## Professional Reference Shelf

#### R4.2 Recycle Reactors

 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 4-15. 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: Xsand X0 Two conversions are usually associated with recycle reactors: the overall conversion, X0, and the conversion per pass, Xs : (CD4-88) (CD4-89) 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 gas-phase 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, (CD4-90) (CD4-91) From the definition for conversion per pass, we can define F A2 and F B3 leaving the reactor, (CD4-92) (CD4-93) 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 (CD4-94) (CD4-95) (CD4-96) where 3. From the balance on the stream intersections, we have (CD4-97)
 Relating the molar flow rates in the various streams (CD4-98) (CD4-99) (CD4-100) (CD4-101) (CD4-102) (CD4-103) (CD4-104) (CD4-105) (CD4-106)
 The volumetric flow rate in the reactor, , is related to the volumetric flow rate entering the reactor by (CD4-107) where X is the number of moles of A reacted per mole of A entering the reactor, and is defined by (CD4-108) The molar flow rate of A within the reactor is (CD4-109)
(CD4-110)
 (CD4-111) These equations for concentration are substituted into the rate law, which is in turn substituted into the design equation and integrated. For a first-order reaction in A and in B, (CD4-114) Recycle reactor volume (CD4-115) where The relationship between the overall conversion and the conversion per pass can be found by equating F A2 from Equations (CD4-107) and (CD4-106): Then using Equation (CD4-97) and simplifying, we have (CD4-116)