Variable pressure permeability

Surface diffusion has been extensively studied in literature. An overview of experimental data is given in Table 6.1. Okazaki, Tamon and Toei (1981), for example, measured the transport of propane through Vycor glass with a pore radius of 3.5 nm at 303 K and variable pressure (see Table 6.1). The corrected gas phase permeability was 0.69 m -m/m -h-bar, while the surface permeability was 0.55 m -m/m -h-bar, and so almost as large as the gas phase permeability (Table 6.1). It is clear from Table 6.1, that the effects of surface diffusion, especially at moderate temperatures, can be pronounced. At higher temperatures, adsorption decreases and it can be expected that surface diffusion will become less pronounced. 

The parameter or variable V" will have the dimensions of permeability times pressure, as previously observed in terms of moles. However, in terms of the total gas volume permeated, and using the pointwise permeability and dealing with volume fractions, then V" would have the dimensions of... 

Permeabilities in Constant Volume/Variable Pressure Apparatus, J, Appl. Polym, Sci,, 20, 1921 (1976) Measurement of Gas Permeability of Polymers. II. Apparatus for Determination of Mixed Gases and Vapurs. J. Appl, Polym. Sci., 20, 287 (1976). 

It is useful to classify permeability methods into two main groups. These are fixed pressure and variable pressure methods. In the former, a steady pressure is applied to a plug of powder and its pneumatic of fluid resistance properties are determined. In variable pressure methods the pressure drop across a powder plug is constandy changing and the rate of change of pressure is measured. 

W.M. Lu, Theoretical and Experimental Analyses of Variable Pressure Filtration and the Effect of Side Wall Friction in Compression-Permeability Cells, PhD dissertation. University of Houston, Texas, 1968. 

Pressure solution. Next, consider the corresponding pressure field. We recall from Equations 12-2 and 12-4a that g(x,y,z) = p(x,y,z) Vk(x,y,z) satisfies 9 g/9 + g/9y + g/9z = 0. If we assume that both the permeabilities and pressures are known at all well positions and boundaries, it follows that g = pVk can be prescribed as known Dirichlet boundary conditions. Then, the numerical methods devised in Chapter 7 for elliptic equations can be applied directly on the other hand, analytical separation of variables methods can be employed for problems with idealized pressure boundary conditions. The general approach in this example is desirable for two reasons. First, the analytical constructions devised for the permeability function (see Equations 12-5b, 12-10, and 12-11) allow us to retain full control over the details of small-scale heterogeneity. Second, the equation for the modified pressure g(x,y,z) (see Equation 12-4a) does not contain variable, heterogeneity-dependent coefficients. It is, in fact, smooth thus, it can be solved with a coarser mesh distribution than is otherwise possible. 

Gas Transport Measurement Permeation measurements were made using a constant volume-variable pressure apparatus (20) at 25 - 300 C and 10 atmosphere feed pressure with a permeate pressure of less than 10 ton. The permeability of a gas through a polymer can be described by equation 1 ... 

Parameters q and W are variables when filtration conditions are changed. Coefficient (rj, is a function of pressure (rj, = f(P). The exact relationship can be derived from experiments in a device called a compression-permeability cell. Once this relationship is defined, the integral of the right hand side of the above equation may be evaluated analytically. Or, if the relationship is in the form of a curve, the evaluation may be made graphically. The interrelation between W and P, is established by the pump characteristics, which define q = f(W) in the integral. Filtration time may then be determined from dq/dt = W, from which we may state ... 

Air flow/air permeability Measure of the amount of air that flows through a filter - a variable of the degree of contamination, differential pressure, total porosity, and filter area. Expressed in either cubic feet/minute/square foot or liters/minute/square centimeter at a given pressure. 

The fifteen layers of constant permeability and porosity were taken as the reservoir zones for which these parameters would be estimated. The reservoir pressure is a state variable and hence in this case the relationship between the output vector (observed variables) and the state variables is of the form y(t,)=Cx(t,). 

The system states (dependent variables) are the pressure, p, and the superficial (Darcy) velocity, v. The density, p, and viscosity, p, are fluid properties, and g is the acceleration of gravity. The porosity, < )(z), and permeability, fc(z), represent the macroscopic properties of the media. Both are spatially dependent and are represented as continuous functions of position z, as explicitly noted. While the per-... 

The fastest HPLC separations are achieved using the maximum available pressure drop. Using reduced variables, Equation 9.6 illustrates a linear relationship between retention time and mobile phase viscosity for packed columns and fixed values of AP (pressure drop), Areq (required efficiency for a given separation) and (a constant that describes the permeability of the packed bed) [4]... 

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