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  

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  

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?      

Here  is  an  example  to  demonstrate  the  relationship  between  microkinetics,  global  kinetics,  and  simplified  (reduced)  kinetics  

Microkinetics  

Reduced  kinetics  

Global  kinetics  

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?  

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*

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:    

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!  

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*

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!  

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  

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  

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.  

Up  next?  •  Deactivation  •  External  mass  transport  effects  •  Internal  mass  transport  effects  •  Estimation  of  activation  energies  etc.    

•  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