reaction# - wordpress.com · lhhw kinetics# sensitivity# analysis pseudo steady#state analysis...
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We focus on kinetics-‐based catalytic reaction models now
Reaction kinetics
Aspects of heat & mass transport
Catalyst Deactivation
Fluid flow
Developing models for catalytic reactors
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Reaction kinetics: • Global (no surface species, few – maybe one – overall reaction)
• Microkinetics (lots of surface species, lots of reactions)
• Other (few surface species, few-‐er reactions)
When the reactor model is simple, we can afford to go crazy on the chemistry model (but we may not want/need to!)
LHHW Kinetics
Sensitivity Analysis
Pseudo-‐Steady State
Analysis
Elementary reaction
mechanisms
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Packed Bed Reactors are common, we can model them similar to ideal PFRs (isothermal)
Catalyst is uniformly distributed
• Material balance equations for each participating species should be written
• What type of equations do we have?
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Here is an example to demonstrate the relationship between microkinetics, global kinetics, and simplified (reduced) kinetics
Microkinetics
Reduced kinetics
Global kinetics
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A preliminary PFR simulation using “detailed kinetics” – multiple reactions to put it simply
Rxn No. Rxn. k0(s-‐1)
E (kcal/mol) k(s-‐1)
1 A-‐-‐>B 1 100 0.951 2 B-‐-‐>C 0.1 20 0.099 T 1000 K u 1m/s P 1 atm
u dCA
dz= −k1CA u dCB
dz= k1CA − k2CB u dCC
dz= k2CB
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 5 10 15 20 25 30 35
A
B
C
Concentrations vs. axial distance
• Three ODEs were solved • Explicit Euler method was
used • CB is seen to go through a
maximum • Can you tell what the inlet
concentrations are?
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PFR microkinetic model simulation for a simple reaction mechanism is done in a straight forward manner using MS-‐ Excel
Rxn No. Rxn. k0 E k
1 A+*-‐-‐>A* 1 100 0.951 2 A*-‐-‐>B* 0.1 10 0.099 3 B*-‐-‐>B+* 0.9 10 0.099
T 1000 K P 1 atm
u dCA
dz= −k1CA (1−CA* −CB*)
u dCA*
dz= k1CA (1−CA* −CB*)− k2CA*u dCB
dz= k3CB*
u dCB*
dz= k2CA* − k3CB*
• Four ODEs were solved • Site conservation was
incorporated into the ODEs • Explicit Euler method was used • B is formed towards the reactor
exit • Can you tell what the surface is
covered by at the inlet? 0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25 30 35 40 45
B*
A*
B
A
C* =1−CA* −CB*
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Here you see the simplification thanks to eliminating the surface species: Only 2 ODEs to be solved in the global model! (number of ODEs = number of gas – phase species)
u dCA
dz= −k1CA (1−CA* −CB*)
u dCA*
dz= k1CA (1−CA* −CB*)− k2CA*u dCB
dz= k3CB*
u dCB*
dz= k2CA* − k3CB*
CA* =k1k2CAC* CB* =
k2k3CA* =
k1k3CAC*
u dCA
dz= −
k1CA
1+ k1k2CA +
k1k3CA
u dCB
dz=
k1CA
1+ k1k2CA +
k1k3CA
C* =1
1+ k1k2CA +
k1k3CA
Microkinetic model
Global kinetics model
Deriving the global kinetics model:
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The prediction of the species concentrations is, however, not in good agreement with the original
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50
Microkinetic-‐A
Microkinetic-‐B
Global-‐A
Global-‐B
• The rate of consumption of A is too high near the inlet!
• If we used the global kinetics model to design the reactor, would be too small or too large?
• The discrepancy is more evident for B
• Close examination of the microkinetic model results indicates that dCA*/dz is not insignificant, while dCB*/dz is)
• Also, CB* is small, CA* is small only in certain parts of reactor
Lost in translation!
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This shows a different model derivation: Three ODEs are solved (reduced by 1!).
u dCA
dz= −k1CA (1−CA* −CB*)
u dCA*
dz= k1CA (1−CA* −CB*)− k2CA*u dCB
dz= k3CB*
u dCB*
dz= k2CA* − k3CB*
CB* =k2k3CA*
Microkinetic model
Global kinetics model
Deriving the reduced kinetics model:
u dCA
dz= −k1CA (1−CA* −
k2k3CA*)
u dCA*
dz= k1CA (1−CA* −
k2k3CA*)− k2CA*u dCB
dz= k2CA*
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The “reduced model” is definitely attractive! However, we should examine the performance of the reduced model at a host of operating conditions for further validation.
• This model shows much better agreement with the microkinetic model
• We could use the reduced kinetics model to design the reactor, it would be just fine!
• In this case, the savings is only in 1 ODE, but in case of larger systems, this might be significant
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25 30 35 40 45
Microkinetic-‐A
Microkinetic-‐B
PARTIAL GLOBAL -‐A Partial Global-‐B
A much better simplification!
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The “reduced model” works well, as far as we can tell. So far so good!
• The reduced model works well at a range of operating temperatures
• The global kinetics model is not really valid at any temperatures
• The influence of the rate constant values may, however, be different
The simplification works at other temperatures
0.0
0.2
0.4
0.6
0.8
1.0
1.2
200 400 600 800 1000 1200 1400 1600
B-‐micro
B-‐global
B-‐reduced
Outlet concentration of B vs. reactor temperature
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See that the global model itself is pretty good for certain rate constant values… In particular, when k3 is of comparable magnitude as k2…
The rate constant values are critical! Rxn No. Rxn. k0 E k
1 A+*-‐-‐>A* 1 0.5 0.78 2 A*-‐-‐>B* 1 1 0.60 3 B*-‐-‐>B+* 1 1 0.60
Rxn No. Rxn. k0 E k
1 A+*-‐-‐>A* 1 0.5 0.78 2 A*-‐-‐>B* 1 1 0.60 3 B*-‐-‐>B+* 0.1 1 0.06
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Conclusions & Summary
In this work, I have shown you • Microkinetic model simulations of catalytic PBR • Generic reduction to eliminate all surface species • Clever reduction methods that use info from microkinetic
simulations (rates, intermediate species concentrations, etc.)
• Issues with blind elimination of species/reactions • Extension of reduced model to other operating conditions:
advantages & drawbacks • Power of simple PFR-‐like models in reaction dominated
situations etc.
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Up next? • Deactivation • External mass transport effects • Internal mass transport effects • Estimation of activation energies etc.
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• Perform 3 simulations using various ki and T and paste the data into a word doc (Check is anything went wrong). • Choose the following: reactor length = 3m; temperature = 900-‐1200K; inlet
composition: stoichiometric CO:O2 • What is the ‘Carbon Balance’ & ‘Oxygen Balance’ mean?
• Derive the PE based global kinetic model in your notebook, & check if the model is correctly incorporated in the second worksheet. Type up the final reaction rate expression you get into the word doc.
• Discuss the reasons why this global kinetic model fails (briefly).
• If time permits, make a simulation of a PSSA based reduced model, and compare results with the microkinetic simulation. Hint: Use “goalseek” to get the solution
• Email me the word doc later today
Catalytic Reactor Class Simulation Exercise