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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: ksuratsawade@eng.psu.ac.th, 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
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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. Mole Balances Equation1.4 Continuous-flow Reactor
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. Mole Balances Equation1.4 Continuous-flow Reactor
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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2. Conversion and ReactorSizing
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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2. Conversion and ReactorSizing
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. Conversion and ReactorSizing
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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2. Conversion and ReactorSizing
[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. Conversion and ReactorSizing
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