Pressure porosity diffusion

The process of pressure-porosity diffusion, the fourth solution mentioned in Section 7, requires solid-fluid coupling to exist. If the pore liquid cannot flow, as is likely in the case of ductile smectitic shales (Dusseault 2003), or if the liquid is present as a fully occluded phase so that it is in the form of liquid bubbles in the solid mineral, as in a vesicular basalt, the wave cannot exist. This also... 

The third solution is porosity diffusion. In this solution the fluid is unable to compress because the motions are too slow, therefore it releases the stresses imparted on it by the matrix through fluid motions observed as pressure and porosity diffusion. Apparently, the compressible-incompressible transition comes at about a frequency of strain excitation of 10 to 10° Hz for the common range of liquids and phase compressibilities. Above this transition frequency, the fluid will compress (strain) in response to excitation. 

The fourth and last solution is a pressure-porosity wave in which fluid flow at the incompressible limit of fluid motions is coupled to elastic deformations of the matrix. The attenuation of this wave is highly frequency dependent, but it is quite conservative at low frequencies. Unlike the previous three solutions which each exist as an independent process, this solution is always coupled to porosity diffusion. It can leave behind an increase in pressure as it propagates, converting some of the inertial energy associated with the... 

The basic equations of motion contain coefficients of shear viscosity for the fluids. This gives rise to a dependency of porosity diffusion on the rate of fluid transmission through the pore space. In low viscosity cases such as crustal fluids in deep interconnected fracture networks, transmission is relatively rapid in reservoirs largely saturated with viscous oil, transmission of pressure effects can be quite slow. For a 10,(XX) cP oil filling 88% of the pore space of a 30% porosity 2-3 Darcy sand, it took about 5 weeks to see a substantial response at distances of 300 m from the excitation well which was being aggressively pulsed at the right frequency (Spanos et al., 2003). 

In summary, slow catalytic reaction rates are proportional to the internal surface area of the catalyst whereas fast reactions may be either proportional to the pore volume (porosity) of the catalyst and independent of surface area (for the case of low pressures, small pores, Knudsen flow) or may be proportional to the square root of both pore volume and surface area (for the case of large pores, high pressures, ordinary diffusion). 

Metal carbonate decompositions proceed to completion in one or more stages which are generally both endothermic and reversible. Kinetic behaviour is sensitive to the pressure and composition of the prevailing atmosphere and, in particular, to the availability and ease of removal of C02. The structure and porosity of the solid product and its relationship with the reactant phase controls the rate of escape of volatile product by inter-and/or intragranular diffusion, so that rapid and effectively complete withdrawal of C02 from the interface may be difficult to achieve experimentally. Similar features have been described for the removal of water from crystalline hydrates and attention has been drawn to comparable aspects of reactions of both types in Garner s review [ 64 ]. 

As well as depending on catalyst porosity, the reaction rate is some function of the reactant concentrations, temperature and pressure. However, this function may not be as simple as in the case of uncatalyzed reactions. Before a reaction can take place, the reactants must diffuse through the pores to the solid surface. The overall rate of a heterogeneous gas-solid reaction on a supported catalyst is made up of a series of physical steps as well as the chemical reaction. The steps are as follows. 

Figure 1. Schematic illustration of factors influencing the production and migration of radon in soils and into buildings. Geochemical processes affect the radium concentration in the soil. The emanating fraction is principally dependent upon soil moisture (1 0) and the size distribution of the soil grains (d). Diffusion of radon through the soil is affected primarily by soil porosity ( ) and moisture content, while convective flow of radon-bearing soil gas depends mainly upon the air permeability (k) of the soil and the pressure gradient (VP) established by the building.

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

If the porosity of the material is insufficient, the time lired to effect separation is unduly long. It may, in connection, be mentioned that it has from time to been suggested that by means of diffusion it would )Ossible to separate a mixture of gases of different sities without the consumption of power. How-, in practice this has not been found to be the case, n order to obtain a reasonable speed of separation, fference of pressure between the two sides of the ision material has to be maintained. 

One crifical paramefer fhaf affecfs fhe fhickness of fhe diffusion layer is fhe compression force used in fhe fuel cell in order fo avoid any gas leaks and to assure good contact between all the components. However, this compressive force can deform the diffusion layer and hence affect the performance of the cell. More information regarding how the compression forces affect the diffusion layer is discussed in Section 4.4.5. Ideally, the material used as the DL should be able to resist this compression force or pressure without affecting most of its parameters. Figure 4.21 shows a schematic of the cell voltage (performance) at a given current density, resistance, and DL porosity as a function of the cell s compression. 

As stated earlier, CEP and CC are the most common materials used in the PEM and direct liquid fuel cell due fo fheir nature, it is critical to understand how their porosity, pore size distribution, and capillary flow (and pressures) affecf fhe cell s overall performance. In addition to these properties, pressure drop measurements between the inlet and outlet streams of fuel cells are widely used as an indication of the liquid and gas transport within different diffusion layers. In fhis section, we will discuss the main methods used to measure and determine these properties that play such an important role in the improvement of bofh gas and liquid transport mechanisms. 

However, this porosity takes into account all the open pores—even those that are not connected between each other, which are useless in fuel cell operation. Therefore, the effective porosity, which counts only the interconnected pores, is more critical when determining the optimal diffusion layer in a fuel cell. This porosity can be determined by using volume filtration techniques. For example, a porous sample is immersed in a liquid that does not enter inside the pores (e.g., mercury at low pressures) and then the total volume of the material can be determined. Next, the specimen is put inside a container of known volume that contains an inert gas, and the changed pressure is recorded. After this, a second evacuated chamber of known volume is connected to the system, and the new pressure is recorded. With these pressures and the ideal gas law, the volume of open pores and thus the effective porosity can be determined [195]. 

J. T. Gostick, M. W. Fowler, M. A. loannidis, et al. Capillary pressure and hydrophilic porosity in gas diffusion layers for polymer electrolyte fuel cells. Journal of Power Sources 156 (2006) 375-387. 

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