l17-1 slides courtesy of prof m l kraft, chemical & biomolecular engr dept, university of...
TRANSCRIPT
L17-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Review: Unsteady State Nonisothermal Reactor Design
An open system (for example, CSTR)
Q
W
Fin
Hin
Fout
Hout
n nsysi i in i i out
i 1 i 1
dE Q W FE FE
dt
rate of heat flow from
surroundings to system
Rate of accumulation of energy in
system
=
Rate of work done by
system on surroundings
- +
Rate of energy added to
system by mass flow in
-
Rate of energy leaving system by mass flow
out
sysdE 0 steady state
dt
sysdE 0 unsteady state
dt
Goal: develop EB for unsteady state reactor
L17-2
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Review: Simplified EB for Well-Mixed Reactors
n
S i0 i i0 RX Ai 1
n
i pii 1
Q W F H H H T r VdTdt
NC
Energy balance for unsteady state reactor
with phase change:
n
S i0 pi i0 RX Ai 1
n
i pii 1
Q W F C T T H T r VdTdt
NC
Energy balance for
unsteady state reactor without phase change:
n n n n
i iS i i i i i i
i 1 i 1 i 1 i 1in out
dH dN dQ W FH FH N H PV
dt dt dt
Total Energy Balance for unsteady state
ipi
dH dTC
dt dt i
i0 i i AdN
F F r Vdt
dPV 0
dt
Constant PV variationMade following substitutions & solved for dT/dt:
L17-3
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Review: Unsteady State EB, Liquid-Phase Reactions
For liquid-phase reactions, often Cp = S iCpi is so small it can be neglectedWhen Cp can be neglected, then:
If the feed is well-mixed, it is convenient to use:
Plug these equations & Ti0 = T0 into the EB:
This equation for the EB is simultaneously solved with the mass balance (design eq) for unsteady state, nonisothermal reactor design
S i0 RX A
n
i pii 1
n
i0 pii 1
Q W T T H T r V
NC
FT
dt
Cd
S
n
i pi A0 ps ps i pii 1
where is the heat capacity of the solNC N C C C ution
S i0 pi A0 psF C F C
S i0 RA
A0
s X
p
0 Ap
s
Q W T T H T
N C
VF C r dTdt
L17-4
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Review: Nonisothermal Batch Reactor Design
n
S i0 pi i0 RX Ai 1
n
i pii 1
Q W F C T T H T r VdTdt
NC
No flow, so:
0
p
S RX
1i i
An
i
Q W H T
CN
r V
p
S RX An
i 1A0 i Api
Q W H T r V dT
CNt
Cd
X
Put the energy balance in terms of conversion:
Solve with the batch reactor design equation using an ODE solver (Polymath):
AA0 A
dXN r V
dt
i A0 i i Ai0
iA
i0
i PpNN
where & CNN
X C
L17-5
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Review: Adiabatic Nonisothermal Batch Reactor Design
S RX An
A0 i pi p Ai 1
Q W H T r V dTdt
N C C X
For negligible stirring work:
i pi psC CSubstitute:Rearrange
00
T
T RX R p R0
XA A
pS p AX 0A0
dT
H T C T T
dX
C C X
p 0 p 0S SA A
RXRX R p R
C T T C T TX X
H TH T C T T
Solve for T: RX 0 A RX 0 A
0 0 np A ps i p A pi
i 1
H T X H T XT T T T
C X CC X C
Solve with the batch reactor design equation using an ODE solver (Polymath)
XAA
A0A0
dXt N
r V
Integrate & solve for XA:
L17-6
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L17 Basic Catalysis & Reaction Mechanisms
•Though we have discussed the use of catalyst in a PBR, we have not discussed the process of catalysis itself
•An understanding of catalysis, the mechanisms, and catalytic reactor design are the subject of the next few lectures
•Catalyst properties•Steps involved in a catalytic reaction•Development of a rate law using steps in catalytic reaction•Different types of catalyst mechanisms•Design of catalytic reactors
L17-7
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Catalysts & Catalysis• ~1/3 of the GNP of materials produced in the US involve a catalytic process• A Catalyst is a substance that speeds up the rate of reaction but is not
changed by the reaction• A catalyst lowers the energy barrier by promoting a different molecular
pathway (mechanism) for the reaction
Many catalyst are porous (high surface area)
• Homogeneous catalysis: catalyst is in solution with at least 1 reactant• Heterogeneous catalysis: more than 1 phase, usually solid and fluid or
solid and gas is present. Reaction occurs at solid/liquid or gas interface.
catalyst
L17-8
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
1. Mass transfer of A to surface
2. Diffusion of A from pore mouth to
internal catalytic surface
3. Adsorption of A onto catalytic surface
4. Reaction on surface
5. Desorption of product B from surface
6. Diffusion of B from pellet interior to pore mouth
7. Diffusion of B from external surface to the bulk fluid (external diffusion)
Steps in a Heterogeneous Catalytic Reaction
Ch 10 assumes steps 1,2,6 & 7 are fast, so only steps 3, 4, and 5 need to be considered
L17-9
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Adsorption Step
A(g) + S ⇌ A·S
S: open (vacant) surface site A·S: A bound to a surface site
The adsorption of A (gas phase) on an active site S is represented by:AI
-S-S-S-
Rate of adsorption = rate of attachment – rate of detachment
AD A A v A A Sr k P C k C partial pressure of A
• Rate is proportional to # of collisions with surface, which is a function of PA
• Rate is proportional to # of vacant (active) sites, Cv, on the surface• Active site: site on surface that can form a strong bond with adsorbed species
Molar conc of vacant sites on surface
A
-S-S-S-
AD A A v A A Sr k P C k C
In terms of the adsorption equilibrium constant KA where AA
A
kK
k
AAD A A v A S
A
kr k P C C
k
A SAD A A v
A
Cr k P C
K
Equation I
Conc of sites occupied by A
L17-10
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Site BalanceCt: Total number of active sites per unit mass of catalyst divided by
Avogadro’s # (mol/g cat)Cv: Number of vacant sites per unit mass of catalyst divided by Avogadro’s #
Ct = Cv + CA·S + CB·S
Surface
Vacant active site
A
Active site occupied by A
B
Active site occupied by B
Site balance:
In the absence of catalyst deactivation, assume the total number of active sites remains constant:
We will use the site balance equation to put Cv in terms of measurable species
Cv is not measurable, but the total number of sites Ct can be measured
L17-11
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Langmuir Isotherm AdsorptionAdsorption of carbon monoxide onto a surface: CO + S ⇌ CO·S
AD A CO v A CO Sr k P C k C CO S
AD A CO vA
Cr k P C
K
AA
A
kK
k
Put Cv in terms of Ct using the site balance; only CO can absorb on the surface:
t v CO SC C C
At equilibrium, rAD = 0:CO S
AD A CO vA
Cr 0 k P C
K
Determine the concentration of CO adsorbed on the surface at equilibrium
Rearrange & solve for CCO·S
CO SCO v
A
CP C
K
t CO S vC C C Insert into eq for CCO·S from rxn rate
CO S A CO vC K P C CO S A CO t CO SC K P C C Solve for CCO·S
CO S A CO t A CO CO SC K P C K P C CO S A CO CO S A CO tC K P C K P C
A CO tCO S
A CO
K P CC
1 K P
Concentration of CO adsorbed on surface vs PCO→ Langmuir Isotherm
CO S A CO vC K P C
L17-12
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Surface Reaction StepAfter the molecule is adsorbed onto the surface, it can react by a few different mechanisms1. Singe site mechanism: Only the site to which the reactant is absorbed is
involved in the reactionAI
-S-⇌
BI
-S-
A·S ⇌ B·SB S
S S A SS
Cr k C
K
SS
S
kwhere K
k
2. Dual site mechanism: Adsorbed reactant interacts with another vacant site to form the product
AI
-S-S-S⇌
B I
-S-S-S-
A·S + S ⇌ S + B·S
B S vS S A S v
S
C Cr k C C
K
Equation IIa
Equation IIb
3. Eley-Rideal mechanism: reaction between adsorbed reactant and a molecule in the gas phase
⇌
C I
-S-S-S-
A·S + B(g) ⇌ C·S
C SS S A S B
S
Cr k C P
K
Equation IIcAI
-S-S-S
B
L17-13
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Desorption StepProducts are desorbed into the gas phase
C I
-S-S-S-⇌
C
-S-S-S-
C·S ⇌ C + S
C vD,C D C S
D,C
P Cr k C
K
DD,C
D
kwhere K
k
Equation III
Note that the desorption of C is the reverse of the adsorption of C
D,C AD,Cr r
Also the desorption equilibrium constant KD,C is the reciprocal of the adsorption equilibrium constant KC
D,CC
1K
K
D,C D C S C C vr k C K P C Substituting 1/KC for KD,C in the rate equation for product desorption gives:
L17-14
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Derive a Rate Law for Catalytic Rxn• Postulate catalytic mechanism, and then derive the rate law for that
mechanism• Assume pseudo-steady state hypothesis (rate of adsorption = rate of
surface reaction = rate of desorption) • No accumulation of species on the surface or near interface• Each species adsorbed on the surface is a reactive intermediate• Net rate of formation of species i adsorbed on the surface is 0, r i·S=0
• One step is usually rate-limiting• If the rate-limiting step could be sped up, the entire rxn would be faster• Although reactions involve all 7 steps, (for chapter 10) only adsorption,
surface reaction, or desorption will be rate limiting• The surface reaction step is rate limiting ~70% of the time!
• Steps to derive the rate law• Select among types of adsorption, surface reaction, and desorption• Write rate laws for each individual step, assuming all are reversible• Postulate which step is rate limiting• Use non-rate-limiting steps to eliminate the surface concentration
terms that cannot be measured
L17-15
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Consider A B and assume the following mechanism is correct:⇌
A SAD A A v
A
Cr k P C
K
1. Adsorption:
2. Surface reaction:
A(g) + S ⇌ A·S
A·S + S ⇌ S + B·SB S v
S S A S vS
C Cr k C C
K
3. Desorption: B·S ⇌ B + SB v
D D B SD
P Cr k C
K
We need to select one of these 3 reactions as the rate limiting step, then derive the corresponding rate equation, and see if this rate eq matches experimental data. Which step is the most logical to start with? a) Adsorptionb) Surface reactionc) Desorptiond) None of the abovee) Any of these would be “logical” - they all have equal probability of being
the rate limiting step
The surface reaction step as is rate limiting ~70% of the time
L17-16
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Consider A B and assume the following mechanism is correct:⇌
A SAD A A v
A
Cr k P C
K
1. Adsorption:
2. Surface reaction:
A(g) + S ⇌ A·S
A·S + S ⇌ S + B·SB S v
S S A S vS
C Cr k C C
K
3. Desorption: B·S ⇌ B + SB v
D D B SD
P Cr k C
K
Derive the rate equation for when the surface reaction is rate limiting (true ~70% of the time)
• For surface reaction-limited mechanisms, kS is small and kA and kD are relatively large
• Therefore rAD/kA and rD/kD are very small, and can be approximated as equal to zero
B S vA S S A S v
S
C Cr ' r k C C
K
1. CA·S, Cv, and CB·S need to be expressed in terms of measurable quantities
2. Use this relationship to eliminate CA·S and CB·S from their respective rate equations and the site balance to eliminate CV
L17-17
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Consider A B and assume the following mechanism is correct:⇌
A SAD A A v
A
Cr k P C
K
1. Adsorption 2. Surface reaction
B S vS S A S v
S
C Cr k C C
K
3. Desorption
B vD D B S
D
P Cr k C
K
Derive the rate equation for when the surface reaction is rate limiting
B S vA S S A S v
S
C Cr ' r k C C
K
Use rAD/kA =0 and rD/kD =0 to eliminate CA·S and CB·S from their respective rate equations and the site balance to eliminate CV
A SAD A A v
D
Cr k P C
K
A SADA v
A A
Cr0 P C
k K
A SA v
A
CP C
K A S A A vC K P C
B vD D B S
D
P Cr k C
K
D B vB S
D D
r P C0 C
k K B vB S
D
P CC
K
Use rAD/kA =0 & rAD equation to solve for CA·S:
Use rD/kD =0 & rD equation to solve for CB·S:
L17-18
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Consider A B and assume the following mechanism is correct:⇌
A SAD A A v
A
Cr k P C
K
1. Adsorption 2. Surface reaction
B S vS S A S v
S
C Cr k C C
K
3. Desorption
B vD D B S
D
P Cr k C
K
Derive the rate equation for when the surface reaction is rate limiting
B S vA S S A S v
S
C Cr ' r k C C
K
A S A A vC K P C rAD/kA =0 & rD/kD =0B v
B SD
P CC
K
Use site balance to solve for CV: t v A S B SC C C C
v t A S B SC C C C Make substitutions for CA·S & CB·S, solve for Cv
B vv t A A v
D
P CC C K P C
K B v
v A A v tD
P CC K P C C
K
Bv A A t
D
PC 1 K P C
K
t
vB
A AD
CC
P1 K P
K
L17-19
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Consider A B and assume the following mechanism is correct:⇌
A SAD A A v
A
Cr k P C
K
1. Adsorption 2. Surface reaction
B S vS S A S v
S
C Cr k C C
K
3. Desorption
B vD D B S
D
P Cr k C
K
Derive the rate equation for when the surface reaction is rate limiting
B S vA S S A S v
S
C Cr ' r k C C
K
A S A A vC K P C B vB S
D
P CC
K tv
A A B D
CC
1 K P P K
Substitute in CA·S, CB·S, &Cv
2 2t tB
A S S A AA A B D S D A A B D
C CPr ' r k K P
1 K P P K K K 1 K P P K
2
t BA S S A A
A A B D S D
C Pr ' r k K P
1 K P P K K K
This is the rate equation in terms of measurable species and rate constants for the mechanism given in the problem statement
L17-20
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Evaluating a Catalytic Reaction Mechanism
• Collect experimental data from test reactor• See if rate law is consistent with data• If not, then try other surface mechanism (i.e., dual-site
adsorption or Eley-Rideal) or choose a different rate-limiting step (adsorption or desorption)
L17-21
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Consider A B and assume the following mechanism is correct:⇌
A SAD A A v
A
Cr k P C
K
1. Adsorption 2. Surface reaction
B S vS S A S v
S
C Cr k C C
K
3. Desorption
B vD D B S
D
P Cr k C
K
Now derive the rate equation for when adsorption is rate limiting:
v
AA AD A A
A
Sr ' r k PK
CC
Conc of vacant and occupied sites must be eliminated from the rate equation
A S
B
SS
S vv
S CC
r CC
k K0
B S v
vS
A SKC
C CC
S
AB S
SKC
C
BB
D
v
D
DS
r P0
C
k KC B v
B SD
P CC
K
If adsorption is rate limiting, kS>>kAD, so rS/kS can be approximated as 0. Then:
B vS S v
S
SA S
Cr k C
KC
C
If adsorption is rate limiting, kD>>kAD, so rD/kD can be approximated as 0. Then:
BB S
vD D
D
P Cr Ck
K
Need to put CB·S in measureable terms
L17-22
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Consider A B and assume the following mechanism is correct:⇌
A SAD A A v
A
Cr k P C
K
1. Adsorption 2. Surface reaction
B S vS S A S v
S
C Cr k C C
K
3. Desorption
B vD D B S
D
P Cr k C
K
Now derive the rate equation for when adsorption is rate limiting:
Conc of vacant and occupied sites must be eliminated from the rate eq
SA
B SSK
CC B
B SD
vPC
K
C
Make substitutions for CA·S & CB·S
B S Bv
Dt
v
SC
C P C
K KC
Bv
B
Dt
v v
DSK K
CP P CC
KC
B B
tS D D
vP P
C 1K K K
C
tv
B B
S D D
CC
P P1
K K K
Solve for Cv using the site balance equation
A B Sv St C CCC
Substitute Cv into the expression for CB·S:
t
B B
S D
B
D
B S
D
C
P P1
K K K
PC
K
Substitute CB·S into CA·S:
B t
B BD
S
A S
DS
D
P C
P P1
KK K
K K
C
v
AA AD A A
A
Sr ' r k PK
CC
L17-23
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
Consider A B and assume the following mechanism is correct:⇌
A SAD A A v
A
Cr k P C
K
1. Adsorption 2. Surface reaction
B S vS S A S v
S
C Cr k C C
K
3. Desorption
B vD D B S
D
P Cr k C
K
Now derive the rate equation for when adsorption is rate limiting:
B tA S
B BS D
S D D
P CC
P PK K 1
K K K
B tB S
B BD
S D D
P CC
P PK 1
K K K
tv
B B
S D D
CC
P P1
K K K
AAD A
A
B t
B BS D
S D D
t
B B
S D D
P C
P PK K
CP P
1K K
1K
KKK K
Pr k
Use these eqs to replace CA·S
& Cv in rAD:
A BAD
B B B BA S D
A t
S D D S D D
P Pr
P P P P1 K K K 1K K K K
C
K
k
K
k
v
AA AD A A
A
Sr ' r k PK
CC
Factor out Ct:
L17-24
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
The gas phase hydromethylation of toluene: C6H5CH3 + H2 → C6H6 + CH4 is to be carried out in a PBR. Plot the conversion and the partial pressures of toluene, hydrogen and benzene as a function of catalyst weight.
FA0 = 50 mol toluene/min, P0 = 40 atm, T= 913K, a= 9.8 x 10-5 kg-1, Feed is 30% toluene (species tol), 45% hydrogen (species H) and 25% inerts (I)
Rate law: ' H tolT
tol tol B B
kP Pr
1 K P K P
k= 0.00087 mol/atm2·kg cat·minKB = 1.39 atm-1 Ktol= 1.038 atm-1
Mole balance:'
tol tol
A0
dX r
dW F
Rate law: ' H tol
Ttol tol B B
kP Pr
1 K P K P
Stoichiometry: tol 0tol tol,0
tol 0
1 X TPC C
1 X P T
tolT T0
tol 0
1 X PC C
1 X P
1Need concentrations in terms of pressure
tol tol tolP V n RT tol tolP C RT toltol
PC
RT tol,0
tol,0P
CRT
tol,0tol tol
tol 0
PP 1 X PRT RT 1 X P
toltol tol,0
tol 0
1 X PP P y where y=
1 X P
tol,0y 1 1 1 1 0 tol,0
Tol,0T0
F 0.3y 0.3
F 1 0.3 0 0
Total P
Total P at inlet
L17-25
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
The gas phase hydromethylation of toluene: C6H5CH3 + H2 → C6H6 + CH4 is to be carried out in a PBR. Plot the conversion and the partial pressures of toluene, hydrogen and benzene as a function of catalyst weight.
FA0 = 50 mol toluene/min, P0 = 40 atm, T= 913K, a= 9.8 x 10-5 kg-1, Feed is 30% toluene (species tol), 45% hydrogen (species H) and 25% inerts (I)
Rate law: ' H tolT
tol tol B B
kP Pr
1 K P K P
k= 0.00087 mol/atm2·kg cat·minKB = 1.39 atm-1 Ktol= 1.038 atm-1
Mole balance:'
tol tol
A0
dX r
dW F
Rate law: ' H tol
Ttol tol B B
kP Pr
1 K P K P
Stoichiometry: tol tol,0 tol0
PP P 1 X y where y=
P
0 tol,0y 0.3
0 tol,0 tol,0 0P y P tol,0P 0.3 40atm 12atm
Use the Ergun equation to evaluate y:
Isothermal rxn & =0, so: 1 2y 1 Wa 1 2tol tol,0 tolP P 1 X 1 Wa
Need an equation for PB & PH
B tol,0 tolP P X y H tol,0 H tol2 2P P X y H2
H2tol
F 0.451.5
F 0.3
L17-26
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
The gas phase hydromethylation of toluene: C6H5CH3 + H2 → C6H6 + CH4 is to be carried out in a PBR. Plot the conversion and the partial pressures of toluene, hydrogen and benzene as a function of catalyst weight.
FA0 = 50 mol toluene/min, P0 = 40 atm, T= 913K, a= 9.8 x 10-5 kg-1, Feed is 30% toluene (species tol), 45% hydrogen (species H) and 25% inerts (I)
Rate law: ' H tolT
tol tol B B
kP Pr
1 K P K P
k= 0.00087 mol/atm2·kg cat·minKB = 1.39 atm-1 Ktol= 1.038 atm-1
Mole balance:'
tol tol
A0
dX r
dW F
Rate law: ' H tol
Ttol tol B B
kP Pr
1 K P K P
Stoichiometry:
0 tol,0y 0.3
0
tol,0P 12atm 1 2tol tol,0 tolP P 1 X 1 Wa
B tol,0 tolP P X y H tol,0 tol2P P 1.5 X y
Finally, calculate the kg cat where P0 = 1atm: 1 2
0
P1 W
Pa 1 25 11atm
1 9.8 10 kg W40atm
1 2y 1 Wa
5 10.000625 1 9.8 10 kg W finalW 10197.7kg
Plug equation in boxes into Polymath to solve
L17-27
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L17-28
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L17-29
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.