Optimal design of non-isothermal reactors

The following reviews the analytieal treatment of (r - T - X ) eharts and develops eomputer programs for this elass of reversible reaetions. 

Most chemical reactions of industrial significance fall within the general class of reversible reactions given by 

If kj and kj denote tlie forward and reverse rate constants respectively, die general rate of disappearance (-r ) for any type of reaction is defined as  

For a constant density system, the concentration of any species, K, Cp, during the course of reaction is given by 

Consider the first order rate of reaetion with respeet to both the reaetants and produets. That is, ttj = = 1. Equation 6-133 beeomes 

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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. 

Not only is this characteristic a design simplification but it also provides a more controlled environment for reaction with respect to completeness of reaction, minimizing by-products and general uniformity of product. For non-isothermal reactions there is also the opportunity to take advantage of the enhanced heat transfer characteristics and to optimize the reactor design by suitable choice of mixer element type and length. 

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