Pore-scale Simulations Research Articles

Evolution of pore-scale concentration PDFs and estimation of transverse dispersion from numerical porous media column experiments

Knowing local concentration distributions is important for transport and mixing, particularly in porous media, yet a comprehensive understanding of them remains a challenge. Computing advancements have enabled high-resolution pore-scale simulations, offering an unprecedented opportunity for in-depth investigation of mixing. In this study we use simulation data to examine concentration distributions at the pore scale in the context of longitudinal (pseudo-one-dimensional) solute transport through a porous column. These distributions arise in a single column from heterogeneous flow at the pore-scale, which gets averaged out when upscaled and are not with reference to statistics across multiple random realizations. To measure these distributions, we first devise a semi-analytical approach to estimate the mean effective transport velocity profile for a non-uniform Darcy-scale fluid velocity, which unavoidably occurs due to the presence of lateral boundaries. This development allows sampling micro-scale concentrations over a moving surface that possesses a well defined Darcy-scale mean concentration, enabling empirical computation of the local concentration distribution. As an added benefit we find that our approach allows for the estimation of transverse dispersion coefficients, which is not typical in traditional column experiments. The implemented approach can estimate it via inverse modeling, and it agrees closely with previously published experimental data across the range of Peclet numbers we studied. We found that the measured pore-scale concentration probability density functions are best represented by a beta distribution, thus validating this longstanding hypothesis with direct evidence. Furthermore, we propose a model to describe the temporal and spatial evolution of the local concentration pdf, as well as its Péclet number dependence.

Numerical investigation on the influence of CO2-induced mineral dissolution on hydrogeological and mechanical properties of sandstone using coupled lattice Boltzmann and finite element model

The impact of CO2-induced mineral reactions, specifically the CO2-water-rock interactions, has been widely recognized for its potential to compromise the hydrogeological and mechanical properties of porous media, thereby deteriorating their integrity and mechanical characteristics. This raises concerns regarding the safety of numerous projects such as CO2 geological storage. However, the mechanism underlying the influence of CO2-induced mineral reactions on these parameters is still not fully understood, thereby introducing uncertainty into the reliability of predicted outcomes. Direct pore-scale simulation plays a crucial role in deepening the understanding of CO2 -water-rock interaction and its associated impacts. The present study proposes a novel simulation model that integrates the lattice Boltzmann and finite element methods to simulate the dissolution of calcite in a 3D sandstone sample invaded by saturated CO2 solution, aiming to investigate the resulting evolution of hydrogeological parameters (i.e., porosity and permeability) and mechanical properties (i.e., bulk and shear moduli). The injection rates of reactive fluid (i.e., CO2 solution) were varied in the model to simulate different operational conditions of CO2 geological storage project. The simulation results demonstrate that the decrease in injection velocity inhibits the dissolution of calcite in the middle and downstream regions, concentrating it near the inlet. These distinct modes of calcite dissolution result in differentiated permeability and mechanical properties within rocks possessing identical porosity levels. In general, the increase in fluid injection velocity leads to a more pronounced enhancement in permeability and a greater attenuation in bulk and shear moduli under the same porosity. Thus, it is confirmed that the utilization of porosity is inadequate in accurately characterizing the evolution of rock permeability and mechanical properties resulting from mineral reactions. We ascertain that the application of fractal parameters, i.e., succolarity and fractal dimension, can more precisely depict the progression of permeability and bulk/shear modulus, respectively.

Effect of Hydrate Saturation on Permeability Anisotropy for Hydrate-Bearing Turbidite Sediments Based on Pore-Scale Seepage Simulation

The permeability of natural gas hydrate (NGH) turbidite reservoirs typically exhibits significant anisotropy, with anisotropy being a crucial basis for evaluating reservoir production. The presence of hydrates, as a crucial constituent of the solid framework, not only impacts the overall permeability but also influences the permeability anisotropy. To investigate the saturation sensitivity of permeability anisotropy, a series of simulations are performed by integrating particle flow and computational fluid dynamics methods to construct the homogeneous and layered numerical samples and compute the evolution of permeability anisotropy. It is shown that the permeability is isotropic for homogeneous sediments and the isotropy remains unchanged regardless of variations in hydrate saturation. The permeability of layered sediments, in contrast, exhibits significant anisotropy due to the presence of dominant channels within the coarse layer. For uniformly distributed hydrates, the more effective blockage in coarse layers results in a reduction in anisotropy. While for preferentially distributed hydrates, the excess blocking of coarse layers makes the dominant channels transfer to the fine layers, the further blocking causes a U-shaped anisotropy–saturation curve characterized by a decrease–increase transformation. During the reservoir production process, the preponderance channels blocked by hydrates will be cleared and the horizontal permeability will significantly increase. As a result, the production efficiency of horizontal wells may exceed expectations. The findings offer a parameter support for production estimation and environmental assessment.

Model PEM water electrolyzer cell for studies of periodically alternating drainage/imbibition cycles

Investigating the counter-current two-phase flow within the anodic porous transport layer (PTL) of polymer electrolyte membrane water electrolyzers (PEMWEs) is a complex yet intriguing challenge. Until now, the gas-liquid invasion processes inside PTLs are only to a limited extent accessible under operation conditions, usually using sophisticated and expensive optical approaches, i.e., neutron imaging. We propose a model-supported experimental method with a fully operating microfluidic PEMWE, that allows to examine pore-scale oxygen-water distributions at the anode with high spatial and temporal resolution. The microfluidic cell is made of transparent Poly-Methyl-Methacrylate (PMMA), and the PTL is simplified by a quasi-2D pore network (PN) with a uniform pore-throat structure in the first preliminary study. The proposed setup is a significant advancement over previous studies, where gas was only injected at a constant flow rate from a single point. Test cases with current densities of 0.1, 1, and 2 A/cm2 and water flow rates of 1, 3, 5, and 10 ml/min were realized in the novel setup. We found periodically alternating invasion of oxygen (drainage) and water (imbibition), which were analyzed based on image sequences as well as voltage measurements. The experimental data is additionally supported by pore-scale Lattice Boltzmann (LB) and PN simulations. The preliminary results with the simplified PN structure are used to study the dominating transport mechanisms, revealing that drainage and imbibition occur simultaneously and are affected by evaporation and wetting liquid films formed in sharp pore corners. These phenomena are also expected to occur in more complex PTL structures. The preliminary results can, therefore, be regarded as an important basis for PTL studies, which are structurally more complex.

Pore-scale simulation of H2-brine system relevant for underground hydrogen storage: A lattice Boltzmann investigation

Underground hydrogen (H2) storage in saline aquifers is a viable solution for large-scale H2 storage. Due to its remarkably low viscosity and density, the flow of H2 within saline aquifers exhibits strong instability, which needs to be thoroughly investigated to ensure safe operations at the storage site. For the first time, we develop a lattice Boltzmann model tailored for pore-scale simulations of the H2-brine system under typical subsurface storage conditions. The model captures the significant contrast of fluid properties between H2 and brine, and it offers the flexibility to adjust the contact angle to suit varying wetting conditions. We show that the snap-off is enhanced in a system with a high capillary number and a small contact angle. These conditions lead to a low recovery factor, which is unfavorable for H2 production from the aquifer. Moreover, the relative permeability curves, computed from the simulation results, exhibit distinct behaviors for H2 and brine. In the case of the wetting phase, the relative permeability can be quantified using the quadratic expression, whereas for the non-wetting phase, the relative permeability exhibits a nearly linear behavior, and saturation alone appears insufficient to characterize the relative permeability at large saturations of non-wetting phase. This implies that different formula for liquid and gas phases may be employed for continuum-scale simulations.

Pore-scale simulations help in overcoming laboratory limitations with unconsolidated rock material: A multi-step reconstruction based on scanning electron and optical microscopy data

This article explores the possibility to assess the flow and transport properties of loosely consolidated rock material—something that is very hard or impossible to achieve in the laboratory due to fragility of cores. We present two cases of weakly consolidated and unconsolidated rocks. We provide a solution based on pore-scale simulations and stochastic reconstructions using scanning electron (SEM) and grain optical microscopy images as input data. The hybrid reconstruction approach is based on 3D grain shape construction out of 2D optical images, packing of grains to match the target porosity measured from SEM imaging, and addition of clay and other cementing phases with the help of phase-recovery method. Note that standard digital rock protocol based on X-ray microtomography did not work for considered samples due to fine-grained particle size distribution (insufficient resolution of X-ray microtomography). After creation of 3D digital replicas of rock samples based on their SEM and optical microscopy images, we applied pore-scale modeling to obtain permeability and two-phase flow properties. Simulated permeability of 259 mD for the first sample was in surprisingly good agreement with laboratory measurements of 248 mD. For the second sample permeabilities deviated by an order of magnitude. After additional studies it was found that the mesh attached to the sample during measurements affected the results. After pore-scale simulations of the grain packing with the mesh we were able to achieve very good agreement with the experiment, confirming that the lab was basically exploring the properties of the mesh clogged with unconsolidated rock material. Thus, pore-scale hybrid rock structure reconstruction technique combined with pore-scale simulations was able to correct inaccurate laboratory assessment and obtain flow properties for unconsolidated rock sample. We believe the developed hybrid reconstruction technique to be robust enough to serve as a basis of the industrial technology for petrophysical studies of weakly and unconsolidated core material.

Pore-scale simulation of diffusion characteristics inside the bi-dispersed pore structure

The classical diffusion models fail to predict the diffusivity of bi-dispersed porous materials, particularly at low macro-porosity. In this work, a pore-scale simulation is carried out to investigate the diffusion process inside ordered and random bi-dispersed pore structures under different growth phases and shapes. The applicability of existing models is evaluated. The results reveal that Maxwell and Nield models are inadequate to predict the diffusivity of the ordered macropore structure under different growth phase types and shapes. Meanwhile, the ordered distribution of microporous spherical particles is superior to that of macropores. For random pore structure, the macropore-macropore diffusion path contributes to the error of the random pore model, which depends on the ratio of the micropore-macropore diffusivity.

A parameter-free and monolithic approach for multiscale simulations of flow, transport, and chemical reactions in porous media

Traditional approaches for transport in porous media rely on empirical hydrodynamic/transport parameters to quantify the interfacial exchange terms between fluid and solid, which leads to considerable uncertainties and also to a narrow application range of each method for realistic investigations of porous media. A parameter-free approach for flow, transport, and chemical reactions in porous media is presented in this paper. This approach adopts a novel, single-domain set of equations that are rigorously derived based on the elementary conservation laws describing the physical, continuous domain. The impact of the solid on nearby fluid being directly quantified in terms of the quantity to be solved, this avoids the introduction of empirical parameters. Various transport problems including external, conjugate, and reactive processes are properly formulated in this context, with the coupling between fluid and porous structures at different scales naturally solved in a monolithic manner. All these equations remain simple in terms of their numerical implementation, with solid structures represented by the porosity field on a background mesh. The application of the present method in both pore-scale and representative elementary volume (REV-scale) simulations are checked by performing a series of test cases, including interfacial momentum/heat/mass transport, conjugate heat/mass transfer, chemical reactions, and two practical applications containing reacting interfaces. An overall first-order convergence rate has been observed in both spatial and temporal accuracy tests.

Pore-scale simulation of flow in porous rocks for wall shear stress analysis

Pore-scale simulation of flow in porous rocks for wall shear stress analysis

Augmenting X-ray micro-CT data with MICP data for high resolution pore-scale simulations of flow properties of carbonate rocks

Pore-scale modeling is essential in understanding and predicting flow and transport properties of rocks. Generally, pore-scale modeling is dependent on imaging technologies such as Micro Computed Tomography (micro-CT), which provides visual confirmation into the pore microstructures of rocks at a representative scale. However, this technique is limited in the ability to provide high resolution images showing the pore-throats connecting pore bodies. Pore scale simulations of flow and transport properties of rocks are generally done on a single 3D pore microstructure image. As such, the simulated properties are only representative of the simulated pore-scale rock volume. These are the technological and computational limitations which we address here by using a stochastic pore-scale simulation approach. This approach consists of constructing hundreds of 3D pore microstructures of the same pore size distribution and overall porosity but different pore connectivity. The construction of the 3D pore microstructures incorporates the use of Mercury Injection Capillary Pressure (MICP) data to account for pore throat size distribution, and micro-CT images to account for pore body size distribution. The approach requires a small micro-CT image volume (7–19 mm3) to reveal key pore microstructural features that control flow and transport properties of highly heterogeneous rocks at the core-scale. Four carbonate rock samples were used to test the proposed approach. Permeability calculations from the introduced approach were validated by comparing laboratory measured permeability of rock cores and permeability estimated using five well-known core-scale empirical model equations. The results show that accounting for the stochastic connectivity of pores results in a probabilistic distribution of flow properties which can be used to upscale pore-scale simulated flow properties to the core-scale. The use of the introduced stochastic pore-scale simulation approach is more beneficial when there is a higher degree of heterogeneity in pore size distribution. This is shown to be the case with permeability and hydraulic tortuosity which are key controls of flow and transport processes in rocks.

Multiscale CFD modelling of porous monoliths for heterogeneous catalysis of Knoevenagel condensation

In this research work, a multi-scale CFD model is developed for a catalytic heterogeneous reaction under continuous flow in a porous monolith. For this purpose, the Knoevenagel condensation was chosen as a model reaction. The model is based on a homogenization approach as well as pore scale modelling by coupling convection, diffusion and reaction within macro-meso porous hierarchical monoliths. The model's accuracy was determined through successful validation against previously available experimental data in the literature. Subsequently, the model was employed to examine the influence on reaction rates of structural and key process parameters like temperature, flow rates and macro/meso porosity. To analyze flow patterns and concentration profiles at the macro pore level, pore-scale simulations were conducted through image processing and CFD modeling of 25x25 µm Scanning Electron Microscopy (SEM) images of the monoliths. These simulations yielded an in-depth comprehension of pore flow and concentration behavior at the macro-meso level, offering valuable insights for optimizing pores in hierarchical structures.

Coupled flow and energy models with phase change in permafrost from pore- to Darcy scale: Modeling and approximation

We consider coupled models of flow and energy with phase change in thawing soils in permafrost at the pore- and Darcy scales. We develop the underlying models from first principles and define robust and conservative discretization algorithms based on cell-centered finite volume discretization on Cartesian grids and implicit time stepping for individual models. To couple the models we consider sequential approaches as well as time-lagging of some of the nonlinear properties. We also derive practical new surrogate models to obtain Darcy scale data from the pore-scale simulations. Finally, we study the sensitivity of models to the data in realistic scenarios. In particular we find that for the dynamics at the time scale of days, the nonlinear flow parameters have most significant impact on pressure, while temperature is less sensitive to data.

Surface wetting characterization in pore-scale multiphase flow simulations: A Ketton carbonate case study

Direct numerical simulations are commonly applied to X-ray computed microtomography images of porous rocks to measure petrophysical properties, such as relative permeability. To complement and/or expand laboratory data with useful simulations, such simulations need to reflect the true wetting condition of reservoir rock. It is therefore important to investigate approaches for assigning surface wetting conditions in pore-scale multiphase flow simulations. Two-phase Lattice-Boltzmann simulations are conducted on a Ketton carbonate image using different effective wetting models and then compared to pore-scale experimental data on the same rock, which is published elsewhere in (Scanziani et al., 2018). Two different wetting models are established based on the aging of the Ketton sample with crude oil at connate water saturation. Model 1 provides uniform wetting on all oil treated surfaces. Model 2 attempts to capture the multiscale nature of carbonate by allowing for spatially varying wetting conditions on oil treated surfaces based on local microporosity. Assessment criteria are based on pore-scale morphological measures, which include oil surface area coverage, oil phase topology, fluid/fluid curvatures, and contact angles. Overall, Model 1 with an assigned contact angle of greater than +10° above the geometrically measured contact angle from the experimental data provided the best results based on our assessment criteria.

Effects of microscopic pore-throat structure on gas–liquid relative permeability: Porous media construction and pore-scale simulation

The porous media structure of the oil/gas reservoir changes greatly after long-term development, which subsequently influences the macroscopic relative permeability. To clarify the effects of microscopic pore-throat structure on macroscopic relative permeability, we first proposed a method to generate two-dimensional porous media images with adjustable structure parameters. The method is based on Delaunay triangulation and is similar to the pore-network generation process, which can provide binary images for direct numerical simulation of flow through porous media. Then, we established the single component multiphase Shan–Chen lattice Boltzmann method coupling the real gas equation of state. Finally, we discussed the effect of pore radius, coordination number, pore-throat ratio, pore shape, and wettability on the gas–liquid relative permeability curve using the lattice Boltzmann simulation. This study provides an effective method to generate porous media and explain the mechanism of relative permeability change at the pore scale.

Multiphase flow simulation in hybrid porous structure

Recent research has primarily focused on creating biporous and hybrid porous structures with multiple pore sizes and length scales to optimize capillary pressure and permeability. Despite numerous experimental investigations on biporous and hybrid media, there is a noticeable absence of numerical simulations that explore the multiphase flow within these media. Therefore, the present study aims to conduct a pore-scale numerical simulation of two-phase flow in a biporous structure. The biporous structure is proposed by arranging clusters of solid particles in a staggered regular pattern, with each cluster consisting of closely packed particles. The dimensions and characteristics of the simulated structure are based on previous experimental literature on biporous and hybrid media. A monoporous structure simulation is also included for comparison with biporous results. ANSYS Fluent is utilized to carry out the numerical simulations of capillary pumping flow. The simulation results indicate that the permeability and average capillary pressure of the biporous media are four times and over one and a half times higher, respectively, compared to those of the monoporous media. The presence of smaller pathways within each cluster of a biporous and hybrid porous media enhances the capillary effect in comparison to conventional monoporous structures. Additionally, the larger pores between the clusters contribute to a higher permeability of the hybrid porous structure. As a result, the combined effect of increased capillary action and higher permeability leads to improved performance of the hybrid porous structure. Overall, the proposed simplified biporous geometry accurately models fluid flow in real, complex biporous and hybrid structures.

Expression of Concern: Lattice Boltzmann Method Pore-scale simulation of fluid flow and heat transfer in porous media: effect of size and arrangement of obstacles into a channel

Expression of Concern: Lattice Boltzmann Method Pore-scale simulation of fluid flow and heat transfer in porous media: effect of size and arrangement of obstacles into a channel

Effects of Nafion content in the catalyst layer of PEMFC on the transport phenomenon among nanoscale particles

Nafion, as a key component in the catalyst layer, plays a crucial role in the mass transport and electrochemical reactions within the catalyst layer. In this study, a numerical method is employed to reconstruct the three-dimensional nanoscale microstructure of the catalyst layer, including pores, Nafion, carbon particles, and Pt phases. A pore-scale model in which the Knudsen effect is taken into account is used to simulate the impact of Nafion contents on the interparticle transport and electrochemical reactions within the catalyst layer. The results show that the pore-scale simulation based on the reconstructed model can clearly reveal the mass transport process and highly uneven distribution of each physical quantity in the nanoscale particles and pores; When the Nafion content is relatively higher, the proton current distribution at the Pt/Nafion interface is relatively more uniform and the proton supply is sufficient. However, there is an inverse correlation between the oxygen mole concentration on the Pt surface and the Nafion content, which is the dominant factor affecting the electrochemical reactions on the Pt particle surface. When the Nafion content is lower, the proton supply becomes the dominant factor in the electrochemical reaction on the surface of Pt particles due to the weak connectivity of Nafion between the agglomerates. The combined effect of oxygen and proton transport result in the optimal Nafion volume fractions of 0.296 and 0.262 at voltages of 0.8 V and 0.7 V, respectively. The optimal Nafion volume fraction ranges between 0.224 and 0.262 at 0.6 V. As the voltage decreases, the effect of oxygen transport becomes more significant, and the optimal Nafion content decreases accordingly.

Thermo-Hydrodynamic Performance Evaluation of a Mini-Channel Inserted With TPMS-Based Porous Lattice

Abstract The coupled pore-scale and Darcy-scale numerical simulations are used in this work to investigate heat transport and hydrodynamic characteristics within a porous channel constructed by using a primitive lattice based on triply-periodic-minimal-surface. The pore-scale simulation is used in void subdomain, whereas the microporous-solid subdomain is simulated by Darcy-scale simulation for a range of mass transfer rates 4×10−7 to 2×10−3 kg/s (corresponding Reynolds numbers 0.1<Re<500). The liquid-water (Pr=7) is used as the working fluid. The Darcy number and inertial drag coefficient are calculated using the pressure drop in the channel along with the heat transfer coefficient (Nusselt number) on both internal and external walls. The quantifiable deviation from local thermal equilibrium (LTE) is also established. The results reveal two distinct, namely passive and active regimes, depending upon the permeability of the microporous-solid subdomain. It is found that the Nusselt number is almost constant for permeability values Kμ<10−11m2(passive regime). However, significant variation is observed in the Nu for higher value of permeability Kμ≥10−11m2(active regime). The Darcy number and effective Nusselt number are found to be increasing, while the inertial drag coefficient and deviation from LTE are found to be decreasing with the permeability in the active regime only.

Data-driven discovery of interpretable water retention models for deformable porous media

The water retention behavior—a critical factor of unsaturated flow in porous media—can be strongly affected by deformation in the solid matrix. However, it remains challenging to model the water retention behavior with explicit consideration of its dependence on deformation. Here, we propose a data-driven approach that can automatically discover an interpretable model describing the water retention behavior of a deformable porous material, which can be as accurate as non-interpretable models obtained by other data-driven approaches. Specifically, we present a divide-and-conquer approach for discovering a mathematical expression that best fits a neural network trained with the data collected from a series of image-based drainage simulations at the pore-scale. We validate the predictive capability of the symbolically regressed counterpart of the trained neural network against unseen pore-scale simulations. Further, through incorporating the discovered symbolic function into a continuum-scale simulation, we showcase the inherent portability of the proposed approach: The discovered water retention model can provide results comparable to those from a hierarchical multi-scale model, while bypassing the need for sub-scale simulations at individual material points.

The Method of Finite Averages: A rigorous upscaling methodology for heterogeneous porous media

Rigorous upscaling techniques offer accurate and computationally-efficient strategies for modeling the average behaviors of multi-physical, multiscale phenomena in geological porous media. However, such techniques often rely on a variety of methodological assumptions that prohibit their rigorous application to practical systems (e.g., systems involving heterogeneous porous media, system-scale boundary conditions, and fine-scale dynamics that are not diffusion-dominant). In this work, we aim to formulate an upscaling methodology with few methodological assumptions to provide high levels of model generality and foster the utilization of rigorously-derived upscaled models in practice. In particular, we introduce the Method of Finite Averages (MoFA), a novel upscaling methodology for rigorously modeling heterogeneous porous media and system-scale boundary conditions. We detail MoFA’s implementation for the advective–diffusive transport of a single species and compare the methodology with classic numerical techniques, as well as other rigorous upscaling techniques, to highlight MoFA’s unique combination of rigor and generality. We then validate the derived model while demonstrating its benefits in three numerical experiments. The results suggest that (1.) the applicability and a priori error guarantees of MoFA models do not directly depend on system geometry, (2.) a model’s applicability and error guarantees can be can arbitrarily expanded and reduced, respectively, with further computational expense, and (3.) downscaling with MoFA provides an efficient strategy for generating accurate pore-scale solutions from upscaled results. Ultimately, the results evidence that upscaled models can be rigorously derived for heterogeneous porous media systems and resolved in a fraction of the time it takes to perform the equivalent pore-scale simulations.