The reactor analysis and design acquires another level of complexity when the reactor is operated under nonisothermal conditions; that is, the temperature of the reactor varies with time or position in the reactor, mostly due to the substantial heat effects associated with most reactions. As the temperature varies, the rate constant also changes according to the Arrhenius equation, and a single governing equation is not sufficient to solve for two variables (T and XA or T and V). The second equation needed is obtained by performing an energy balance on the system.
The simple conversion-concentration relationship described by equation 9.20 is valid only for a constant volume system. Gas-phase reactions involving changes in pressure, temperature, or the number of moles experience a volume change, and the conversion is not merely a function of concentration but also of these other variables. Additional governing equations are required to describe these situations.
It can be seen that a chemical engineer will be required to solve problems in chemical engineering kinetics that range from simple linear equations to highly complex, multiple, simultaneous differential equations. The representative examples presented in section 9.2 utilize the mathematical relationships that are obtained when the concepts of chemical engineering kinetics are applied to different situations. The development of these mathematical relationships itself requires an in-depth knowledge of concepts and is not covered in this text.
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