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. | |||
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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. | |||
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Two conversions: |
Two conversions are usually associated with recycle reactors: the overall conversion, X0, and the conversion per pass, Xs : | ||
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(CD5-88) (CD5-89) |
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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 |
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Then: | |||
Design equation: | |||
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Rate law: | |||
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with | |||
Stoichiometry: 1. From the definition from the overall conversion, we can define F A3 and F B3 leaving the system, |
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(CD5-90) (CD5-91) |
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From the definition for conversion per pass, we can define F A2 and F B3 leaving the reactor, | |||
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(CD5-92) (CD5-93) |
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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 | |||
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(CD5-94) (CD5-95) (CD5-96) |
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where | |||
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3. From the balance on the stream intersections, we have | |||
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(CD5-97) |
Relating the molar flow rates in the various streams |
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The volumetric flow rate in the reactor, , is related to the volumetric flow rate entering the reactor by | |||||
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(CD5-107) | ||||
where X is the number of moles of A reacted per mole of A entering the reactor, and is defined by | |||||
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(CD5-108) |
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The molar flow rate of A within the reactor is | |||||
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(CD5-109) |
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(CD5-111) | ||||
(CD5-112) (CD5-113) |
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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, | |||||
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(CD5-114) | ||||
Recycle reactor volume |
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(CD5-115) | |||
where | |||||
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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): | |||||
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Then using Equation (CD5-97) and simplifying, we have | |||||
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(CD5-116) |