The character of the stationary state of exothermic processes

Abstract

The temperature level of exothermic processes is in some cases completely and in most cases at least partly determined by the heat of reaction itself. Because of the exponential dependency of the reaction rate on temperature, these processes very often have different stationary solutions for a given set of boundary conditions: two stable solutions, one at low temperature and low degree of conversion and one at high temperature and high degree of conversion, and in between an unstable ignition state. A necessary condition for this is a feed back of heat along the reaction path. This feed back may be due to convection (mixed reactor), conduction (flame) or to heat exchange (e.g. between outlet and inlet). Assuming a simple first-order Arrhenius rate equation different cases are considered: the ideal mixer, a piston-flow reactor with heat exchange between outlet and inlet, and a piston-flow reactor with longitudinal conduction of heat. It can be shown that the character of the system, that is to say either one stable solution, or two stable solutions with an ignition state in between, depends on the value of two dimensionless parameters: the adiabatic temperature rise for complete conversion and the temperature necessary to obtain a degree of conversion 1/ e, both temperatures being expressed in units E/ R, E being the activation energy.