Pore-scale Simulations Research Articles

Pore-Scale Analysis of the Permeability Damage and Recovery during Cyclic Freshwater and Brine Injection in Porous Media Containing Non-Swelling Clays

Permeability damage in subsurface porous media caused by clay mobilization is encountered in many engineering applications, such as geothermal energy, water disposal, oil recovery, and underground CO2 storage. During the freshwater injection into rocks containing brine, the sudden decrease in salinity causes native clay fines to detach and clog pore throats, leading to a significant decline in permeability. The clay fines detach due to weakened net-attractive forces binding them to each other and the grain. Past experiments link this permeability damage on the immediate history of the salinity and the direction of flow. To better understand this phenomenon, we conducted pore-scale simulations of cyclic injection of freshwater and brine into sandstone containing Kaolinite clay. Our simulations establish a link between the clay-fine trajectory and the permeability trend observed by Khilar and Fogler (1983). For a uniform clay size of 3 microns, we observe a permeability decline by two orders of magnitude during freshwater injection with respect to brine injection. Increasing salinity and simultaneously reversing flow direction restores the permeability. The permeability restoration upon reversing the brine flow direction is attributed to the unblocking of pore throats in the reverse direction by the movement of the clay particles along the grain surfaces by the hydrodynamic force and the strong net-attractive force under high salinity.

Pore-scale resolved simulation of quenching, acceleration, and transition to detonation of hydrogen explosions by metal foams

Pore-scale simulations of quenching, acceleration, and transition to detonation of gaseous hydrogen explosions by metal foams were performed. The model solves the three dimensional compressible reactive Navier-Stokes equations with detailed chemistry in a closed square channel with a metal foam placed inside. The structures of the foam were fully resolved using an immersed boundary method. Stoichiometric mixtures of hydrogen-oxygen and hydrogen-air were considered. An explosion in the channel was initiated with a high-pressure and high-temperature spark. The simulation results show that the explosion can be quenched, accelerate, or transition to detonation depending on the foam pores-per-inch (PPI). Hydrogen-air explosions were quenched with foams of ∼39 PPI or higher due to heat losses from the flame, which is consistent with experimental observations. The explosion was not quenched by foams with low PPI. Instead the low PPI foams exacerbated the explosion by causing flame acceleration. Worse, a 78 PPI foam caused a stoichiometric H2 and O2 mixture to transition to detonation. Hydraulic resistance due to products venting away from the flame surface was found to produce strong pressure gradients within the foam. This causes a self-pressurizing effect that grows as the flame propagates further into the foam. The pressure within the foam grows and steepens into a shock. The shock initiated the detonation by a Mach reflection, which is similar to deflagration-to-detonation transition mechanisms in traditional obstacle-laden channels. Statement of SignificanceMetal foam structures are often used as devices to inhibit flames in scenarios where explosion hazards are a concern. Direct numerical simulations were performed to increase understanding of how flames and explosions interact with metal foams. The simulation results show that high pores-per-inch (PPI) foams quench the explosion by removing heat from the flame. Lower PPI foams can have the opposite effect and exacerbate the explosion by promoting flame acceleration or even transition to detonation. Flames self-pressurize as they propagate through low PPI foams due to hydrodynamic friction and gas-dynamic effects from flowing product gases. In extreme cases, the pressure waves near the flame can steepen into a shock and initiate a detonation. These results indicate that improperly selected metal foam flame arresters can exacerbate the explosion.

Digital core reconstruction based on discrete element and Markov chain-Monte Carlo methods

The digital core is an essential platform for pore-scale flow simulation in geoenergy exploitation, CO2 storage, and hydrogen storage. However, the existing reconstruction methods, such as the Markov chain-Monte Carlo (MCMC) method, can not obtain the digital core reflecting the influence of complex stress. Moreover, the discrete element method (DEM)-based reconstruction, which can consider the effect of stress, has yet to be reported to consider the actual particle shape. To this end, a hybrid reconstruction method based on DEM and MCMC methods is proposed in this study. Firstly, watershed and level set algorithms are used to segment and extract the contours of rock particles, and clump in PFC2D is used to fill the contours to establish a clump template library. Then, the initial condition (ground condition) digital core slice is established with clump packing based on porosity and particle size distribution. Subsequently, the stress loading simulation is carried out to obtain 2D digital core slices with different stress combinations. Finally, the MCMC method obtains 3D digital cores. This proposed method is used to reconstruct the digital core of Belgian fieldstone with different stresses and effective moduli, and the evolution of pore structure characteristics is analyzed. Results show that the stress compresses the range of the pore radius distribution curve, resulting in the shortening of the throat length distribution; the conductivity of the model is poor. The maximum reduction of porosity and permeability is 6.56% and 24.81%, respectively. The model with a large effective modulus has a stronger resistance to deformation and can protect the pore structure. These results prove that the method proposed can obtain the digital core reflecting the stress effects and provide a reference for accurately describing the in-situ rocks' pore structure and the pore-scale flow simulation.

Effect of natural convection on charging of phase change materials in graded metal foam: Pore-scale simulation

Open-cell metal foams (MFs) possess exceptional thermal conductivity and are often utilized to enhance the phase transition efficiency of phase change materials (PCMs) that have insufficient thermal conductivity. The movement of energy within MFs during phase transition is influenced by natural convection and heat conduction. In this study, pore-scale numerical simulation (PNS) was employed to study the effect of natural convection on the phase transition of graded MFs (positive gradient foam-PGF, homogenous foam-HF, and negative gradient foam-NGF). Simplified tetrakaidecahedron cells were used for PNS to capture the primary geometric features of MFs. Results have shown that natural convection significantly influences the phase transition process of PCMs. Compared to pure thermal conductivity, the full melting times (FMTs) of PCMs in PGF, HF, and NGF were reduced by 85.2% - 88.3% when natural convection was considered. Furthermore, the integrated average temperature response rates of PCMs in PGF, HF, and NGF, considering natural convection, were improved by 378.4%, 301.9%, and 342.5%, respectively. The presence of natural convection resulted in a gradient in the phase interface distribution and temperature field. The PNS method proved useful in illustrating the influence of metallic ligaments on phase interface and temperature distributions.

Effect of Rock Dissolution on Two-Phase Relative Permeabilities: Pore-Scale Simulations Based on Experimental Data

Relative phase permeability is an important characteristic of multiphase flow in porous media. Its assessment is an urgent issue when the pore structure changes due to rock dissolution. This article examines the effect of carbonate rock dissolution on two-phase flow based on images obtained by X-ray microcomputed tomography with a spatial resolution of ~18 µm. The characteristics of the two-phase flow were calculated through pore network modeling. The studies were conducted on 20 sub-volumes, which were extracted from cylindrical samples A and B with permeabilities of 0.72 and 0.29 D. HCl solutions (12% and 18%) were injected into samples A and B at a rate of 8 and 2 mL/min, respectively. Due to rock dissolution, the porosity and absolute permeability of the sub-volumes increased by 1.1–33% and 44–368%, respectively. Due to dissolution, the residual oil and water saturations decreased by 20–46% and 25–60%, respectively. These results showed that an increase in absolute permeability led to a significant reduction in residual oil and water saturations. These results also demonstrated that rock dissolution resulted in a change in the spatial heterogeneity of the relative phase permeabilities. The spatial heterogeneity increased in sample A after rock dissolution, while in sample B, it decreased.

Investigation of Natural Gas Hydrate Microscopic Occurrence Types and Pore-Scale Flow Simulation Based on Digital Cores

Investigation of Natural Gas Hydrate Microscopic Occurrence Types and Pore-Scale Flow Simulation Based on Digital Cores

Pore-Scale Simulation of Fracture Propagation by CO2 Flow Induced in Deep Shale Based on Hydro-Mechanical Coupled Model

Summary The depletion of conventional reservoirs has led to increased interest in deep shale gas. Hydraulic fracturing addresses the challenge of developing low-permeability shale, involving hydro-mechanical coupling fracture propagation mechanics. Supercritical CO2 (SC-CO2) has become a promising alternative to fracturing fluids due to its ability to be buried underground after use. The high temperature, pressure, and stress of deep shale lead to the flow of fracturing fluid to plastic deformation of rock, resulting in microfractures. In this paper, we simulate the fracture propagation process of deep shale fractured by SC-CO2 based on the coupling of the Darcy-Brinkman-Biot method, which adopts the Navier-Stokes-like equation to solve the free flow region, and the Darcy equation with Biot’s theory to solve flow in the matrix. To clearly probe the mechanism of deep fracturing from a microscopic perspective, the plastic rock property is taken into consideration. We investigate the effects of injection velocity, rock plastic yield stress, formation pressure, and gas slippage effect on fluid saturation and fracture morphology, and find that increasing the injection rate of fracturing fluid can form better extended fractures and complex fracture networks, improving the fracturing effect. Furthermore, we find that it is more appropriate to adopt SC-CO2 as a fracturing fluid alternative in deep shale with higher plastic yield stress due to higher CO2 saturation in the matrix, indicating greater carbon sequestration potential. High confining pressure promotes the growth of shear fractures, which are capable of more complex fracture profiles. The gas slip effect has a significant impact on the stress field while ignoring the flow field. This study sheds light on which deep shale gas reservoirs are appropriate for the use of SC-CO2 as a fracturing fluid and offers recommendations for how to enhance the fracturing effect at the pore scale.

Integrated Formation Evaluation for Site-Specific Evaluation, Optimization, and Permitting of Carbon Storage Projects

Participation in over 80 carbon capture and sequestration (CCS) projects spanning 25 years has led to the evolution of a recommended well-based appraisal workflow for CO2 sequestration in saline aquifers. Interpretation methods are expressly adapted for CCS applications to resolve key reservoir parameters, constrain field-scale modeling, provide answers required for the permitting process, and de-risk unique CCS evaluation challenges, such as Storage capacity Injectivity Containment. A challenge complicating all of the above is the eventual impact of three-way interaction among rock matrix, brine, and (impure) CO2 streams. Most logging, sampling, and laboratory techniques are adapted from established domains such as enhanced oil recovery, underground gas storage, and unconventional reservoir evaluation, though some CCS-specific innovation is also needed. Storage evaluation begins with established methods for lithology, porosity, permeability, and pressure, while special core analysis (SCAL) determines CO2 storage efficiency and relative permeability. Containment evaluation spans multiple disciplines and methods: the petrophysicist’s task to quantify seal capacity relies heavily on laboratory analysis, while geologists leverage downhole imaging tools to verify caprock structural/tectonic integrity. Geomechanics engineers define safe injection pressure via mechanical earth models (MEMs) built on advanced acoustic logs calibrated by core geomechanics, wellbore failure observations, and in-situ stress tests. The impact of rock-brine-CO2 interactions is studied via custom SCAL experiments and/or pore-scale digital rock simulations that rigorously represent chemical and thermal processes. Wireline formation tester samples provide representative formation brine as feedstock for SCAL. Water samples also enable operators to prove injection within regulatory limits while establishing baselines for future monitoring programs. Examples applied to recent CCS projects in North America are presented. All of the above data need to be integrated into a CCS model predicting the CO2 plume behavior across the area of interest and within multiple horizons.

Morphology and Transport Characterization of Catalyst Layers for CO2 Reduction

Gas diffusion electrodes (GDEs) help to reduce transport limitations in devices for electrochemical CO2 reduction. Homogenized modeling of such devices requires input of morphological characteristics and effective transport properties of the porous structure, which can be obtained by pore-scale methods. Due to the small pore sizes and layer thicknesses, such characterization of the catalyst layer (CL) is difficult. In this work, CL structures digitalized by FIB-SEM nano-tomography were analyzed to obtain a set of morphological descriptors and were considered as geometrical domains in direct pore-scale simulations to calculate tensors of effective diffusion coefficient, permeability, tortuosity, and effective ionic and electronic conductivity. The CL properties vary significantly depending on the diffusion and flow direction, and samples of similar composition and synthesis technique exhibit different transport behaviors. The reported results provide a quantitative morphological analysis and a reliable set of effective properties to be used in homogenized device modeling, a net improvement over the most commonly used empirical or analytical formulations. The data set was obtained directly from the pore-scale structure of real CLs and contributes to making device-scale homogenized modeling of GDEs more accurate and reliable.

Direct pore-scale simulation of the effect of capillary number and gas compressibility on cyclic underground hydrogen storage & production in heterogeneous aquifers

Understanding the flow dynamics of hydrogen-water in aquifers is critical to maximizing hydrogen storage and recovery. By using direct computational fluid dynamics at elevated pressure, this paper aims at detailed pore-scale investigation of the effect of flow regime, compressibility, and hysteresis on flow pattern, trapping mechanisms and the efficiency of hydrogen storage and recovery. The results reveal that the favorable rates during hydrogen injection and production differ and a medium flow rate corresponding to drainage capillary number of ∼10−7 and imbibition capillary number of ∼10−5 can minimize both capillary and viscous fingering mechanisms, leading to more storability and recovery factor. We show that neglecting the local compression and expansion of hydrogen and a low working pressure, typical in modeling and experimental studies, result in misinterpretation of flow regimes and hydrogen storability. Finally, we report that during the cyclic process, the trapped hydrogen bubbles produce a “self-cushion gas" effect, improving hydrogen storage.

Brinkman double-layer model for flow at a free-porous interface

The phenomenon of the Stokes–Darcy flow in coupled systems comprising a clear channel and a complex 3D porous medium is investigated through both numerical and theoretical approaches. A quartet structure generation set (QSGS) method is used to generate random complex 3D porous structures imitating real structures in nature. Pore-scale flow simulations are performed using the Lattice Boltzmann method, enabling detailed analysis and characterization of the interfacial flow phenomena. Four key parameters with clear physical meanings are introduced to quantitatively capture essential aspects of the flow dynamics, revealing intriguing linear relationships with the square root of permeability – a fundamental characteristic length scale dominating the phenomenon. Several existing models are examined by these parameters. To address the limitations of existing models, a Brinkman double-layer(BDL) model is proposed. By comparing with several classic models, the present BDL model stands out due to its simplicity, accuracy and robustness, providing a comprehensive understanding of the complex flow behavior in the coupled system.

Sub-volume analysis of pore-network simulations: Determining the asymptotic longitudinal dispersion coefficient

This work introduces a new method called sub-volume analysis (SVA) to calculate macroscopic model parameters with their uncertainties from pore-scale simulations. We apply the SVA to calculate the longitudinal dispersion coefficient of the advection–dispersion model (ADM) from continuous tracer injection problems simulated with pore-network models. The SVA application presented here allows for verifying if a given network has enough length to reach an asymptotic dispersion regime where ADM applies. We tested the method using statistically constructed pore networks and pore networks built by joining several network units extracted from Berea sandstone images. There is complete agreement within the error margins for the asymptotic longitudinal dispersion coefficients obtained with the SVA and those obtained from breakthrough curve fitting. We also showed that the SVA gives more accurate results than those from the breakthrough curve fitting and much more accurate results than those from the method of spatial moments. Unlike the other methods, the SVA estimates the parameter uncertainty using a single pore-network realization.

Estimating the permeability of soils under different tillage practices and cropping systems: Roles of the three percolating pore radii derived from X-ray CT

Soil permeability associated with pore characteristics is a critical factor affecting water and nutrient transport in agricultural fields. However, which soil pore characteristics determine soil permeability remains inconclusive due to high heterogeneity of soil pore structure affected by soil and crop management practices. The objective of this study was to compare the pore characteristics of soils under various field management and assess the performance of different pore radii in estimating soil permeability. In this study, we utilized X-ray computed tomography (XCT) to quantify the pore characteristics of soil cores from three treatments: no-tillage under continuous maize cropping (NT-MM), no-tillage under continuous soybean cropping (NT-SS) and conventional tillage under continuous maize cropping (CT-MM). Subsequently, we calculated the permeability with pore-scale numerical simulations directly based on XCT images. Our results revealed that compared to the NT-MM treatment, the NT-SS and CT-MM treatments significantly increased soil porosity of > 200 µm pore classes (soil depths of 2–8 cm and 2–14 cm), as well as pore compactness, specific surface area, fractal dimension, and global connectivity. Among the three XCT-derived pore radii, the critical pore radius (CR) exhibited excellent performance in estimating permeability for samples from the NT-SS and CT-MM treatments, surpassing the hydraulic radius (HR) and mean pore radius of the limiting layer (MRLL). For samples from the NT-MM treatment, the CR and MRLL had similar estimation capabilities (R2 = 0.429, P = 0.110), but both were not as good as the HR (R2 = 0.539, P = 0.060). Furthermore, when estimating the permeability of all the aforementioned soil samples, the CR demonstrated the best estimation performance (R2 = 0.838, P < 0.001). In conclusion, utilizing CR as a predictor for estimating permeability in naturally structured soils is a good choice, which provides valuable insights into improving the accuracy of estimating soil permeability.

Pore-scale numerical simulation of supercritical CO2-brine two-phase flow based on VOF method

CO2 capture and storage technology is favorable for the reduction of CO2 emissions. In recent years, a great number of research achievements have been obtained on CO2 geological storage from nano scale to oil/gas reservoir scale, but most studies only focus on the flow behaviors in single-dimension porous media. Besides, the physical experiment method is influenced by many uncertain factors and consumes a lot of time and cost. In order to deeply understand the flow behaviors in the process of CO2 geological storage in microscopic view and increase the volume of CO2 geological storage, this paper established 2D and 3D models by using VOF (Volume of Fluid) method which can track the dynamic change of two-phase interface, to numerically simulate supercritical CO2-brine two-phase flow. Then, the distribution characteristics of CO2 clusters and the variation laws of CO2 saturation under different wettability, capillary number and viscosity ratio conditions were compared, and the intrinsic mechanisms of CO2 storage at pore scale were revealed. And the following research results were obtained. First, with the increase of rock wettability to CO2, the sweep range of CO2 enlarged, and the disconnection frequency of CO2 clusters deceased, and thus the volume of CO2 storage increased. Second, with the increase of capillary number, the displacement mode transformed from capillary fingering to stable displacement, and thus the volume of CO2 storage increased. Third, as the viscosity of injected supercritical CO2 gradually approached that of brine, the flow resistance between two-phase fluids decreased, promoting the "lubricating effect". As a result, the flow capacity of CO2 phase was improved, and thus the volume of CO2 storage was increased. Fourth, the influence degrees of wettability, capillary number and viscosity ratio on CO2 saturation were different in multi-dimensional porous media models. In conclusion, the CO2-brine two-phase flow simulation based on VOF method revealed the flow mechanisms in the process of CO2 geological storage at pore scale, which is of guiding significance to the development of CCUS technology and provides theoretical guidance and technical support for the study of CO2 geological storage in a larger scale.

Tight and Shale Oil Exploration: A Review of the Global Experience and a Case of West Siberia

Shale and tight oil reservoirs, with horizontal wells and hydraulic fractures, typically have a recovery ratio of around 10%. The exploration of tight oil and shale in North America has proven economically viable, thanks to advancements, such as horizontal wells, hydraulic fracturing, and other enhanced oil recovery techniques. Taking inspiration from the global experience (the North American shale experience), the exploration and development of the West Siberian tight and shale reserves was more focused on the reported best practices of the exploration of North American shale. In this study, the advance in the specific areas of shale and tight oil exploration was considered, with more emphasis placed on the progress in the exploration of West Siberian shales. According to the review literature, thermal enhanced recovery methods capable of converting organic matter into hydrocarbons were studied more than other methods of enhanced oil recovery. Aligned with global trends, there has been a growing focus on research aiming to integrate data-driven approaches and pore-scale simulations to enhance recovery from tight and shale formations. Multiple pilot studies have showcased promising prospects for implementing multistage hydraulic fracturing. Nevertheless, there are limited pilot studies dedicated to enhanced oil recovery methods for West Siberian shale.

Pore-Scale Investigation of Decomposition-Methods-Dependent Fluid Flow Properties in Hydrate-Bearing Sediments

Summary Depressurization (PD) and thermal stimulation (TS) are the primary methods for producing gas from natural gas hydrate (NGH) sediments. Fluid flow properties of the hydrate sediment, such as permeability, are fundamental parameters for simulating both processes. Most of the existing formulated permeability models are based on the numerical or experimental investigation of hydrate morphology evolution without considering the decomposition methods. In this study, we investigate the hydrate-decomposition-methods (PD and TS processes)-dependent fluid flow properties of hydrate sediments, which is achieved by microcomputed tomography (micro-CT) scanning of hydrate morphology evolution during PD- and TS-induced decomposition, as well as pore-scale modeling of fluid flow in the extracted 3D fluid-rock-hydrate images. We find that the decomposition behavior during TS is much more complicated than that during PD. The retardation zone in the PD sample increases the heterogeneity of the pore structure, while the secondary hydrates generated during TS cause even more heterogeneity in the pore space. The better facilitation of the TS method on hydrate split is favorable for the continuity of the gas phase. The pore-scale fluid flow simulation shows that the modified Kozeny-Carman (K-C) model is the best to describe the evolution of the normalized permeability with hydrate saturation during PD. However, a single model is not sufficient to describe the normalized permeability during TS decomposition due to the stronger heterogeneous porous structure reformed by the local accumulation of secondary hydrates. The two-phase flow capability is best at the initial stage of PD decomposition, while the two-phase flow region becomes wider as TS decomposition progresses. These results provide significant references for the simulation of the natural hydrate extraction process using different decomposition methods.

Reactive transport modeling for assessing coupled hydrogeochemical processes at interfaces in deep geological repositories: from the laboratory to the real world

Abstract. Deep geological repositories with a multi-barrier concept are foreseen by various countries for the disposal of high-level radioactive waste. Simulation tools for a close-to-reality description of repository evolution scenarios are required, especially to resolve the challenging task of comparing and assessing the long-term safety of different repository concepts in different host rocks within the German site-selection process. Chemical, thermal, and pressure gradients at the interfaces of the different barriers in a repository can lead to mineral dissolution and precipitation, generating non-linear responses in transport and mechanical properties of barrier materials and host rocks. Reactive transport modeling (RTM) can be applied to investigate these perturbations and processes across temporal and spatial scales to assess subsurface evolution. Nevertheless, implementing RTM at the continuum scale while accounting for pore-scale heterogeneities and geometry evolution remains a challenge. Pore-scale simulations offer the potential to capture the complex evolution of porous media over a broad range of Peclet and Damköhler numbers, and they can be utilized to improve the RTM by using upscaling methods (Prasianakis et al., 2020). In this context, we developed “lab-on-a-chip” experiments, combining time-lapse high-resolution optical microscopy and confocal Raman spectroscopy to test extended constitutive equations to classically employed Archie's law to improve the description of changes in transport properties (e.g., diffusivity) in evolving porous media in RTM. The 3D Raman tomography of the porous media combined with pore-scale modeling enabled the derivation of upscaled transport parameters. Our results highlight the importance of calibrating pore-scale models with quantitative experiments prior to simulations over a wide range of Peclet and Damköhler numbers, whose results can be further used for the derivation of upscaled modeling parameters. The derived and parameterized constitutive equations based on simple systems have been tested in reactive transport models as a sensitivity case study to evaluate uncertainties in the predictions of the evolution of real subsurface systems such as clay–cement interfaces in deep geological repositories.

Effects of carbon aggregates and ionomer distribution on the performance of PEM fuel cell catalyst layer: A pore-scale study

An in-depth understanding of the structure-performance relationship of the catalyst layer is crucial for its optimal design. In this work, the effects of carbon aggregation and ionomer distribution morphologies on the performance of the catalyst layer are investigated by pore-scale simulation. First, an optimized stochastic algorithm that can control the carbon aggregation degree and ionomer morphology is proposed to reconstruct realistic catalyst layer structures. The structural characteristics of the catalyst layer, such as pore size distribution, agglomerate size, and ionomer connectivity, are analyzed. A pore-scale model based on the lattice Boltzmann method is developed to simulate the reactive transport processes in the catalyst layer. The results indicate that the reasonable aggregation degree of carbon supports can balance the pore and cross-ionomer transport resistances of the oxygen to achieve optimal catalyst layer performance. The uniform ionomer coating in the catalyst layer can further improve the performance, and the optimal ionomer content is determined by balancing the electrochemical active surface area and the oxygen transport resistance. Based on the simulation results, a key principle for the optimal design of the catalyst layer is also proposed.

Pore Scale Simulation of Rheology Properties on Residence Time of Polymer Hydrogel and Hydraulic Conductivity of Bentonite Polymer Composite Geosynthetic Clay Liners

Flow in an idealized bentonite polymer composite geosynthetic clay liner (BPC-GCL) containing bentonite comprising two idealized circular granules was simulated using a COMSOL hydrodynamic model. The effect of the polymer rheology properties, including viscosity, surface tension, and contact angle, on the hydraulic conductivity of BPC-GCLs was investigated. The results showed that the hydraulic conductivity of BPC-GCLs significantly decreased by 2–4 orders of magnitude with polymer loadings of 3.3%, 6.5%, and 9.8% compared to conventional geosynthetic clay liners (GCLs). The polymer rheology properties are critical to the residence time and the hydraulic conductivity of BPC-GCLs. The residence time increases with the viscosity, surface tension, and contact angle of polymer hydrogel. In the overall study, the hydraulic conductivities increased significantly from 2.80 × 10−9 m/s to 1.40 × 10−7 m/s when the residence time was insufficient. When the viscosity of the polymer hydrogel is 5000 Pa∙s, 1 × 104 Pa∙s, and 1 × 105 Pa∙s, the residence time of the polymer hydrogel in the domain of BPC-GCLs is 14 min, 23 min, and 169 min, respectively. When the surface tension of the polymer hydrogel is 0 N/m, 0.01 N/m, and 0.02 N/m, the residence time of the polymer hydrogel in the domain of BPC-GCLs is 9 min, 17 min, and 23 min, respectively. When the contact angle between the polymer hydrogel and the NaB granules is 30° to 60°, the residence time of the polymer hydrogel in the domain of BPC-GCLs is 9 min and 33 min. These few minutes can approximate the actual passage of several days in physical time. When the viscosity, the surface tension, and the contact angle are higher than 1 × 106 Pa∙s, 0.03 N/m, and 60°, the residence time of the polymer hydrogel in the domain of BPC-GCLs tends to be very long, which means that a very low hydraulic conductivity of BPC-GCLs can be maintained in the very long term. This research unveils a nuanced and profound correlation between the rheological properties of the polymer hydrogel and the resulting hydraulic conductivity. This discovery enhances the understanding of the potential to tailor hydrogel characteristics for BPC-GCLs. The advanced model developed in this study also lays the groundwork for constructing a more realistic model that considers irregular geometries, interconnected pores, and diverse polymer distributions within the pore spaces.

Modeling the 4D discharge of lithium-ion batteries with a multiscale time-dependent deep learning framework

The lithium-ion battery (LIB) field is moving towards the direction of investigating spatially resolved physical phenomena in the 3D porous microstructure of electrodes. These pore-scale simulations give new insights into the local dynamics of lithiation/de-lithiation and charge transport. Nevertheless, the computational time of these simulations limits the integration of these models in optimization workflows of cycling conditions or electrode manufacturing processes.Machine learning models present a way of assessing in real-time the performance of materials. While several successful techniques for replicating simulations with machine learning have been proposed, this case study presents a more demanding problem, due to the necessity of understanding the behavior of heterogeneous 3D local data, as it evolves in time: this poses both a scientific and a technical challenge.To this end, we propose an autoregressive multiscale convolutional neural network model to predict relevant quantities at the pore-scale in the solid phase: the lithium concentration (in the active material) and potential (in the active material and carbon binder). These are ultimately used to reconstruct the battery discharge curve. 3D images of the electrode microstructures are the input to the network, trained with a dataset of finite element method simulations to predict the discharge behavior of the cathode side in lithium ion batteries.We propose this machine learning model as a proof-of-concept of the applicability of multiscale networks for time-dependent physics problems. The trained model exhibits very high accuracy (with errors lower than 2%) in forecasting the discharge behavior of new unseen cathodes.