Mathematical Modeling of a Membrane Reactor Using Numerical Methods:Comparison of Orthogonal Collocation with Finite Difference

Three different numerical methods such as orthogonal collocation, finite difference and shooting method are performed comparatively for modeling a straight membrane gas reactor and the results have been compared by analytical solution. The performance of the reactor is studied by a hypothetical gas phase reaction DCBA+⇔+ which occurs in a dense polymeric catalytic membrane reactor (DOPMR). In this work, the effect of Thiele modules parameter () has been studied on the variation of the outlet concentration. As the results, shooting method showed instability in prediction of the model responses, although both orthogonal collocation and finite difference exhibited stable results in the range of studied conditions. For the lower number of grids in the bed length (n<20), the results revealed orthogonal collocation was more accurate procedure than the finite difference method, whereas for higher number of step sizes (n>20) finite difference could predict the results with more accuracy.

Keywords:

membrane reactor , numerical modeling , orthogonal collocation