Distribution of Residence Times for Reactorslibvolume2.xyz/.../nonidealreactors/nonidealreactorspresentation1.pdf · Similarly, in an ideal batch reactor, all the atoms of materials

ERT 208/4 REACTION ERT 208/4 REACTION ERT 208/4 REACTION ERT 208/4 REACTION

ENGINEERING: ENGINEERING: ENGINEERING: ENGINEERING:

Distribution of Residence Distribution of Residence Distribution of Residence Distribution of Residence

Times for ReactorsTimes for ReactorsTimes for ReactorsTimes for Reactors

(PART A)(PART A)(PART A)(PART A)

By; By; By; By; MrsMrsMrsMrs HafizaHafizaHafizaHafizaBintiBintiBintiBinti ShukorShukorShukorShukor

ERT 208/4 REACTION ENGINEERING

SEM 2 (2009/2010)

Students should be able to; Students should be able to; Students should be able to; Students should be able to; Students should be able to; Students should be able to; Students should be able to; Students should be able to; DEFINE and DESCRIBE DEFINE and DESCRIBE DEFINE and DESCRIBE DEFINE and DESCRIBE the cumulative the cumulative the cumulative the cumulative F(t), external age E(t), and internal age I(t) F(t), external age E(t), and internal age I(t) F(t), external age E(t), and internal age I(t) F(t), external age E(t), and internal age I(t) residence time distribution (RTD) functions residence time distribution (RTD) functions residence time distribution (RTD) functions residence time distribution (RTD) functions

RECOGNIZERECOGNIZERECOGNIZERECOGNIZE these function for PFR, CSTR these function for PFR, CSTR these function for PFR, CSTR these function for PFR, CSTR and laminar flow reactions. and laminar flow reactions. and laminar flow reactions. and laminar flow reactions.

APPLY these functions to CALCULATE the APPLY these functions to CALCULATE the APPLY these functions to CALCULATE the APPLY these functions to CALCULATE the conversion and concentrations exiting a conversion and concentrations exiting a conversion and concentrations exiting a conversion and concentrations exiting a reactorreactorreactorreactor using the segregation model and using the segregation model and using the segregation model and using the segregation model and maximum maximum maximum maximum mixednessmixednessmixednessmixedness model for both single model for both single model for both single model for both single and multiple reactions.and multiple reactions.and multiple reactions.and multiple reactions.


SEM 2 (2009/2010)

OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW;

Learn about Learn about Learn about Learn about nonidealnonidealnonidealnonideal reactorsreactorsreactorsreactors, that is reactors do , that is reactors do , that is reactors do , that is reactors do

not follow the models we have developed for ideal not follow the models we have developed for ideal not follow the models we have developed for ideal not follow the models we have developed for ideal

CSTRs, PFRs and PBRs.CSTRs, PFRs and PBRs.CSTRs, PFRs and PBRs.CSTRs, PFRs and PBRs.

Describe Describe Describe Describe nonidealnonidealnonidealnonideal reactors reactors reactors reactors using ;using ;using ;using ;

A)residence time distribution function, E(t)A)residence time distribution function, E(t)A)residence time distribution function, E(t)A)residence time distribution function, E(t)

B) The mean residence time, tB) The mean residence time, tB) The mean residence time, tB) The mean residence time, tmmmm

C) The cumulative distribution C) The cumulative distribution C) The cumulative distribution C) The cumulative distribution fuctionfuctionfuctionfuction, F(t), F(t), F(t), F(t)

D)The variance, D)The variance, D)The variance, D)The variance, σ2222


SEM 2 (2009/2010)

OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW; OVERVIEW;

Evaluate E(t), tm, F(t) and Evaluate E(t), tm, F(t) and Evaluate E(t), tm, F(t) and Evaluate E(t), tm, F(t) and σ2222 for ideal for ideal for ideal for ideal

reactor, reactor, reactor, reactor, so we have a reference point as to so we have a reference point as to so we have a reference point as to so we have a reference point as to

how for our real (how for our real (how for our real (how for our real (nonidealnonidealnonidealnonideal)))) reactorreactorreactorreactor

Recognize all these functions & Recognize all these functions & Recognize all these functions & Recognize all these functions & apply to apply to apply to apply to

calculate the conversion & concentrations calculate the conversion & concentrations calculate the conversion & concentrations calculate the conversion & concentrations

exiting a reactor exiting a reactor exiting a reactor exiting a reactor using certain model.using certain model.using certain model.using certain model.


SEM 2 (2009/2010)

ResidenceResidenceResidenceResidenceResidenceResidenceResidenceResidence--------time distribution (RTD) time distribution (RTD) time distribution (RTD) time distribution (RTD) time distribution (RTD) time distribution (RTD) time distribution (RTD) time distribution (RTD)

function…function…function…function…function…function…function…function…In an In an In an In an ideal plug flow reactorideal plug flow reactorideal plug flow reactorideal plug flow reactor, all the , all the , all the , all the atoms of atoms of atoms of atoms of

material leaving the reactor material leaving the reactor material leaving the reactor material leaving the reactor have been inside it for have been inside it for have been inside it for have been inside it for

exactly the exactly the exactly the exactly the same amount timesame amount timesame amount timesame amount time....

Similarly, in an ideal batch reactor, all the atoms of Similarly, in an ideal batch reactor, all the atoms of Similarly, in an ideal batch reactor, all the atoms of Similarly, in an ideal batch reactor, all the atoms of

materials within the reactor have been inside it for an materials within the reactor have been inside it for an materials within the reactor have been inside it for an materials within the reactor have been inside it for an

identical length of time.identical length of time.identical length of time.identical length of time.

The The The The time the atoms have spent in the reactor time the atoms have spent in the reactor time the atoms have spent in the reactor time the atoms have spent in the reactor is is is is

called the called the called the called the RESIDENCE TIME RESIDENCE TIME RESIDENCE TIME RESIDENCE TIME of the atoms in the of the atoms in the of the atoms in the of the atoms in the

reactor.reactor.reactor.reactor.ERT 208/4 REACTION ENGINEERING

SEM 2 (2009/2010)


functionfunctionfunctionfunctionfunctionfunctionfunctionfunction…cont……cont……cont……cont……cont……cont……cont……cont…

The The The The idealized plugidealized plugidealized plugidealized plug----flow flow flow flow and and and and batch reactors batch reactors batch reactors batch reactors are are are are the only 2 classes of reactors in which the only 2 classes of reactors in which the only 2 classes of reactors in which the only 2 classes of reactors in which all the all the all the all the atoms in the reactors have the same residence atoms in the reactors have the same residence atoms in the reactors have the same residence atoms in the reactors have the same residence time.time.time.time.

In all In all In all In all other reactor typesother reactor typesother reactor typesother reactor types, the , the , the , the various atoms in various atoms in various atoms in various atoms in the feed spend different times inside the the feed spend different times inside the the feed spend different times inside the the feed spend different times inside the reactorreactorreactorreactor, that is a , that is a , that is a , that is a DISTRIBUTION OF DISTRIBUTION OF DISTRIBUTION OF DISTRIBUTION OF RESIDENCE TIMES RESIDENCE TIMES RESIDENCE TIMES RESIDENCE TIMES of the material within of the material within of the material within of the material within the reactor.the reactor.the reactor.the reactor.


SEM 2 (2009/2010)


functionfunctionfunctionfunctionfunctionfunctionfunctionfunction…cont……cont……cont……cont……cont……cont……cont……cont…

The residenceThe residenceThe residenceThe residence----time distribution (RTD) of the time distribution (RTD) of the time distribution (RTD) of the time distribution (RTD) of the reactor is a reactor is a reactor is a reactor is a characteristic of the mixing that characteristic of the mixing that characteristic of the mixing that characteristic of the mixing that occurs in the chemical reactor.occurs in the chemical reactor.occurs in the chemical reactor.occurs in the chemical reactor.

There is There is There is There is no axial mixing in a plug flow reactor no axial mixing in a plug flow reactor no axial mixing in a plug flow reactor no axial mixing in a plug flow reactor and this omission is reflected in the RTD. and this omission is reflected in the RTD. and this omission is reflected in the RTD. and this omission is reflected in the RTD.

The CSTR is thoroughly mixed and processes The CSTR is thoroughly mixed and processes The CSTR is thoroughly mixed and processes The CSTR is thoroughly mixed and processes a far different kind of RTD than the plug flow a far different kind of RTD than the plug flow a far different kind of RTD than the plug flow a far different kind of RTD than the plug flow reactor. reactor. reactor. reactor.


SEM 2 (2009/2010)

MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…RTD is RTD is RTD is RTD is determined experimentally by injecting an determined experimentally by injecting an determined experimentally by injecting an determined experimentally by injecting an inert chemical, molecule, or atom called a tracer, inert chemical, molecule, or atom called a tracer, inert chemical, molecule, or atom called a tracer, inert chemical, molecule, or atom called a tracer, into the reactor at some timeinto the reactor at some timeinto the reactor at some timeinto the reactor at some time t=0 and then measuring t=0 and then measuring t=0 and then measuring t=0 and then measuring the tracer concentration, C in the effluent stream as a the tracer concentration, C in the effluent stream as a the tracer concentration, C in the effluent stream as a the tracer concentration, C in the effluent stream as a function of time.function of time.function of time.function of time.

Tracer Tracer Tracer Tracer –––– nonreactive nonreactive nonreactive nonreactive species that species that species that species that easily detectable easily detectable easily detectable easily detectable (similar physical properties to reacting mixture and (similar physical properties to reacting mixture and (similar physical properties to reacting mixture and (similar physical properties to reacting mixture and be completely soluble in the mixture) and should not be completely soluble in the mixture) and should not be completely soluble in the mixture) and should not be completely soluble in the mixture) and should not adsorb on the walls @ other surface in the reactor.adsorb on the walls @ other surface in the reactor.adsorb on the walls @ other surface in the reactor.adsorb on the walls @ other surface in the reactor.

EgEgEgEg; ; ; ; coloredcoloredcoloredcolored & radioactive materials & radioactive materials & radioactive materials & radioactive materials along with inert along with inert along with inert along with inert gasses are the most common type of tracer.gasses are the most common type of tracer.gasses are the most common type of tracer.gasses are the most common type of tracer.


SEM 2 (2009/2010)

MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…MEASUREMENT OF RTD…

�2 most used 2 most used 2 most used 2 most used methods of injection methods of injection methods of injection methods of injection ::::

A) pulse inputA) pulse inputA) pulse inputA) pulse input

B) step inputB) step inputB) step inputB) step input


SEM 2 (2009/2010)

a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…

An amount of An amount of An amount of An amount of tracer, tracer, tracer, tracer, NNNNoooo is suddenly is suddenly is suddenly is suddenly

injected in one shot into the feed injected in one shot into the feed injected in one shot into the feed injected in one shot into the feed

stream entering the reactor in as stream entering the reactor in as stream entering the reactor in as stream entering the reactor in as short short short short

time time time time as possible.as possible.as possible.as possible.

The The The The outlet outlet outlet outlet concconcconcconc is then measured as a is then measured as a is then measured as a is then measured as a

function of timefunction of timefunction of timefunction of time....


SEM 2 (2009/2010)

a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…a) Pulse input…cont..cont..cont..cont..cont..cont..cont..cont..

Typical Typical Typical Typical concconcconcconc----time curve time curve time curve time curve at the inlet & outlet of at the inlet & outlet of at the inlet & outlet of at the inlet & outlet of an arbitrary reactor are shown below;an arbitrary reactor are shown below;an arbitrary reactor are shown below;an arbitrary reactor are shown below;


SEM 2 (2009/2010)

C

C C

t t

Pulse injectionPulse injectionPulse injectionPulse injection

Step injectionStep injectionStep injectionStep injection

Pulse responsePulse responsePulse responsePulse response

Step responseStep responseStep responseStep response

2 most used 2 most used 2 most used 2 most used

methods of methods of methods of methods of

injection :injection :injection :injection :

A) pulse inputA) pulse inputA) pulse inputA) pulse input

B) step inputB) step inputB) step inputB) step input


The effluent The effluent The effluent The effluent concconcconcconc----time curve time curve time curve time curve is referred to as the is referred to as the is referred to as the is referred to as the

C curve C curve C curve C curve in RTD analysis.in RTD analysis.in RTD analysis.in RTD analysis.

We shall analyze the injection of a tracer pulse We shall analyze the injection of a tracer pulse We shall analyze the injection of a tracer pulse We shall analyze the injection of a tracer pulse

for a for a for a for a singlesinglesinglesingle----input input input input & & & & singlesinglesinglesingle----output output output output system in which system in which system in which system in which

only flow (no dispersion) only flow (no dispersion) only flow (no dispersion) only flow (no dispersion) carries the tracer carries the tracer carries the tracer carries the tracer

material across system boundaries.material across system boundaries.material across system boundaries.material across system boundaries.


SEM 2 (2009/2010)


Step;Step;Step;Step;

Choose an increment of time ∆t sufficiently small that the Choose an increment of time ∆t sufficiently small that the Choose an increment of time ∆t sufficiently small that the Choose an increment of time ∆t sufficiently small that the concconcconcconc of tracer, C(t)of tracer, C(t)of tracer, C(t)of tracer, C(t)

Exiting between time Exiting between time Exiting between time Exiting between time t t t t and and and and t+∆t t+∆t t+∆t t+∆t is essentially the same.is essentially the same.is essentially the same.is essentially the same.

The The The The amount of tracer material, ∆N amount of tracer material, ∆N amount of tracer material, ∆N amount of tracer material, ∆N leaving the reactor leaving the reactor leaving the reactor leaving the reactor between time, t and t+∆t is then between time, t and t+∆t is then between time, t and t+∆t is then between time, t and t+∆t is then

Where, Where, Where, Where, υ is the effluent volumetric flow rateis the effluent volumetric flow rateis the effluent volumetric flow rateis the effluent volumetric flow rate....

∆N is the amount of material exiting the reactor that has ∆N is the amount of material exiting the reactor that has ∆N is the amount of material exiting the reactor that has ∆N is the amount of material exiting the reactor that has spent an amount of time between timespent an amount of time between timespent an amount of time between timespent an amount of time between time t and t+∆t in the t and t+∆t in the t and t+∆t in the t and t+∆t in the reactor.reactor.reactor.reactor.


SEM 2 (2009/2010)

tvtCN ∆=∆ )(


Divide the total amount of material that was injected Divide the total amount of material that was injected Divide the total amount of material that was injected Divide the total amount of material that was injected into the reactor, into the reactor, into the reactor, into the reactor, NNNNoooo, we obtain, we obtain, we obtain, we obtain

Which represents the Which represents the Which represents the Which represents the fraction of material that has a fraction of material that has a fraction of material that has a fraction of material that has a residence time in the reactor between time t and t+∆tresidence time in the reactor between time t and t+∆tresidence time in the reactor between time t and t+∆tresidence time in the reactor between time t and t+∆t....

For pulse injection, we define,For pulse injection, we define,For pulse injection, we define,For pulse injection, we define,

So that;So that;So that;So that;


SEM 2 (2009/2010)

tvtCN ∆=∆ )( tN

tvC

N

N

oo

∆=∆ )(

oN

tvCtE

)()( =

ttEN

N

o

∆=∆

)(


The quantity The quantity The quantity The quantity E(t) is called the residenceE(t) is called the residenceE(t) is called the residenceE(t) is called the residence----time time time time distribution function distribution function distribution function distribution function that describes in quantitative that describes in quantitative that describes in quantitative that describes in quantitative manner how much time different fluid elements have manner how much time different fluid elements have manner how much time different fluid elements have manner how much time different fluid elements have spent in the reactor.spent in the reactor.spent in the reactor.spent in the reactor.

The quantity The quantity The quantity The quantity E(t)E(t)E(t)E(t)dtdtdtdt is the is the is the is the fraction of fluid exiting the fraction of fluid exiting the fraction of fluid exiting the fraction of fluid exiting the reactor that has spent between time t and reactor that has spent between time t and reactor that has spent between time t and reactor that has spent between time t and t+dtt+dtt+dtt+dt inside inside inside inside the reactor.the reactor.the reactor.the reactor.

If If If If NNNNoooo is not known directly, it can be obtained from is not known directly, it can be obtained from is not known directly, it can be obtained from is not known directly, it can be obtained from the outlet concentration measurements by summing the outlet concentration measurements by summing the outlet concentration measurements by summing the outlet concentration measurements by summing up all the amounts of materials, ∆N between time up all the amounts of materials, ∆N between time up all the amounts of materials, ∆N between time up all the amounts of materials, ∆N between time equal to zero and infinityequal to zero and infinityequal to zero and infinityequal to zero and infinity....


SEM 2 (2009/2010)


Writing in differential form Writing in differential form Writing in differential form Writing in differential form

yields,yields,yields,yields,

And then integrating, we obtainAnd then integrating, we obtainAnd then integrating, we obtainAnd then integrating, we obtain

The volumetric flow rate, v is usually The volumetric flow rate, v is usually The volumetric flow rate, v is usually The volumetric flow rate, v is usually

constant, so we can constant, so we can constant, so we can constant, so we can define E(t) define E(t) define E(t) define E(t) as,as,as,as,


SEM 2 (2009/2010)

dttvCdN )(=

tvtCN ∆=∆ )(

dttvCNo

)(0

∞∫=

dttC

tCtE

)(

)()(

0

∞∫=


The The The The integral in the denominator integral in the denominator integral in the denominator integral in the denominator is the is the is the is the area area area area under the C curve.under the C curve.under the C curve.under the C curve.

An alternative way of interpreting the An alternative way of interpreting the An alternative way of interpreting the An alternative way of interpreting the residenceresidenceresidenceresidence----time function is in its time function is in its time function is in its time function is in its integral formintegral formintegral formintegral form::::


SEM 2 (2009/2010)

dttC

tCtE

)(

)()(

0

∞∫=

Fraction of material

leaving the reactor that has

resided in the reactor for

times between t1 and t2

= dttEt

t)(2

1∫


We know that the fraction of all the material that has We know that the fraction of all the material that has We know that the fraction of all the material that has We know that the fraction of all the material that has

resided for a time t in the reactor resided for a time t in the reactor resided for a time t in the reactor resided for a time t in the reactor between t=0 and between t=0 and between t=0 and between t=0 and

t=∞ is 1.t=∞ is 1.t=∞ is 1.t=∞ is 1. Therefore:Therefore:Therefore:Therefore:

Next example will show how we can calculate and Next example will show how we can calculate and Next example will show how we can calculate and Next example will show how we can calculate and

interpret E(t) from the effluent concentrations from interpret E(t) from the effluent concentrations from interpret E(t) from the effluent concentrations from interpret E(t) from the effluent concentrations from

the response to a pulse tracer input to a real the response to a pulse tracer input to a real the response to a pulse tracer input to a real the response to a pulse tracer input to a real

((((nonidealnonidealnonidealnonideal) reactor.) reactor.) reactor.) reactor.


SEM 2 (2009/2010)

1)( =∫∞

dttEo

A sample of the A sample of the A sample of the A sample of the tracer tracer tracer tracer hytanehytanehytanehytane at 320K was injected at 320K was injected at 320K was injected at 320K was injected as a pulse as a pulse as a pulse as a pulse to a reactor to a reactor to a reactor to a reactor

and the and the and the and the effluent concentration effluent concentration effluent concentration effluent concentration was measured as a function of time, was measured as a function of time, was measured as a function of time, was measured as a function of time,

resulting in the data shown in table below.resulting in the data shown in table below.resulting in the data shown in table below.resulting in the data shown in table below.

The measurements represent the exact concentrations at the time listed The measurements represent the exact concentrations at the time listed The measurements represent the exact concentrations at the time listed The measurements represent the exact concentrations at the time listed

and not average values between the various sampling tests.and not average values between the various sampling tests.and not average values between the various sampling tests.and not average values between the various sampling tests.

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


SEM 2 (2009/2010)

Example: Constructing the C(t) and E(t) Example: Constructing the C(t) and E(t) Example: Constructing the C(t) and E(t) Example: Constructing the C(t) and E(t)

Curves (Pulse Input)Curves (Pulse Input)Curves (Pulse Input)Curves (Pulse Input)

t(min) 0 1 2 3 4 5 6 7 8 9 10 12 14

C

(g/m3)

0 1 5 8 10 8 6 4 3 2.2 1.5 0.6 0

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

Solution:Solution:Solution:Solution:

C(t) as function of time C(t) as function of time C(t) as function of time C(t) as function of time ---- By plotting C as a By plotting C as a By plotting C as a By plotting C as a fuctionfuctionfuctionfuction of time, using the data of time, using the data of time, using the data of time, using the data

in table before, the curve shown in figure below obtain.in table before, the curve shown in figure below obtain.in table before, the curve shown in figure below obtain.in table before, the curve shown in figure below obtain.


SEM 2 (2009/2010)


Curves (Pulse Input)Curves (Pulse Input)Curves (Pulse Input)Curves (Pulse Input)…cont……cont……cont……cont…

C(t)

Time (min)

To obtain the E(t) curve from the C(t) curve, we just To obtain the E(t) curve from the C(t) curve, we just To obtain the E(t) curve from the C(t) curve, we just To obtain the E(t) curve from the C(t) curve, we just divide C(t) by the divide C(t) by the divide C(t) by the divide C(t) by the

integral integral integral integral which is just the which is just the which is just the which is just the area under the C curvearea under the C curvearea under the C curvearea under the C curve. Because . Because . Because . Because

one quadrature (integration) formula will not suffice over the entire one quadrature (integration) formula will not suffice over the entire one quadrature (integration) formula will not suffice over the entire one quadrature (integration) formula will not suffice over the entire

range of data in the table given, we range of data in the table given, we range of data in the table given, we range of data in the table given, we break the data into 2 regions (0break the data into 2 regions (0break the data into 2 regions (0break the data into 2 regions (0----10 10 10 10

min & 10min & 10min & 10min & 10----14min). 14min). 14min). 14min). The area under the C curve can now be found The area under the C curve can now be found The area under the C curve can now be found The area under the C curve can now be found

using the using the using the using the numerical integration formulas (Appendix in text book)numerical integration formulas (Appendix in text book)numerical integration formulas (Appendix in text book)numerical integration formulas (Appendix in text book)....


SEM 2 (2009/2010)



dttCo

)(∞∫

dttCdttCdttCo

)()()(14

10

10

0∫+∫=∫

∞


SEM 2 (2009/2010)



dttCdttCdttCo

)()()(14

10

10

0∫+∫=∫

∞

3

10

0

min/.4.47

)5.1(1)2.2(4)0.3(2)4(4)6(2

)8(4)10(2)8(4)5(2)1(4)0(1

3

1)(

mg

dttC

=

++++

++++++=∫

[ ]3

14

10

min/.6.2

0)6.0(45.13

2)(

mg

dttC

=

++=∫

3

3

min/.0.50

min/.)6.24.47()(

mg

mgdttCo

=

+=∫∞

We now calculate,We now calculate,We now calculate,We now calculate,

With the following resultsWith the following resultsWith the following resultsWith the following results


SEM 2 (2009/2010)



3min/.50

)(

)(

)()(

mg

tC

dttC

tCtE

o

=∫

= ∞

t(min) 0 1 2 3 4 5 6 7 8 9 10 12 14

C

(g/m3)

0 1 5 8 10 8 6 4 3 2.2 1.5 0.6 0

E(t)

(min-1)

0 0.02 0.1 0.16 0.2 0.16 0.12 0.08 0.06 0.044 0.03 0.012 0

Solution:Solution:Solution:Solution:

E(t) as function of time curve E(t) as function of time curve E(t) as function of time curve E(t) as function of time curve


SEM 2 (2009/2010)



E(t)

Time (min)

Tail-the long

time portion

of the E(t)

curve

b) Determine both the fraction of material leaving the reactor that has b) Determine both the fraction of material leaving the reactor that has b) Determine both the fraction of material leaving the reactor that has b) Determine both the fraction of material leaving the reactor that has

spent between 3 and 6 min in the reactorspent between 3 and 6 min in the reactorspent between 3 and 6 min in the reactorspent between 3 and 6 min in the reactor


SEM 2 (2009/2010)



E(t)

Time (min)

Shaded area Shaded area Shaded area Shaded area represents the fraction

of material leaving the reactor that

has resided in the reactor between 3

and 6 min.

63

51.0

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

3

_)(6

3

=

+++=

=∫ areashadeddttE

51% of the material leaving the 51% of the material leaving the 51% of the material leaving the 51% of the material leaving the

reactor spends between 3 and 6 reactor spends between 3 and 6 reactor spends between 3 and 6 reactor spends between 3 and 6

min in the reactormin in the reactormin in the reactormin in the reactor

cccc) Determine the fraction of material leaving the reactor that has spent ) Determine the fraction of material leaving the reactor that has spent ) Determine the fraction of material leaving the reactor that has spent ) Determine the fraction of material leaving the reactor that has spent

between 7.75 and 8.25 min in the reactor.between 7.75 and 8.25 min in the reactor.between 7.75 and 8.25 min in the reactor.between 7.75 and 8.25 min in the reactor.


SEM 2 (2009/2010)



Because of the time between 7.75 and 8.25 min is very small

relative to a time scale of 14min, we shall use alternative technique

to determine this fraction to reinforce the interpretation of the

quantity E(t). The average value of E(t) between these times is average value of E(t) between these times is average value of E(t) between these times is average value of E(t) between these times is

0.06/min.0.06/min.0.06/min.0.06/min.

Consequently, 3% of the fluid leaving the reactor has been in the 3% of the fluid leaving the reactor has been in the 3% of the fluid leaving the reactor has been in the 3% of the fluid leaving the reactor has been in the

reactor between 7.75 and 8.25minreactor between 7.75 and 8.25minreactor between 7.75 and 8.25minreactor between 7.75 and 8.25min

03.0min)5.0(min06.0)( 1 == −dttE

Quiz………(5 min)Quiz………(5 min)Quiz………(5 min)Quiz………(5 min)Quiz………(5 min)Quiz………(5 min)Quiz………(5 min)Quiz………(5 min)


SEM 2 (2009/2010)

Define the following terms;

a)Ideal reactor

b)Non ideal reactor

End For Part AEnd For Part AEnd For Part AEnd For Part A


SEM 2 (2009/2010)

Documents

Distribution of Residence Times for Reactorslibvolume2.xyz/.../nonidealreactors/nonidealreactorspresentation1.pdf · Similarly, in an ideal batch reactor, all the atoms of materials