Temperature control in semi-batch reactors

Many chemical reactions are preferably carried out batchwise, occasionally in a pure batch mode, where all reactants are mixed before the reaction starts, but more often in a semi-batch mode, where at least one reactant is added gradually. 

A pure batch reactor, used for a rapid exothermic reaction, is inherently very unstable. A well known example of such a reactor is a bomb. When we want to control a chemical reaction effectively, also in the laboratory, the semi-batch mode is usually preferred. A certain amount of one reactant (A) is put into the reactor, and heat to a temperature that makes the reaction possible. The other reactant (B) is introduced into the reactor with a controlled rate. When the reactor has adequate cooling, the reactor temperature can be kept effectively within desired limits. The practical problem is a how to adjust the cooling rate to the strongly varying reaction rate. 

Controlling the cooling rate can be achieved in several ways, e.g., by controlling 

The required knowledge of the process consists of a kinetic model, such as described by eqs. (3.25a,b), and a heat balance. This can be written in the following way 

The symbols are are the same as in section 8.3.2, the dashes refer to the cooling medium. When both reactant concentrations are found from eqs. (3.25a,b) as functions of time, the reactor temperature is given as a function of time and of the feed rate F (of reactant B) and the flow rate of die cooling medium F (note that AT is also dependent on F ). 

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