Random Porous Media Research Articles

A fractal model of effective mechanical properties of porous composites

In this work, a simple but effective fractal model is proposed to predict the mechanical properties of complex porous composites. By extending the Mori-Tanaka and Double Inclusion models, we develop a computationally efficient algorithm based on the mean-field homogenization, to quickly determine the macroscopic elastic properties of the random porous media by the fractal theory. The random pore sizes and locations are properly characterized by a single fractal dimension, and the fractal model agrees well with the numerical results obtained by the finite element homogenization technique and the existing experimental data from literature. Moreover, the effect of pore size distribution has been investigated, indicating that the elastic properties decrease with the increase in the fractal dimension. In particular, the computation time can be reduced from 4 h for the finite element analysis to 15 s based on the fractal model. Based on the mathematically analogous governing equations, the present fractal modeling has great potential to determine the other significant physical properties such as thermal conductivity and coefficient of thermal expansion.

Lattice Boltzmann simulation of three phase reactive flow in random porous media at pore-scale

In this study, the process of carbonate rock acidification with three-phase immiscible fluids reactive flow at pore-scale is simulated by a multiphase multicomponent lattice Boltzmann method. Besides, the dissolved solid mass is calculated by Volume of Pixel method. The effects of pressure difference, wettability, oil interfacial tension and porous media porosity on the dissolution reaction are investigated numerically, and the results show that: the increasing pressure difference, oil interfacial tension and porosity promotes the dissolution reaction. The influence of wettability on dissolution and acid breakthrough rates depend on the phase distribution of non-acidic fluids. In addition, the dissolution dead zone may appear when the inlet flow rate or solid particle size is small. Increasing the interfacial tension of the oil facilitates its separation from the porous medium.

Lagrangian dynamics and heat transfer in porous-media convection

Abstract

Flow Pattern Map of Flow Boiling in a Rectangular Channel Filled with Porous Media

A flow visualization study was carried out for flow boiling in a rectangular channel filled with and without metallic random porous media. Four main flow patterns are observed as intermittent slug-churn flow, churn-annular flow, annular-mist flow, and mist flow regimes. These flow patterns are clearly classified based on the high-speed images of the channel flow. The results of the flow pattern map according to the mass flow rate were presented using saturation temperatures and the materials of porous media as variables. As the saturation temperatures increased, the annular-mist flow regime occupied a larger area than the lower saturation temperatures condition. Therefore, the churn flow regime is narrower, and the slug flow more quickly turns to annular flow with the increasing vapor quality. The pattern map is not significantly affected by the materials of porous media.

Analysis of flow resistance in fractal porous media based on a three-dimensional pore-throat model

Flow resistance in porous media is a difficult problem due to its importance and complexity of the fluid flow. Based on the original aligned and staggered pore-throat models, a new three-dimensional pore-throat model is established, and the analytical correlation of flow resistance is derived by employing the fractal theory in random porous media. The correlation is the function of porosity, ratio of porous diameters, sphericity coefficient of particles and Reynolds number. Prediction comparison among the proposed model, Yu model, Zheng model, Ergun model and experimental data in relevant literatures are carried out, and good agreement between the proposed model prediction and experiment data of literatures is obtained, and our model can obtain better predicting precision when the ratio of minimum capillary diameter λ min and maximum capillary diameter λ max equals to 10−3.

On the p-Adic analog of Richards’ equation with the finite difference method

In this paper, with the help of a variant of Schauder fixed point theorem in the real Banach algebra together with the finite difference method (FDM), we take a brief look at the [Formula: see text]-adic analog of Richards’ equation derived by Khrennikov et al. [Application of [Formula: see text]-adic wavelets to model reaction–diffusion dynamics in random porous media, J. Fourier Anal. Appl. 22 (2016) 809–822], and study the solvability and solution of this problem. This equation is formulated by a kinetic equation during the modeling of the reaction–diffusion dynamics in random porous media. Moreover, in order to guarantee the convergence of the presented iterative schemes, some sufficient conditions would be presented.

Investigation of flow through triply periodic minimal surface-structured porous media using MRI and CFD

Advances in additive manufacturing technology are making ordered porous media, such as those based on triply periodic minimal surfaces (TPMS), increasingly feasible alternatives to random porous media for applications ranging from chromatography to heat exchange. Process performance in these applications is controlled by the flow characteristics within the channels. In this work, magnetic resonance imaging (MRI) experiments and computational fluid dynamics (CFD) simulations were used to study flow through a Schwarz Diamond TPMS column for Reynolds numbers up to 30. The CFD simulations were in good quantitative agreement with the MRI experiments. The velocity images illustrate a transition from creeping flow to inertial flow. The inertial flow regime exhibits flow splitting in each channel, where recombination depends on the extent of inertia. These results demonstrate that MRI and CFD are both suitable techniques for understanding the mechanisms underlying reported enhanced transfer performance (e.g. low axial dispersion) in TPMS devices.

Application of half-way approach to discrete unified gas kinetic scheme for simulating pore-scale porous media flows

Simulation of pore-scale porous media flows is generally considered to be a non-trivial task due to the complicacy of geometry structures involved. In the recent decades, the mesoscopic scheme of lattice Boltzmann equation (LBE), combined with the inherent half-way (HW) bounce-back boundary method has been proved to efficiently handle those complex flows. More recently, a new mesoscopic method called discrete unified gas kinetic scheme (DUGKS) is proposed in the literature, which is partially derived from the LBE. In view of that, the HW-type boundary approach is introduced to the DUGSK in this study, which is accomplished within the framework of the ghost-cell (GC) method. The HWGC-DUGKS is then developed for extending the application of DUGKS to the complex flows in the porous media. The simulations of the cylindrical Couette flow, flow through a square array of cylinders and flow in the random porous media are performed to validate the present HWGC-DUGKS. The results demonstrate the accuracy and feasibility of the method for pore-scale porous media flows, and the non-uniform mesh and rarefied effect can be conveniently incorporated into the method.

Shale gas permeability upscaling from the pore-scale

The effective permeability of large shale samples provides useful insights into shale gas production. However, its determination can only be achieved through upscaling, since the direct pore-scale simulation of gas flows in large rock samples is not feasible due to the high computational cost and absence of pore connectivity in sample images. Although the Brinkman formulation is widely used in the permeability upscaling of conventional rocks, how to choose the effective viscosity in this coarse-scale model is not clear. Moreover, its application in shale rocks, where the rarefaction effects are important so that the conventional Navier–Stokes equations are inadequate, is rare, and its accuracy has not been assessed. This study aims to address the above two problems, by comparing the Brinkman solutions of several two-dimensional and three-dimensional random porous media containing fractures with the fine-scale solutions of the Stokes and Boltzmann equations (for continuum and rarefied gas flows, respectively). It is found that the use of the fluid viscosity in the Brinkman model, instead of the controversial effective viscosity, leads to accurate results for the cases considered. Additionally, the macroscopic quantity in rarefied gas flows in shale rocks is well predicted by the Brinkman model for a wide range of gas rarefaction, since the error is found to be less than 7%, while neglecting the rarefaction effects leads to significant underestimation of effective permeability (up to 90% in the cases studied). Although heterogeneity and anisotropy of the porous medium increase the error of the effective permeability derived from the Brinkman model, generally speaking, the effective permeability extracted from this coarse-scale model compares favorably to its fine-scale counterpart.

Phase distributions in a porous medium after the first breakthrough

In this study, we analyze experimentally the immiscible displacement of an oil phase from a porous medium. A 2D pore network etched in resin was considered as a random porous medium. This micromodel is made with a transparent material to allow direct visualization of the drainage process. In all experiments, the porous model is initially saturated with an oil-phase, which is displaced by an air phase. Air is injected continuously at a constant flow rate in a centre point of the micromodel. In this paper, we present an experimental characterization of the evolution of the gas cluster after the first breakthrough. We discuss the dependence of the phase distributions on viscous forces, capillary forces and flow rate injection. We have noticed that for low air rates injection, the main gas cluster is detached and connected at the permeable edge. The detachment and the connection durations are periodic and depend on fluids properties.

Study of gas emission law at the heading face in a coal‐mine tunnel based on the Lattice Boltzmann method

AbstractGas distribution ahead of the coal tunnel is the key risk factor controlling coal and gas outburst. Based on an analysis of the influence of the stress state on the porosity of the coal seam, an improved quartet structure generation set (QSGS) random porous media generation tool is used to reconstruct the coal structure. Adopting the reconstructed pore structure of the coal as the boundary of the flow field, the Lattice Boltzmann method (LBM) is used to simulate the gas dynamic distribution law ahead of the coal tunnel. The gas pressure of the coal seam decreases obviously in the fracture zone only, and the change in gas pressure is very small in the stress concentration zone and ahead of the coal seam. This research is of significance for gas drainage and the prevention of coal and gas outburst hazards in the working face during coal tunneling.

UNCERTAINTY QUANTIFICATION FOR NATURAL CONVECTION IN RANDOM POROUS MEDIA WITH INTRUSIVE POLYNOMIAL CHAOS EXPANSION

The paper presents a framework for the construction of a stochastic projection method for the natural convection in random porous media under the local thermal nonequilibrium conditions. In this approach, the input stochastic field (porosity) is represented by the Karhunen−Loeve expansion and the output fields (e.g., velocity, pressure, fluid phase temperature, and solid phase temperature) are expressed by the polynomial chaos expansion. Using the spectral decomposition, the stochastic problem in random porous media is reformulated to a set of deterministic problems to be solved for each polynomial chaos. A stochastic projection method is implemented to obtain the chaos coefficients in the corresponding deterministic governing equations and the statistics of the numerical solution is obtained. The prediction results are compared against results obtained using a Monte Carlo method. Excellent agreement between these results indicates the efficiency and accuracy of the proposed method.

Liquid-vapor phase equilibrium of a simple liquid confined in a random porous media: Second-order Barker-Henderson perturbation theory and scaled particle theory

A simple analytical theory for the thermodynamic properties of a multicomponent liquid mixture adsorbed in a random porous media is proposed. The mixture is modeled by an n-component fluid of hard-sphere Morse (HSM) particles and the media is represented by the matrix of HSM obstacles randomly distributed in a configuration of HS fluid quenched at equilibrium. We combine scaled particle theory (SPT) and the corresponding version of the second-order Barker-Henderson (BH2) perturbation theory to describe the thermodynamics of the system. To assess the accuracy of the theory, Monte Carlo computer simulations are performed to determine the structure of the corresponding reference system and the chemical potential of the HSM liquid confined in a random HSM matrix. Based on agreement between the theoretical predictions and Monte Carlo simulation data, the structure of the reference system is shown to be accurately predicted using radial distribution functions of the n + 1-component hard-sphere mixture with the n component representing the fluid and the one component representing the matrix obstacles. Theoretical predictions for the chemical potential are also in a very good agreement for the model for systems with weak fluid-matrix attractive interactions, though slight deviations are observed as the strength of the fluid-matrix attraction and/or matrix density is increased. With minimal adjustment of the HSM potential, the phase behavior of the Lennard-Jones and square-well fluids adsorbed in the matrix are also described. Due to its simplicity, the theory could be used in a number of applications to predict the properties of simple fluid mixtures with any number of components adsorbed in the porous media.

Computational identification of adsorption and desorption parameters for pore scale transport in periodic porous media

Computational identification of unknown adsorption and desorption rates is discussed in conjunction with reactive flow considered at pore scale. The reactive transport is governed by incompressible Stokes equations, coupled with convection–diffusion equation for species transport. The surface reactions, namely adsorption and desorption, are accounted via Robin boundary conditions. Henry and Langmuir isotherms are considered. Measured concentration of the specie at the outlet of the domain has to be provided to carry out the identification procedure. Deterministic and stochastic parameter identification approaches are considered. The influence of the noise in the measurements on the accuracy of the identified parameters is discussed. Multistage identification procedure is suggested for the considered class of problems. The proposed identification approach is applicable for different geometries (random and periodic) and for a range of process parameters. In this paper the potential of the approach is demonstrated in identifying parameters of Langmuir isotherm for low Peclet and low Damkoler numbers reactive flow in a 2D periodic porous media with circular inclusions. Simulation results for random porous media and other regime parameters are subject of follow up papers. Finite element approximation in space and implicit time discretization are exploited.

Volume averaging theory (VAT) based modeling for longitudinal mass dispersion in structured porous medium with porous particles

In this study, to investigate the mass transport characteristics in a structured porous medium with porous particles under an interfacial concentration discontinuity, a macroscopic solute transport equation is proposed based on the volume averaging theory. A typical three-dimensional geometry (a body center cubic arrangement of spheres) was chosen as the representative elementary volume. The corresponding closure problem was solved to obtain the longitudinal mass dispersion. Based on the numerical results, a new correlation of the longitudinal mass dispersion for a structured porous medium with porous particles is presented. Through a comparison with the correlation of the longitudinal mass dispersion for a random porous medium, it can be determined that, for a mechanical dispersion, the dependence of a random porous medium and that of a structured porous medium on the Péclet number Pe are linear and quadratic, respectively. Furthermore, it was also determined that for a holdup dispersion, a structured porous medium is less dependent on the ratio of diffusivity of the fluid phase to the diffusivity of the porous particle phase. In addition, it is more dependent on the inverse ratio of the solubilities of the solute in the fluid and in the catalyst particles than in a random porous medium.

Flow-pattern-based experimental analysis of convective boiling heat transfer in a rectangular channel filled with open-cell metallic random porous media

This paper reports a visualization study on the flow boiling of R245fa in a rectangular channel filled with an open-cell random porous structure made of copper. The boiling heat transfer of the two-phase vertical upward flow inside the channel was measured while the refrigerant was asymmetrically heated by a hot-water-source channel. An experiment was conducted with a constant saturation pressure of 5.9 bar, inlet vapor quality of 0.05–0.99, channel heights of 3 and 5 mm, and mass flux of 133–300 kg/m2 s. The results are compared with those of a plain channel in the same operating conditions. The two-phase flow characteristics are discussed along with the trend of the boiling heat transfer coefficient and mean vapor quality according to the flow patterns obtained with and without the metallic porous media. A non-dimensional analysis was also conducted for comparison.

Anomalous percolation flow transition of yield stress fluids in porous media

Microfluidic experiments and simulations reveal an anomalous percolation transition for the flow of a yield stress fluid through a random porous medium. The evolution of the fluidized network results in a highly nonlinear flow conductivity and reveals a novel dispersion mechanism.

Linear Stability Analysis of Time-Dependent Electrodeposition in Charged Porous Media

We study the linear stability analysis of time-dependent electrodeposition in a charged random porous medium, whose pore surface charges can generally be of any sign, that is flanked by a pair of planar metal electrodes. Discretization of the linear stability problem results in a generalized eigenvalue problem for the dispersion relation that is solved numerically, which agrees well with the analytical approximation obtained from a boundary layer analysis valid at high wavenumbers. Under galvanostatic conditions in which an overlimiting current is applied, in the classical case of zero pore surface charges, the voltage and electric field at the cathode diverge when the bulk electrolyte concentration there vanishes at Sand's time. The same phenomenon happens for positive surface charges but at a time earlier than Sand's time. In contrast, negative surface charges allow the electrochemical system to sustain an overlimiting current via surface conduction past Sand's time, keeping the voltage and electric field bounded. Therefore, at Sand's time, negative surface charges greatly reduce the electrode surface instabilities while zero and positive surface charges magnify them. We compare theoretical predictions for overall electrode surface stabilization from the linear stability analysis with published experimental data for copper electrodeposition in cellulose nitrate membranes and demonstrate good agreement between theory and experiment. We also use the linear stability analysis as a tool to analyze how the crystal grain size changes with duty cycle during pulse electroplating.

Flow Resistance Characteristics of Power Low Fluid Flow Through the Structured Porous Media

The flow characteristics of power law fluid in finite wall three-dimensional structured packed beds of spheres was investigated experimentally. The packed beds of spheres was in Simple Cubic configuration and enclosed in square cross-section duct, and the Partially Hydrolyzed Polyacrylamide (HPAM) solutions with different concentrations and temperatures was chosen as the working fluids (a power-law type non-Newtonian fluids). The relationships between the friction factor and Reynolds number was verified by the modified Ergun type equations. And found that the coefficients ' E A and ' E B had certain relations with the power index and would vary for different concentrations and temperatures of the fluids. However, the results showed that the existing Ergun correlations for random porous media failed to predict the resistance factor for finite wall structured beds, and the new modified Ergun correlation was proposed and verfied to be valid for power law fluid. At last, the study highlighted the need for pinpointing of the different flow regimes.

Pressure statistics from the path integral for Darcy flow through random porous media

The path integral for classical statistical dynamics is used to determine the properties of one-dimensional Darcy flow through a porous medium with a correlated stochastic permeability for several spatial correlation lengths. Pressure statistics are obtained from the numerical evaluation of the path integral by using the Markov chain Monte Carlo method. Comparisons between these pressure distributions and those calculated from the classic finite-volume method for the corresponding stochastic differential equation show excellent agreement for Dirichlet and Neumann boundary conditions. The evaluation of the variance of the pressure based on a continuum description of the medium provides an estimate of the effects of discretization. Log-normal and Gaussian fits to the pressure distributions as a function of position within the porous medium are discussed in relation to the spatial extent of the correlations of the permeability fluctuations.