Simulating catalytic membrane reactors using orthogonal collocation with spatial coordinates transformation

Abstract

It is presented in this study a new numerical scheme using orthogonal collocation together with an independent variable (spatial coordinate) transformation, useful for solving the model equations associated to membrane reactors with catalytic membranes. This new scheme takes advantage of a noticeable feature of the concentration profile inside a catalytic membrane: close to the membrane surfaces, this profile becomes steeper and steeper with the Thiele modulus. Using traditional numerical methods for solving the model equations of a catalytic membrane reactor, namely finite differences with equispaced intervals or orthogonal collocation, for example, may lead to imprecise results. In order to illustrate the ability of this new numerical scheme for solving such equations, it is applied to the resolution of a case where an analytical solution is available (a generic A ⇌ B reaction carried out in a catalytic membrane with perfectly mixed flow pattern in both retentate and permeate sides). Then, the same numerical scheme is used for solving a model describing the cyclohexane dehydrogenation, A ⇌ B + 3 C , carried out in a porous membrane with the same flow pattern as above—and the results are compared with the ones obtained using an adaptive wavelet-based method. For these two models, solutions were also obtained using straight orthogonal collocation and finite differences with homogeneously distributed grid points for the sake of the comparison. The results show that the new numerical approach is useful in dealing with this kind of problems, especially for high Thiele modulus values, showing high accuracy and demanding low computation time. Finally, this new scheme is applied to the resolution of a more complex model: a generic reaction 2 A ⇌ B , carried out in a dense catalytic cylindrical membrane with plug–flow pattern for both retentate and permeate sides.