Diffusion Processes In Porous Media Research Articles

Numerical study and parameters estimation of anomalous diffusion process in porous media based on variable-order time fractional dual-phase-lag model

The primary objective of this study is to provide an accurate prediction of thermal transport in a porous media, and more significantly develop a model based on variable-order fractional calculus to better describe the anomalous diffusion process in thermal transport. The variable-order time fractional model based on the dual-phase-lag theory (VOFDPL) has been presented, then numerically solved and the results obtained have been compared to experimental data and other theoretical models to highlight the advantage and capability of this model. The comparison reveals that the results of VOFDPL model can well fit the experimental data, which proves the application of this model to conduct the thermal response of porous media, the non-equilibrium state and the microscale interactions between two phases (solid and fluid) with different thermophysical properties. Also, the heat conduction equations based on the Fourier’s law, single/double-phase-lag (SPL/DPL) models and also their fractional forms i.e., fractional single-phase-lag (FSPL) and fractional dual-phase-lag (FDPL) models have been solved and their results have been compared to experimental data, but the deviation between the results obtained and experimental data illustrates that these models cannot accurately predict the temperature response of porous media. We show that the VOFDPL model developed is an improvement over these models, leading to the most accurate prediction of thermal transport in porous media. In fact, the two lagging times and also the time derivative term with variable order as a time-dependent function can describe the local non-equilibrium condition, microscale thermal interaction between two phases and the anomalous diffusion process respectively Moreover, the two lagging times in the VOFDPL model have been estimated by using an inverse analysis based on the Levenberg–Marquardt algorithm, for the thermal response of porous media at different locations of sensors through the computational domain.

Study on CO<SUB align="right">2 diffusion process in heavy oil saturated porous media using experiment and simulation

To explore the CO2 diffusion in heavy oil saturated porous media, a mathematical model was developed to simulate the diffusion process by coupling the gas state equation. Then the experiment of CO2 diffusion in heavy oil saturated porous media was carried out and CO2 diffusion coefficient was determined by fitting the experimental data with the established model. Using the measured diffusion coefficient as an input parameter, the CO2 diffusion process in porous media was simulated and the factors that affected the diffusion process were analysed in this paper. The simulation results show that diffusion direction on the rock surface is in the tangential direction of the rock and points to where the CO2 concentration potential decreases. Furthermore, the contact area of the heavy oil and CO2 has a vital impact on the CO2 diffusion amount and CO2 concentration distribution. [Received: November 24, 2019; Accepted: August 7, 2020]

Study of the Factors Influencing Diffusive Tortuosity Based on Pore-Scale SPH Simulation of Granular Soil

Tortuosity quantitatively reflects the complexity of porous media. For the diffusion process in porous media, diffusive tortuosity is inevitably an important research topic. A simulation experimental method is proposed to study diffusive tortuosity in granular soil based on 3D pore-scale simulation by smoothed particle hydrodynamics (SPH). On the basis of the simulation results, the relationships between diffusive tortuosity and microstructural parameters are discussed. Simulation experiments are implemented on 3D granular soil columns generated by PFC software and soil layers formed by periodic expansion of the soil columns. The accuracy of the pore-scale SPH diffusion model is verified by the analytic solution for the particular case of a pure water column. The results show that the dimensionality does affect the diffusive tortuosity. 2D profiles cannot represent the original 3D medium in terms of the diffusion characteristics. Within the limited range of the variation of porosity during soil compression, the relationship between porosity and diffusive tortuosity can be considered to be linear. In addition, for the case of uniform granule size, diffusive tortuosity is almost linearly related to the specific surface area. Tortuosity values for soil columns are larger than those for the soil layer, which denotes that the effect of the sidewall on diffusion cannot be overlooked for a centimeter-scale soil column.

Analysis of gas diffusivity in coal using micro-computed tomography

As coalbed methane (CBM) becomes an increasingly important resource in the global natural gas market, gas transport in CBM reservoirs remains a crucial research topic that has not been fully understood. Gas migration in coal matrix is identified as a diffusion process which is quantified by effective diffusivity. This paper aims to explore the diffusion process in coal and measure the effective diffusivity using X-ray microcomputed tomography (micro-CT) imaging. By visualising the krypton gas migration process using micro-CT imaging, we are able to simulate the gas transport and better understand the diffusion mechanism of adsorptive gas in coal. The effective diffusivity of krypton that we obtain in the coal matrix is estimated to be 3.4 × 10−11 m2/s which falls in the mid-range of reported value in the literature. In this paper, we develop a method based on using micro-CT imaging and high X-ray attenuated gas to visualise gas transport and quantitatively analyse diffusion process in porous media. The experiment can be conducted at in situ pressure conditions to mimic CBM storage and production process. This method is ought to provide more insights into the gas diffusion mechanism in coal while preserving the original rock structure.

Mathematical modeling of the simultaneous convection–anomalous diffusion processes in porous media

ABSTRACTAfter a brief overview of most important general features of the nonclassical diffusion on the base of the extended irreversible thermodynamics, the relevant mathematical formulae are incorporated into general formalism of the simultaneous convection–diffusion processes taking place in porous media. Then, using the simplest variant of the convection–diffusion equation, novel-type analytic solutions are derived for transport processes with both subdiffusion and superdiffusion characters in Lagrangian representation.

Time-Dependent Methane Diffusion Behavior in Coal: Measurement and Modeling

In-depth understanding of how methane diffuses in porous media like coal is critical for enhanced coalbed methane recovery and coal seam methane drainage. However, the classic unipore gas diffusion model can only describe methane diffusion behavior in coal at the early time diffusion stage. Describing the whole methane diffusion behavior in coal has not been reasonably addressed in the coalbed methane field. Considering the large surface-to-volume ratio of coal, the authors proposed a time-dependent gas diffusion model to describe the whole diffusion process. This work first proposed a power–law relationship between diffusion coefficient and time according to previous studies of the time-dependent gas diffusion process in porous media. Then, both the analytical solution and its approximation solution for the time-dependent gas diffusion model were derived. Six methane diffusion tests in crushed coal were conducted to validate the proposed model under different pressures (0.5, 1.5, 2.5 MPa) and temperatures (20 and \(30\,{^{\circ }}\hbox {C}\)). Modeling results show that the time-dependent gas diffusion model is superior to the classic unipore gas diffusion model for describing the whole methane diffusion process in coal. Increasing temperature always accelerates methane diffusion in coal; the higher the temperature the larger the diffusion coefficient.

PORE STRUCTURE RECONSTRUCTION AND MOISTURE MIGRATION IN POROUS MEDIA

Three kinds of porous media (isotropic, perpendicular anisotropic and parallel anisotropic porous media) with the same porosity, different pore size distributions and fractal spectral dimensions were reconstructed by random growth method. It was aimed to theoretically study the impact of microscopic pore structure on water vapor diffusion process in porous media. The results show that pore size distribution can only denote the static characteristics of porous media but cannot effectively reflect the dynamic transport characteristics of porous media. Fractal spectral dimension can effectively analyze and reflect pores connectivity and moisture dynamic transport properties of porous media from the microscopic perspective. The pores connectivity and water vapor diffusion performance in pores of porous media get better with the increase of fractal spectral dimension of porous media. Fractal spectral dimension of parallel anisotropic porous media is more than that of perpendicular anisotropic porous media. Fractal spectral dimension of isotropic porous media is between parallel anisotropic porous media and perpendicular anisotropic porous media. Other macroscopic parameters such as equilibrium diffusion coefficient of water vapor, water vapor concentration variation at right boundary in equilibrium, the time when water vapor diffusion process reaches a stable state also can characterize the pores connectivity and water vapor diffusion properties of porous media.

Direct simulation of the influence of the pore structure on the diffusion process in porous media

In this paper, we numerically study the influence of pore structures on diffusion processes in porous media. The porous media geometry models are constructed based on two-dimensional Voronoi diagrams, and they feature randomly connected channels with large pores embedded to simulate the heterogeneity of porous media. A link-type two-relaxation-time (LTRT) lattice Boltzmann (LB) method is employed to solve the diffusion equation. The tortuosity is characterized as a function of porosity and pore structure. From numerical results, a correlation for the tortuosity as a function of porosity is derived for Voronoi geometries without large pores. Geometries with large pores at the same total porosity have higher tortuosity, which indicates that geometric heterogeneity slows down the diffusion.

Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise

In this paper one surveys and sharpens some recent results obtained by the authors on the finite time extinction property of solutions to stochastic diffusion equations of the form d X − ρ Δ X m d t = X d W and d X − ρ Δ sgn X d t = X d W , where 0 < m < 1 , ρ > 0 . These equations arise as models for nonlinear diffusion processes in porous media, plasma and self-organized criticality under stochastic Gaussian perturbation. These equations can be also viewed as control systems governed by fast diffusion porous media equations with a stochastic feedback controller X d W .

A backward problem for the time-fractional diffusion equation

We consider a backward problem in time for a time-fractional partial differential equation in one-dimensional case, which describes the diffusion process in porous media related with the continuous time random walk problem. Such a backward problem is of practically great importance because we often do not know the initial density of substance, but we can observe the density at a positive moment. The backward problem is ill-posed and we propose a regularizing scheme by the quasi-reversibility with fully theoretical analysis and test its numerical performance. With the help of the memory effect of the fractional derivative, it is found that the property of the initial status of the medium can be recovered in an efficient way. Since our solution is established on the eigenfunction expansion of elliptic operator, the method proposed in this article can be used to higher dimensional case with variable coefficients.

Investigation on mass diffusion process in porous media based on Lattice Boltzmann method

The mass diffusion process inside a porous medium is difficult for numerical simulation due to complex and stochastic nature of its structure. Based on the lattice Boltzmann method and reconstruction technology, this article presents an approach for simulating mass diffusion process and predicting the effective mass diffusivity in porous media, which is validated by comparing theoretical and experimental data. The concentration distribution and effective mass diffusivity inside porous media can be obtained.

Nonlinear diffusion under a time dependent external force: q-maximum entropy solutions

Nonlinear diffusion equations provide useful models for a number of interesting phenomena, such as diffusion processes in porous media. We study here a family of nonlinear Fokker-Planck equations endowed both with a power-law nonlinear diffusion term and a drift term with a time dependent force linear in the spatial variable. We show that these partial differential equations exhibit exact time dependent particular solutions of the Tsallis maximum entropy (q-MaxEnt) form. These results constitute generalizations of previous ones recently discussed in the literature [C. Tsallis, D.J. Bukman, Phys. Rev. E 54, R2197 (1996)], concerning q-MaxEnt solutions to nonlinear Fokker-Planck equations with linear, time independent drift forces. We also show that the present formalism can be used to generate approximate q-MaxEnt solutions for nonlinear Fokker-Planck equations with time independent drift forces characterized by a general spatial dependence.

Transient diffusion of heat, mass species and momentum in cylindrical pellets during catalytic oxidation of CO

Transient diffusion of heat, mass species, and momentum in cylindrical pellets during catalytic oxidation of CO is investigated. Experimental measurements of intrapellet temperature distributions are reported for CuOAl 2O 3 pellets, 0·25 in. dia., which are subjected to cross-flow of binary mixtures of CO and O 2, the pellets initially being saturated with pure oxygen. Mole fraction CO and temperature in the free stream ranged from 0·026 to 0·105 and 70 to 200°C, respectively. The Reynolds number based on pellet diameter ranged from 25 to 110. The effects of pellet porosity and copper content were also investigated. Of particular interest is the asymmetric nature of the problem wherein angular variations in free surface transfer rates result in markedly non-isothermal and non-symmetric pellet characteristics. Further insight into the temporal behavior of the intrapellet problem is extracted from an analysis of unsteady diffusion processes in porous media, using the dusty gas model to formaulte mass species and energy fluxes. A quasi-one-dimensional approximation of the problem is solved numerically. Preliminary results indicate that a simple first-order representation of the kinetics as inferred from static experiments is inadequate for predicting the experimental transient behavior of a catalyst pellet.