Diffusion In Porous Media Research Articles

Analysis of degenerate Burgers' equations involving small perturbation and large wave amplitude

We only focus on the shock waves to Burgers system by considering the porous medium diffusion and singularity in energy estimates. In this paper, the conditions and are considered. Moreover, we establish the existence of shock waves through the phase plane. The weighted function is employed to handle the singularity in the weighted energy estimates under small perturbations and arbitrary wave amplitudes. Finally, the weighted energy estimates are then used to prove the stability of shock waves.

Numerical simulation study on the effect of temperature on the restricted diffusion in porous media

It is of great significance to study how temperature affects the restricted diffusion in pores for an accurate evaluation of reservoir physical properties by using nuclear magnetic resonance (NMR) diffusion-transverse relaxation (D-T2) spectrum under reservoir temperature conditions. In this paper, we simulate the restricted diffusion and two-dimensional (2D) NMR D-T2 spectra of water molecules at different temperatures using random-walk method. The one-dimensional (1D) restricted diffusion simulation results show that the diffusion coefficient in the pore at room temperature decays with the diffusion time and eventually reaches a plateau. Under the condition of long-time diffusion, the ratio of restricted diffusion coefficient to bulk diffusion coefficient at different temperatures tends to be the same constant. With the increase in temperature, the simulated D-T2 spectra also gradually move upward. The simulated D-T2 spectra at all temperatures are consistent with the Padé interpolation equation. In addition, the results calculated by Padé interpolation equation demonstrate that the degree of temperature influence on the D-T2 spectrum of rock is quantitatively related to the pore radius, porosity and cementation index.

Pore-scale hydro-mechanical modeling of gas transport in coal matrix

We present a 3D model coupling a discrete element model and a pore network model specifically developed to describe the different diffusion mechanisms at stake in coal matrix as well as the associated adsorption induced deformations. The material is assumed to be saturated with gas and diffusion occurs through the combination of Knudsen diffusion within the pore space, surface diffusion at the solid surface, and adsorption–desorption at the pore-solid interface. The model is hydro-mechanically coupled in the sense that changes in pore pressure produce hydrostatic forces that deform the solid skeleton, while deformation of the pore space induces pore pressure changes that promote interpore flow. Sorption induced deformations are taken into account by considering an additional pressure term related to the concentration of gas within the medium (the so-called solvation pressure). The implemented transport models are verified against analytical solutions describing diffusion in porous media with and without sorption–desorption, and a comparison is made with a swelling experiment performed on a coal specimen to illustrate the relevance of the proposed approach for describing adsorption induced deformation. As a result, this new pore-scale model offers a precise way to assess coal matrix sorption induced deformation and contributes to the knowledge of CBM storage and transport processes.

General framework to construct local-energy solutions of nonlinear diffusion equations for growing initial data

This paper presents an integrated framework to construct local-energy solutions to fairly general nonlinear diffusion equations for initial data growing at infinity under suitable assumptions on local-energy estimates for approximate solutions. A delicate issue for constructing local-energy solutions resides in the identification of weak limits of nonlinear terms for approximate solutions in a limiting procedure. Indeed, such an identification process often needs the maximal monotonicity of nonlinear elliptic operators (involved in the doubly-nonlinear equations) as well as uniform estimates for approximate solutions; however, even the monotonicity is violated due to a localization of the equations, which is also necessary to derive local-energy estimates for approximate solutions. In the present paper, such an inconsistency is systematically overcome by reducing the original equation to a localized one, where a (no longer monotone) localized elliptic operator is decomposed into the sum of a maximal monotone operator and a perturbation, and by integrating all the other relevant processes. Furthermore, the general framework developed in the present paper is also applied to the Finsler porous medium and fast diffusion equations, which are variants of the classical PME and FDE and also classified as a doubly-nonlinear equation.

Diffusion Model of Cement Slurry in Porous Media Considering Porosity Variation and Percolation Effect

The porosity of porous media is a key factor affecting cement slurry diffusion. In this paper, a theoretical model of cement slurry diffusion in porous media considering the variation of porosity is proposed. The model is validated through comparison with the experimental results in the literature. The influence of injection parameters (i.e., the water–cement ratio and the pore fractal dimension) on the porosity and strength of porous media is analyzed. The results indicate that: under the same pore fractal dimension, the porosity of the specimen increases gradually with the increase in diffusion distance, and the rate increases rapidly in the later stage. However, when the fractal dimension of porosity increases to 2.1, the porosity of the consolidated body after grouting does not change with the diffusion distance. The water–cement ratio also affects the porosity of the sample. At a distance below 1.0 m, the sample porosity is larger at a larger water–cement ratio of 1.5. When the distance is more than 1.0 m, the smaller the porosity decreases with increasing water–cement ratios. With the increase in distance, the compressive strength of the specimen first decreases slowly, and then rapidly from 90 kPa to 0 kPa. This is further verified by the pore variation law obtained by SEM. The model is applied to selecting grouting parameter design in road maintenance. The pavement deflection after grouting is effectively reduced, verifying the theoretical model’s applicability.

WHAT IS THE MAXIMAL POSSIBLE SOIL METHANE UPTAKE?

WHAT IS THE MAXIMAL POSSIBLE SOIL METHANE UPTAKE?

Parabolic methods for ultraspherical interpolation inequalities

<p style='text-indent:20px;'>The <i>carré du champ</i> method is a powerful technique for proving interpolation inequalities with explicit constants in presence of a non-trivial metric on a manifold. The method applies to some classical Gagliardo-Nirenberg-Sobolev inequalities on the sphere, with optimal constants. Very nonlinear regimes close to the critical Sobolev exponent can be covered using nonlinear parabolic flows of porous medium or fast diffusion type. Considering power law weights is a natural question in relation with symmetry breaking issues for Caffarelli-Kohn-Nirenberg inequalities, but regularity estimates for a complete justification of the computation are missing. We provide the first example of a complete parabolic proof based on a nonlinear flow by regularizing the singularity induced by the weight. Our result is established in the simplified framework of a diffusion built on the ultraspherical operator, which amounts to reduce the problem to functions on the sphere with simple symmetry properties.</p>

Diffusivity of porous media considering the coupling influence of pore shape- and size-polydispersities on the percolation: Theoretical and numerical studies

Aggressive media in the environment will penetrate into the porous media through the connected pore channels, causing damage to the microstructure and reducing the working performance. In statistical physics, the connectivity of porous network is usually described by the concept of percolation. A critical yet unresolved subject has been how to adequately capture the percolation thresholds of these complex porous network including polyshaped–polysized pores, and their quantitative implications on the transport property of porous media. This paper presents theoretical and numerical approaches for precisely determining the effects of pore shape- and size-polydispersities on percolation thresholds and diffusivity of porous media. Combining the Monte Carlo simulation with finite-size scaling analysis, the statistical values of percolation thresholds are obtained. Incorporating the proposed pore size-polydispersity degree with the excluded volume, the influences of pore shape- and size-polydispersities on the percolation thresholds are characterized. Substituting the percolation thresholds into generalized effective medium theory, the diffusivities of porous media are theoretically predicted. Moreover, the lattice Boltzmann method is employed to numerically calculate the diffusivity. Comparison with the theoretical, numerical and experimental results reveals the present model can accurately predict the percolation thresholds and diffusivities of porous media. The results indicate that the enhancing of the pore excluded volume and the decline of the pore size-polydispersity degree will decrease the percolation threshold and increase the diffusivity. This work can provide novel insights into understanding the complex interactions between the composition (pore shape- and size-polydispersities), microstructure (percolation threshold), and macro-property (diffusivity) of porous media.

A chemotaxis‐Stokes system with nonhomogeneous boundary condition: Global large‐datum solution and asymptotic behavior

AbstractIn this paper, we study the global solvability and stabilization to a chemotaxis‐Stokes model with porous medium diffusion and mixed nonhomogeneous boundary value conditions in three‐dimensional space. When m is slightly bigger than 1, we can get a solution with strong regularity, but when m is close to 1, the regularity of the solution becomes weak. Specifically, our results are divided into two cases: (i) and (ii) . For case (i), we obtain a global bounded weak existence with good regularity for any initial datum, and for decay incoming oxygen, we also prove that the bounded solution will converge to a constant steady state. But for case (ii), it is hard to obtain the boundedness of solutions, and a global “very” weak solution is obtained.

CO2 transport and carbonate precipitation in the coupled diffusion-reaction process during CO2 storage

During geological CO2 storage and utilization, CO2 plume migration forms widespread static retention regions including the dead-end fractures and pores in the host rock, where the mass transfer is dominated by diffusion. A series of packed column experiments with natural olivine were conducted to investigate how the coupled CO2 diffusion–reaction process influences the CO2 transport and the temporal-spatial evolution of carbonate precipitation in diffusion-limited zones. The carbonate precipitations were mainly magnesite, and some dolomite due to the combined effect of carbonate precipitation kinetics and the low Ca content of the solution with Mg enrichment. Compared with the pure diffusion in porous media, the geochemical gradients in the pore solution resulting from the coupled diffusion–reaction interaction promoted mass transfer and broad migration, which led to an increase in effective diffusion coefficients of CO2 by approximately-one order of magnitude. The free water layer and pressure mode could affect the distribution of carbonate precipitation and the overall sequestration capacity. In particular, the coupled CO2 diffusion–reaction interaction under pressure decay mode could accelerate the carbonation in the deep region in the water-saturated column. This study advances the fundamental understanding on the transport and reaction of injected CO2 for mafic and ultramafic formations.

Mechanism and influence factor of hydrocarbon gas diffusion in porous media with shale oil

Due to the compactness of shale reservoir matrix and the high conductivity of fractures, the hydrocarbon gas injection huff and puff method or displacement is the most realistic technology to improve shale oil recovery. The diffusion mechanism plays an important role in shale oil development; therefore, it is crucial to figure out the factors influencing diffusion, which could enhance shale oil recovery. In this paper, a physical simulation experiment is designed to evaluate the diffusion ability of hydrocarbon gas. Diffusion experiments are conducted to simulate diffusion in the bulk fluid and in the porous media, to learn about how the pressure, permeability and fracture affect the diffusion behavior. The diffusion coefficients between the bulk diffusion and core sample diffusion are compared. The experimental results show that the diffusion coefficient and mass transfer capacity are positively correlated with permeability and pressure: increasing these parameters can promote the diffusion process. The diffusion coefficient of hydrocarbon gas in a saturated oil core is significantly less than that in crude oil, which indicates that the porous media seriously affects the process of gas diffusion in crude oil. Fractures have little impact on the diffusion behavior. Combined with numerical simulation, the influencing factor of diffusion on the development effect of hydrocarbon gas injection is clarified. The recovery enhances and then decreases with the increasing diffusion coefficient. Cited as: Wanyan, Z., Liu, Y., Li, Z., Zhang, C., Liu, Y., Xue, T. Mechanism and influence factor of hydrocarbon gas diffusion in porous media with shale oil. Advances in Geo-Energy Research, 2023, 7(1): 39-48. https://doi.org/10.46690/ager.2023.01.05

Convolutional neural network based prediction of effective diffusivity from microscope images

This study presents a method to predict the effective diffusivity of porous media from a limited set of scanning electron microscope images using deep learning. The electrodeposited nickel oxide film over carbon nanostructure, meant to provide electrochemical capacitance based on diffusion of ions through the film's pore space, was observed under the scanning electron microscope. Gray scale SEM images were converted to binary images, and the effective diffusivity was found using lattice Boltzmann simulations. A convolutional neural network (CNN) model comprising two sets of convolution and pooling layers and a fully connected layer was trained with lattice Boltzmann method data, where the choices of kernel size and stride were made, keeping the homogeneity of the image in perspective. An initial attempt to train a CNN with 900 training instances predicted effective diffusivity with a relative error of 13.33%, 43.49%, and 36.41% for the training, validation, and test set, respectively. However, it was over-predicting the diffusivities for images with very low connectivity. Isolated pores within the images were identified and were eliminated to solve this issue before using the images to train another CNN. This second network worked well for images with low connectivity and brought down the mean relative error from 36.41% to 25.43% for the test set. The error was found to vary across the images due to highly non-even representation of different image types, increasing by complex pore connectivity at lower porosity for which the number of training instances is the least, and overfitting of networks on medium porosity images that are present in greater numbers. The SEM images were further classified based on porosity as well as pore connectivity. The training was performed with one category of images, and the testing was conducted with images of another category at the other end of the spectrum to evaluate CNN efficacy upon encountering a new category of images. The results show the ability of the network to extend the prediction to an unknown electrode morphology, which is critical for the analysis of SEM images.

Bounded weak and strong time periodic solutions to a three-dimensional chemotaxis-Stokes model with porous medium diffusion

In this paper, we study the time periodic problem to a three-dimensional chemotaxis-Stokes model with porous medium diffusion Δnm and inhomogeneous mixed boundary conditions. By using a double-level approximation method and some iterative techniques, we obtain the existence and time-space uniform boundedness of weak time periodic solutions for any m > 1. Moreover, we improve the regularity for m≤43 and show that the obtained periodic solutions are, in fact, strong periodic solutions.

Modelling of filamentous phage-induced antibiotic tolerance of P. aeruginosa.

Filamentous molecules tend to spontaneously assemble into liquid crystalline droplets with a tactoid morphology in environments with high concentration on non-adsorbing molecules. Tactoids of filamentous Pf bacteriophage, such as those produced by Pseudomonas aeruginosa, have been linked to increased antibiotic tolerance. We modelled this system and show that tactoids composed of filamentous Pf virions can lead to antibiotic tolerance by acting as an adsorptive diffusion barrier. The continuum model, reminiscent of descriptions of reactive diffusion in porous media, has been solved numerically and good agreement was found with the analytical results, obtained using a homogenisation approach. We find that the formation of tactoids significantly increases antibiotic diffusion times which may lead to stronger antibiotic resistance.

Multi-factor sensitivity analysis of chloride ingression: A case study for Hangzhou Bay Bridge

The transport of chloride into concrete is affected by many factors, including temperature, relative humidity, load cracks, and material properties. The purpose of this paper is to analyze the influence of various factors on the chloride ingression process through a case study for Hangzhou Bay Bridge located in marine environment. Firstly, based on the concentration of free chloride in pore solution, a porous media diffusion model is derived, considering the chloride adsorption term. Then, chloride adsorption isotherm, time-varying diffusion coefficient, temperature, relative humidity, and macroscopic cracks are simulated respectively by the porous media diffusion model. The main conclusions are as follows: (1) The chloride adsorption effect and time-varying diffusion coefficient have a great influence on the numerical results, which cannot be ignored in any case. (2) The natural temperature and relative humidity conditions of the case have a small effect on the simulation results. (3) Under the marine atmospheric environment, the macroscopic load cracks have a small influence on chloride ingression in the long term.

Fractal analytical solution of gas diffusivity in heterogeneous porous media over the entire saturation range

The gas diffusivity of porous media under dry and wet conditions is valuable in many science and engineering fields, but its accurate measurement remains challenging and time-consuming. This study develops a fractal theoretical model to predict the diffusion behavior of gas in heterogeneous porous media over the entire saturation range. In this model, the pore space is conceptualized as an assembly of heterogeneous capillaries and the gas diffusion within different ranges of pore size is divided into three regimes (i.e., ordinary, Knudsen and transition diffusions). Two heterogeneous factors χ and χs are introduced to capture the heterogeneity of porosity and saturation, respectively. Together with volume averaging technology, the fractal theory is then used to upscale the diffusion behavior from pore scale to representative element volume scale. The model is then verified by the numerical and experimental data published in the literature and the results are in good agreement. It is revealed that under the dry state, the porosity heterogeneity significantly inhibits the molecular diffusion, leading to a reduction in gas diffusivity. When the media is wetted, the resistance of molecular diffusion also extremely depends on the local heterogeneity of saturation distribution, not just on the bulk saturation, causing a two-stage feature in the variation of gas diffusivity with saturation. Moreover, the proposed model can achieve a much better prediction than the power-law model and Moldrup model. The newly introduced heterogeneity factors can capture the physical behavior of media that is strongly sensitive to local conditions, expecting to overcome the difficulties in applying the volume averaging technology on the continuum scale to heterogeneous materials.

Numerical study on the parabolic flow of MHD fluid past a vertical plate in a porous medium

AbstractA numerical investigation on MHD fluid flow in parabolic mode has been performed to point out its significant properties. Thermal radiation, porous medium, heat generation, chemical reaction, and thermal diffusion along with variable temperature and concentration are taken into consideration in the analysis. The novelty of the work is the inclusion of heat generation and thermal diffusion along with exponentially varying temperature and concentration. The constituent governing equations are solved by using finite difference schemes in explicit form. The fluctuations in velocity, concentration, and temperature are observed and discussed with the help of graphs as well as numerical data. Their gradients are also calculated and analyzed the flow properties by using numerical tables. The existence of heat generation, as well as viscous dissipation, creates an increment in the temperature. The gradient of heat transfer rises with the impact of Prandtl number and decay in it is examined under the existence of a source of heat and viscous dissipation.

Global solvability to a cancer invasion model with remodeling of ECM and porous medium diffusion

Global solvability to a cancer invasion model with remodeling of ECM and porous medium diffusion

Insights on cellulose hydrolysis in the porous structure of biomass particles using the lattice Boltzmann method

Lignocellulose biomass has been recognized as one of the most promising sources of low-cost and renewable biofuels, and its conversion into alternative fuels and valuable platform molecules has attracted widespread attention. The porous solid residue from lignocellulose biomass, which was pretreated by steam-stripping, is catalyzed by dilute sulfuric acid to form levulinic acid (LA). The process includes porous media diffusion, multicomponent reactive transport, liquid-solid interface reaction, and cellulose dissolution. Understanding the interactions between these complex physicochemical processes is the basis for optimizing the performance of the hydrolysis reaction. In this study, a porous reaction transport model based on the lattice Boltzmann method (LBM) was established to simulate the conversion of cellulose to LA which was catalyzed by dilute acid. The simulation results were compared with the existing experimental results to verify the accuracy of the model. The simulation results showed that temperature has a significant effect on hydrolysis and the highest carbon yield was obtained at 180 °C. Without considering the lignin reaction, the higher the sulfuric acid concentration, the better is the hydrolysis efficiency in the range of 4% – 8%. The influence of cellulose content and steam-stripping the residue porosity on the dissolution rate of cellulose was also evaluated. The average dissolution rate of cellulose is the highest within 75 min, when the porosity is 0.7 and the cellulose content is 50%.

Hydrodynamic couplings of colloidal ellipsoids diffusing in channels

The hydrodynamic interactions (HIs) of two colloidal spheres characterized by the translation–translation (T–T) couplings have been studied under various confinements, but little is known regarding the HIs of anisotropic particles and rotational motions, which are common in nature and industry. Here, we study the T–T, rotation–rotation (R–R) and translation–rotation (T–R) hydrodynamic couplings of two colloidal ellipsoids sediment on the bottoms of channels in experiment, theory and simulation. We find that the degree of confinement and the particle shape anisotropy are critical tuning factors resulting in anomalous hydrodynamic and diffusive behaviours. The negative R–R coupling reflects the tendency of opposite rotations of two neighbouring ellipsoids. The positive T–R coupling reflects that an ellipsoid rotates away from the channel axis as another ellipsoid approaches. As the channel width increases, the positive T–T coupling changes to an abnormal negative coupling, indicating that the single-file diffusion can exist even in wide channels. By contrast, only positive T–T couplings were observed for spheres in channels. The T–T coupling increases with the aspect ratiop. The R–R coupling is the maximum at a moderatep ~ 2.8. The T–R coupling is the maximum at a moderate degree of confinement. The spatial range of HIs is longer than that of spheres and increases withp. We propose a simple model which reproduces some coupling phenomena between two ellipsoids, and it is further confirmed by low-Reynolds-number hydrodynamic simulation. These findings shed new light on anisotropic particle diffusion in porous media, transport through membranes, microfluidics and microrheology.