Packed bed reactor analysis by orthogonal collocation

Abstract

The equations governing a packed bed reactor with radial temperature and concentration gradients are solved using the orthogonal collocation method. The method is shown to be faster and more accurate than finite difference calculations. Using the orthogonal collocation method it is straightforward to extend one-dimensional (lumped parameter) models to the two-dimensional models needed when radial temperature and concentration gradients are important. The two-dimensional model is necessary for large Biot numbers, h w R/ k e, where h w is the wall heat transfer coefficient, R is the tube radius, and k eis the tube radius, and k e is the effective thermal conductivity. For Biot number less than one, seventy-five per cent of the resistance to heat transfer is at the wall, and a one-dimensional (lumped parameter) treatment gives good results. Computations are illustrated for both plug flow and radially-varying velocity. In the latter case the velocity profile induces effective thermal conductivity and diffusivity profiles. Calculations made using the velocity profile predict a heat transfer coefficient which is used in the plug flow model. Good agreement is obtained between the models.