Nonadiabatic Batch Reactors

The temperature varies with the reaction time in the nonisothermal batch reactor. To perform the energy balance, we use the same energy balance equation 14.67, annulling the molar flow terms, but considering the variation of sensible heat with temperature and time. Then, 

Integrating Xa between 0 and Xa, T between To and T, being t the common variable. 

Substituting the external heat as a function of the overall heat transfer coefficient  

This is the energy balance equation for a batch reactor, in which T is the temperature of reaction, Tj is the temperature of the cooling/heating coil, and To is the initial temperature of the system. All other parameters have already been defined. 

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Closed Systems Closed systems exchange energy with their environment through their boundaries, but they do not exchange matter. The simplest example is the nonadiabatic batch reactor. These systems also tend towards a thermodynamic equilibrium with time, again characterized by maximal entropy, or the highest possible degree of disorder. 

Sizing or analysis of a nonadiabatic batch reactor, with a single homogeneous reaction taking place, requires the simultaneous solution of a mass balance and the macroscopic energy balance. 

If the batch reactor operation is both nonadiabatic and nonisothermal, the complete energy balance of equation 12.3-16 must be used together with the iiaterial balance of equation 2.2-4. These constitute a set of two simultaneous, nonlincmr, first-flijer ordinary differential equations with T and fA as dependent variables and I as Iidependent variable. The two boundary conditions are T = T0 and fA = fAo (usually 0) at I = 0. These two equations usually must be solved by a numerical procedure. (See problem 12-9, which may be solved using the E-Z Solve software.)... 

NONISOTHERMAL, NONADIABATIC BATCH, AND PLUG-FLOW REACTORS... 

A Closed System does not exchange matter with the surroundings but exchanges energy. Thermodynamically it tends to the state of thermodynamic equilibrium (maximum entropy). An example is a batch nonadiabatic reactor. 

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