale gas production.

Towards multifield discrete element modeling of concrete structures

AbstractConcrete structures are built extensively all over the world. The prediction of the lifetime of a structure is very important in terms of costs and usability. A numerical modeling concept is presented that can describe concrete on the mesoscale. The focus of the model development is on the coupling of mechanics, heat conduction and chemical reactions. The Discrete Element Method (DEM) is used to describe the aggregates with spherical bonded particles. A voronoi tessellation provides access to the free space between the aggregates and leads to a pore network model (PNM) approach accounting for transport phenomena. Chemical reactions are handled within a processzone which couples the DEM and PNM. In the scope of this framework the sulfate attack on concrete is modeled and computed. The local deterioration in the concrete matrix is directly captured and the impact on the macroscopic behavior is presented.

Carbon felt electrodes for redox flow battery: Impact of compression on transport properties

In a flow battery setup, carbon felt materials are compressed to obtain higher performance from the battery. In this work, a commercially available carbon felt material, commonly used as electrodes in Vanadium Redox Flow Battery setups was evaluated for the transport properties (diffusivity, permeability, pressure drop required for maintaining flow, among others) while under seven set levels of compression, using an image analysis coupled with pore network modeling approach. X-ray computed tomography has been used to obtain the microstructure of a commercially available electrode under compressed conditions. An open-source pore network modeling tool, OpenPNM has been used to investigate the transport properties of the porous felt material at each of the set compression levels. The results from the modeling are compared against experimentally obtained electrolyte transport patterns visualized using synchrotron X-ray radiography. The electrical resistance of the carbon felt electrode was measured experimentally using a four-probe method. The compression resulted in a 58% reduction in permeability, and a 25% reduction in single-phase diffusion. This combination of ex-situ characterization of the electrical and fluid transport through the electrodes provides valuable data for modeling flow battery systems, and validating hypothesis from in situ testing.

Multiscale Reconstruction of Vuggy Carbonates by Pore-Network Modeling and Image-Based Technique

Summary Vugular carbonate rocks have a complicated flow behavior because of their multimodal porosity system, with different interconnectivity at the pore scale. In this study, a new hybrid algorithm to reconstruct a bimodal vugular porous medium is introduced by coupling the pore-network modeling approach (i.e., stochastic) with the image-based network technique (i.e., process-based). This work implements image-processing techniques to generate a lattice-based network of secondary porosity (i.e., vugs) on top of an initial pore-network model at the pore scale. The resulting multiscale model is designed to preserve vug-to-vug and vug-to-pore connectivity of overlapping vugs. Modifying the effective conductance of the overlapped vugs enables the calculation of permeability of the dual-porosity network by applying mass conservation and the Poiseuille law. The method is validated on samples from an Iranian carbonate formation. The matrix micropores obtained from the mercury-intrusion laboratory measurements are statistically reconstructed by a Nelder-Mead optimization algorithm. Our results show that during the addition of vugs into a network, the absolute permeability of the network increases monotonically with rising porosity before vug percolation. However, once vuggy pores percolate, the absolute permeability of the network increases tremendously. Moreover, the availability of vugs makes the network structure more complex as determined by the off-diagonal complexity measure. The results of this study help in understanding the behavior of vuggy formations observed in carbonate reservoirs.

Electrolyte Flow in Vanadium Redox Flow Batteries

The redox reactions inside a Vanadium Redox Flow Battery (VRFB) are catalyzed by a porous carbon felt electrode, through which the vanadium containing electrolyte is pumped. Thus, a high Electrochemically Active Surface Area (ECSA), corresponding to a high saturation of the porous electrode, is beneficial to the performance. Maintaining a low mass transport resistance inside the flow felt is important to reduce parasitic pumping losses, which decrease the overall efficiency of the battery system. The pressure drop was measured, as it is directly related to the pumping losses caused by the flow through the pores. X-ray tomography and X-ray radiography were used to visualize the distribution of the electrolyte inside the pores. The effect of thermal activation (400 °C, 25 h) and compression of the carbon electrode on the wetting behavior of the electrolyte was investigated, as it correlates with the ECSA and the oxygen content on the electrode surface1. Furthermore, the changes in flow behavior of the redox active vanadium species with a different oxidation number are of interest, as it could imply separate optimization parameters for the anode side and the cathode side. The redox-active vanadium species in the electrolyte exist in four different states, V(II), V(III), V(IV), and V(V). In this work, the X-ray based techniques were used in an ex situ injection setup2. VRFB electrolytes (V(IV), V(V), V(II), V(III), all 0.1 M in 2M H2SO4) were injected into a commercially available porous carbon felt electrode ((GFA 6EA) from SIGRACELL® battery electrodes (SGL Carbon, Germany)) under controlled degrees of compression (20%, 50%, 70% of the uncompressed height). After an initial imbibition of the electrode, which was stopped immediately after the electrode wicked the electrolyte, a higher flow-rate was applied to simulate operating conditions. Synchrotron X-ray radiography shows the invasion and progression of the liquid electrolyte into the pores and indicates that capillary forces are initially dominant, but numerical simulation of the flow-through suggests that other forces come into play as well at higher flow velocities3. The study shows that the thermal activation plays the major role in the wetting behavior, increasing the saturation inside the electrode by more than 200% and decreasing the pressure drop by a factor of two when the electrolyte is injected into a thermally activated electrode, in agreement with Banerjee et al.3. The influence of the vanadium species in the electrolyte is relatively weak and it shows a slightly higher saturation for V(III), but this effect is outweighed by a stronger effect of compression. Synchrotron X-ray tomography highlights the occurrence of the Cassie-Baxter effect (the emergence of trapped air bubbles inside the electrode) and implies movement of these bubbles during continuous flow, in agreement with Greco et al.1. Figure 1: a) Saturation after injection of various electrolyte species into thermally activated carbon felt electrodes under different degrees of compression. b) Effect of compression on the pressure during the simulation of continuous flow-through conditions. The bar color corresponds to the color of the electrolyte solution in both figures. 1 Greco, K. V., Forner-Cuenca, A., Mularczyk, A., Eller, J. J. & Brushett, F. R. Elucidating the Nuanced Effects of Thermal Pretreatment on Carbon Paper Electrodes for Vanadium Redox Flow Batteries. ACS Applied Materials & Interfaces 10, 44430-44442, doi:10.1021/acsami.8b15793 (2018). 2 Bevilacqua, N., George, M. G., Galbiati, S., Bazylak, A. & Zeis, R. Phosphoric Acid Invasion in High Temperature PEM Fuel Cell Gas Diffsuion Layers. Electrochim. Acta 257, 89-98, doi:10.1016/j.electacta.2017.10.054 (2017). 3 Banerjee, R., Bevilacqua, N., Eifert, L. & Zeis, R. Characterization of carbon felt electrodes for vanadium redox flow batteries - A pore network modeling approach. Journal of Energy Storage 21, 163-171, doi:10.1016/j.est.2018.11.014 (2019). Figure 1

An efficient coupling of free flow and porous media flow using the pore-network modeling approach

Macro-scale models of coupled free flow and flow through a permeable medium often lack the capabilities to account for process-relevant complexities on the pore scale. Direct numerical simulation of such systems, on the other hand, inherently includes these micro-scale features but is only feasible for problems of very limited spatial and temporal extent. A new class of hybrid models aims to combine the individual strengths, i.e., computational efficiency and local accuracy on the micro scale, of models of different dimensionality.We propose, to our knowledge for the first time, a fully coupled model concept that involves a (Navier-) Stokes model for the free flow and a pore-network model for the porous domain. As a first step, we consider isothermal single-phase flow with and without component transport, but the model is open for extension for more complex physics. Appropriate coupling conditions guarantee the continuity of mass and momentum fluxes across the interface between the two domains. The coupled model is implemented in DuMu▪ , an open-source toolbox for the simulation of flow in porous media. We use a monolithic approach, i.e., all balance equations are assembled into a single system matrix and no coupling iterations between the submodels are required. Newton's method is applied to solve the potentially non-linear system of equations.The model is able to handle both structured and unstructured, randomly-generated networks. For the structured porous domains, the simulation results of the coupled model were compared to numerical reference solutions where excellent agreement was found, both for Reynolds numbers below one and around 400 in the free-flow channel. When applied to a geometrically complex unstructured network and considering compositional flow, clear paths of preferential flow could be identified which also locally affect the adjacent region of free flow at the respective interface. The ability to account for such pore-scale characteristics makes the model an interesting option, e.g., for simulating coupled flow problems that feature non-Fickian transport behavior or multi-phase flow, which will be investigated in future work.

Characterization of carbon felt electrodes for vanadium redox flow batteries – A pore network modeling approach

Abstract Carbon felt electrodes are commonly used as porous electrodes in Vanadium redox flow batteries for large-scale energy storage. The transport properties of these electrodes are an important parameter as the transport resistance can form a significant parasitic power loss depending on the configuration of the flow battery. Therefore, to better predict the overall parasitic power losses and devise strategies for the improvement of overall battery efficiency, the transport properties need to be properly understood. In this work, four commercially available carbon felt electrodes have been investigated for their transport properties. It has been shown that the non-activated electrode is hydrophobic in nature, while after activation, the electrodes become hydrophilic. The single-phase diffusion and permeability were found to decrease linearly with an increase in electrode thickness. The imbibition characteristics were similar for the four electrodes, although the change in wettability had a strong impact on the pressure required for the electrolyte to invade into the electrode.