Recycle reactors are used when the reaction is autocatalytic, or when it is necessary to maintain nearly isothermal operation of the reactor or to promote a certain selectivity (see Section 5.6.6). They are also used extensively in biochemical operations. To design recycle reactors, one simply follows the procedure developed in this chapter and then adds a little additional bookkeeping. A schematic diagram of the recycle reactor is shown in Text Figure 415.  


The recycled stream is drawn off at point Q and merged with the fresh feed at Point P. We shall define the recycle parameter R as the moles recycled per mole of product removed at point Q.  


Two conversions: 
Two conversions are usually associated with recycle reactors: the overall conversion, X_{0}, and the conversion per pass, X_{s} :  

(CD488) (CD489) 

The only new twist in calculating reactor volumes or conversions for a recycle reactor is a mole balance at the stream intersections (points P and Q) to properly express the species concentrations as a function of conversion. Consider the gasphase reaction
occuring in our reactor. Let X be the conversion of A in the reactor per mole of A fed to the reactor. The design equation is 



Then:  
Design equation:  


Rate law:  


with  
Stoichiometry: 1. From the definition from the overall conversion, we can define F _{A3 } and F _{B3} leaving the system, 


(CD490) (CD491) 

From the definition for conversion per pass, we can define F _{A2} and F _{B3} leaving the reactor,  

(CD492) (CD493) 

2. From the definition for the recycle parameter, R, we can define F _{AR } and F _{BR} and the total molar flow rate in the recycle stream, F _{tR}  

(CD494) (CD495) (CD496) 

where  


3. From the balance on the stream intersections, we have  

(CD497) 
Relating the molar flow rates in the various streams 
(CD498) (CD499) (CD4100) (CD4101) (CD4102) (CD4103) (CD4104) (CD4105) (CD4106) 
The volumetric flow rate in the reactor, , is related to the volumetric flow rate entering the reactor by  

(CD4107)  
where X is the number of moles of A reacted per mole of A entering the reactor, and is defined by  

(CD4108) 

The molar flow rate of A within the reactor is  

(CD4109) 

(CD4111)  
These equations for concentration are substituted into the rate law, which is in turn substituted into the design equation and integrated. For a firstorder reaction in A and in B,  

(CD4114)  
Recycle reactor volume 

(CD4115)  
where  


The relationship between the overall conversion and the conversion per pass can be found by equating F _{A2} from Equations (CD4107) and (CD4106):  


Then using Equation (CD497) and simplifying, we have  

(CD4116) 