Porous media methods

Estimate the effective diffusivity of naphthalene in saturated sediment collected from Campus Lake on the LSU campus in Baton Rouge using the following properties of the material and the saturated porous media method described in Chapter 5. 

The technique just described requires the porous medium to be sealed in a cell, so It cannot be used with pellets of irregular shape or granular material. For such materials an alternative technique Introduced by Eberly [64] is attractive. In Eberly s method the porous pellets or granules are packed into a tube through which the carrier gas flows steadily. A sharp pulse of tracer gas is then injected at the entry to the tube, and Its transit time through the tube and spreading at the exit are observed. A "chromatographic" system of this sort is very attractive to the experimenter,... 

Several alternative methods have been considered in order to increase the energy density of natural gas and facilitate its use as a road vehicle fuel. It can be dissolved in organic solvents, contained in a molecular cage (clathrate), and it may be adsorbed in a porous medium. The use of solvents has been tested experimentally but there has been little improvement so far over the methane density obtained by simple compression. Clathrates of methane and water, (methane hydrates) have been widely investigated but seem to offer little advantage over ANG [4]. Theoretical comparison of these storage techniques has been made by Dignam [5]. In practical terms, ANG has shown the most promise so far of these three alternatives to CNG and LNG. 

In order to be useful in practice, the effective transport coefficients have to be determined for a porous medium of given morphology. For this purpose, a broad class of methods is available (for an overview, see [191]). A very straightforward approach is to assume a periodic structure of the porous medium and to compute numerically the flow, concentration or temperature field in a unit cell [117]. Two very general and powerful methods are the effective-medium approximation (EMA) and the position-space renormalization group method. 

Because the fluid in a porous medium follows a tortuous path through channels of varying size and shape, one method of describing the flow... 

With the supposition that the slip layer is thin and the slip velocity is constant, various analyses have been developed in the search for the ideal experimental method to define slip. The Mooney analysis (20) for both tube flow and concentric cylinder flow has been applied to a wide range of materials including polymer solutions (21), filled suspensions (22), semisolid foods (23), fruit purees (24), and ketchups (25). Alternate estimates of slip velocity have been determined experimentally from, parallel plate torsion flow (26), from flow data in channels and inclined planes, and from porous medium geometries (8). 

Associated with the mass balance of water and the mechanical equilibrium equation, relations (7) and (8) give a model of solution transport in a deformable porous medium. The result of an incremental numerical method was... 

In the last section, convection in a two-dimensional porous medium is presented as a physical problem. Porous media is important in environmental heat transfer studies, transpiration cooling, and fuel cells, as some examples. Using the slug flow assumption, the energy equation is solved using an alternating implicit method to show its effectiveness. 

The approximate integral equation method that was discussed in Chapters 2 and 3 can also be applied to the boundary layer flows on surfaces in a porous medium. As discussed in Chapters 2 and 3, this integral equation method has largely been superceded by purely numerical methods of the type discussed above. However, integral equation methods are still sometimes used and it therefore appears to be appropriate to briefly discuss the use of the method here. Attention will continue to be restricted to two-dimensional constant fluid property forced flow. 

As discussed in Chapters 2 and 3, in the integral method it is assumed that the boundary layer has a definite thickness and the overall or integrated momentum and thermal energy balances across the boundary layer are considered. In the case of flow over a body in a porous medium, if the Darcy assumptions are used, there is, as discussed before, no velocity boundary layer, the velocity parallel to the surface near the surface being essentially equal to the surface velocity given by the potential flow solution. For flow over a body in a porous medium, therefore, only the energy integral equation need be considered. This equation was shown in Chapter 2 to be ... 

As a last example of the use of the integral equation method consider again two-dimensional flow about an isothermal cylinder in a porous medium. The situation considered is shown in Fig. 10.22. 

Use the integral equation method to derive an expression for the variation of the local heat transfer rate along a wide flat plate buried in a porous medium through which... 

Oosthuizen. P.H. and Paul, J.T.. "Natural Convection in a Rectangular Enclosure with a Partially Heated Wall and Partly Filled with a Porous Medium", Proc. Eighth Int. Conf. on Numerical Methods in Thermal Problems. Vol. VIII. Part I, Pineridge Press, Swansea, U.K., 1993, pp. 467-478. 

The methods described so far for studying self-diffusion are essentially based on an observation of the diffusion paths, i.e. on the application of Einstein s relation (eq 3). Alternatively, molecular self-diffusion may also be studied on the basis of the Fick s laws by using iso-topically labeled molecules. As in the case of transport diffusion, the diffusivities are determined by comparing the measured curves of tracer exchange between the porous medium and the surroundings with the corresponding theoretical expressions. As a basic assumption of the isotopic tracer technique for studying self-diffusion, the isotopic forms are expected to have... 

Operations like pressure swing adsorption involve the condensation of the liquid in the porous medium. Several researchers developed predictive models of the configuration of liquid phase in the wet, unsaturated, porous media. The method developed by Silverstein and Fort (2000) is based on simulated annealing with random swapping of gas and liquid elements in the system to achieve a global energy minimum defined by... 

There are methods for measuring the surface area using the flow of gases through a porous medium, by finding a pressure drop across the particle. The equation relating the mole gas flow rate J and the pressure drop AP can be written as [13]... 

The phenomenon of capillary condensation provides a method for measuring pore-size distribution. Nitrogen vapor at the temperature of liquid nitrogen for which cos(0) = 1 is universally used. To determine the pore size distribution, the variation in the amount of nitrogen inside the porous particle is measured when the pressure is slightly increased or decreased. This variation is divided into two parts one part is due to true adsorption and the other to capillary condensation. The variation due to adsorption is known from adsorption experiments with nonporous substances of known surface area, so the variation due to condensation can be calculated. The volume of this amount of nitrogen is equal to the volume of pores with the size as determined by the Kelvin equation. Once a certain model has been selected for the complicated pore geometry, the size of the pores can be calculated. Usually it is assumed that an array of cylindrical capillaries of uniform but different radii, and randomly oriented represents the porous medium. So the Kelvin equation in the form of Equation 3.9 is used. Since condensation is combined with adsorption, the thickness of the adsorption layer... 

All these different mechanisms of mass transport through a porous medium can be studied experimentally and theoretically through classical models (Darcy s law, Knudsen diffusion, molecular dynamics, Stefan-Maxwell equations, dusty-gas model etc.) which can be coupled or not with the interactions or even reactions between the solid structure and the fluid elements. Another method for the analysis of the species motion inside a porous structure can be based on the observation that the motion occurs as a result of two or more elementary evolutions that are randomly connected. This is the stochastic way for the analysis of species motion inside a porous body. Some examples that will be analysed here by the stochastic method are the result of the particularisations of the cases presented with the development of stochastic models in Sections 4.4 and 4.5. 

The classic and stochastic methods used for the analysis of liquid flow inside a porous medium are strongly related. These interactions are given by the relationships between the parameters of both types of models. We show here that the analysis of the flow of a liquid through a porous medium, using a stochastic model, can describe some of the parameters used in deterministic models such as ... 

The theoretical basis of the Hg-injection method is defined by Laplace law. By using a capillary model where the porous medium is assimilated to a bundle of cylindric capillary tubes the capillary pressure is Pc = y(l/Rci+l/Rc2) = 2y cos0 /Rc (3) where Pc is the capillary pressure Rd and Rc2 are mutually perpendiculcir radii of a surface segment R is the average pore-throat size (pm) 0is the angle between mercury menisc and pore wall (for mercury 0=140°) y is the interfacial tension (for mercury y = 0.480 N/m). 

Gas permeability method. Like the gas flow method, this technique is also based on the measurement of the flow rate of a gas through a porous medium such as a membrane. The flow rate is monitored as a function of the pressure drop across the thickness of the membrane. But unlike the gas flow method, the gas used in this method is a pure, nonadsorbable and noncondensable gas. 

A promising method of controlling and evaluating the structural parameters of plastic foams is the acoustic (ultrasonic) pulse method This method is based on the propagation of elastic waves in a porous medium depending on shape, distribution and volumetric content of the GSE. 

The method that has received the most attention belongs to the first category. Specifically, the particular model is the capillary tube model for porous medium and the power law model for the emulsion (J6). The shear-stress (t) rate relationship for a power law fluid is given by... 

A critical review of emulsion flow in porous media has been presented. An attempt has been made to identify the various factors that affect the flow of OAV and W/O emulsions in the reservoir. The present methods of investigation are only the beginning of an effort to try to develop an understanding of the transport behavior of emulsions in porous media. The work toward this end has been difficult because of the complex nature of emulsions themselves and their flow in a complex medium. Presently there are only qualitative descriptions and hypotheses available as to the mechanisms involved. A comprehensive model that would describe the transport phenomenon of emulsions in porous media should take into account emulsion and porous medium characteristics, hydrodynamics, as well as the complex fluid-rock interactions. To implement such a study will require a number of experi-... 

The electrochemical behavior of the powdered active carbon electrode depends on the surface chemistry, and cyclic voltammetry can be used as a simple method of characterizing active carbon materials. A new heterogeneous copper catalyst was developed using highly porous active carbon as the catalyst support [282]. The advantages of a porous-medium supported catalyst are that the active phase could be kept in a dispersed but stable state, and that, as an example, the oxidized organic pollutant is adsorbed onto carbon, thereby enhancing its surface concen-... 

In the near future, the development of the molecular simulation methods and the availability of results of comparison studies for a wide range of microporous sorbents should make the situation clearer However, these methods are always based on the same kind of experimental data a N2 adsorption isotherm at 77 K. These experimental conditions are very often far from those prevailing in the industrial applications. The use of a single adsorption isotherm within standard conditions could be considered as an advantage as it simplifies the experimental part of the characterization procedure. On the other hand, the possibility of using adsorption data in a wider temperature and pressure domain of conditions and for a large range of adsorbates should be helpful to prove or to invalidate the efficiency of the theoretical treatments. Besides, it would allow to adapt the complete characterization procedures and thus the choice of the experimental conditions in order to fit the final application in which the porous medium will be involved. 

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