Temperature and Energy Considerations in Tubular Reactors

In this section we treat the material and energy balance equations for a plug flow reactor. For steady-state operation the energy balance analysis leading to equation (10.1.4) is appropriate  

These equations must be solved simultaneously using a knowledge of the temperature dependence of reaction rate expression. 

If one considers the rate at which heat is being supplied to a differential length of a tubular reactor, geometric considerations imply that 

A material balance on this differential reactor volume yields the following result  

The summation involves the effluent molal flow rates. This equation and equation (10.4.2) must be solved simultaneously to determine the tubular reactor size and to determine the manner in which the heat transfer requirements are to be met. For either isothermal or adiabatic operation, one of the three terms in equation (10.4.7) will drop out, and the analysis will be much simpler than in the general case. In the illustrations that follow, two examples are treated in detail to indicate the types of situations that one may encounter in practice and to indicate in more detail the nature of the design calculations. 

---