A mathematical model is developed for predicting the mixing characteristics of fixed beds of spheres. The model is based on a two-dimensional network of perfectly stirred tanks. By means of the conventional partial differential equation description of flow in fixed beds, the predictions of the new model are compared with experimentally observed axial and radial mixing characteristics. The introduction of a capacitance effect is shown to enable the model to predict the abnormally low axial Peclet numbers observed in liquid-phase systems in the unsteady state.
The mathematical model developed in the first part of this paper is extended to cover chemical reaction in a cylindrical fixed bed of porous catalyst spheres. The mathematical effect on the model of various controlling rate steps, nonconstant property values, and multiple, non-first-order reactions is discussed. After the general discussion a simplified system is chosen to indicate the practical advantages of the model. A single, first-order, irreversible, exothermic reaction is considered to proceed according to an effectively homogeneous rate expression, which varies exponentially with the inverse of absolute temperature. Both steady state and transient cases are calculated for a reactor, the walls of which are maintained at constant temperature.