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4. ISOTHERMALREACTORDESIGN

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 isshown 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:

XsandX0

Two conversions are usually associated with

recyc le reactors: the overall conversion,X0,

and the conversion per pass,Xs:

(CD4-88)

(CD4-89)

The only new twist in calculating reactor

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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 ofconversion. 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 FA3 and FB3leaving the system,

(CD4-90)

(CD4-91)

From the definition for conversion per pass,

we can define F A2and FB3leaving the

reactor,

(CD4-92)

(CD4-93)

2. From the definition for the recycle

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parameter, R, we can define FAR andFBRand the total molar flow rate in the recycle

stream, FtR

(CD4-94)

(CD4-95)

(CD4-96)

where

3. From the balance on the streamintersections, we have

(CD4-97)

Relating

themolar

flow

rates in

the

variousstreams

(CD4-

98)

(CD4-

99)

(CD4-

100)

(CD4-

101)

(CD4-

102)

(CD4-

103)

(CD4-

104)

(CD4-

105)

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(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 permole 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)

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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,

(CD4-

114)

Recycle

reactor

volume

(CD4-115)

where

The relationship between the overall conversion and the

conversion per pass can be found by equating FA2from

Equations (CD4-107) and (CD4-106):

Then using Equation (CD4-97) and simplifying, we have

(CD4-

116)

Fogler & Gurmen

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