Area averaging of packed bed in continua conservation equations in axial flow

Abstract

AbstractA novel averaging of the conservation equations for axial flow in packed beds is presented to express the momentum, continuity, and energy equations in terms of the cross‐sectional averages of concentration, temperature, and superficial velocity. The model integrates the radial fluctuations of the intrinsic variables into the partial differential equations of the model and presents a method for the design and analysis of catalytic reactors at a broad range of Reynolds numbers without the necessity of adjusting the operating conditions to minimize the impact of the radial profiles of velocity, concentration, and temperature. Since the control of the industrial reactors is dependent on the average values of the concentration and temperature, the model can be directly employed for design, optimization, and control processes with the added advantage of time and cost savings for both the numerical resolution and laboratory testing expenses. The model is limited to reaction systems with Péclet numbers of less than 700 with an average void fraction of for which the ratio of the bed length‐to‐particle diameter to particle Péclet number exceeds . The model was applied to the simulation of steam methane reforming (SMR). The results indicate that the average equations predict the responses of the SMR properly and thus the model could be reliably utilized for process design, operation, and control.