Ch 1-4 Chemical Kinetics Part 1

7/31/2019 Ch 1-4 Chemical Kinetics Part 1

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230-620 ADVANCED CHEMICAL ENGINEERINGKINETICS AND CHEMICAL REACTOR DESIGN

Prince of Songkla University

Suratsawadee Kungsanant, Ph.D.

Department of Chemical Engineering, Room: KE302

Email: [email protected], Tel.: 7308


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Chemical Kinetics

Chemical kinetics - speed or rate at whicha reaction occurs

How are rates of reactions affected by

Reactant concentration?

Temperature?

Reactant states?

Catalysts?


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Kinetics

Considerations of the rate at which achemical process occurs.

Besides information about the speed atwhich reactions occur, kinetics also shedlight on the reaction mechanism (exactlyhowthe reaction occurs).


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Factors That Affect Reaction Rates

Physical State of the Reactants: In order to react, molecules must come in

contact with each other.

The more homogeneous the mixture ofreactants, the faster the molecules can react.

Concentration of Reactants: As the concentration of reactants increases,

so does the likelihood that reactant

molecules will collide. Temperature:

At higher temperatures, reactant moleculeshave more kinetic energy, move faster, and

collide more often and with greater energy.


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1. Mole Balances Equation

2. Conversion and Reactor Sizing3. Rate Laws and Stoichiometry

4. Isothermal Reactor Design

Fundamental of Chemical Engineering

Kinetics and Reactor Design


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1. Mole Balances Equation


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Three ways a chemical species can lose itschemical identity:

1.decomposition

2.combination

3.isomerization

A chemical species is said to have reacted when it

has lost its chemical identity. The identity of a chemicalspecies is determined by the kind, number, and configurationof that species' atoms.

Chemical Identity
http://e/html/01chap/frames.htmhttp://e/html/01chap/frames.htm


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1. Mole Balances Equation1.1 Definition of the Rate of the Reaction, -rA

The reaction rate is the rate at which a species

looses its chemical identity per unit volume.

The rate of a reaction can be expressed as the

rate of disappearance of a reactant or as the rate of

appearance of a product.


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1. Mole Balances EquationConsider species A:

rA = the rate of formation of species A per unit volume

-rA = the rate of a disappearance of species A per unit

volume

rB = the rate of formation of species B per unit volume


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-rA = moles of A reacting (disappearing)/(time.volume)

= [ ] moles / (s.dm3) = rA= rate of formation of product

For a catalytic reaction,

-rA

= number of mole A reacted

/ (time. Mass of catalyst)= [ ] moles / (s.g of cat.)

For a catalytic reaction, we refer to -rA', which is therate of disappearance of species A on a per mass of catalystbasis.


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For a constant volume batch reactor,

The reactants were mixed together at time t =

0 and the concentration of one of the reactants, CA,was measured at various times t.

Let:

rA = the rate of formation of A per unit volume

dt

dC

r

A

A

(from t=0 to t=t)


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1. Mole Balances Equation1.2 The General Mole Balance Equation

FjoFj

Gj

System Volume To perform amole balance on anysystem, the systemboundaries must first be

specified.

The volume

enclosed by theseboundaries will be

referred to as thesystem volume


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A mole balance on

species j at any instanttime, t, yields thefollowing equation:

Fjo FjGj

System Volume

[Rate of j flowinto the

system(moles/time)]

[Rate of jflow out of

the system

(moles/time)]

+ -[Rate ofgeneration of j bychemical

reaction within

the system(moles/time)]

= [Rate ofaccumulation of jwithin the

system(moles/time)]

Mole Balance: In + Generationout = AccumulationFjo + GjFj = dNj/dt (1-3)


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1. Mole Balances EquationGeneral Mole Balance EquationIN - OUT + GENERATION = ACCUMULATION


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1. Mole Balances Equation1.3 Batch Reactor

A batch reactor has neither inflow nor outflow of

reactants or products while the reaction is being carriedout; Fjo = Fj = 0


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if the reaction is perfectly mixed, so that there is no

variation in the rate throughout the reactor volume, we

can take rj out of the integral and write the mole balance

in form

= dNj/dt

= dNj/dt

GBE for Batch reactor:In + Generationout = Accumulation

FjoFj + = dNj/dtV jdVr0 0

V

j dVr

Vrj


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1. Mole Balances Equation1.4 Continuous-flow Reactor

1.4.1 Continuous-Stirred Tank Reactor (CSTR)

A type of reactor used very commonly in industrial

processing is a stirred tank operated continuously. The CSTR isnormally run at steady state and is usually operated so as to bequite well mixed.


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FjoFj + = 0

GBE for CSTR reactor (operated at steady state):In + Generationout = Accumulation

FjoFj + = dNj/dtV jdVr0

V

j dVr

Vrj

FjoFj + = 0

j

jj

r

FFV

0

0AF

AF


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The molar flow rate Fj is just the product ofthe concentration of species j and the volumetric

flow rate v:

timevolume

volumemoles

timemoles

vCFjj


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1.4.2 Plug Flow Reactor (PFR)

It consists of a cylindrical pipe and is normally operated at

steady state, as is the CSTR. The flow insides the reactor is highlyturbulent.

The reactants are continuously consumed as they flow

down the length of the reactor. The concentration variescontinuously in the axial direction through the reactor. Thereaction rate will also vary axially.


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GBE for PFR reactor (operated at steady state):In + Generationout = Accumulation

FjoFj + = dNj/dtV jdVr0

VrdVr j

V

j

V

y y yy 0jF exitjF ,

)(yFj)( yyFj

0)()( VryyFyF jjj

0)()( VryyFyF jjj

yAV

j

jjAr

y

yFyyF

]

)()([


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V

y y yy 0jF exitjF ,

)(yFj)( yyFj

j

jj

y

Ary

yFyyF

])()(

[lim0

j

jAr

dydF

j

j

Ardy

dF

j

jjr

dV

dF

Ady

dF

j

jr

dV

dF


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1.4.3 Packed-bed Reactor (PBR)

The reaction rate is based on mass of solid catalyst, W,

rather than on reactor volume, V.The mass of solid is used because the amount of catalyst is

what is important to the reaction rate of the reaction. The reactor

volume that contains the catalyst is of secondary significance.

For a fluid-solid heterogeneous system, the rate of reactionof a substance A is defined as

'Ar g mole A reacted/s.g catalyst


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GBE for PBR reactor (operated at steady state):In + Generationout = Accumulation

W

W WW 0AF AF

)(WFA )( WWFA

0)()(' WrWWFWF AAA

time

molesAcatalystofmass

catalystofmasstime

AmoleWrA )(

))((

'

As with the PFR, the PBRis assumed to have no radial

gradients in concentration,temperature, or reaction rate.

After dividing by and takingthe limit as , yields:

W0W

'

AA r

dW

dF

A

A

F

F A

A

r

dFW

0

'


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Example 1-3: How large is it?


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2. Conversion and Reactor Sizing


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2. Conversion and ReactorSizing

2.1 Definition of Conversion

Choose one of the reactants as the basis ofthe calculation

Relate the other species involved in the

reaction to this basis


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dDcCbBaA (2-1)A: The upper letters represent chemical species.

a: The lower letters represent stoichiometric coefficients.

Taking specie A as a basis of calculation, thereaction expression is divided through by thestoichiometric coefficient of specie A

C


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DadC

acB

abA

aa

(2-2)Da

dC

a

cB

a

bA

Put every quantity on a per mole of A basis


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Assume, 1 mole of A is used in the reaction.Then, in the reaction we must use

B = b/a mole

and we obtain

C = c/a moleD = d/a moleBasis 1 mole of A, the conversion of this reaction

(xA) is

xA = (mole of A reacted) /(mole of A fed)


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The conversion (xA) is the answer of thesequestions.

How can we quantify how far a reaction has

progress?

How many moles of C are formed for everymoles A consumed?

2 C i d R


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2.2 Design Equations2.2.1 Batch Systems

Conversion (xA) = f (time reactants spend in the reactor)

If A is reactant,

NA0 is the initial number of mole ANA0X is the number of mole A that reacted after a time t

[mole of Aconsumed] [mole ofA fed] mole of A reacted /mole of A fed= x

[NA0] [X]= x[NA]

2 C i d R


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[mole of A

consumed] [mole of Aat t=0] mole of A that havebeen consumed bychemical rxn.= -

[NA0] [NA0X]= -

At t=t, NA =

[NA]NA = NA0(1-X)

The number of mole A in the reactor after aconversion X has been achieved.


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(2-2)

Da

dCa

cBa

bA

In general reaction,

A is disappearing, so eq. (2-5) is multiply by -1; yields

=

GBE for Batch reactor:In + Generationout = Accumulation

FjoFj + =V

AdVr0 0

V

A dVr

=VrA (2-5)

dt

dNA

dt

dNA

dt

dNA

=Vr

A

dt

dNA


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In batch reactor, we are interested in determining

how long to leave the reactants in the reactor to achieve acertain conversion XThus, from XNNN AAA 00

dt

XNd

dt

dN

dt

dN AAA )( 00

dt

dXN

dt

dNA

A0

0

Vr

dt

dN

dt

dXN A

AA 0

Vrdt

dXN AA 0

Batch reactor design equation!

The differential

form of the design

equations often

appear in reactoranalysis and are

partially useful in

the interpretation

of reaction ratedata.


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)(

0

0

tX

A

AVr

dXNt

The integral form for

Constant-volume Batch reactor design equation!

Vrdt

dXN AA 0

2 C i d R t


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2.2 Design Equations2.2.2 Flow system 0A

F

AF

If ,

FA0 is the molar flow rate of species A fed to a systemoperated at steady state

FA0X is the molar flow rate at which species A is reachingwithin the entire system

][][ 0 XFF AA Moles of A fed/time . Moles of A reacted/Moles of A fed ][ 0XFF AA Moles of A reacted /time= The molar flow rate of

A leaving the system


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[molar flow

rate at which A

is fed to thesystem] - =

[FA0

X]

[FA0

]

[molar flow rate

at which A is

consumed within

the system]

[molar flow

rate at which A

leaves thesystem]

[FA

]

)1(0 XFF AA (2-10)The entering molar flow rate, FA0 (mol/s) = The

entering concentration, CA0 (mol/dm3). The enteringvolumetric flow rate, v0 (dm3/s)

000 AA CF


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CSTR or Backmix Reactor

The equation resulting from mole balance onspecies A of the reaction

(2-2)Da

dC

a

cB

a

bA

occuring in a CSTR

GBE for CSTR reactor:In + Generationout = Accumulation

0dt

dNdVrFF A

V

AAA

0

00

VrFF AAAVrFF AAA 0

VrXFFF AAAA )( 000 VrXF AA 0exitA

A

r

XFV

,

0)(

0AF

AF


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exitA

A

r

XFV

,

0

)(

(2-13)

Eq. (2-13) is applied for determine the CSTR

volume necessary to achieve a specific conversion XSince the exit composition from the reactor is

identical to the composition inside the reactor, the rate ofreaction is evaluated at the exit condition.


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For PFR,A

A rdV

dF

AAAA r

dVXdF

dVXFFd )()( 0

00

X

A

Ar

XdFV

0

0

)(

For PBR,'

0 AA rdW

dXF

X

A

Ar

XdFW

0

'0

)(


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Example 2-1 using the ideal gas law to calculate CA0

Ch 1-4 Chemical Kinetics Part 1

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