cre ii l20-21
TRANSCRIPT
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L -21 External Mass Transfer
Effects
Prof. K.K.Pant
Department of Chemical EngineeringIIT Delhi.
mailto:[email protected]:[email protected] -
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Thermofer Catalytic cracking unit (MBR,Used for reactions with moderate
decay)
Fresh/regenerated catalyst enters from top
of reactor=> gets coked as moves down
and exits in a furnace where air is uded toburn off carbon (C+ O2-CO2 )
Catalyst pellet size ~ 1/8 in inch in dia)
CATALYST DEACTIVATION
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L -21 External Mass Transfer
Effects
Prof. K.K.Pant
Department of Chemical EngineeringIIT Delhi.
mailto:[email protected]:[email protected] -
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Thermofer Catalytic cracking unit (MBR,Used for reactions with moderate
decay)
Fresh/regenerated catalyst enters from top
of reactor=> gets coked as moves down
and exits in a furnace where air is uded toburn off carbon (C+ O2-CO2 )
Catalyst pellet size ~ 1/8 in inch in dia)
CATALYST DEACTIVATION
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Ist Order deactivation
IInd order Rate
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Straight through Transport Reactor
(Circulating Fluidized bed reactor)
Used when deactivation is rapid.Used for production of gasoline
Catalyst pellet and feed enter
together and transported rapidly.Bulk density of the catalyst is low
compared to Moving bed.
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STTR : Used when coking is rapid.
Bulk density of catalyst is smaller than
MBR. Particle velocity = gas velocity.
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Mole balance
rA= brA
Or
Z= Height (m),and Up is velocity of catalyst
(m/s)
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a
1 R 1= ln +T E Ta o
Temperature/Time Trajectories
A control strategy involves maintaining a constant
conversion with catalyst decay by increasing
operating temperature.
develop a temperature/time trajectory to find T -t
relationship: How T should increase with time.
-rA (t=0,T0) = -rA (t= t,T) = a(t ,T)[-rA (t=0,T) ]
k T a T,t = ko
E1 1a -
R T To
k e a = ko o
Arrhenius type T dependence
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Temperature/Time Trajectories
a
0
E1 1d -
R T Tda o n
r = - = k ed ddt
decay law is:
a
Ed- lnaE
da a n- = k e
ddt o
a
E
dn-Ea
= kdo
a
1 R 1= ln +
T E Ta o
Substitute T value
Integrate with a=1 at t=0
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Temperature/Time Trajectories
1- n+ E Ead1- at =
k 1-n+ E Ead d
o
a
1 R 1= ln +T E T
a o
E 1 1a -R T T
oa = e
E -n E +Ea a 1 1d -R T T
o1-e
=E
dk 1-n+d
Eo a
aa
E
d-n+E
a tda = -k dt1 0d
o
Ed-n 1
Ea
For
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13
External Diffusion effects in Heterogeneous Reactions
TWO TYPES of Diffusion Resistance
1. External diffusion
2. Internal Diffusion
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Mass Transfer FundamentalsDiffusion : Spontaneous intermingling or mixing of Atoms or molecules
by random thermal motion.
Gives rise to motion of the species relative to motion of mixtures.
WA or NA= Molar flux of A relative to a fixed coordinates (Vector)
Molar flux of A = Diffusive flux (J A) + Convective flux (BA)(in direction of concn. Gradient)
BA = CAV due to bulk fluid motin, V = Molar average velocity , V= yivi
For Binary system
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Or
For Equi molar Counter Diffusion (EMCD): WA= -WB
EMCD
Ficks Law of diffusion
B d C diti
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Boundary Conditions
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For Equi molar counter diffusion
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Ist Order deactivation
IInd order Rate
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Straight through Transport Reactor
(Circulating Fluidized bed reactor)
Used when deactivation is rapid.
Used for production of gasoline
Catalyst pellet and feed enter
together and transported rapidly.Bulk density of the catalyst is low
compared to Moving bed.
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STTR : Used when coking is rapid.
Bulk density of catalyst is smaller than
MBR. Particle velocity = gas velocity.
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a
1 R 1= ln +T E Ta o
Temperature/Time Trajectories
A control strategy involves maintaining a constant
conversion with catalyst decay by increasingoperating temperature.
develop a temperature/time trajectory to find T -t
relationship: How T should increase with time.
-rA (t=0,T0) = -rA (t= t,T) = a(t ,T)[-rA (t=0,T) ]
k T a T,t = ko
E
1 1a -R T To
k e a = ko o
Arrhenius type T dependence
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Temperature/Time Trajectories
a
0
E1 1d -
R T Tda o n
r = - = k ed ddt
decay law is:
a
Ed- lnaE
da a n- = k e
ddt o
a
E
dn-Ea
= kdo
a
1 R 1= ln +
T E Ta o
Substitute T value
Integrate with a=1 at t=0
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Temperature/Time Trajectories
1- n+ E Ead1- at =
k 1-n+ E Ead do
a
1 R 1= ln +
T E Ta o
E 1 1a -R T T
oa = e
E -n E +Ea a 1 1d -R T T
o1-e
=E
dk 1-n+d
Eo a
aa
E
d-n+Ea t
da = -k dt1 0do
Ed-n 1
Ea
For
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External Diffusion effects in Heterogeneous Reactions
TWO TYPES of Diffusion Resistance
1. External diffusion
2. Internal Diffusion
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27
Mass Transfer FundamentalsDiffusion : Spontaneous intermingling or mixing of Atoms or molecules
by random thermal motion.
Gives rise to motion of the species relative to motion of mixtures.
WA or NA= Molar flux of A relative to a fixed coordinates (Vector)
Molar flux of A = Diffusive flux (J A) + Convective flux (BA)(in direction of concn. Gradient)
BA = CAV due to bulk fluid motin, V = Molar average velocity , V= yivi
For Binary system
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Or
For Equi molar Counter Diffusion (EMCD): WA= -WB
EMCD
Ficks Law of diffusion
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Boundary Conditions
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Boundary Conditions
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For Equi molar counter diffusion
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32Solve for concentration profile CAvs z
=>
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Diffusion through Stagnant Gas (Evaporation or
gas absorption)
Gas B is stagnant then there is no net flux of B
with respect to a fixed coordinate.
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External mass transfer / boundary layer
Diffusion through a film to a catalyst particle
CAb= concn of gas A at the ext. boundary of gas film B (dilute gas)
Cas = at the external cat surface
Correlation for mass transfer for flow around a
spherical pellet
Frossling correlation
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Boundary layer around a catalyst pellet
External Resistance to Mass Transfer
Diffusion and Reaction
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Isomerisation Reaction
Diffusion and reaction
LHHW surface
reaction
For weak adsorption or at high T,
=>
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For rapid reaction : sp. reaction rate constant is much greater than mass
transfer coefficient
For slow reaction
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Mass transfer and reaction in a
packed bed
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'AzA b
AbAz AB Ab
2'Ab Ab
AB A b2
dW- +r = 0
dz
where
dCW = -D +C U and
dz
U = superficial velocity
hence
d C dCD -U +r = 0
dz dz
Mole balance in flux form, where Acis
constant and FA= AcWAz
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Diffusion and Reaction in a Porous Catalyst
c
D p cD =e
where
Actual distance a molecule travels btw 2 points = tortousity =
Shortest distance btw 2 points
Volume of void space = pellet porosity =p
Total volume(voids and solids)
= Constriction factor,c f( )
Effective Diffusivity: Bulk diffusion ( Large pore)and
Knudsen diffusion(small pore) Dk(cm2/s)=9.7 *103r (cm) (TK/M)
1/2
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Effective Diffusivity: Pores are not straight cylindrical.
These are a series of Tortuous, interconnecting paths of
varying cross sectional area.
Pellet porosity = volume of void space/ total volume
(voids and solids)
Constriction factor , ( )accounts for the variation in thecross sectional area that is normal to the diffusion. It is a
function of the ratio of maximum to minimum pore areas
().
= f(), =1 if =1. =0.5 if = 10. Typical value=0.8.
tortuosity,t = 3.0
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Derivation of the Differential Equation
~ Diffusion and Reaction in a spherical pellet
dr
dCD
dr
dycDW Ae
AeAr
0)( 22 rr
dr
rWdcA
Ar
0])/([ 22
rrdrrdrdCDd cAAe
=r+r
Moles = WAr(4 r2)r
Boundary
conditions
Order of
reaction?-rA=c(-rA)
r=0, CA finite, r=R, CA=CAS
Molar flux
Inoutdisappearance =0
WAr(4 r2)r - WAr(4 r
2)r+ r - rA (4 r2c
r) =0
Dividing by -4 r
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Lets simply consider 1storder
0])/([ 22
rrdr
rdrdCDdcA
Ae
0])/([ 122
AAe CkrdrrdrdCDd
c(-rA)=-rA volumetric
-rA=kCA
What about n-th order ?
0])/([ 2
2
n
AnAe Ckr
dr
rdrdCDd
Differentiation &
Divide byr2De
Differentiation &
Divide byr2De
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Lets simply consider 1storder
What about n-th order ?
02
2
2
n
A
e
nAA CD
k
dr
dC
rdr
Cd
02 12
2
A
e
AAC
D
k
dr
dC
rdr
Cd
Di i l F f th E ti
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Dimensionless Form of the Equation
Dimensionless symbol was normally introduced to
Reduce complexity in equation
Simplify operation of calculation Scale-up the reactor
Let = CA/CAs and =r/R
dCA/dr= (dCA/d)(d/dr)= (d/d)(dCA/d
)x
(d/dr)
=> dCA/dr = (d/d)(CAS/R)d2CA/dr
2= d/dr(dCA/dr)= (d2/d2)(CAS/R2)
When
CA=CAsat r=R, =1 and =1
CA=finite at r=0, =finite and =0
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Dimensionless eq.1storder
About for n-th order ?
0
22
2
n
A
e
nAA
CD
k
dr
dC
rdr
Cd
02 1
2
2
A
e
AAC
D
k
dr
dC
rdr
Cd0
2 212
2
dr
d
rd
d
0
2 22
2
n
ndr
d
rd
d
Thiele
Module
Thiele
Module
eDRk 2
1
e
n
Asn
D
CRk 12
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Thiele Modulus, n
2 n-1 n
2 n As n Asn
e e As
k R C k RC "a" surface reaction rate = = =D D [(C -0)/R] "a" diffusion rate
A 1
As 1
C sinh 1 = =
C sinh
If n is largeinternal diffusion limits the
overall rate
If n is smallthe surface reaction limits theoverall rate
y=
d2y/d 2- 2y=0
y= A Cosh + B Sinh
A=0 as must be finite
at the centre
(B. C =0, cos h 1;
1/ , and Sinh 0.
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Calculation of Catalytic Effectiveness FactorCatalytic Effectiveness Factor:
where
- Thiele Modulus
1storder reaction rate:
Spherical Pellet
Cylindrical Pellet
Slab Pellet
)313(1
Coth
DekSaR p/3
DekSa
Rp
/2
DekSaL p/
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Internal Effectiveness Factor
InternaleffectivenessFactor, is:ranged 01
for a first-orderreaction in aspherical catalystpellet
As s
Actual overall rate of reaction
= Rate of reaction that would result if entire
interior surface were exposed to the external
pellet surface conditions C ,T
' "
A A A
' "
As As As
-r -r -r = = =
-r -r -r
1 121
3 = coth -1
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Internal Effectiveness Factor
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Falsified Kinetics
Measurement of the apparentreaction orderand activation energy results primarily wheninternal diffusion limitations are present.
This becomes serious if the catalyst pellet
shape and size between lab (apparent) andreal reactor (true) regime were Too different.
Smaller catalyst pelletreduces the diffusion
limitationhigher activation energy moretemperature sensitive
RUNAWAY REACTION CONDITIONS!!!!
F l ifi d Ki i
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Falsified Kinetics
Apostrophe/ prime sign denotes the
apparent parameter vice versa
With the same rate of production, reaction
order and activation energy to be measured
R t f ti
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Rate of reaction, -rA
= (Actual overall rate of reaction) divided by
(rate that would result if the entire surface
were exposed to the bulk conditions, CAb,Ts)
"
1 a b c c
" " "
A Ab 1 Ab
' " "
A A b A a b 1 Ab a b
=1+k S /k a
-r = (-r ) = k C
-r =-r = -r S = k C S
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Axial diffusion, can be neglected when
FAis very large
so
Finally, the conversion for
1storder reaction in PBR is
'
0 p A b p
a 0 Ab
U d -r d>>
D U C
2
Aba 2
d CDdz
"
Ab b aAb
dC k S=- C
dz U
Remember the
forced
convection in
binary external
diffusion, JAisalso neglected
b a-( k"S L)/UAb
Ab0
CX =1- =1-e
C
Mass transfer and reaction in a packed bed
cont.
Determination of limiting situation from
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Determination of limiting situation from
reaction data
Type ofLimitation
Variation of Reaction Rate with:
Velocity
Particle
Size TemperatureExternaldiffusion
U (dp)-1/2 Linear
InternalDiffusion Independent (dp)-1 Exponential
SurfaceDiffusion
IndependentIndepende
ntExponential