Chapter 5: Isothermal Reactor Design: Conversion

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R5.2 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. 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 below.



	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: X_sand X₀	Two conversions are usually associated with recycle reactors: the overall conversion, X₀, and the conversion per pass, X_s :

		(CD5-88) (CD5-89)

	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,

		(CD5-90) (CD5-91)

	From the definition for conversion per pass, we can define F _A2 and F _B3 leaving the reactor,
		(CD5-92) (CD5-93)

	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

		(CD5-94) (CD5-95) (CD5-96)

	where


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

		(CD5-97)

Relating the molar flow rates in the various streams

(CD5-98)

(CD5-99)

(CD5-100)

(CD5-101)

(CD5-102)

(CD5-103)

(CD5-104)

(CD5-105)

(CD5-106)


The volumetric flow rate in the reactor, , is related to the volumetric flow rate entering the reactor by

		(CD5-107)

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

	(CD5-108)

The molar flow rate of A within the reactor is

	(CD5-109)

(CD5-110)



		(CD5-111)

		(CD5-112) (CD5-113)

	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,

		(CD5-114)

Recycle reactor volume		(CD5-115)

	where


	The relationship between the overall conversion and the conversion per pass can be found by equating F _A2 from Equations (CD5-107) and (CD5-106):



	Then using Equation (CD5-97) and simplifying, we have

		(CD5-116)