Approximate models of concentration-polarization in Pd-membrane separators. Fast numerical analysis

Several approximate solutions are derived to predict the concentration polarization effect in a shell-andtube Pd-membrane empty separator with permeate flow either in the tube or in the shell. The first two approximations (Nekhamkina and Sheintuch (2015) [221) are governed by ODEs describing the axial profiles of the average variables coupled with algebraic relations that describe the radial profiles of velocity components and species concentrations. The hydrogen membrane flux is approximated by a mass transfer coefficient k=D(partial derivative c(H2)/(partial derivative)r)w/(< CH2 >) - c(H2w)) expressed via the Sherwood number Sh=kd/D which is a geometry-dependent parameter (D is hydrogen diffusivity, C-H2w = p(H2,w)(ret)/RT is its membrane wall concentration and d a characteristic length). Here Sh is obtained by 2-D CFD simulations in a wide range of parameters and when plotted vs the separator length, it reaches an asymptotic value that matches the predicted values and is independent of operating conditions. ; The third approximation reduces the polarization effect to an algebraic equation by approximating the effectiveness factor eta = [(p(2,w)(retH)) 5 (p(H2)(per))]/[<(p(H2)(ret))>(0.5)] (p(H2)(per))(0.5)] which depends mainly on the ratio of the mass-transfer coefficient to the membrane permeance parameter Gamma=Gamma(Sh). This expression can be used for fast design of separators that avoids or accounts for polarization effects. The three approximations offer a trade-off between accuracy and ease of application. (C) 2015 Elsevier B.V. All rights reserved.