Design Equations for Non-Isothermal Reactors

Design calculations for non-isothermal reactors should account for the effect of temperature on rate. Thus, the rate equation used in the design calculations is treated as a function of both conversion x and temperature T, -ry = -rJ Xj, T)). 

Tf femperafure of fhe fluid in fhe reactor vessel Cao- feed concenfrafion of A Tq feed femperafure 

An equation relating temperature T and conversion Xa is required to design the non-isothermal reactors. This relationship between temperature T and conversion is obtained by setting up a heat balance equation around the reactor (Section 3.1.5.3). In certain cases, reactor temperature T is deliberately varied with conversion by regulating the heat supply to the reactor or heat removal from the reactor. One such case is the non-isothermal reactor in which a reversible exothermic reaction is carried out. In the case of a reversible exothermic reaction, there is an optimum temperature T for every value of conversion x at which the rate is maximum. A specified conversion Xaj will be achieved in a CSTR or a PFR with the smallest volume or in a batch reactor in the shortest reaction time if the temperature in the reaction vessel is maintained at the optimum level. This optimal temperature policy in which temperature is varied as a function of conversion x,i is known as the optimal progression of temperature presented in the following section. 

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