Transport in Porous Media最新文献

This study deals with the thermal gravitational convection of a variable viscosity fluid in a closed two-dimensional cavity in the presence of a porous layer. In addition, at the lower edge of the region there is a heat-conducting energy source with periodic heat release. The problem has been solved in dimensionless non-primitive parameters including stream function and vorticity using the finite difference schemes on a uniform structured mesh. The influence of the defining characteristics of heat transfer such as the Darcy and Rayleigh numbers, the height of the porous layer, the heater location, as well as the frequency of the heat dissipation from the heater, has been studied. The results have been demonstrated using isolines of the stream function and temperature combined with time dependences of the integral characteristics of heat transport for various values of dimensionless parameters. The conclusions obtained have demonstrated that the periodic nature of heat dissipation completely determines the periodicity of convective processes in the cavity. In addition, the presence of a porous layer and the ability to change the position of the heater make it possible to control heat removal.

Experimental, analytical, and numerical investigations, addressing the onset and development of Rayleigh–Taylor convection in porous media, often give results, which do not agree with each other quantitatively. The reason of this discrepancy can be related to different fields of small perturbations, which always present in a system as a “hidden parameter”. Computational methods provide an opportunity to introduce small perturbations explicitly and investigate the response of fluid system to them. In the present work, numerical study of Rayleigh–Taylor convection of miscible fluids in a weak heterogeneous porous medium is conducted. Small random perturbations of porosity and permeability are considered. It was found that parameters of the convection onset and long-time evolution, which are analyzed statistically, depend on the amplitude of perturbations significantly. Particularly, the convection onset time increases by a factor of 15, if the amplitude of porosity perturbations, normalized by the average porosity, decreases from (mathtt{10^{-2}}) to (mathtt{10^{-10}}). To do conditions for the convection development identical, a periodic impact on the fluid system at the initial time is added. As obtained, the convection onset time under the periodic impact may become independent of the field of random perturbations. This finding may be employed to improve compatibility between different investigations. In addition, the periodic impact changes dramatically the long-time fluid behavior, which is studied in detail. We conduct in our work a representative statistical analysis, find the ensemble averages, and estimate standard deviations about the averages.

Species separation is usually achieved in closed vertical thermogravitational columns (TGC). To obtain continuous separation, the initially homogeneous binary solution, saturating the porous medium is introduced at a constant volumetric flow rate through one of the two vertical slots of the TGC and retrieved through the opposite slot. However, this process requires the horizontal dimension of the two vertical walls of the cell to be sufficiently large for the mass regime at the exit slot to reach the steady state. The analytical resolution obtained using the parallel flow approximation and numerical simulations developed are in very good agreement. The vertical mass fraction gradient,({m}^{*},) at steady state was shown not to admit an optimum with respect to the thickness (e) for a fixed (Delta T) or with respect to (Delta T) for a fixed (e), unlike the gradient m obtained in a vertical TGC. The ratio of the two simplified analytical expressions ({m}_{s}^{*}) and ({m}_{s}), respectively, obtained for the two columns filled with the same binary fluid in porous or fluid media, led to an expression depending only on the ratio of the thermodiffusion coefficient, ({D}_{T},) to the corresponding coefficient, ({D}_{T}^{*},) in the porous medium, the column thickness (e,) and the permeability of the porous medium. To increase the degree of separation of this mixture, we could simply add another column of height (h), at the outlet of the first column of height (H,) with (h<H), and restart the process with a mass fraction higher than the initial fraction, ({C}_{0}). This technique could be repeated as often as necessary.

The linear stability analysis of Darcy–Brinkman–Bénard convection (DBBC) in a binary fluid-saturated porous layer is studied numerically using (n) term Galerkin approach for rigid–rigid, isothermal boundaries. The occupied binary fluid and porous medium are assumed to be in thermal non-equilibrium. Thus, two energy equations are used for each phase. The critical values of the Darcy–Rayleigh and wave numbers for the onset of convection are obtained by considering ten terms in the Galerkin solution. The effect of the five parameters of the model, namely the Darcy number, Da, the modified ratio of thermal conductivity (gamma), the Lewis number Le, the separation ratio coefficient, (chi), and the inter-phase heat transfer coefficient, H, on the stability of the system is discussed in detail and presented with the aid of plots and tables. The onset of convection in a binary fluid-saturated porous medium is delayed for realistic boundary conditions compared with ideal boundary conditions (stress-free, isothermal boundary conditions). Increasing the values of the Darcy number, inter-phase heat transfer coefficient, and the separation ratio coefficient stabilizes DBBC. In contrast, the thermal conductivity ratio and Lewis number are destabilize the system. Furthermore, convective cell size remains unaltered with increasing (chi). Convection is delayed in the pure fluid medium compared to the binary fluid medium. Local thermal non-equilibrium ceases for small and large inter-phase heat transfer coefficient values.

The effects of pressure and temperature on foam flow through porous media, critical for applications such as subsurface gas storage and enhanced oil recovery, have yet to be completely understood. This study provides valuable new insights into foam behavior by directly measuring both pressure drop and capillary pressure during a series of foam quality scan experiments conducted at 20 °C and 50 °C and under ambient and 500 psi pressures. A key innovation of this work is the development of an in-house-designed capillary pressure probe, which captures capillary pressure dynamics at the mid-length of the sandpack This allows for precise measurements of foam stability mechanisms as a function of foam quality. Experiments were conducted in two sandpacks with identical silica sand, one with a translucent polycarbonate tube for ambient conditions and another with a stainless-steel tube for high-pressure and temperature experiments. Results reveal that foam strength increases with pressure at moderate flow rates due to increased pressure oscillations that promote foam generation, while higher temperatures reduce foam strength, driven by reduced liquid viscosity and accelerated gas diffusivity. These findings challenge the conventional understanding of “limiting capillary pressure” by showing that foam in homogeneous sandpacks becomes generation-limited at high qualities, providing a foundation for improved modeling and application of foam in porous media.

Fast, data-driven prediction of transport properties of porous media from 2D images is important for materials design and optimization. This work presents prediction of liquid transport in 3D materials using geometric characteristics of pore cross sections. A dataset of 1733 digital structures, of which about a half has impermeable non-percolated systems of isolated pores, was generated using coarse-grained simulations mimicking formation of porous glasses and porous polymer membranes. 2D pore cross sections were characterized by the surface area, perimeter, and asymmetry. Liquid permeability and self-diffusion coefficients of tracers of varying sizes were calculated using lattice Boltzmann and Monte Carlo simulations, correspondingly. On these simulation results, machine learning models were built for (a) distinguishing permeable (percolated) from impermeable (non-percolated) structures and (b) predicting transport properties from pore cross-section characteristics. Very reasonable accuracy was achieved, despite a wide permeability range of the dataset. Gradient boosting method was employed with two-step learning: First, classification model distinguished the permeable samples, and second, a regression model predicted the dynamic properties. The total pore volume and the non-circular shape of the pore cross sections made the strongest influence on the transport properties, but no single feature was dominant. The model trained on synthetic polymer structures was applied to several sandstone samples, with a reasonable predictive accuracy for permeabilities within the training range, and demonstrating the robustness of the proposed approach. In addition, a separate gradient boosting model was trained on a semi-real dataset based on augmented real images, achieving high determination score and confirming the potential of the method for broader range of materials.

In this study, a novel path-percolation algorithm is introduced to simulate inhomogeneous porous channels. Furthermore, a novel double-path-percolation model was developed to simulate porous channels with lower-tortuosity void paths for fluid transfer and solid paths for heat and electron transfer. Micro-computed tomographies of two actual gas diffusion layer materials used in polymer electrolyte fuel cells were digitized and used in diffusion simulations to provide morphology precisely. A single-phase fluid flow through the inhomogeneous porous channels was simulated using a two-dimensional lattice Boltzmann model, where the fluid flow codes were ported on Nvidia GPUs using CUDA. The effective diffusion equations as a function of effective porosity and tortuosity were developed for single- and double-path-percolation models, respectively, and tested using the micro-computed tomographies of the gas diffusion layers.

Darcy’s law provides a fundamental framework for understanding fluid flow through porous media. However, deviations from its linear superficial velocity-hydraulic gradient (v-i) relationship have been widely reported, at high and low flow rates. While previous studies have attributed the low flow rate deviations to factors such as fluid properties, boundary effects, and experimental artifacts, the role of material heterogeneity has received less attention. This study employs neutron imaging to investigate how rock heterogeneity influences macroscopically observed flow behavior. Volume-controlled percolation tests were conducted on Idaho Gray sandstone cores under near-single-phase conditions using heavy water (D₂O) and normal water (H₂O) across a wide range of flow rates. Bulk measurements (pore pressure at the sample boundaries and the controlled injection flow rate) revealed a decline in hydraulic conductivity at lower injection rates. Through a novel method for interpreting the breakthrough curves (BTC) derived from the neutron imaging data, we are able to quantify the volume of pores active in the flow during each test. The neutron radiography imaging acquired during the flow tests revealed that flow paths were strongly influenced by the rock’s heterogeneous pore structure, with higher flow rates promoting more uniform front propagation. This suggests greater pore space access at higher injection rates and implies the presence of threshold pressure gradients needed to access different parts of the pore network. The BTC analysis from neutron image shows a decrease in the volume of pores active in the flow (effective porosity) with decreasing injection rates, aligning with the observed reduction in hydraulic conductivity. By linking nonlinearity in vi-curves to variations in effective porosity, this study highlights the critical role of heterogeneity in controlling the fluid flow behavior. These findings underscore the importance of understanding the role of spatial variability in porous media when interpreting macroscopic (bulk) permeability measurements, especially when interpreting apparent deviations from Darcy’s law.

This study corrects the micro-continuum model to improve the accuracy of simulating porous media flows. The correction includes adding the second Brinkman term to the averaged momentum balance equation and discretizing the gradients of this term using the Gaussian scheme with a harmonic interpolation in the finite-volume method. The corrected micro-continuum model better applies the no-slip immersed boundary condition at the solid–fluid interface. We compared the absolute permeability obtained from direct numerical simulation of the flow in different 2D and 3D porous media using the corrected and uncorrected micro-continuum models and the Navier–Stokes model. Considering all flow simulations on coarse meshes of 2D and 3D porous media, we observed errors of up to 54.2% in determining absolute permeability with the micro-continuum model without correction, which is reduced to a maximum of 4.3% using the corrected micro-continuum model. Due to this gain of accuracy, the corrected micro-continuum model with a coarse mesh can be as accurate as the uncorrected micro-continuum model in a much finer mesh. For the 2D bed of particles, this led to a speedup of 8483. Besides, we developed a methodology to compare the relative errors in the absolute permeability in 2D and 3D porous media using the number of mesh cells in the mean throat diameter. Our analysis indicates that meshes from 3D microtomography are usually coarse enough to require the corrected micro-continuum model in its flow simulation.

Produced water re-injection (PWRI) is the water management strategy with least environmental impact during petroleum recovery. A major challenge, however, is clogging of pores in the injection reservoir by particles suspended in the produced water. Basic understanding of transport and retention of particles in porous media is required to better handle this injectivity decline. Here, a microfluidic technique was used to study the transport and retention of monodisperse silica particles in a porous network. The amount of particle retained in the network, the distribution of the particles in the network and the aggregation state of the particles depended on particle–particle and particle–pore wall interactions. These interactions were modulated by varying the salinity of the suspension introduced into the network and by adsorbing surface-active additives (a non-ionic surfactant, a cationic flocculant and an anionic flocculant) onto the particles. The latter was done to mimic how adsorption of production chemicals onto solid particles in produced water influence their transport in reservoirs. In accordance with the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, high-energy barriers prevented both aggregation of particles and retention of particles in the pore network at low salinities. A threshold salinity was reached, where the energy barriers were reduced so that individual particles were retained in the pore network. Further increase in the salinity resulted in aggregation of particles prior to the network and most of the aggregates were accumulated close the entrance of the network. Adsorption of a non-ionic surfactant provided sufficient steric hindrance to prevent aggregation of particles at high salinities, and the retention of particles became more evenly distributed in the network. The adsorption of the anionic flocculant resulted in steric hindrances that reduced the retention of particles in the network, while the opposite was seen when the cationic flocculant was adsorbed onto the particles. The extent of re-mobilization of retained particles indicated the strength of the particle–pore wall interactions.