Ideal Isothermal Tubular Recycle Reactor

It is sometimes advantageous to divide the product stream of a reactor and return a portion to the entrance, for example, to charge or discharge reaction heat outside of the reactor in the recycle line and thus limit the increase or decrease of temperature 

The recycle ratio R is defined (for a constant volume reaction) as the ratio of the flow rate of fluid returned to the reactor entrance to the flow rate of the fresh feed entering the system  

For a first-order reaction with respect to reactant A (va— 1) constant volume, combination of Eqs. (4.10.33) and (4.10.34) leads to  

The concentration of reactant A at the entrance of the reactor (ca.,) after mixing of the fresh feed (Ca.o) with the recycle stream (Ca,2 = Ca.oui) is given by  

For the first border case of a negligibly small recycle ratio (R 0), Eq. (4.10.38) approaches the equation for a plug flow reactor, Eq. (4.10.25)  

---

Another view is given in Figure 3.1.2 (Berty 1979), to understand the inner workings of recycle reactors. Here the recycle reactor is represented as an ideal, isothermal, plug-flow, tubular reactor with external recycle. This view justifies the frequently used name loop reactor. As is customary for the calculation of performance for tubular reactors, the rate equations are integrated from initial to final conditions within the inner balance limit. This calculation represents an implicit problem since the initial conditions depend on the result because of the recycle stream. Therefore, repeated trial and error calculations are needed for recycle... 

---