Criteria for the use of 1D and 2D models in catalytic membrane reactor modeling

A criterion was developed to determine the necessity of using 1D or 2D methods for modeling a concentric tubular membrane reactor for hydrogen-producing reactions. Four dimensionless parameters were defined to provide a complete description of the physical and chemical systems, and the effects of each parameter on the difference between a 1D and 2D model were explored. The membrane reactor geometry consisted of a tube-and-shell configuration with a catalyst bed in the tubular section and a perm-selective membrane in the interphase. The four dimensionless parameters consisted of the Damk & ouml;hler number (Da), which relates the reaction and axial convection rates, the P & eacute;clet number (Pe), which relates the radial diffusion and axial convection rates, the transport parameter (theta), which relates the axial convection and membrane permeation rates, and the equilibrium parameter (epsilon), which is a measure of the favorability of the reaction. A cutoff at which 1D and 2D model results have less than a 1% difference in final concentrations was used to define a critical Pe value, or Pe(crit). Then, a criterion equation was fitted using non-linear regression so that any system can be calculated and compared against Pe(crit). Using this criterion, a model above the cutoff (Pe > Pe(crit)) can reduce computation time by selectively calculating a simple 1D model for conditions, while a model below the cutoff (Pe <= Pe(crit)) should use a more computationally expensive 2D model to assure accuracy. The final criterion was validated against literature data for both 1D and 2D models.