2.5.4 Comparing the CSTR and PFR Reactor Volumes and Reactor Sequencing

If we look at Figure E2-5.2, the area under the curve (PFR volume) between X = 0 and X = 0.2, we see that the PFR area is greater than the rectangular area corresponding to the CSTR volume, i.e., V_PFR > V_CSTR. However, if we compare the areas under the curve between X = 0.6 and X = 0.65, we see that the area under the curve (PFR volume) is smaller than the rectangular area corresponding to the CSTR volume, i.e., V_CSTR > V_PFR. This result often occurs when the reaction is carried out adiabatically, which is discussed when we look at heat effects in Chapter 11.

In the sequencing of reactors, one is often asked, “Which reactor should go first to give the highest overall conversion? Should it be a PFR followed by a CSTR, or two CSTRs, then a PFR, or ...?” The answer is “It depends.” It depends not only on the shape of the Levenspiel plot (F_A0/–r_A) versus X, but also on the relative reactor sizes. As an exercise, examine Figure E2-5.2 to learn if there is a better way to arrange the two CSTRs and one PFR. Suppose you were given a Levenspiel plot of (F_A0/–r_A) vs. X for three reactors in series, along with their reactor volumes V_CSTR1 = 3 m³, V_CSTR2 = 2 m³, and V_PFR = 1.2 m³ and were asked to find the highest possible conversion X. What would you do? The methods we used to calculate reactor volumes all apply, except the procedure is reversed and a trial-and-error solution is needed to find the exit overall conversion from each reactor. See Problem P2-5_B.

The previous examples show that if we know the molar flow rate to the reactor and the reaction rate as a function of conversion, then we can calculate the reactor volume necessary to achieve a specified conversion. The reaction rate does not depend on conversion alone, however. It is also affected by the initial concentrations of the reactants, the temperature, and the pressure. Consequently, the experimental data obtained in the laboratory and presented in Table 2-1 as –r_A as a function of X are useful only in the design of full-scale reactors that are to be operated at the identical conditions as the laboratory experiments (temperature, pressure, initial reactant concentrations). However, such circumstances are seldom encountered and we must revert to the methods we describe in Chapters 3 and 4 to obtain –r_A as a function of X.

It is important to understand that if the rate of reaction is available or can be obtained solely as a function of conversion, –r_A = f(X), or if it can be generated by some intermediate calculations, one can design a variety of reactors and combinations of reactors.

Ordinarily, laboratory data are used to formulate a rate law, and then the reaction rate–conversion functional dependence is determined using the rate law. The preceding sections show that with the reaction rate–conversion relationship, different reactor schemes can readily be sized. In Chapters 3 and 4, we show how we obtain this relationship between reaction rate and conversion from rate law and reaction stoichiometry.

2.6 Some Further Definitions

Before proceeding to Chapter 3, some terms and equations commonly used in reaction engineering need to be defined. We also consider the special case of the plug-flow design equation when the volumetric flow rate is constant.