Properties Of Porous Media Research Articles

Precise derivations of radiative properties of porous media using renewal theory

This work uses the mathematical machinery of Renewal/Ruin (surplus risk) theory to derive preliminary explicit estimations for the radiative properties of dilute and disperse porous media otherwise only computable accurately with Monte Carlo Ray Tracing (MCRT) simulations. Although random walk and Lévy processes have been extensively used for modeling diffuse processes in various transport problems and porous media modeling, relevance to radiation heat transfer is scarce, as opposed to other problems such as probe diffusion and permeability modeling. Furthermore, closed-form derivations that lead to tangible variance reduction in MCRT are widely missing. The particular angle of surplus risk theory provides a richer apparatus to derive directly related quantities. To the best of the authors’ knowledge, the current work is the only work relating the surplus risk theory derivations to explicit computations of ray tracing results in porous media. The paper contains mathematical derivations of the radiation heat transfer estimates using the extracted machinery along with proofs and numerical validation using MCRT.

Resolution-Dependent Multifractal Characteristics of Flow in Digital Rock Twin Simulated Using the Lattice Boltzmann Method

Digital rock twins are widely used to obtain hydraulic properties of porous media by simulating pore-scale fluid flow. Multifractal characteristics of pore geometry and flow velocity distribution have been discovered with two-dimensional (2D) images and three-dimensional (3D) models, whereas the dependency of results on the resolution is not well known. We investigated resolution-dependent multifractal properties of 3D twin models for a sandstone sample with originally 3 μm resolution images. 3D pore-scale water flow was simulated with the lattice Boltzmann method (LBM). As indicated by multifractal analyses, the generalized dimension spectra, the Hölder exponent spectra, and singularity spectra of the flow velocity are similar to that of the pore geometry but different in ranges and sensitivities to the change in the model resolution. Nonlinear dependencies of 2D/3D porosity, holistic/slice permeability, equivalent pore radius squared, and multifractal parameters on the resolution were discussed.

Analysis of complete boiling process inside double pipe porous heat exchanger filled with NanoFluids

This study involves an investigation on fully evaporation process inside annular porous heat exchanger using Cu/distilled water nano-fluid. Emphasis has been placed on how the use of Cu/distilled water affected two-stage flux predictions. Two-phase mixture model, based on the considerations of Local Thermal Equilibrium (LTE), has been reformulated to involve the influences of employing nano-fluid instead of only water. To display the actions of employing nano-fluid, the predictions of liquid saturation and temperature, obtained using Cu/distilled water and only water, have been presented and compared for a wide ranges of geometric conditions, operating conditions and properties of porous media. The outcomes displayed that the using Cu particle to water has a large impacts on the heat diffusivity, where the boiling and condensation fronts are considerably moved to downstream and upstream sections, respectively, as compared to the predictions of only water due to rising the axial diffusion. The temperature at the pipe exit is considerably decreased when adding Cu particles to water as compared to the pure water case. The predications of Cu/distilled water show that the nano-fluid volume fraction, geometric parameters, operating parameters and porous structure properties have high actions on the locations of initiation and termination of phase change process. Since the fluid temperature for pure water case is extremely high at the superheated vapour region, the addition of Cu particles to water considerably reduces the fluid temperature in this region and hence, the use of nano-fluid can be considered as a safety factor in the applications that used heat exchangers (boiling processes) due to it improves the mechanism of heat transfer during the boiling process.

Second-order accurate implicit finite volume method for two-dimensional modeling of PFAS transport in unsaturated porous media with variable surface tension

Per- and polyfluoroalkyl substances (PFASs) have become emerging contaminants of critical concern. Comprehensive understanding of the transport and fate of PFAS in the vadose-zone, a type of water-unsaturated porous media, is key to determination of the risks of the PFAS contamination in the subsurface and to the development of the effective remediation strategies. Accurate modeling of the PFAS transport in the unsaturated porous media is still a challenge due to the variable surface tension induced by the adsorption of PFAS to the air-water interfaces. In an effort to address this challenge, we propose a multidimensional modeling framework for the transient PFAS transport in the unsaturated porous media based on the second order accuracy finite volume method. In the modeling, the adsorption of PFAS to the solid surfaces and to the air-water interfaces is described by the two-domain sorption kinetics model, i.e., both the instantaneous and the rate limited PFAS adsorptions are taken into account. The diffusive and convective terms in the governing equations for the PFAS transport and the water flow are discretized by the central difference and the quadratic upstream interpolation for convective kinetics schemes, respectively. We investigate the effects of the convergent criteria, coupling method, and variation of the surface tension on the average and the local PFAS concentration and water content in the computational domain. We find that the convergent criteria should be chosen carefully so as to get the accurate results. The differences between the different coupling methods are affected by the boundary conditions. The variation in the surface tension due to the variation of the PFAS concentration cannot be neglected. The dimensionless parameters relevant to the properties of porous media as well as the relation between the surface tension and the PFAS concentration play an important role in transport of PFAS in the unsaturated porous media. The effects of the Péclet number, Damköhler values, and fraction of instantaneous sorption are not significant in the ranges studied in this work. These findings provide a better understanding of transport of PFAS in the vadose zone.

Pore-morphology-based pore structure characterization for various porous media

Quantitative characterization of pore structure plays an important role in predicting properties of porous media and it has significant applications in energy and chemical engineering. Mercury injection capillary pressure experiments and gas adsorption experiments are the major pore structure characterization techniques, but they are time-consuming, costly, and destructive. In this paper, a simple pore-morphology-based method is developed to simulate the mercury injection and gas pore condensation in CT image for obtaining the pore structure characteristics. The main idea of the developed algorithm is to utilize some of the morphological operations to capture the pore geometry and topology, and then combine with the invasion phase connectivity analysis to implement the mercury injection and gas pore condensation. The algorithm is designed in several ways with an improved computational speed and characterization accuracy. The algorithm is user-friendly and can be applied on 2D and 3D images. Various porous media are used to assess the performance of the algorithm and the characteristics of pore structures. The results are compared to the available results in the literature. Findings show that the algorithm can reliably quantitatively characterize the pore structure for a wide variety of porous media. The general pore radius distribution, pore throat radius distribution, and strict throat radius distribution involved in pore structure characterization are clarified. The characterization of heterogeneous pore structures and the effects of pore roughness on capillary pressure are discussed.

Local thermal equilibrium analysis of complete phase change process inside porous diffuser using NanoFluids

This works implements an investigation on two-phase flow inside porous diffuser using Cu/water nanofluid instead of pure water. Interesting has been focused on how the using Cu/water affect the predictions of complete boiling process. Two-phase mixture model (TPMM), based on the assumptions of Local Thermal Equilibrium (LTE), has been converted to implement the actions of combining nano-fluid rather only water. The governing equations are solved by finite volume method. For the purpose of comparison, the solutions of temperature and liquid saturation, obtained employing Cu/water and only water as working fluid, have been displayed for a wide ranges of geometric parameters, operating parameters and properties of porous media to investigate impacts of using nanofluid. The findings illustrated that the adding Cu particle to water has a high influences on the heat diffusivity inside the diffuser as compared to the solutions of only water due to enhancing the axial diffusion. By employing Cu/water, the boiling and condensation fronts are considerably moved to downstream and upstream sections, respectively. The exit temperature is significantly reduced when utilizing Cu/water as compared to the only water solution. The findings of Cu/water show that the volume fraction of nano-fluid, operating conditions, geometric conditions and porous structure properties have large impacts on the locations of liquid and steam fronts. Accordingly, the nano-fluid is supposed as a safety key in the boiling applications since it improves the technique of heat transfer while simulating the complete boiling process.

A direct methanol fuel cell with outstanding performance via capillary distillation

Facing the severe challenge of methanol crossover, direct methanol fuel cell (DMFC) can hardly operate under high-concentration fuel supply without additional structures, which inevitably restrains its energy density and increases integration difficulty. To address this problem, capillary distillation has been applied for the first time in this work to regulate methanol–water evaporation where a reduced relative volatility of methanol/water and a decreased methanol flux have been realized. A theoretical model has been established to illustrate the impact of porous media properties on the evaporation procedure, followed by a specifically designed experiment which intuitively proves the reduced methanol/water relative volatility via the chosen carbon aerogel. The proposed approach significantly alleviates methanol crossover and water starvation by providing a suitable methanol/water ratio in the vapor supply for DMFCs and thus it could directly operate under high-concentration methanol with a minimal structure, showing an outstanding performance (22 mW cm−2 at 16 mol/L) and stability (a stable output of 20 mW cm−2 for 6 h). The proposed approach not only opens a brand-new window for the design of an all-solid-state /flexible DMFC of high specific energy density, but also expands the potential of DMFC integration, tremendously promoting its development and application in microsystems.

Digital Core Permeability Computation by Image Processing Techniques

Calculation of REV (representative elementary volume) properties of geological porous media refers to the process of creating a 3D digital representation of a rock sample, typically obtained from imaging techniques such as X-ray microtomography. This technique allows for a detailed analysis of the internal structure and the properties of rocks, as well as precise calculation of various flow parameters. However, one major challenge with calculation of REV properties of geological porous media is the high computational cost required to generate accurate results, especially for large and complex samples. In this study, we constructed 3D digital cores of dune sand and fractured shale using CT scanning technology, and then used two image processing techniques, namely digital core image resampling and cutting, to reduce the computational cost of calculating digital core permeability. Next, a fast permeability calculation method is employed to reduce the complexity of permeability calculation. Finally, we summarized the applicability of different image processing methods to different rock samples, and provided prerequisites for high computational cost digital core permeability calculation.

Moment analysis for predicting effective transport properties in hierarchical retentive porous media

We report on a new homogenization approach to solve, with drastically improved speed and accuracy, the general advection-diffusion equation in hierarchical porous media with localized diffusion and adsorption/desorption processes, thus opening the way to a much deeper understanding of the band broadening process in chromatographic systems. The proposed robust and efficient moment-based approach allows us to compute the exact local and integral concentration moments and hence provides exact solutions for the effective velocity and dispersion coefficients of migrating solute particles. Innovative to the proposed method is also that it not only produces the exact effective transport parameters of the long-time asymptotic solution, but also their entire transient. The analysis of the transient behaviour can be used, for example, to properly identify the time and length scales needed to achieve the macro-transport conditions. If the hierarchical porous media can be represented as the periodic repetition of a unit lattice cell, the method only requires the solution of the time-dependent advection-diffusion equations for the zeroth order and first-order exact local moments, exclusively on the unit cell. This implies an enormous reduction of the computational efforts and a significant improvement of the accuracy of the results when compared to the direct numerical simulation (DNS) approaches which require flow domains that are long enough to achieve steady-state conditions, and hence often cover tens to hundreds of unit cells. The reliability of the proposed method is verified by comparing its predictions with DNS results, in one, two and three dimensions, in both transient and asymptotic conditions. The influence of top and bottom no-slip walls on the separation performance of chromatographic columns with micromachined porous and nonporous pillars is discussed in detail.

On the Optimal Conductivity of Packed Two-Dimensional Dispersed Composites

Optimal packing is applied in physics for investigation of macroscopic properties of composites and porous media. The present paper demonstrates that the optimal packing of perfectly conducting disks on the plane corresponds to the minimal effective conductivity for macroscopically isotropic composites. Such an optimal location is studied and compared to the pure geometric problem for disks packing on the flat torus. The hexagonal (triangular) array of disks solves the problem for the triangle lattice numbers . The rest of the cases are investigated separately by minimization of structural sums constructed by means of the Eisenstein functions.

Estimating Permeability and Its Scale Dependence at Pore Scale Using Renormalization Group Theory

AbstractInvestigating hydraulic and petrophysical properties of porous media has been an active area of research. Despite numerous progress in modeling flow and transport over the past decades, we are still far from accurately estimating the scale dependence of soil and rock properties. In this study, we propose applying renormalization group theory (RGT) at the pore scale. Using the RGT, we determine the scale dependence of effective pore‐throat radius (rteff) and develop two theoretical models to estimate permeability (k) in pore networks of various sizes. The first theoretical model estimates k(L) from the rteff(L) and simulated formation factor F(L), while the second model uses information at the smallest scale (L = Lmin) in addition to rteff(L) and F(L). By comparing with 25 pore‐network simulations, we show that the RGT estimates the scale‐dependent k reasonably well. The first model estimates k(L) with average relative errors ranged between −53.1% and −3.0%, while the second model between −1.0% and 14.33%. We also conduct fluid flow simulations in 40 other pore networks above the representative elementary volume and compare the results of the RGT with those of the effective‐medium approximation (EMA). Results showed that both RGT and EMA accurately estimate k from pore‐throat radius distribution and formation factor with root mean square log‐transformed error = 0.119 and 0.096, respectively.

Comparing methods for permeability computation of porous materials and their limitations

AbstractEfficient numerical simulations of fluid flow on the pore scale allow for the numerical estimation of effective material properties of porous media, e.g. intrinsic permeability or tortuosity. These parameters are essential for various applications where hydro‐mechanical properties on larger scales have to be known. Numerical tools based intrinsically on pore scale simulations are known e.g. as Digital Rock Physics in geosciences and have even more and more replaced physical experiments. For these reasons, the validation of numerical methods as well as the establishment of clear limits regarding the application areas play an important role. Here, we compute single‐phase flow through a porous matrix, e.g. irregular sphere packings, sandstones, artificially created thin porous media, on the pore scale. Therefore we implement on the one hand a Smoothed Particle Hydrodynamics algorithm for solving the Navier‐Stokes equations and on the other hand a Finite Difference solver for the Stokes equations. Both methods work directly and seamlessly on voxel data of porous materials which are generated by µXRCT‐scans or by microfluidic experiments that have undergone segmentation and binarization. We compare both solvers from a parallel performance point of view as well as their results for flows in the Darcy regime. In addition, we investigate the limitations of the solvers using the example of a porous material whose pore geometry changes over time and precipitation affects the flow conditions.

Understanding the role of water evaporation and condensation in applied smoldering systems

Accurately resolving the way energy is stored and transferred is critical to applied smoldering systems in porous media. Water evaporation and condensation are important mechanisms in the energy conservation of smoldering. This is particularly important when significant water presence can affect the potential for self-sustained smoldering as it occurs in a broad range of practical applications. This paper describes a one-dimensional smoldering model considering water phase change. The model was calibrated to a series of wet smoldering experiments of GAC varying initial water saturation from 5 to 20%. The results show that introducing simple calibration constants on the thermal properties of a wet porous medium can accurately predict the transient and spatial resolution of the progression of evaporation, condensation, and smoldering reactions. A sensitivity analysis suggests that wet smoldering could be improved by increasing fuel concentration and injected airflow, which provides practical insights into wet smoldering applications. In addition, the model was applied to establish five characteristic zones for the wet smoldering front: evaporation, condensation, pre-heating, smoldering, and cooling. The evaporation and condensation zones challenge smoldering propagation due to the high water saturation. The pre-heating zone represents the region separating the smoldering front and evaporation zone, which serves as an important dry buffer and requires a minimum thickness (4 mm) to avoid extinction.

The effects of water table fluctuation on LNAPL deposit in highly permeable porous media: A coupled numerical and experimental study

Light Non-Aqueous Phase Liquid (LNAPL) flow on the water table is highly mobile and is sensitive to the fluctuation of groundwater. This process is highly complex and involves the migration of three immiscible phases (i.e. water, LNAPL and air) which need the explicit definition of multiple parameters. A coupled experimental and numerical simulation methodology is performed by using Time Domain Reflectrometer (TDR) and multiphase simulation of a controlled environment to mimic the water table fluctuation and its effect on the LNAPL residual saturation. TDR probes are installed in different locations of a 2D tank (i.e. a cuboid box with relatively low off-plane thickness) and the bulk permittivity of the phases are measured through artificially imposed boundary conditions. The bulk permittivity is then translated into saturation of the three different phases. The translated residual saturations along with the previously measured porous media properties (e.g. porosity and saturated permeability) are then inserted into the numerical simulator (i.e. COMSOL Multiphysics®) and the migration of the three phase in porous media is simulated. The numerical exponents and entry pressures needed for the simulation of the multiphase flow are estimated using the temporal experimental values. The exponents of water LNAPL relative permeability were estimated to be around 2 while the exponents gas LNAPL relative permeability were estimated to be closer to 3. The results, simulated with the optimized parameters, are then evaluated with pictures taken from the transparent face of the 2D tank different stages of the experiment. The temporal evolution of different phase saturation has been compared and validated between the experimental results obtained and interpreted by the TDR probe measurements and the simulations. The relative error stays in the 5 % confidence level for most reported points and only in the highly dynamic flow time steps the error reaches around 12% which are discussed in the text and is accepted due to the highly nonlinear nature of the problem.

A Three-Phase Relative Permeability Model for Heavy Oil Emulsion System

Chemical flooding is important and effective enhanced oil recovery processes are applied to improve the recovery of heavy oil reservoirs. Emulsification occurs during chemical flooding processes, forming an oil-in-water (O/W) emulsion system. In this work, the heavy oil emulsion system is characterized as a three-phase (continuous oil phase, dispersed oil phase, and continuous water phase) system. Based on a capillary tube model, a new relative permeability model is proposed to describe the flow of the emulsion system in porous media quantitatively, considering the physicochemical properties of emulsions and the properties of porous media. A resistance factor is derived in this model to describe the additional resistance to the emulsion flow caused by the interaction between dispersed oil droplets and the pore system. Three dimensionless numbers related to the emulsion porous flow process were proposed and their different effects on the three-phase relative permeability are investigated. To validate the reliability of the proposed model, a one-dimensional O/W emulsion–oil displacement experiment is simulated. The maximum absolute error between the simulated results and experimental data is no more than 10%, and the new model can be used to describe the flow behavior of heavy oil emulsions in porous media.

Deep learning for multiphase segmentation of X-ray images of gas diffusion layers

High-resolution X-ray computed tomography (micro-CT) has been widely used to characterise fluid flow in porous media for different applications, including in gas diffusion layers (GDLs) in fuel cells. In this study, we examine the performance of 2D and 3D U-Net deep learning models for multiphase segmentation of unfiltered X-ray tomograms of GDLs with different percentages of hydrophobic polytetrafluoroethylene (PTFE). The data is obtained by micro-CT imaging of GDLs after brine injection. We train deep learning models on base-case data prepared by the 3D Weka segmentation method and test them on the unfiltered unseen datasets. Our assessments highlight the effectiveness of the 2D and 3D U-Net models with test IoU values of 0.901 and 0.916 and f1-scores of 0.947 and 0.954, respectively. Most importantly, the U-Net models outperform conventional 3D trainable Weka and watershed segmentation based on various visual examinations. Lastly, flow simulation studies reveal segmentation errors associated with trainable Weka and watershed segmentation lead to significant errors in the calculated porous media properties, such as absolute permeability. Our findings show 43, 14, 14, and 3.9% deviations in computed permeabilities for GDLs coated by 5, 20, 40, and 60 w% of PTFE, respectively, compared to images segmented by the 3D Weka segmentation method.

Multiscale reconstruction of porous media based on multiple dictionaries learning

Digital modeling of the microstructure is important for studying the physical and transport properties of porous media. Multiscale modeling for porous media can accurately characterize large-pores and fine-pores in a large-FoV (field of view) high-resolution three-dimensional pore structure model. This paper proposes a multiscale reconstruction algorithm based on multiple dictionaries learning, in which edge patterns and fine-pore patterns from homology high-resolution pore structure are introduced into low-resolution pore structure to build a fine multiscale pore structure model. The qualitative and quantitative comparisons of the experimental results show that the results of multiscale reconstruction are similar to the real high-resolution pore structure in terms of complex pore geometry and pore surface morphology. The geometric, topological and permeability properties of multiscale reconstruction results are almost identical to those of the real high-resolution pore structures. The experiments also demonstrate the proposal algorithm is capable of multiscale reconstruction without regard to the size of the input. This work provides an effective method for fine multiscale modeling of porous media.

A novel analytical model for porosity-permeability relations of argillaceous porous media under stress conditions

Argillaceous rocks, such as sandstones, shales, and mudstones, are widely distributed in nature and constitute approximately 50% of the global sedimentary rocks. They are the conventional reservoir rocks for hydrocarbon resources. To better characterize hydrocarbon resources, it is essential to understand the fundamental physical properties of argillaceous porous media (APM), and one of the most crucial properties is the porosity-permeability relationship (PPR). However, due to the enormous complexity of pore structures in APM, the effects of relevant factors on PPR remains unclear, and the major factors controlling PPR are still open questions. In this work, experimental tests were carried out on 43 artificial argillaceous sandstone samples to evaluate the porosity and permeability relations under stress dependence. An analytical model was then proposed to interpret the experimental results. The analytical solutions are consistent with the experimental data and the simulation results obtained from the Lattice Boltzmann method. It indicates that the derived model can precisely capture the PPR of APM. The analysis results show that the PPR of APM under stress dependence is related to clay volume content, effective stress, initial irreducible water saturation, rock lithology, and pore structure parameters (e.g., the maximum pore radius, the minimum pore radius, pore fractal dimension and tortuosity fractal dimension). These findings can enhance the understanding of the PPR and coupled flow-deformation behavior in APM and set the stages for a proper investigation of PPR in APM.

Influence of inter-grain cementation stiffness on the effective elastic properties of porous Bentheim sandstone

Effective elastic properties of porous media are known to be significantly influenced by porosity. In this paper, we investigated the influence of another critical factor, the inter-grain cementation stiffness, on the effective elastic properties of a granular porous rock (Bentheim sandstone) using an advanced numerical workflow with realistic rock microstructure and a theoretical model. First, the disparity between the experimentally tested elastic properties of Bentheim sandstone and the effective elastic properties predicted by empirical equations was analysed. Then, a micro-computed tomography (CT)-scan based approach was implemented with digital imaging software AVIZO to construct the 3D (three-dimensional) realistic microstructure of Bentheim sandstone. The microstructural model was imported to a mechanics solver based on the 3D finite element model with inter-grain boundaries modelled by cohesive elements. Loading simulations were run to test the effective elastic properties for different shear and normal inter-grain cementation stiffness. Finally, a relation between the macroscale Young's modulus and inter-grain cementation stiffness was derived with a theoretical model which can also account for porosity explicitly. Both the numerical and theoretical results indicate the influence of the inter-grain cementation stiffness, on the effective elastic properties is significant for porous sandstone. The calibrated normal and shear stiffnesses at the inter-grain boundaries are 1.2 × 105 and 4 × 104 GPa/m, respectively.

Double-diffusive magneto-natural convection of nanofluid in an enclosure equipped with a wavy porous cylinder in the local thermal non-equilibrium situation

The emphasis of this study is the numerical analysis via finite volume method of magneto-natural convection induced by double-diffusion of a nanofluid within an enclosure equipped with a wavy porous cylinder. The porous cylinder which is under the local thermal non-equilibrium (LTNE) situation is modeled using Darcy-Brinkman-Forchheimer design as momentum equation. Results are interpreted and evaluated in terms of the dimensionless controlling variables such as Rayleigh number (Ra), Lewis number (Le), Hartman number (Ha), buoyancy ratio parameter (N), Darcy number, (Da), and medium's porosity (ε) at a given heat transfer coefficient for the solid/fluid inter-phase (H) and modified conductivity ratio (γ) of the porous wavy cylinder region. Corcione's correlations with 4% of Al2O3 nanoparticles is used to estimate nanofluid's thermal conductivity and viscosity. Findings show that the heat and mass transfers are improved by Ra, Da, and ε augmentation and Ha and Le diminution. In general, as Le increases, the mass transfer rate rises while the corresponding heat transfer rate drops. Also, we identified a value of N where Le-dependent heat and mass transfer rates are minimal. Moreover, the heat transfer rate is found to be more sensitive to the changes in the porous medium's properties of the wavy porous cylinder than the mass transfer rate. Furthermore, the LTNE situation everywhere exists in the porous wavy cylinder except for the center where the LTE is realized.