Permeation of Gases through a Porous Slug

Equations 9.1 and 9.2 contain five unknown variables the partial pressures and fluxes of the components and the total pressure. To find the fluxes five additional equations are necessary. One obvious equation is 

The boundary conditions at the opposite surfaces of the septum give the other four. Assuming there is no mass transfer resistance other than inside the septum, these boundary conditions can be written as 

Thus there are two first-order differential equations (Equations 9.1 and 9.2) and five algebraic equations (Equations 9.4 - 9.6) with which to determine the two integration constants and the five variables. Different numerical techniques can be used to solve the problem. One way is to linearize Equations 9.1 and 9.2 and apply the iteration procedure described by Kerkhof [5]. An equation describing the variation of the total pressure inside the septum, 

For this specific situation, it may be assumed that dP/dz = 0. Now, the flux of component B can be eliminated from Equation 9.7, which yields 

The fluxes can be obtained by direct numerical integration of Equation 9.10  

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