Dr Salam-Topic 8 Week 12

7/30/2019 Dr Salam-Topic 8 Week 12

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Residence time distribution

State of aggregation of the flowing

streamEarliness of mixing

Reference: Fogler and Levenspiel

TOPIC 8

Non-ideal Reactors


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Residence time distribution

Residence time distribution (RTD) is used to:

-characterize reactor

-predict exit conversion and concentration

-diagnose faulty operation of a reactor

All above can be done using

-age distribution of fluid (pulse and step

experiment)

-cumulative distribution time


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State of aggregation of flowing stream can be inthe state of microfluid or macrofluid or micro-

macrofluid.

Single phase system

The state exist is either microfluid or macrofluid .

State of aggregation


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Two phase system

The state is micro-macrofluid, depending on the

contacting scheme.


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Mixing of reactants can be divided into 3 which are

Early mixing, Uniform mixing, Late mixing

Single stream flow can mix with each other, either

early or late mixing, which has little effect onoverall behaviour.

Two entering reactant stream mixing can be very

important towards the fluid behaviour.

Earliness of mixing


6/15

Residence-Time Distribution (RTD) Function

~The time the atoms have spent in the reactor is called the residencetime of the atoms in the reactor.

~In any reactor, the distribution of residence times can significantly

affect its performance.

~The residence-time distribution (RTD) of a reactor is a characteristic

of the mixing that occurs in the chemical reactor.

~Not all RTDs are unique to a particular reactor type; markedly different

reactors can display identical RTDs.

~The RTD exhibited by a given reactor type yields distinctive clues to

the type of mixing occurring within it and is one of the most informative

characterizations of the reactor.

The RTD is determined experimentally by injecting an inert chemical,

molecule, or atom, called a tracer, into the reactor at some time t=0 and

then measuring the tracer concentration, C, in the effluent stream as a

function of time.

Residence-Time Distribution (RTD) Function


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Age distribution of fluid, E(t)

0

)(

)()(

dttC

tCtE

T

T

reactorin thedt)(tand(t)

betweenspent timehavethat

reactortheexitingmoleculesofFractionE(t)


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Example 13-1

A sample of the tracer hytane at 320 K was injected as pulse to a reactor, and the effluent

concentration was measured as a function of time, resulting in the data shown in Table E13-

1 . 1 .

The measurement represent the exact concentrations at the times listed and not average

values between the various sampling tests.

(a) Construct figures showing C(t) and E(t) as functions of time.

(b) Determine both the fraction of material leaving the reactor that has spent between 3 and6 min in the reactor and the fraction of material leaving the reactor that has spent between

7.75 and 8.25 min in the reactor, and

(c) determine the fraction of material leaving the reactor that has spent 3 min or less in the

reactor.


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Solution

(a)

dt)t(Cdt)t(Cdt)t(C14

10

10

00

314

10

3

10

0

min/6.2]0)6.0(45.1[3

2)(

min/4.47

)8(4)5(2)1(4)0(1[3

1)(

mgdttC

mg

dttC

3

14

10

10

00

min/0.506.24.47

)()()(

mg

dttCdttCdttC


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vdt)t(C

)t(C)t(E

0

3

0mmin/g0.50dt)t(C

(b)

51.0]12.0)16.0(3)2.0(316.0)[1(8

3dt)t(E

6

3

We find that 51% of material leaving the reactor spends

between 3 and 6 min in the reactor.

03.0min)75.725.8min)(06.0(tEdt)t(E average25.8

75.7

We find that 3% of material leaving the reactor

spends between 7.75 and 8.25 min in the reactor.

Cumulative distribution time, F(t)


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(c)

area=0.2

0

We see that 20% of the material has

spent 3 min or less in the reactor.

We see that 80% of the material has spent 3 min or more in thereactor.



12/15


t

dttEtF

0

)()(


13/15

dt)t(tE

dt)t(E

dt)t(tEt

0

0

0m

We have a reactor completely filled with maize molecules. At time t=0 we start

blue molecules to replace the maize molecules that currently fill the reactor.

Initially, the reactor volume V is equal to the volume occupied by the maize

molecules. Now, in a times dt, the volume of molecules that will leave the reactoris (vdt). The fraction of these molecules that have been in the reactor a time t or

greater is [1-F(t)]. Because only the maize molecules have been in the reactor a

time t or greater, the volume of maize molecules, dV, leaving the reactor in a time

dt is

)]t(F1)[vdt(dV )]t(F1)[vdt(dV dt)]t(F1[vV 0

volumetric flow

is constant

0

dt)]t(F1[vV 1

0

1

00tdF0tdF)]t(F1[t

v

V

Mean Residence Time


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dt)t(E)tt(0

2m

2

Variance or square of the standard deviation is defined as:

The magnitude of this moment is an indication of

the spread of the distribution; the greater the

value of this moment is, the greater a istributions

spread will be.

dt)t(EdF m

0tdt)t(tE

v

V

For liquid reactions, no change involumetric flow rate.

For gas reactions, no pressure drop,

isothermal operation, and no

change in the total number of moles

(

=0).

)X1/(tm

Mean Residence Time


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Mean residence time & variance

0

)( dtttEtm

0

22 )()( dttEttm

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Dr Salam-Topic 8 Week 12