Проницаемость двумерной пористой среды из волокон квадратного сечения (ячеечная модель)

This investigation attempts to describe and simulate the alcohol displacement process by means of a cell model, as employed in chemical engineering practice. The proposed model is more simple than previously proposed models, and utilizes parameters chosen on a theoretical basis. The model successfully reproduced the formation of the stabilized bank and the breakthrough of alcohol, the latter depending on one of the model parameters, which may be correlated with the length of the porous medium. Moreover, the effects of the phase behavior of the liquid system involved, as observed in experimental studies, were reproduced. Several variations of the basic model were devised and tested on a digital computer. These included the cases in which: the actual value of fractional flow was used in cell-to-cell computations; the number of cells was varied within the same run; and incomplete rather than complete phase equilibrium was assumed within each cell. The proposed cell model clarifies the basic mechanism of the process. Detailed concentration profiles obtained for each cell, for instance, showed the mechanism of bank formation in relation to the phase behavior characteristics. The results obtained indicated a varying degree of phase equilibrium concommitant with changes in the velocities of the phases in an actual alcohol displacement. This condition was approximated by changing the number of cells during the simulation. Interesting information was obtained on the influence of path length on the efficiency of alcohol displacement, which has been the subject of some controversy. Certain limitations preclude the use of the proposed model as a substitute for experimental studies. The results obtained were, nevertheless, of value in interpreting the experimental results. Introduction During recent years considerable effort has been directed toward an understanding of alcohol displacement, the process whereby oil and water are recovered from a porous medium by the continuous injection of a solvent. The complex nature of the physical process involved has so far defied a complete mathematical treatment. Other methods of approach, amounting to an overall material balance, have been proposed, yielding useful information on certain aspects of the process. Taber et al, in particular, defined the displacement mechanism in terms of the phase behavior of the alcohol-oil-brine system involved. Wachmann reported a mathematical treatment of alcohol displacement subject to certain simplifying assumptions. Donohue proposed the use of a "cell model" for simulating alcohol displacement. The nature of the assumptions involved limited the utility of the model. The present work attempts to examine the variables involved in the simulation of alcohol displacement and discusses several possible versions of the basic cell model. Under certain conditions the model results are similar to the experimental results. In particular, the spontaneous formation of the stabilized bank and the effects of the system phase behavior were successfully reproduced. PREVIOUS WORK ON CELL MODELS Cell models and the theoretical plate concept are often used in solving chemical engineering problems in which an explicit mathematical solution may be difficult or impossible to obtain. Examples of such applications occur in distillation, gas-liquid chromatography, reactor technology, absorption, etc. In petroleum engineering, such a model was used by Attra to describe non-equilibrium gas drive, and by Higgins and Leighton to calculate sweep efficiency in water flooding. Aris and Amundsen pointed out the equivalence between the diffusion model and perfectly mixed cells connected in series. SPEJ P. 89ˆ

An investigation of the transient electrophoresis of conducting colloidal particles in porous media using a cell model

Correlations between air drag and movement of water droplets in fibrous media

Pd–Au nanoparticles supported by TiO2 fibers for catalytic NO decomposition by CO

Compression in the processing of polymer composites 2. Modelling of the viscoelastic compression of resin-impregnated fibre networks

Acoustically enhanced porous media enables dramatic improvements in filtration performance

We are examining the thermophoretic movement of a uniform mixture of spherical aerosol particles, all with the same properties, as they are situated within a porous material. These particles can have various thermal conductivity and surface characteristics. This analysis focuses on situations where the Péclet and Reynolds numbers are small. The influence of particle interactions is carefully considered by using a unit cell model, a well-established method known for its accurate predictions in the context of sedimentation for monodisperse suspensions of spherical particles. The porous medium is represented as a Brinkman fluid characterized by a Darcy permeability, which can be determined directly from experimental observations. This medium is considered to be uniform and isotropic, and the solid matrix is in thermal equilibrium with the fluid flowing through the voids of the medium. The Knudsen number is assumed to be low, enabling the description of fluid flow through the porous medium using a continuum model that includes temperature jump, thermal creep, frictional slip, and thermal stress slip at the aerosol particle’s surface. The conservation equations for energy and momentum are individually tackled within each cell. In this model, each cell represents a spherical particle enclosed by a concentric shell of surrounding fluid. The thermophoretic particle migration velocity is determined across different cases. We derive analytical expressions for this average particle velocity, expressing it in terms of the particle volume fraction. It is observed that different cell models yield somewhat varied results for particle velocity. Generally, with a fixed permeability parameter characterizing the porous medium, an increase in the thermal stress slip coefficient tends to decrease the normalized thermophoretic velocity across the different cell models. The results are in good agreement with the available data as documented in the existing literature. Additionally, a parallel examination of aerosol sphere sedimentation is provided.

Nitrified municipal wastewater effluent was passed upward through an anaerobic filter containing gravel media to effect denitrification. Using methanol as a supplementary carbon source for the denitrifying bacteria, 90% nitrogen removal was obtained with a detention time as short as 1.5 hr in pilot plant studies. Further laboratory studies were conducted using fiber media in upflow and horizontal flow filters. The highly porous fiber media performed comparably to the gravel media in the upflow filter; however, media configuration and poor flow distribution limited the success of the horizontal flow filters. The anaerobic filter process has several advantages over other methods of denitrification. These are low initial and operating cost, simplicity of operation, long solids retention times, and absence of any sludge recycle or disposal equipment. The major operating cost for the process is for the methanol. The quantity required increases with increasing dissolved oxygen and nitrate nitrogen and decreasing effluent BOD. The total cost, not including the cost of nitrifying the secondary effluent and reaerating the denitrified effluent, may run as low as $12.00 per million gallons.

Electrically conductive porous Si/SiC fiber media were prepared by infiltration of liquid silicon into porous carbon fiber preforms. The series rule of mixture for the effective electrical conductivity was applied to the disc shaped samples to estimate their silicon content, effective electrical conductivity and porosity. The electrical conductivity was estimated by assuming the disc sample as a plate of equivalent geometry, i.e., same thickness, electrode distance and volume. As the volumetric content of silicon in a sample increases from 0.026% to 0.97%, the estimated electrical conductivity increases from 0.17 S/cm to 2.09 S/cm. The porosity of the samples measured by Archimedes principle was in the range of 75~83% and 1~4% less than the one estimated by the series rule of mixture for the effective electrical conductivity.

The steady electroosmosis and electric conduction in a fibrous medium constructed by a homogeneous array of parallel, identical, charged, circular cylinders filled with an electrolyte solution is analytically examined. The imposed electric field is constant and normal to the axes of the cylinders. The electric double layer surrounding each dielectric cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model that allows for the overlap of the double layers of adjacent cylinders is employed. The electrokinetic equations that govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution surrounding the charged cylinder in a cylindrical cell are linearized assuming that the system is only slightly distorted from equilibrium. Through the use of a regular perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the cylinder as the small perturbation parameter. Analytical expressions for the electroosmotic velocity of the fluid solution and the effective electric conductivity in the array of cylinders are obtained in closed forms as functions of the porosity of the fiber matrix and other characteristics of the porous system. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. The cell model predicts that, under otherwise identical conditions, the electric conductivity in a porous medium composed of an array of parallel cylinders in the transverse direction in general is smaller than that of a suspension of spheres, but there are some exceptions. The effect of interactions among the cylinders or spheres on the effective conductivity can be significant under appropriate conditions.

Time-varying Brinkman electrophoresis of a charged cylinder-in-cell model

The reduction of platinum loading is essential for lowering the cost of Proton Exchange Membrane Fuel Cells (PEMFCs). However, low platinum loadings typically lead to performance losses due to reduced electrochemical active surface area as well as additional local transport losses within the catalyst layer. Experimentally, limiting current analysis provides a helpful tool to investigate the oxygen transport limitations. In this method the limiting current (obtained at cell voltages of about 0.2 V) is measured for different oxygen concentrations and total pressures. The oxygen transport resistance is then calculated from the ratio of oxygen concentration and limiting current. The pressure variation allows separating the pressure dependent and pressure independent parts of this resistance, which are related to transport in the channels, molecular diffusion in the Gas Diffusion Layer (GDL), Knudsen diffusion through the Micro Porous Layer (MPL) and cathode catalyst layer (CCL) plus local transport losses within the CCL, respectively. However, the method does not allow to easily break down the contributions of each cell component and processes to the total resistance, which requires the variation of the components[1].Therefore, within the project FURTHER-FC[2] we develop a multiscale modeling approach for interpreting the experimentally observed transport losses and to quantify the contributions of the different cell components based on their microstructure. On the sub-µm scale a Lattice Boltzmann model is developed to describe the transport within the CCL on the agglomerate scale, taking into account the transport through the ionomer film. This model is used to parametrize the effective local transport resistance[3] for calculation of the reaction kinetics in the cell model. For the GDL/MPL Direct Numerical Simulation (DNS) applied to the real microstructures[4] is used to obtain the effective diffusion coefficients, which are then applied in the cell model. The 2D PEMFC model considers the multicomponent transport, i.e., free flow in the gas channels and transport through the porous media according to Darcy’s law, charge transport, water transport in the ionomer, energy transport as well as the electrochemical reactions. Model validation is performed with limiting current analysis on MEAs with different platinum loading under various pressures and relative humidity. By analyzing the local concentrations within the cell, the model is then used to quantify the contributions of each cell component to the overall oxygen transport resistance. The project FURTHER-FC [2] has received funding from the Fuel Cells and Hydrogen 2 Joint Undertaking (now Clean Hydrogen Partnership) under Grant Agreement No 875025. This Joint Undertaking receives support from the European Union’s Horizon 2020 Research and Innovation program, Hydrogen Europe and Hydrogen Europe Research. [1] Daniel R. Baker et al, J. Electrochem. Soc. (2009) 156 B991[2] https://further-fc.eu/[3] T. Jahnke and A. Baricci, J. Electrochem. Soc. 169 (2022) 094514[4] M. Ahmed-Maloum et al., Journal of Power Sources 561 (2023) 232735 Figure 1

In this paper, the permeability of fiber fabric used in liquid composite molding (LCM) is predicted by the method of numerical simulation. The three-dimensional finite element model of unit cell representing the periodic micro-structure of a plaid is established. In the process of numerical simulation, each fiber bundle in unit cell is treated as a porous medium. Stokes equation and Darcy's law are employed to model the saturated flow between the fiber bundles and the saturated flow in the fiber bundle, respectively. Steady state flow of the finite element model of unit cell is simulated. The effective permeability of the plaid is obtained from the postprocessing of the simulation results by using Darcy's law.

Effective thermal conductivity of a porous medium is a key thermos-physical parameter in characterizing heat transfer properties in many applications. In this study, a new cell model to predict the porous medium effective thermal conductivity is developed by treating the cells as being variables in size in relation to porosity. In the new model, the interaction of a particle with the surrounding is conceptualized as a fluid cell surrounding the particle and the particle size distribution is explicitly taken into account by the variations of cell size in the porous medium. While the fluid volume fraction varies in different cells, the total fluid volume fraction in the porous medium is required to be the same as the porosity. The developed effective thermal conductivity model is then compared with experimental data sets from the literature. The effect of cell size variations on the effective thermal conductivity of porous medium is quantified and discussed. The results demonstrate that the model that incorporates cell size variations can capture scattered experimental data in the literature. The cell size variations significantly affect the effective thermal conductivity of porous medium and the non-uniformity of cell size enhances the effective thermal conductivity.

An improved mathematical hydrodynamic quasi-two-dimensional model of cells, CELSUB3, is presented for simulating drainage systems that consist of pumping well fields or subsurface drains. The CELSUB3 model is composed of an assemblage of algorithms that have been developed and tested previously and that simulate saturated flow in porous media, closed conduit flow, and flow through pumping stations. A new type of link between aquifer cells and drainage conduits is proposed. This link is verified in simple problems with well known analytical solutions. The correlation between results from analytical and mathematical solutions was considered satisfactory in all cases. To simulate more complex situations, the new proposed version, CELSUB3, was applied in a project designed to control the water-table level within a sewer system in Chanar Ladeado Town, Santa Fe Province, Argentina. Alternative drainage designs, which were evaluated under conditions of dynamic recharge caused by rainfall in a critical year (wettest year for the period of record) and a typical year, are briefly described. After analyzing ten alternative designs, the best technical–economic solution is a subsurface drainage system of closed conduits with pumping stations and evacuation channels.