Nonisothermal reactors: Theory and application of thermal time distributions

Abstract

For reactions in nonisothermal systems, the thermal time distribution is the analog of the residence time distribution. If the reaction can be characterized by a single activation energy, knowledge of the thermal time distribution based on this activation energy can be used to predict the yield of a first order reaction uniquely and to closely bound the yield for reactions of order other than first. Thermal time distributions are a useful conceptual and analytical tool for reaction engineering, particularly in systems where the temperature and velocity profiles are not strongly coupled to the extent of reaction. This situation frequently occurs in the processing of polymer melts, for example in the activation of blowing agents or in chemical modification of the polymer chain. Simplified flow models of heat exchange and extrusion equipment are used to illustrate the application of thermal time distributions and to show that they often differ significantly from the residence time distribution in the same device. In fixed wall heat exchangers, the thermal time distribution shows less uniform reaction conditions than would be true for an isothermal reaction governed by the residence time distribution. In extruders, and particularly for those where viscous dissipation is the major energy input, this situation is dramatically reversed with a reaction environment very similar to that for piston flow and substantially better than would occur in the same equipment operated isothermally.