Improved one-dimensional model of a tubular packed bed reactor

The major drawback of one-dimensional models of tubular fixed bed reactors, which are often used if the computational effort should be small, is the fact that the reaction rate is calculated using the average temperature over the cross-section of the reactor. The difference between this reaction rate and the average reaction rate over the cross-section becomes increasingly significant with increasing temperature difference over the radius of the reactor and with increasing activation energy of the reaction(s). Improved versions of the one-dimensional model, such as that of Hagan et al. [1988. A simple approach to highly sensitive tubular reactors. SIAM Journal of Applied Mathematics 48, 1083–1091] are available, which use an analytical approximation of the radial temperature profile to improve the prediction of the average reaction rate. However, application of these models involves solving of implicit equations. Here, a new model is proposed as an alternative to the existing one-dimensional models. It has the same form as the conventional one-dimensional model and contains only explicit functions. It is demonstrated that, at conditions not too close to runaway, the new model performs better than the well-known α-model.