Reactors 1

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Performance equations for reactors

output = f(input, kinetics, contacting pattern)

e.g. Fig.4.1.1 (Rich) Mixed reactor with first orderreaction kinetics

We have now seen other reaction rate expressions.

These were obtained in batch reactors, so we are

already familiar with them.

There are other reactor types as well.

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Rich, Fig. 4.1.1

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Review of figures from Levenspiel

Fig. 4.1 Reactor types

Fig. 4.2 and Eqn.1 Material balance on a reactorvolume element

Fig. 4.3 and Eqn.2 Energy balance on a reactor volumeelement

Fig. 4.4 Review of notation for batch reactors

Fig 5.3 Notation for a mixed reactor

Fig. 5.5 Notation for a plug flow reactorFig. 5.1 The three ideal reactors

Fig. 11.1 nonidealities in flow patterns

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Notation Summary

C: concentration, mol/L

X: conversion

V: volume, Lv: volumetric flowrate, L/h

F : molar flowrate, mol/h

Subscripts:

A : reactant A0: initial or inlet

f: final or outlet

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Performance equation for a batch reactorreaction = accumulation (no input or output)

tioninterpretagraphicalgivesFigure5.2

1;1

:thesegintegratin

;

:writtenbealsocanwhich

;

0

0

00

0

0

00

AA X

A

A

A

tX

A

A

A

t

A

AA

AA

A

A

A

A

A

dXr

CdtdXVr

Ndt

dt

dXCr

dt

dX

V

Nr

dt

dCr

dt

dNVr

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Performance equation for mixed flow reactorsteady state case: (no accumulation)

A

AA

A

A

A

AAAA

A

AAA

AA

r

XC

v

V

r

X

F

V

VrXFFVrREACTION

XFFOUTPUT

CvFINPUT

0

0

0

00

0

000

s

1

:velocityspaceandtimespaceofsdefinitiontheusing

)1(:

)1(:

:

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Steady state mixed flow reactor

Again, there will be an algebraic relation in terms of

concentrations and the rate constant for each specificcase, e.g. -rA = kCA CA does not change with time

For a well mixed reactor CAis the same at all points

in the reactor and is equal to the outlet concentrationCAf

A

AA

r

XC

v

V

0

0 s1

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Steady state mixed flow reactor

area of rectangle on y vs x coordinates = (y)(x)

Thus Fig 5.4 gives the graphical interpretation of theperformance equation for a mixed flow reactor,comparable to the one for the batch reactor (Fig. 5.2)

A

AA

A

AA

XrC

rXC

vV

1

s

1

0

0

0

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Performance equations

Batch Reactor Mixed Reactor

t

X

A

A

A

dt

dX

r

C

A

0

0

0

1

A

AA

r

XC

0

These can be found in Table 5.1.

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Performance equation for plug flow reactorsteady state case: (no accumulation)

Mass balance on cylindrical element of small thickness:

From the definition of XA, FA=FA0(1-XA)

dFA=-FA0dXA

Substituting, we get: FA0dXA = (-rA) dV

dVrdFFF

NCONSUMPTIOOUTPUTINPUT

AAAA

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Performance equation for plug flow reactor:

AfX

A

A

AdX

rC

0

0

1

But this is exactly what we had for a batch reactor!

Consecutive elements in a plug flow reactor can beanalyzed as individual batch reactors

0

0

000

11

A

A

X

A

A

V

A

C

F

V

dXr

dVF

Af

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Systems with varying density

Fractional change in volume of the system between no conversionand complete conversion of reactant A:

(Equation 64, Chp 3)

Typically negligible for liquid systems.

Can be determined from stoichiometry for gaseous systems

0

01

A

AA

X

XX

A

V

VV

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Systems with varying density

0

0

00

0

00

1

1

:arranging-re

1

1

)1(

)1(

)1()1(

A

A

A

A

A

A

AA

A

A

AA

AAA

A

AAAAA

C

C

C

C

X

X

XC

XV

XN

V

NC

XNNXVV

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Table 5.1 gave performance equations for thecase of constant density, A=0

Table 5.2 gives performance equations forthe case of varying density, A 0

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Example 5.1 demonstrates that we can observe thereaction rate in a mixed flow reactor by observing thesteady state concentrations going in and out of the

reactor We do not even have to use stoichiometry for

observing this but the stoichiometry can also bededuced

Observing the reaction rate does not mean we obtain

a reaction rate expression, or a reaction mechanism

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Example 5.2 demonstrates that we will needmultiple runs in a mixed flow reactor to arrive

at a reaction rate expression

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Example 5.3 demonstrates the design of a mixed flowreactor (i.e. the determination of the size) and theoperating conditions (flowrates) required to achieve a

given objective when the reaction stoichiometry andreaction rate expressions are known (probablydetermined in a batch reactor beforehand, using themethods of Chapter 3)

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Example 5.4 demonstrates the design of a plug flowreactor (the determination of space time, hence thesize for a given flowrate) required to achieve a given

objective when the reaction stoichiometry andreaction rate expressions are known (probablydetermined in a batch reactor beforehand, using themethods of Chapter 3)

It also demonstrates that the integral involved in the

performance equation of a PFR can be evaluatedgraphically or numerically, as well as analyticallywhen that is possible.