Transport Properties Of Porous Media Research Articles

Turbulent Properties of Stationary Flows in Porous Media.

In this study, we investigate the flow dynamics in a fixed bed of hydrogel beads using particle tracking velocimetry to compute the velocity field in the middle of the bed for moderate Reynolds numbers (Re=[124,169,203,211]). We discover that even though the flow is stationary at the larger scales, it exhibits complex multiscale spatial dynamics reminiscent of those observed in classical turbulence. We find evidence of the presence of an inertial range and a direct energy cascade, and are able to obtain a value for a "porous" Kolmogorov constant of C_{2}=3.1±0.3. This analogy with turbulence opens up new possibilities for understanding mixing and global transport properties in porous media.

Diffusion coefficients and MSD measurements on curved membranes and porous media.

We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.

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 FRACTAL MODEL FOR ELECTRICAL CONDUCTIVITY OF POROUS MEDIA EMBEDDED WITH A DAMAGED TREE-LIKE NETWORK

Predicting the electrical conductivity of porous media is important for oil reservoirs, rock physics, and fuel cells. In this work, a cuboid embedded with a damaged tree-like network is employed to denote a portion of porous media. Analytical expressions for the electrical conductivity are then derived with the fractal theory. Various structural parameters have been examined in detail for the influence of electrical conductivity. It is found that the increased number of damaged channels means more difficult ion migration and lower electrical conductivity of porous media. In addition, a decreasing length ratio or an increasing diameter ratio will increase electrical conductivity. Moreover, both the channel distribution fractal dimension and tortuosity fractal dimension result in a decrease in electrical conductivity. A comparison of the results predicted by other models yields a good agreement, validating our proposed model. These results may further interpret the transport properties of porous media.

Effect of gravity on colloidal particle transport in a saturated porous medium: Analytical solutions and experiments.

The colloidal particle transport process in all porous media from laboratory to nature is affected by gravity. In this paper, a mathematical model of colloidal particle migration in a saturated porous medium with the gravity effect is established by combining the gap velocity (advection) with the settling velocity (gravity effect), and an analytical solution of the particle migration problem with time variation of the particle injection intensity is obtained using an integral transformation. The correctness and rationality of the analytical solution are verified by comparing the experimental and theoretical results of the particle migration problem in the point-source transient injection mode. The analytical solution can easily analyze the colloid transport experimental data in a variety of seepage directions. Analysis of the influence of seepage velocities in three different seepage directions on particle transport parameters shows: under the same seepage direction, the peak value of the breakthrough curve increased with an increase in the seepage velocity. The dispersion, adsorption coefficient, and deposition rate decreased with an increase in the seepage velocity. Under the same seepage velocity, the peak value of the breakthrough curve from large to small was vertically downward (VD)> horizontal (H)> vertically upward (VU), the order of dispersion from large to small was vertically downward (VD)>horizontal (H) >vertically upward (VU), the order of the adsorption coefficient and deposition rate of particles from large to small was vertically upward (VU)> horizontal (H) >vertically downward (VD), and the smaller the seepage velocity, the greater the relative differences in the peak value of the breakthrough curve, dispersion, the particle adsorption coefficient, and the deposition rate in the different seepage directions. Therefore, gravity is an important mechanism of particle migration in saturated porous media. The larger the particle size and density were, the smaller the seepage velocity was and the more obvious the effect of gravity. The findings of this study can help for better understanding of colloidal transport properties in porous media under the coupled effects of gravity and hydrodynamics.

Nano-scale Wetting Film Impact on Multiphase Transport Properties in Porous Media

Nano-scale Wetting Film Impact on Multiphase Transport Properties in Porous Media

A new operator-splitting finite element scheme for reactive transport modeling in saturated porous media

The operator splitting approach has been widely accepted since it was introduced as a means to solve reactive transport problems. The conventional operator-splitting finite element scheme (Nodal-OS) handles speciation calculations on nodes, resulting in a mixing of heterogeneous reactions on opposing sides in multi-layer systems. Such mixing, however, is not physically accurate. In this context, we propose a new operator-splitting finite element scheme (IP-OS) for reactive transport modeling in saturated porous media. In contrast to the conventional scheme, speciation calculations are performed on integration points rather than on nodes in the new scheme. The implementation of the IP-OS scheme is verified through comparison with an analytical solution of a coupled diffusion–dissolution problem. On this basis, two representative benchmarks are used to examine the advantages and disadvantages of IP-OS. IP-OS is found to have the following advantages and disadvantages compared to Nodal-OS: (1) IP-OS is more accurate; (2) IP-OS is more straightforward to implement; (3) IP-OS is less sensitive to grid resolution and is numerically more stable with coarser grid spacing; and (4) IP-OS is computationally more expensive. In light of the above pros and cons, we recommend using Nodal-OS in cases where chemical reactions do not affect transport properties, and IP-OS in multi-layer heterogeneous cases where chemical reactions alter transport properties of porous media.

ACCURATE PREDICTION OF PERMEABILITY IN POROUS MEDIA: EXTENSION OF PORE FRACTAL DIMENSION TO THROAT FRACTAL DIMENSION

Fractal characteristic has been considered as the essential parameter to determine transport properties of porous media. Fluid flow in the real porous media is more influenced by the narrow throat system than the relatively large pore system. In this work, the concept of throat fractal dimension is proposed and applied to predict permeability in porous media. First, pore system and throat system of six sandstone rock samples and three carbonate rock samples are divided from the pore network models extracted from rock CT images. Then, fractal dimensions based on the total pore space, pore system and throat system are calculated, respectively, based on the three-dimensional (3D) box-counting method. Three groups of permeabilities are estimated, respectively, using the fractal theory based on the pore space fractal parameter, pore system fractal parameter and the proposed throat system fractal parameter. The results indicate that permeabilities estimated by the proposed throat system fractal parameter are closer to the accurate permeabilities of rock samples compared with that estimated by the pore space fractal parameter and pore system fractal parameter. Our study results reveal that throat fractal dimension should be used to accurately predict fluid transport properties in porous media.

Temperature field prediction for various porous media considering variable boundary conditions using deep learning method

The prediction of temperature fields in porous media is challenging owing to the variable boundary conditions attributed to the working condition and topological structure. In this study, a supervised convolutional neural network (CNN) is built to predict the temperature field and effective thermal conductivity of sphere-packed and irregular porous media under various boundary conditions. Datasets of temperature fields, obtained using lattice Boltzmann method (LBM) simulations based on three-dimensional sphere-packed porous media, are employed to a CNN for training. The CNN achieves an accurate and fast prediction of the temperature field and effective thermal conductivity with different boundary conditions (the temperature differences between the inlet and outlet are 25, 50, 100, 125, 150, 175 °C). The relative errors for the effective thermal conductivity between the CNN and LBM are 0.7–22.8% for the sphere-packed porous media and 3.1–16.0% for the irregular porous media. For a typical case of sphere-packed porous medium with a porosity of 0.6, the computation time using CNN is 1.53 × 10−2 h, while that of LBM is approximately 720 h. These findings mean that the CNN is promising for the prediction of the heat transport properties of porous media with different morphologies and variable boundary conditions.

Pore network modeling of a solid desiccant for dehumidification applications

The development of desiccant-based dehumidification requires a profound understanding of the adsorption–desorption performance and transport properties of porous media. The characterization and modeling of porous media is fundamental to all adsorption and transport studies in porous media. The characteristic properties of porous media, such as pore size distribution (PSD) and connectivity, are usually extracted from complex geometrical and topological information. Pore network modeling (PNM) can also capture these properties without a large computational cost, in contrast to continuum models. In this study, PNM was adopted for the characterization of a silica-based micro sphere gel (M. S. Gel). The PSD of the M. S. Gel was estimated from the adsorption isotherm using a modified Kelvin equation (the Barrett–Joyner–Halenda (BJH) method), which was then corrected by comparison with the PSD obtained from grand canonical Monte Carlo (GCMC) analyses. By contrast, the connectivity was estimated from the desorption isotherm using PNM simulations incorporating the percolation effect, in which the PSD estimated from the adsorption isotherm was employed. Finally, a pore network model of the M. S. Gel with the assigned PSD, connectivity, and porosity without any special pore arrangement was constructed, and the diffusivity of water vapor inside the model was evaluated.

Deciphering porosity clogging at barrier interfaces in deep geological repositories for radioactive waste

Abstract. The disposal of spent nuclear fuels and high-level radioactive wastes in deep geological repositories represents one of the greatest scientific-technical and societal challenges of our times. Most disposal concepts rely on a multibarrier system, consisting of a combination of engineered materials, geotechnical and geological barriers to provide a safe containment of the radioactive waste to protect humans and the environment against dangers arising from ionizing radiation. A reliable safety assessment of a deep geological repository over assessment time scales of several 100 000 years requires a profound and comprehensive understanding of the complex coupled physical (thermal, hydraulic, mechanical), chemical and biogeochemical (THM/CB) processes that govern the long-term evolution of the repository system. As a result of thermal and chemical gradients at the interfaces of different components and materials of the multi-barrier system (e.g. interfaces between metallic waste containers and bentonite backfill or between structural concrete and clay host rock), mineral dissolution and precipitation reactions are promoted; thus the (local) porosity, the volume filled with gas and/or water, can increase or decrease leading to changes in the macroscopic transport properties of the respective media. Although a reduction of the porosity (porosity clogging) appears to be desirable to inhibit radionuclide migration, it can also be detrimental, particularly in the case of gas pressure build-up due to canister corrosion or bacterial activity. So far, porosity clogging at barrier interfaces and associated consequences on solute or gas transport remain poorly understood; currently used mathematical descriptions of porosity clogging in reactive transport codes usually fail to capture respective experimental observations (Chagneau et al., 2015; Deng et al., 2021). In this context, we are developing a “lab-on-a-chip” set-up, which combines time lapse optical microscopy imaging and in operando Raman spectroscopy (Poonoosamy et al., 2019, 2020) to determine (i) whether complete clogging is possible and permanent, (ii) which parameters control the porosity clogging and (iii) which changes in transport properties of porous media are induced due to porosity clogging. Our approach comprises micronized counterdiffusion experiments with in situ visualization and monitoring of the evolution of mineralogy and microstructure/pore architecture with time. Complementary pore scale modelling will be used to derive key relationships that describe changes in transport properties due to mineral precipitation-induced porosity clogging. This approach will help to improve reactive transport codes and their predictive capabilities thus enhancing confidence and reduce uncertainties in long-term predictions, leading to more realistic descriptions of the evolution of complex repository systems.

Pore-Scale Prediction of the oxygen effective diffusivity in porous battery electrodes using the random walk theory

This study developed a predictive model to calculate the effective diffusivity of oxygen in porous electrodes. The model integrates the random walk method and the tomographic technique. We reconstructed pore-scale structures of battery electrodes, and quantitatively studied the effective diffusivity of oxygen in non-wetted and wetted digital geometry. Both the reconstructed geometry and the random walk model were well validated. This model can simulate effective diffusivity with reasonable accuracy and low computational time. Results show that the effective diffusivity of oxygen is very sensitive to the porosity and the electrolyte saturation. A higher porosity improves the oxygen diffusion in a porous medium. On the contrary, the oxygen diffusivity drops significantly when the porous medium is wetted by the electrolyte. At higher saturation (> 0.79), the effective diffusivity is similar to the diffusivity in the liquid. The findings from this study have a strong potential to enhance oxygen mass transfer in porous electrodes and will accelerate the deployment of metal-air batteries. In addition, the advantages of low computational cost, real-time capture of material structures, and wide applicability make this model a powerful and convenient tool to predict transport properties of porous media in a wide range of science and engineering fields.

A FRACTAL MODEL FOR EFFECTIVE THERMAL CONDUCTIVITY OF DUAL-POROSITY MEDIA WITH RANDOMLY DISTRIBUTED TREE-LIKE NETWORKS

It is very difficult to characterize the transport properties of porous media due to the disorder of pores distribution in porous media. In this paper, we study heat conduction through porous media with randomly fractures which are considered as tree-like networks. An expression for effective thermal conductivity (ETC) of saturated dual-porosity media is derived based on the fractal characteristics of pores diameter and fractures size. It is shown that the ETC is a function of structure parameters of the fractal dimension ([Formula: see text]), the porosity ([Formula: see text]), the tortuous fractal dimension ([Formula: see text]) and the maximum diameter ([Formula: see text]) for the porous matrix; the fractal dimension ([Formula: see text]), the porosity ([Formula: see text]), the maximum diameter ([Formula: see text]), the diameter ratio ([Formula: see text]), the length ratio ([Formula: see text]) and the branching levels (n) for the fracture networks. The dependence of structure parameters on the ETC is studied in detail. The results of our model are compared with the available experiments, which show good agreement. The proposed model for the ETC does not contain empirical parameters. The model is useful for predicting the heat conduction of materials.

A fractal-based approach to evaluate the effect of microstructure on the permeability of two-dimensional porous media

The complex and heterogeneous microstructure of underground porous media usually results from geological processes such as deposition, compaction, cementation and fluid-mineral interactions. Variations in these microstructural characteristics largely determine the differences in the transport properties of porous media. The fractal geometry theory has been successfully applied to characterize the microstructure and transport properties of underground reservoirs. In this study, two-dimensional porous media with differently heterogeneous structures are reconstructed by utilizing the quartet structure generation set method. Fractal dimension and lacunarity are implemented to quantify the complex microstructure and analyze the relationships among these parameters. Under specific porosity, the fractal dimension increases with the reduction of lacunarity according to a power law relationship. Meanwhile, permeability has a perfect power law relationship with porosity under the same heterogeneity. The stronger heterogeneity increases the degree of pore aggregation, resulting in increased pore radius for fluid flow. For porous media with the same porosity, permeability has a significant positive power law relationship with lacunarity and a negative relationship with fractal dimension. The results demonstrate that fractal parameters are helpful to fully understand the influence of complex microstructure and chemical reactions on the macroscopic physical properties of porous media.

A Pore‐Scale Investigation of Mineral Precipitation Driven Diffusivity Change at the Column‐Scale

AbstractMineral precipitation affects the pore structure and thus transport properties of porous media. In this study, we investigated the pore‐scale dynamics of precipitation in diffusion controlled systems and the resulting impacts on the effective diffusivity, using a micro‐continuum reactive transport model. Forty two‐dimensional pore structures representing both idealized and realistic geometries were simulated with consideration of different precipitation scenarios and rates. A homogeneous nucleation scenario reproduced patterns observed in previous experimental study showing mixing‐induced precipitation, and a surface growth scenario captured the pattern for mineral precipitation on a substrate with the same or similar mineral structures. In all cases, local precipitation resulted in the reduction in the average porosity of the domain (Φ) until the cessation of diffusive transport and the termination of precipitation. The minimum porosity reached was referred to as the critical porosity (Φc). The effective diffusivity (Deff) decreased with Φ and dropped sharply to effectively zero, that is, the critical effective diffusivity (Deffc), as Φc was reached. These pore‐scale dynamics can be captured by a revised relationship that explicitly considers the critical porosity and the corresponding effective diffusivity, and the pre‐exponential coefficient and the exponent of the relationship varied with initial pore structure and the precipitation kinetics. Overall, the homogeneous nucleation scenario results in systematically larger Φc and coefficients that give rise to a sharper decrease in diffusivity as Φc is approached, compared to the surface growth scenario. The revised relationship was also implemented at continuum scale and used to examine column scale diffusivity change and reactions.

The impact of flow displacement patterns on hydraulic tortuosity for unsaturated flow

Hydraulic tortuosity is one of the key parameters used to characterize the fluid transport properties of porous media. One of the existing debates on hydraulic tortuosity is whether it is an intrinsic property or a correction factor to match the experimental data with a particular model. In this study, a series of immiscible displacement simulations with different capillary numbers and contact angles were established by using the phase field method based on three-dimensional micro-computed tomography images of porous media. Then, the vector-based tortuosity method based on the flow velocity field is used to predict the dynamic evolution of hydraulic tortuosity of unsaturated porous media. Interestingly, the transient hydraulic tortuosity at different flow displacement patterns shows different dynamic evolutions where the quasi-steady-state hydraulic tortuosity is related to both the fluid saturation and the characteristics of the trapped voids in the porous media. These phenomena can be explained by the complex and interesting pore-scale displacement events, including viscous self-correcting smoothing, noncooperative Haines jumps, capillary self-correcting smoothing, and corner flow.

Advances in porous media science and engineering from InterPore2020 perspective

Natural, artificial, and biological porous media can be seen everywhere in our daily lives. Transport phenomena in porous media, such as flow, diffusion, reaction, adsorption and deformation, are encountered in a wide variety of practical applications and scientific interests over widely disparate length scales, from molecular, to pore, core, and field scales. However, determination of transport properties in porous media remains a challenging issue. During the 12th Annual Meeting of the International Society for Porous Media (InterPore), held online from August 31-September 4, 2020, advances on porous media science and engineering in very broad areas were presented. The meeting was attended by more than 750 participants from across the globe, and a significant milestone was achieved in the history of InterPore conferences due to its online interactive platform. Participants could access the pre-recorded talks, leave comments and questions, chat with each other, one week before the conference. Then, all the feedback related to a talk was discussed in the presence of the author during several Q&A sessions. Invited and Keynote talks were live, and were also recorded. Each Q&A session was moderated by two experts, who first reviewed the 8 contributions of their session and then summarized the questions for each talk. The author could further elaborate their work and answer the questions. Cited as : Cai, J., Hajibeygi, H., Yao, J., Hassanizadeh, S.M. Advances in porous media science and engineering from InterPore2020 perspective. Advances in Geo-Energy Research, 2020, 4(4): 352-355, doi: 10.46690/ager.2020.04.02

A new fractal model for porous media based on low-field nuclear magnetic resonance

Fractal geometry has been successfully applied to the study of structures and transport properties of porous media due to its scaleinvariant property. A new fractal probability density (FPD) model is developed to characterize the pore structures of porous media in this paper. Mechanical press filtration (MPF) is performed on pre-dewatered sludge samples in order to achieve different porous structures. The pore structures and water contents of the dewatered porous sludge cakes are then measured by low-field nuclear magnetic resonance (NMR). The pore fractal dimensions are determined with the proposed FPD model based on NMR results. It has been found that the pore fractal dimension increases with porosity under fixed pore size range. The value of the pore fractal dimension of porous samples is larger than 2.6, which indicates highly heterogeneous pore structures. The present work may provide insight on the multiscale structures of porous media based on NMR technique.

A fractal capillary model for multiphase flow in porous media with hysteresis effect

Multiphase flow in unsaturated porous media exhibiting hysteretic phenomenon is of great significance to oil and gas recovery, agriculture, and hydrology etc. Water retention curve (WRC) and relative hydraulic conductivity function (RHC) as well as relative air permeability function (RAP) are usually employed to characterize the transport properties of porous media. A new fractal capillary model accounting for the hysteresis effect is developed in this paper for the multiphase flow in unsaturated porous media. The analytical expressions for WRC, RHC and RAP under drying and wetting paths are derived accordingly. The proposed fractal capillary model shows good consistent with available experimental results. It has been found that the pore-throat structure in the proposed fractal capillary model takes an important influence on the hysteresis effect and fluid flow, especially for the non-wetting phase. The present work may be helpful for understanding the complex mechanisms of hysteresis effect and transport processes in unsaturated porous media.

Predicting Effective Diffusivity of Porous Media from Images by Deep Learning

We report the application of machine learning methods for predicting the effective diffusivity (De) of two-dimensional porous media from images of their structures. Pore structures are built using reconstruction methods and represented as images, and their effective diffusivity is computed by lattice Boltzmann (LBM) simulations. The datasets thus generated are used to train convolutional neural network (CNN) models and evaluate their performance. The trained model predicts the effective diffusivity of porous structures with computational cost orders of magnitude lower than LBM simulations. The optimized model performs well on porous media with realistic topology, large variation of porosity (0.28–0.98), and effective diffusivity spanning more than one order of magnitude (0.1 ≲ De < 1), e.g., >95% of predicted De have truncated relative error of <10% when the true De is larger than 0.2. The CNN model provides better prediction than the empirical Bruggeman equation, especially for porous structure with small diffusivity. The relative error of CNN predictions, however, is rather high for structures with De < 0.1. To address this issue, the porosity of porous structures is encoded directly into the neural network but the performance is enhanced marginally. Further improvement, i.e., 70% of the CNN predictions for structures with true De < 0.1 have relative error <30%, is achieved by removing trapped regions and dead-end pathways using a simple algorithm. These results suggest that deep learning augmented by field knowledge can be a powerful technique for predicting the transport properties of porous media. Directions for future research of machine learning in porous media are discussed based on detailed analysis of the performance of CNN models in the present work.