Graphical Interpretation of the Design Equations

In the discussion of graphs of (l /—rj ) versus x, the term isothermal will be used to mean that the temperature does not change as xa changes. This definition is consistent with the definitions, given previously, for isothermal ideal batch reactors and isothermal ideal plug-flow reactors. However, this definition of isothermal is more general and can apply to a CSTR or to a series of reactors. 

The shape of the (—1/rA) versus xa curve is not always normal. This curve can be very different if the reaction is exothermic and the reactor is adiabatic, or if the rate equation does not obey Generalization III. 

let s reexamine one form of the design equation for an ideal CSTR  

In order to discriminate between the variable xa and the outlet conversion from the CSTR, let s call the latter xa,c ( e for effluent ), and write the design equation as 

Now we can compare the volumes (or weights of catalyst) required to achieve a specified conversion in each of the two ideal, continuous reactors. Suppose we have an ideal CSTR and an ideal PFR. The same reaction is being carried out in both reactors. The PFR is isothermal and operates at the same temperature as the CSTR. The molar feed rate of Reactant A to both reactors is Fao- If the kinetics are normal, which reactor will require the smaller volume to produce a specified conversion, xa,c, in the effluent stream  

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The graphical interpretation of the design equations for the two ideal continuous reactors has been illustrated using fractional conversion to measure the progress of the reaction. The analysis could have been carried out using the extent of reaction with Eqns. (3-18) and (3-34). Moreover, for a constant-density system, the analysis could have been carried out using the concentration of Reactant A, Ca, with Eqns. (3-24) and (3-37). 

The definitions of the three ideal reactors, and the fundamentals of ideal reactor sizing and analysis are covered in Chapters 3 and 4. Graphical interpretation of the design equations (the Levenspiel plot ) is used to compare the behavior of the two ideal continuous reactors, the plug flow and continuous stirred-tank reactors. This follows the pattern of earlier texts. However, in this book, graphical interpretation is also used extensively in the discussion of ideal reactors in series and parallel, and its use leads to new insights into the behavior of systems of reactors. 

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