08 Introduction to Non-Ideal Reactors....by akash agrawal.itis good for every one: I THINK GIFTING...

7/22/2019 08 Introduction to Non-Ideal Reactors....by akash agrawal.itis good for every one: I THINK GIFTING IS GOOD TECH

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Chapter 8

Introduction to

Non-ideal Reactors

Our treatment on reactor design in the

previous chapters is based on the assump-

tion that the reactorsare ideal

What are ideal reactors?

For CSTRs,

they must be well-mixed the concentration of the exit

stream is equal to that of fluid in

the reactor


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For PFRs, theflowin the reactor must

be in order, i.e. there are

no overtaking () no backmixing ()

With these idealbehaviours/character-istics, at steady state, the concentrationof

the fluidflowing outof the reactor is

uniform(or constant)

In reality, however, no reactorsare

ideal, i.e. theflow patternin the reactor

(either CSTRs or PFRs) is non-ideal


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The main reasonsof the non-ideal

flow (or the deviation of the ideal flow) are:

1) the residence time distribution(RTD)

For ideal reactors, it is assumed

that the residence time(or space time, )

ofall substances(all molecules) in the

reactors are identical, i.e. all molecules

that enter the reactor at the same time

must exit the reactor at the same residence

time; no molecules stay in the reactor

shorter or longer than the residence time


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For non-ideal reactors(or real

reactors), there may be some molecules

whose flow rates are slower or faster than

those of others

Channellingof fluid causes some

molecules to havefasterflow ratethan

others, as illustrated below

Channelling of Fluid


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A stagnant(/) zone

in the reactor, on the contrary, delaysthe

flowof some molecules, causing such

molecules to flow out of the reactor slower

than others

Stagnant zone in a CSTR

Stagnant Zone


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2) State of aggregationFor ideal reactors, all molecules

are assumed to be negligibly small(when

compared to the reactor); thus, they can

move freely

In reality, a group ofmolecules

are combined together(i.e.aggregationof

molecules) to form macrofluid molecules

(as apposed to microfluid molecules as

per ideal reactors)

These macrofluid molecules move

in package(or in aggregates), thus causing

non-ideal flowbehaviour to occur


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Microfluid

Macrofluid

3) Earliness or lateness of mixingFor an ideal CSTR, it is assumed

that the reactor is well-mixed, meaningthat the concentrations at any position

(point) of the CSTR are identical throughout

the reactor


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The mixing in the non-idealCSTR,

on the contrary, is NOTideally perfect,

causing the concentrationsin the CSTR

vary from position to position

For an ideal PFR, it is assumed

that there are no overtaking and/or no

backmixing (i.e. the flow is uniform or in

order)

In a real PFR, however, there may

be some overtaking or backmixing, which

results in early mixing or late mixing in the

PFR as illustrated on the next Page


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Uniform Mixing

(Ideal Flow in a PFR)

EarlyMixing

LateMixing


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RTD Function (or The Age Distribution

of Fluid)

As mentioned earlier, the residence

timesof molecules in a real (actual)

reactor are NOTidenticalas per the ideal

reactor

In other words, there is a distribution

of the residence timesoffluidentering

and leaving the reactor

The distribution of these times for the

stream of fluid leavingthe reactor is called

the exit age distribution, E (we shall

discuss about Ein detail later)


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In order to determine the distribution of the

residence times (or the degree of the non-ideal

of the flow), a small amount of substance

(called a tracer) is injected into the reactor,

and the concentrations of the tracer flowing

out of the reactor are recorded

A tracershould be

easy to analyse for itsconcentration(using an ordinary

equipment available in a common

laboratory, e.g., pH meter, gas

chromatograph: GC)

stable(i.e. it is not decomposed easily) inactive(i.e. it does not react with any

other species in the reactor)


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To introduce (or inject) tracerinto the

reactor, it can be done by

apulseexperiment a stepexperiment

The Pulse Experiment

In thepulseexperiment, a known

amount of tracer is injected into the

reactor onlyonceat any instant of time

Assume that a tracer in the amount of

M kg or kmol (kg-mol) is injected into thefluid entering the reactor (or vessel) with

the volumetric flow rate ofv m3/s


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The concentration vstime (which can

be called time-resolved concentration) of

the tracer leaving the reactor is monitored,

and the plot between the concentration of

the tracer ( )pulseC and time ( )t for an ideal

reactor and a non-ideal reactor can beillustrated on the following Pages (Pages

1415)


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For an ideal flow

For the case of an idealflow, after a

certain period of time (which is, in fact, the

residence time), the tracershall leave the

reactor at oncewith the concentration

equalto that enteringthe reactor

Cpulse

tResidence time

=out inC C


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For a non-ideal flow

For a non-idealflow pattern (or a non-

ideal reactor), there is a distributionoftimesthat the tracer leaves the reactor

from = 0t to t=

Cpulse

t


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The area under the pulseC vs t curve for a

non-ideal reactor from = 0t to t= is

( )0

C t dt

The unit of the integral is, for example,

[ ]mol mol s

sL L

=

or

[ ]3 3kg kg ssm m

=


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Multiplying the integral with the

volumetric flow rate gives

( )0

v C t dt

and the unit of the resulting multiplication

is, for example,

L mol s

s L

= mol

or

3

3m kg s kgs m

=


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By considering the unit of the term

( )0

v C t dt

, it leads to the fact that this term

is, in fact, the total amount of the tracer

leaving the reactor, which, by employing

the principle of the mass conservation, is

equal to that entering the reactor

Thus,

( )0

M v C t dt

= (8.1)

which can be re-arranged to

( )

= =

0

Area under

the curve

from 0

M C t dtv

(8.2)


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If the integration is performed from = 0t

to t t= ,

( )0

t

C t dt

we obtain the fact that

( )0

t

m v C t dt = (8.3)

which can be re-arranged to

( )

= ==

0

Area under

the curvefrom 0

tm

C t dtvt

(8.4)

where m is the mass (or moles) of the

tracer leaving the reactor between the time

period of = 0t to t t= as shown graphically

on the next Page


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Cpulse

t t=t

( )0

Area under

the curvefrom 0

t

mC t d t

vt

= =


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Dividing throughout Eq. 8.3:

( )0

t

m v C t dt =

(8.3)

withM

vand re-arranging yields

( )0

t

v C t dtm

M M

v v

=

( )0

t

v C t dt

mvMM

v

=

( )0

t

C t dtm

MM

v

=

(8.5)


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It is defined that

( )

( )0

0

t

t

C t dt

E t dtM

v

= (8.6)

Thus, the meaning ofE (the exit age

distribution) or ( )E t is, in fact,

( )( )C t

E tM

v

= (8.7a)

pulseCE

M

v

= (8.7b)

( )

pulse pulse

0

Area under

the curve

from 0

C C

EC t dt

= =

(8.7c)


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In other words, we can obtain Eat any

instant of time by simply dividing the value

of the concentration of a tracer ( )pulseC by

M

vor by ( )

0

C t dt

or by the area under the

curve from 0t= to t=

From Eq. 8.6, when t= , we obtain the

fact that

( )

( )0

0

C t dt

E t dtM

v

=

(8.8)

but, from Eq. 8.2, ( )0

MC t dt

v

=


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Hence, Eq. 8.8 becomes

( )0

1

M

vE t dt M

v

= = (8.9)

( )E t is also called the RTD functionwhose graph are as shown below

E

t


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It is evident that the E vs tplot is

identical to that ofC vs t, as E is, in fact,

impulseCE

M

v

= (8.7b)

Since the area under the curveof the C

vs tplot from 0t= to t= or ( )0

C t dt

is

M

v(see Page 18), the area under the

curveof the E vs tplot from 0t= to t=

or ( )0

E t dt

or0

Edt

is 1, as illustrated

mathematically on Page 24 (Eq. 8.9)

Note that by dividing Cor pulseC with a

constant (i.e.Mv ), it is called normalisation


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We can employ the RTD function to

calculate the average (or mean) residence

time using the following relationship:

( )0

t tE t dt

= (8.10)

or

( )

( )

0

0

tC t dt

t

C t dt

=

(8.11)

which can be proved mathematically as

follows


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From Eq. 8.8, we obtain the fact that

( )

( )0

0

C t dt

E t dtM

v

= (8.8)

but, from Eq. 8.2,

( )0

M C t dtv

= (8.2)

Combining Eq. 8.8 with Eq. 8.2 results

in

( )

( )

( )

0

0

0

C t dt

E t dt

C t dt

=

(8.12)


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Multiplying throughout Eq. 8.12 with t

gives

( )

( )

( )

0

0

0

tC t dt

tE t dt

C t dt

=

(8.13)

but, from Eq. 8.10, which is defined that

( )0

t tE t dt

= (8.10)

Thus, Eq. 8.13 is, in fact,

( )

( )

0

0

tC t dt

t

C t dt

=

(8.11)


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Example To determine the non-ideal

behaviour of a reactor with a volume of

180 L, a pulse experiment is carried out by

injecting a tracer only once in the amount

ofM = 1.2 kg into the inlet stream flowing

into the reactor with volumetric flow rate of

11 L/min

The concentration vs timedata of the

tracer in the outlet stream of the reactor

within the period of 035 min are as shown

in the Table on the next Page

Determine

a) the mean residence time( )t ofthe flow in this reactor

b) the residence time in this reactorif the flow is ideal


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Time [min] C[g/L]

05

101520253035

03

554210

The plot ofC vs tof this pulse

experiment is as illustrated on the next

Page (Page 31)

Determining the area under the curve

(try doing it yourself) gives

( )0

M

C t dtv

= (8.2)

which can also be written in thepractical

form as

( )iM C t tv

= (8.14)


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0

1

2

3

4

5

6

0 10 20 30 40

Time [min]

Concen

tration

oftracer[g/L]

The meaning of Eq. 8.14 is that the

integral ( )0

C t dt

can practically be obtained

by summing the multiplication ofC (at any

instant of time) and t (or 1n nt t+ )


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The area under the curve of the graph

on the previous Page (Page 31) is found to

be 100 g min

L ; thus,

( )0

g min100

L

MC t dt

v

= =

and

g min100

L L11

min

g min L 100 11L min

M

M

=

=

1,100 g= = 1.1 kgM


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It is given that the tracer is injected

into the reactor in the amount of1.2 kg,

but the data from the outlet streamyield

the fact that the total amountof the

tracer leavingthe reactor is 1.1 kg

Although there is a discrepancy (

), but it seems to be acceptable, as

the error is only1

~ 100 8.3%

12

=

The mean or average residence time ( )t

can be calculated using Eq. 8.11

( )

( )

0

0

tC t dt

t

C t dt

=

(8.11)


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which can also be written in thepractical

form as follows

( )( )

i i

i

t C t t t

C t t

=

(8.15)

Note that the term( )i

C t t

(or the

denominator: ) is, in fact, ( )0

C t dt

,

which is the area under the Cpulse vs tcurve

and is equal tog min

100L

(see Page 32)

The computation of the value of

( )0

tC t dt

or ( )( )i it C t t is illustrated



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t [min] iC [g/L] t ( ) i it C t 0 0

5 3 5 535 = 75

10 5 5 1055 = 25015 5 5 1555 = 37520 4 5 2045 = 40025 2 5 2525 = 25030 1 5 3015 = 15035 0 5 3505 = 0

= 1,500

Thus, by employing Eq. 8.15, we can

calculate the mean residence time ( )t as

follows

( )

( )2g min

1,500 Lg min

100L

i i

i

t C t t t

C t t

=

=

15 mint =

a)


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The residence timefor the ideal-flow

pattern ( ) can simply be calculated using

the following equation:

180 L

L11min

V

v =

=

16.4 min =

b)

It is evident that the mean residence

time ( )t for the non-idealflow (or the

actualcase) is shorterthan the ideal-flow

residence time (15 min vs16.4 min)


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This implies that, on average, the

molecules stay in the reactor shorter

than the required residence time, which

should lead to the fact that the conversion

may be lower than expected

The reasons that the mean residence

time is lower than the ideal residence time

may include the following:

There is a channellingof the flow inthe reactor

There is a stagnant zonein thereactor, which makes the volume( )V of the reactor smaller than the

actual one; thus,V

v = is lower

than expected


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The Step Experiment

Another way of determining the non-

idealflow pattern of the reactor is to carry

out a step experiment

In the stepexperiment, at any instant of

time ( )or at 0t= , a tracer is introduced

into the inlet stream flowing into the

reactor (volume = V m3) with the volume-

tric flow rate ofv m3/s

The traceris injected continuouslyintothe reactor with the concentration

(relative to the inlet stream) of maxC


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The concentration of the tracer in the

outlet stream leaving the reactor can be

presented graphically as follows

Let

( )

( )

max

C t

F t C=

(8.16)

Cstep

t

Cmax


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The concentration of the tracer at any

instant of time, C or ( )C t , is defined asm

V

(on massbasis) or

( )m

C tV

= (8.17)

where m is the total amount of mass

leaving the reactor from 0t= to t t=

Let concentration of maxC be

max

MC

V= (8.18)

Combining Eqs. 8.17 & 8.18 with Eq.8.16 yields

( )( )

max

mC t VF t

MC

V

= = (8.19)


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For a constant-V system, Eq. 8.19

becomes

( ) ( )

max

C t mF t

C M= = (8.20)

but, as we have learned previously (or from

Eq. 8.3)

( )0

t

m v C t dt = (8.3)

and Eq. 8.1

( )0

M v C t dt

= (8.1)

which can be combined to form

( )

( )

( )0

0

0

t

tv C t dt

mE t dt

Mv C t dt

= =

(8.21)


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Combining Eqs. 8.20 & 8.21 together

yields

( )( )

( )max 0

tC t mF t E t dt

C M= = =

or

( ) ( )0

t

F t E t dt = (8.22)

Eq. 8.22 is the relationshipbetween F

(from a stepexperiment) and E(from a

pulseexperiment)


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Eq. 8.22 can be written in the differential

form as follows

( ) ( )dF t

E tdt

= (8.23)

which implies mathematically that the

value ofEor ( )E t can be obtained by

differentiating the graph ofF vs tat any

given time ( )t

Note that

max

MC

V=

can also be written as

max

MmtC

V v

t

= =

(8.24)

where m

is the mass flow rate of the tracer


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The shaded area on the stepC vs t curve:

is

max

step

0

C

tdC

max

max

0

Shaded

area

C

tdC

=

Cstep

t

Cmax


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Thus, the average residence time( )t for

the stepexperiment can be calculated

using the following equation:

max max

max

step step

0 0

max

step

0

C C

C

tdC tdC

tC

dC

= =

(8.25)

Eq. 8.25 can be written in thepractical

form as

( )

max

i it CtC

= (8.26)


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Conversion in Non-ideal Flow Reactors

In the previous chapters, our treatment

on reactor design is based on the ideal

model, in which the conversionis affected

by

thermodynamic constraint[maximum possible conversion

(how faror how much) or K:

equilibrium constant]

rate (how fast) of the Rxn. (or k:rate constant)

design equation of the reactor (ortype)


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For the non-idealreactors, in addition

to those factors, the following additional

factors must also be taken into

consideration in determining/calculating

the conversion of the system (or reactor)

RTD of fluid in the reactor

Micro- or macro-fluid behaviour Earliness & lateness of mixing

As we have learned previously, these

factors cause the reactor to deviate

() from the ideal behaviours


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We have just learned the effect of the

RTDon the non-ideal behaviours of the

reactor

In the subsequent sections, lets

consider the effects of the earliness & late-

ness of mixingand the state of aggregation

(or the macrofluidbehaviour)

If the early mixingtakes place in the

plug flow reactor (PFR) as shown below

EarlyMixing

the section in which the early mixing is

occurring will behave as a CSTR


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Thus, the concentration in this section

will

reduce substantially be uniform quickly

The resulting lowconcentration of thereactant will then proceed its conversion

along the length of the PFR

On the contrary, if the late mixing

occurs in the PFR:

LateMixing


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the concentration of the reactantwill decrease gradually along the

length of the PFR during the first

stage of the reaction

but it will drop quickly after itenters the mixing zone, whichbehaves as a CSTR

In either case (early or late) of mixing, if

the order of the Rxn. ( )n is lowerthan unity( )1 : e.g., n = 0.5

or

0.5

A A

r kC = (8.27)

the rate of Rxn. ( )Ar would be

decreasing at the rate slowerthan AC (e.g.,

when AC decreases by 2 folds, Ar would be

decreasing at the rate of 0.52 = 1.44 folds)


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higherthan unity: e.g., n = 2 or2

A Ar kC = (8.28)

the rate of Rxn. ( )Ar would be

decreasing at the ratefasterthan AC (e.g.,

when AC decreases by 3 folds, Ar would be

decreasing at the rate of 23 = 9 folds

Hence, to obtain as high conversion as

possible, when

n< 1, we want the reactor to havean earlymixing, in order to enable

AC to drop substantially during the

early stage of the reaction n> 1: we desire to have a late

mixing, to obtain as high rate of

Rxn. during the early stage of the

reaction as possible


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The relationship between the

concentration of A (reactant) at any instant

of time ( )AC and its initial concentration

( )oA

C for a PFR or a BR for the nth order

Rxns. are as follows

1st order Rxn.:

( )expo

A

A

Ckt

C= (8.29)

2ndorder Rxn.:1

1o o

A

A A

C

C kC t =

+(8.30)

nthorder Rxn.:

( )

11 1

1 1 oo

nA n

AA

C

n C kt C

= + (8.31)


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For the non-idealPFR or BR, since the

concentration of A does NOT leave the

reactor at once (i.e. it leaves the PFR or BR

with the different value from 0t= to t= ,

as shown as a graph on Page 15), the

average concentration ofA

C ( )AC that

leaves the reactor during the time interval

of 0 must be used instead of the exact

value of AC


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The average (or mean) concentrationof A

with reference tooA

C o

A

A

C

C

for the non-

idealPFRs or BRs can be calculated using

the following equation:

0o o

A A

A A

C C EdtC C

=

(8.32)

and by employing the same principle, the

average conversionof A ( )Ax can be

computed using the following equation:

0

A Ax x Edt

= (8.33)


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Example The reaction with the rate

equation of A Ar kC = , where k = 0.307

min-1, is taken place in a 180-L reactor

with a volumetric flow rate of the inlet

stream of 11 L/min

Determine the conversion of A ( )Ax ifa) the reactor is the idealPFRb) the reactor is the non-idealPFR

(use the data of the Example on

Pages 2930 to determine the non-

ideal behaviour of the reactor)


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56

For PFRs and 1st order Rxns.,

( )expo

A

A

Ck

C

= (8.29)

Assume that this is a constant-V system

Thus,

( )1oA A A

C C x= (1.24)

Combining Eq. 1.24 with Eq. 8.29 and

re-arranging results in

( )( )

( ) ( )

1exp

1 exp

o

o

A A

A

A

C xk

C

x k

=

=

( )1 expAx k= (8.34)


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For an ideal PFR,

180 L16.4 min

L11min

V

v

= = =

Hence, the conversion of A for the ideal

PFR can be calculated, using Eq. 8.34, as

follows

( ) ( )[ ]1 exp 0.307 16.4

1 0.00651

Ax =

=

0.993Ax =

a)


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58

If the reactor is non-ideal, the average

conversion ( )Ax can be computed using

Eq. 8.33:

0

A Ax x Edt

= (8.33)

The value ofEcan be calculated using

Eq. 8.7c

( )

pulse pulse

0

Area under

the curve

from 0

C CE

C t dt

= =

(8.7c)

From the previous Example, the area

under the C vs tcurve or ( )0

MC t dt

v

= was

found to beg min

100L


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59

Thus, in this Example, the value ofEis,

in fact,

pulse

100 100

C CE= =

The conversion at any given residence

time can be computed using Eq. 8.34:

( )1 expAx k= (8.34)

From the given data (on Pages 2930),

we can compute the mean conversion of A

( )Ax using Table as shown on the next

Page


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60

t CE=

C/100( )= 1 expAx k Ax E t

0

5

101520253035

0

3

554210

0

0.03

0.050.050.040.020.01

0

1 exp[-(0.307)(5)]= 0.7850.9540.9900.9980.999

11

0.785

0.03

5= 0.11780.23850.24750.19960.09990.05

0 = 0.953

Note that the term0

Ax Edt

can be

written in a practical form as follows

( )Ax E t (8.35)


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Thus, the average conversion of A

( )A

x , or0

A

x Edt

or ( )

A

x E t

, for the

non-ideal PFR is found to be 0.953

b)

Note that, in this Example, the

conversion of the non-idealPFR is lower

than that of the idealone (0.953 vs0.993)


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62

In the case ofCSTRs, whose design

equation is

oA A

A

C C

r

=

(1.40)

If the Rxn. is of 1st order:

A Ar kC =

by combining the rate equation (1st order)

with the design equation (of a CSTR), we

obtain

oA A

A

C C

kC

= (8.36)

Re-arranging Eq. 8.36 gives

oA A

A

C Ck

C

=

1oA

A

C

k C =


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63

1oA

A

Ck

C= +

1

1o

A

A

C

C k=

+(8.37)

Thus, for a non-idealCSTR and the 1st

order Rxn., we obtain the following

equation:

0o o

A A

A A

C C EdtC C

=

0

1

1o

A

A

CEdtC k

= + (8.38)


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64

Example Repeat the Example on Page 55

but for ideal and non-idealCSTRs

Since the volume of the reactor (CSTR),

V, and the volumetric flow rate, v, of the

inlet stream are still the same as per the

previous Example, the residence time of

the ideal CSTR is also the same; i.e.

180 L16.4 min

L11min

= =

Substituting 16.4 min = and 0.307k=

-1min into Eq. 8.37 yields

( ) ( )

1

1 0.307 16.4o

A

A

C

C=

+

0.166o

A

A

C

C=


65/76

65

Re-arranging Eq. 1.24:

( )1oA A A

C C x= (1.24)

results in

( )1o

AA

A

Cx

C=

1o

AA

A

Cx

C= (8.39)

Thus,

1 1 0.166 0.834o

AA

A

Cx

C= = =


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66

For the non-ideal CSTR,

0o o

A A

A A

C CEdt

C C

=

(8.32)

The above equation (Eq. 8.32) can be

written for the 1st

order Rxn. taken placein a CSTR as

0

1

1o

A

A

CEdt

C k

=

+ (8.38)

Applying Eq. 8.39 for the non-ideal

reactor (can be any type of reactor; BR,

CSTR, or PFR) yields

1o

AA

A

Cx

C= (8.40)


67/76

67

Combining Eq. 8.40 with Eq. 8.38 gives

0

11

1Ax Edt

k

=

+ (8.41)

which can be written in a practical form as

follows

11 1

Ax E tk

= +

(8.42)

From the given data, we can compute

the value ofo

A

A

C

Cfor a CSTR and 1st order

Rxn. or

1

1 E tk

+ as illustrated



68/76

68

t CE=

C/100

1

1+k

1

1 + E tk

0

5

1015202530

35

0

3

55421

0

0

0.03

0.050.050.040.020.01

0

1/[1+(0.307)(5)]= 0.3940.2460.1780.1400.1150.098

0.085

0.394 0.5 5= 0.05910.06150.04450.02800.01150.0049

0 = 0.210

Thus,0

1

1Edt

k

+ or

1

1E t

k

+

oro

A

A

C

Cis

0.210o

A

A

C

C

=


69/76

69

Hence, the average conversion for the

non-ideal CTSR in this Example can be

calculated, using Eq. 8.40, as follows

1 1 0.210

0.790

o

AA

A

Cx

C= =

=

b)

The conversion of the non-idealCSTR

is found to be lowerthan the idealone(0.834 vs0.790)


70/76

70

In the case that the fluid in the reactor

behaves as a macrofluid, the residence

time distribution (RTD) of the tracer in the

outlet stream for thepulseexperiment is

as shown in the following Figure

Cpulse

t


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71

The graph on the previous Page

illustrates that the fluid are combined

together to become a lump or a group of

fluid

This lump of fluid moves together from

one place to another, and, eventually, it

comes out of the reactor as a lump of fluid

The example of the calculations

concerning the non-ideal, macrofluid

behaviour is illustrated in the following

Example


72/76

72

Example The liquid A in the form of

macrofluidhas an initial concentration

( )oAC of 2 mol/L is decomposed according

to the rate equation of

2 L; 0.5

mol min

A Ar kC k = =

The RTD for the pulse experiment is as

shown below

Determine the conversion of this Rxn. if

it is taken place in a BR

Cpulse

[mol/L]

t[min]

2

1 3


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73

Since this is a non-ideal, macrofluid

flow pattern, we can employ the following

relationships:

0o o

A A

A A

C CEdt

C C

=

(8.32)

and

1o

AA

A

Cx

C= (8.40)

For the 2nd order Rxn.,

1

1o o

A

A A

C

C kC t =

+(8.30)

Combining Eq. 8.30 with Eq. 8.32 yields

0

1

1o o

A

A A

CEdt

C kC t

= +

(8.43)


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74

We have learned that

( )

pulse pulse

0

Area underthe curve

from 0

C CE

C t dt

= =

(8.7c)

In the Example, the area under thecurve from 0 - can be computed as

follows

( ) ( )[ ]

pulse

Area under

the curve

2 mol/L 3 1 min

C t

=

=

Area under mol min4the curve L

=


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75

Hence,

pulse -1

mol2

L 0.5 minmol minArea under4

Lthe curve

CE= = =

Substituting corresponding numericalvalues into Eq. 8.43 and integrating gives

( ) ( )

( )[ ]

( ) ( )[ ]

( )

0

0

3

1

3

1

1

1

10.5

1 0.5 2

10.5

1

0.5 ln 1

0.5 ln 1 3 ln 1 1

0.5 ln4 ln2

40.5ln2

o o

A

A A

CEdt

C kC t

dtt

dtt

t

= +

= +

=+

= +

= + +

=

=


76/76

0.5 ln2 0.347o

A

A

C

C= =

but, from Eq. 8.40, 1o

AA

A

CxC

=

Thus, the average conversion of A for

non-ideal, macrofluid in this Example can

be computed as follows

1

1 0.347

0.653

o

AA

A

A

Cx

C

x

=

=

=

Question: What is the conversion of A forthe ideal BR for the residence time of 3

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08 Introduction to Non-Ideal Reactors....by akash agrawal.itis good for every one: I THINK GIFTING...

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