[PPT] - Extent- -based Incremental Identification based Incremental PowerPoint Presentation

SLIDE 1

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Extent Extent-

based Incremental Identification

based Incremental Identification

f Reaction Kinetics from Spectroscopic Data
f Reaction Kinetics from Spectroscopic Data

Julien Billeter, Sriniketh Srinivasan and Dominique Bonvin

Ecole Polytechnique Fédérale de Lausanne Laboratoire d’Automatique Switzerland

XIII Conference on Chemometrics in Analytical Chemistry (CAC 2012) 25 – 29 June 2012, Budapest – Hungary

SLIDE 2

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Kinetic investigation From data to rate expressions

1. Computation of extents
2. Individual identification of rate expressions

Estimation of rate parameters

( ) ( )

number of number of = measured species computed extents

( ) ( )

number of number of = measured species computed rates

2/23

SLIDE 3

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Homogeneous reaction systems Balance equations

Homogeneous reaction system containing S species, R independent reactions, p inlets and 1 outlet

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

T T

,

ut

in

ut

in in in

u t t V t t t t m t q t V t t t t V t N W n n r u n n r C q n N = + − = = + − 

Mole balance for S species

( )

x 1 S

( )

x S R (

)

x 1 R

( )

x S p (

)

x 1 p

( ) ( ) ( ) ( )

( )

( ) ( ) ( ) ( ) ( ) ( )

T

1 , , , , ,

S w w i

m t t m t t t t V t t t V t ρ φ ρ = = = = n M n n M ρ c

Mass m, density , volume V and concentrations c

ρ

, ,

in in in in

C q W u

, u

ut
ut

q n

3/23

SLIDE 4

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Homogeneous reaction systems 4-way decomposition into extents

Assumption: Vessel extents of reaction xr and of flow (xin and xout)



( )



( )



( ) ( )

x 1 x 1 x

T T T T T T T T T

1 1

R R p R p p R

ut

r in in r r

ut

in in in in i R p n

ut

in in

ut

S R p

ut

iv

u V m u V m u V m x x

I I

x S N r S W u x x x M N r M W u x x q N r u q x W λ λ λ λ

− −

= + − = = + − = = + − = = − = =      

( )

T

rank 1

in

R p   = + +   N W n

T T T r in

S x n x M n q λ

ψ

        ⎯⎯ → =        

4/23

SLIDE 5

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Homogeneous reaction systems 4-way decomposition into extents

Assumption: Vessel extents of reaction xr and of flow (xin and xout)

( )

T

rank 1

in

R p   = + +   N W n

( ) ( ) ( ) ( )

1 1

ut

r r r

ut

in in in in R p

ut
ut
ut

u V m u m u m x x λ λ λ λ = − = = − = = − = = − = x r x x x x x u   

Reconstruction: ( ) ( ) ( ) ( )

T in r in

ut

t t t x t = + + − n N n x W n x

T T T r in

S x n x M n q λ

ψ

        ⎯⎯ → =        

5/23

SLIDE 6

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Homogeneous reaction systems Reaction Variant (RV) form

When

Compute xin and xout using uin, uout and m
Compute nRV (RV-form of n)
Compute xr from nRV

( )

T

rank 1

in

R p   < + +   N W n

( ) ( ) ( ) ( ) ( )

T RV in in

ut

r

t t t x t t = − − + = n n n W x n N x

( ) ( ) ( ) ( ) ( )

( )

T+ T+ RV r in in

ut

t t t t x t = = − − + x N n N n n W x n

( ) ( ) ( )

1

ut

in in in in p

ut
ut
ut
ut

u m u x x x m = − = = − = x u x x  

6/23

SLIDE 7

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems Assumptions

Assumptions:

the gas and liquid phases are homogeneous
the reactions take place in the liquid bulk
the mass transfer is described by the two-film theory

with no accumulation in the boundary layer

ζ

Gas-liquid reaction system containing pg inlets and 1 outlet in the gas phase, and inlets and 1 outlet in the liquid phase. The two phases are connected with pm mass transfer rates . By convention, a positive sign (+) is assigned to a mass transfer from the gas to the liquid. p

g

p

gas inlets Gas outlet

,

ut g

u

, ,

,

in g in g

W u p liquid inlets

, ,

,

in in

W u

 

Liquid outlet

,

ut

u



Gas phase Liquid phase

,

g g

m n , m n



ζ + ζ −

Mass transfer

7/23

SLIDE 8

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems Balance equations

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

T , , , ,

,

m

in ut in

u t t V t t t t t m t n r u N W n n n W ζ = + + − =

         



Mole balance in the Liquid phase

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

T ,

1 , ,

S w

m t t m t t V t t t V t ρ = = = n M n c

        

Mass , density , volumes and , and concentrations

( ) ( ) ( ) ( ) ( ) ( ) ( )

, , , ,

,

m g in g g

ut g

g in g g g g

u t t t t t m t ζ = − + − = n u n W W n n 

Mole balance in the Gas phase

m V c

g

V

ρ

( ) ( )

g tot

V t V V t = −



( ) ( )

( )

,

, ,

w i

t t ρ φ = c M ρ

   

8/23

SLIDE 9

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems 5-way decomposition into extents

Assumption: Vessel extents of reaction xr and of flow (xin and xout)

( )

T , ,

rank 1

m in m

R p p   = + + +   N W n W

   

( ) ( ) ( ) ( ) ( )

, , , , , , , , , , , , ,

1 1

m

ut

r r r R

ut

in in in in p

ut
ut
ut
ut

m m m p

u V m u m u m x m x u x r x x x u x x x x x ζ λ λ λ λ = − = = − = = − = = − = − = =



                     

   

Reconstruction:

( ) ( ) ( ) ( ) ( )

T , , , , , r in in

ut

m m

t t t x t t = + + + − W x n n N x W x n

        T T , , T , , T m in in m r

S x x M n n x M q λ

ψ

        ⎯⎯ → =            

         9/23

SLIDE 10

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems

Reaction & Mass-transfer Variant (RMV) form

When

Compute and using ,

and

Compute

(RMV-form of )

Compute xr and from

( )

T , , ,0

rank 1

m in m

R p p   < + + +   N W W n

   

( ) ( ) ( ) ( ) ( ) ( )

T , , , , , RMV in in

ut

r m m

t t t x t t t = − − + = + n n n W x n N x W x

        

( ) ( ) ( ) ( ) ( ) ( )

( )

T T , , , , , , RMV r m m in in

ut

m

t t t t x t t

+ +

      = = − − +         x N W n N W n n W x n x

         

( )

, , , , , , , , ,

1

ut

in in in in p

ut
ut
ut
ut

u m u x x x m = − = = − = x u x x



          

 

, in

x

 ,

ut

x

 , in

u

 ,

ut

u



m

RMV

n

, m

x

 RMV

n n

10/23

SLIDE 11

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Individual identification of reaction rates from the extents of reaction

Identification of the rate expression and estimation of the associated kinetic parameters for each i-th reaction by comparing the computed extents and the simulated extents of reaction

( ) ( )

( )

( ) ( ) ( ) ( )

, , , ,

,

ut

r i r i r i i i

u t x V t t x t x m t r = − = c θ

   

   

i

r

i

θ

( )

, r i

x t

( )

, r i

x t 

11/23

SLIDE 12

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Incremental identification using spectroscopic data

( ) ( )

ˆ

prog v

t t = n F a



( ) ( ) ( )

T T , , 0

ˆ

r m m

t t t x S n x M     =        

   

( ) ( )

ˆ

prog v

t t = n F a

( ) ( )

T 0 ˆ r t

t x S n =

Homogeneous reaction systems Gas-liquid reaction systems

( ) ( ) ( )

v t

t V t = a a



Fprog is the prognostic matrix (S x L) from calibration, with dimension (L x 1)

( ) ( ) ( )

T , ,

ˆ

RMV r m m

t t t x N W n x

+

    =      

  

( ) ( )

T+ˆRV r t

t x N n =

( )

,

prog c c

ϕ = F C Y

( )

, ,

,

prog c c

ϕ = F C Y

 

Calibration step Numbers of moles Extents using or

ˆ n

using Extents can subsequently be used for model identification

ˆRV n ˆRMV n

12/23

SLIDE 13

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Homogeneous reaction systems Acetoacetylation of pyrrole

The acetoacetylation of Pyrrole (A) with Diketene (B) catalyzed by Pyridine (K) involves seven species (S = 7). Four reactions (R = 4) produce 2-acetoacetyl pyrrole (C), Dehydroacetic acid (D), Oligomers (E) and a By-product (F).

,

in in

q C

( )

t a

ut

q

1 1 2 2 2 3 3 4 4

R1: R2: R3: R4:

K A B K K B K B K C B K

A B C r k c c c B B D r k c c B E r k c C B F r k c c c + ⎯⎯ → = + ⎯⎯ → = ⎯⎯ → = + ⎯⎯ → = 1 1 1 2 0 1 1 0 1 1 1 1 − −   −   = −   − −   N 0.72 0.09 0.01 0.02 5       =         n 0.58

in

      =         C

The experiment is performed in a CSTR, assuming a constant density, with one inlet (p = 1) and one outlet.

1 L V =

13/23

SLIDE 14

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Homogeneous reaction systems Acetoacetylation of pyrrole

Pure Component Spectra :

1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] Absorptivity [L mol-1] 500 1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] Absorptivity [L mol-1]

A: Pyrrole B: Diketene C: 2-acetoacetyl pyrrole D: Dehydroacetic acid E: oligomer F: By-product K: Pyridine

500

Calibration set (10 spectra):

500 1500 Wavenumber [cm-1] Absorbance [-]

Ac

( )

7 x 1000

prog

S L F E+ = = =

( )

noise 0, 0.1% max N E =    

( )

noise 0, 0.1% max

c

N C E =    

14/23

SLIDE 15

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Homogeneous reaction systems Acetoacetylation of pyrrole

( )

T T T

, ,

in prog

S N C n M F q

ψ

    =    

( )

t a

Wavenumber [cm-1] Time [min] 145 1500 500

( ) ( ) ( )

v t

t V t = a a

( )

T

rank 6 1

in

R p N C n   = = + +  

1.8 145 Time [min]

( ) ( ) [ ]

T

mol

r prog v

t t x S F a =

R1 R2 R3 R4

145 Time [min] 0.8

0.8

( ) ( ) ( ) [ ]

T T

L

in prog v

ut

t t t M x F a x q     =        

in

x

ut

x −



( )

noise 0, 3% max N t c E   =  

prog

F E+ =

simulation experiment −−

simulation

experiment −−

15/23

SLIDE 16

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Homogeneous reaction systems Acetoacetylation of pyrrole

ssq 2.802 0.114 0.100 0.064 line

1

r

A B K

kc c c

B K

kc c

A K

kc c

A B

kc c

145 Time [min] 0.45

( ) [ ]

,1

mol

r

x t

Simulation Fitting Model k Model k CI (99%) R1 M1 0.0530 E : M1 PCR : M1 PLS : M1 0.0525 0.0536 0.0536 0.0516 – 0.0534 0.0528 – 0.0543 0.0528 – 0.0543 R2 M2 0.1280 E : M2 PCR : M2 PLS : M2 0.1287 0.1294 0.1294 0.1269 – 0.1304 0.1278 – 0.1309 0.1278 – 0.1309 R3 M3 0.0280 E : M3 PCR : M3 PLS : M3 0.0280 0.0280 0.0280 0.0276 – 0.0283 0.0276 – 0.0285 0.0276 – 0.0285 R4 M4 0.0030 E : M4 PCR : M4 PLS : M4 0.0029 0.0030 0.0030 0.0027 – 0.0031 0.0028 – 0.0032 0.0028 – 0.0032

2

M1: , M2: , M3: , M4:

A B K B K B C B K

r k c c c r k c c r k c r k c c c = = = =

Fitting of each extent individually

PCR and PLS calibrations performed with 7 factors

R1

fitting experiment −−

16/23

SLIDE 17

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems Chlorination of butanoic acid

The reaction of Butanoic acid (BA) with chlorine (Cl2) involves seven species (S = 7). Two reactions (R = 2) produce α-mono-chloro-butanoic acid (MBA), α-di-chloro-butanoic acid (DBA) and Hydrochloric acid (HCl). Ethanol (EtOH) is used as liquid solvent and Air is initially present in the reactor.

1 1 1 1 1 2 0 2 1 N − −   = − −    

Species in the Liquid phase ( = 6):

S

Transferring species (pm = 2): Species in the Gas phase (Sg = 3): BA, Cl2, MBA, HCl, DBA and EtOH Cl2, HCl, (Air) Cl2, HCl

2 2

in 2 1 1 , , , in 2 2 2 1 ,

R1: R2: 2 2

EtOH BA Cl MBA EtOH Cl

BA Cl MBA HCl r k c c c BA Cl DBA HCl r k r c + ⎯⎯⎯ → + = + ⎯⎯⎯ → + =

   

17/23

SLIDE 18

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems Chlorination of butanoic acid

Liquid phase

One inlet of BA ( = 1) and one outlet The density changes with the composition The outlet is regulated to maintain the mass of the liquid constant

Gas phase

One inlet of Cl2 (pg = 1) and one outlet The outlet is regulated to maintain the total pressure at 10 bar

5

10 100 n

−

    =        

 ,

0.0141

in g

W   =     0.095

g

n   =    

,

1 1

m

W     =        



p

,

1 1

m g

W   =    

kmol kmol

1

g

p =

gas inlet Gas outlet

,

ut g

u

2

, ,

,

in g in Cl

W u

Gas phase Liquid phase

( )

2,

, Cl HCl Air

2

Cl

ζ +

HCl

ζ −

Mass transfer

2

, , , , , BA Cl MBA HCl DBA EtOH

3

10 m

tot

V = 1 p =



liquid inlet

, ,

,

in in BA

W u



Liquid outlet

,

ut

u



18/23

SLIDE 19

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems Chlorination of butanoic acid

Pure Component Spectra :

1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] 500 1500 Wavenumber [cm-1] Absorptivity [L mol-1]

BA Cl2 MBA HCl DBA

500

Calibration set (10 spectra):

500 1500 Wavenumber [cm-1] Absorbance [-]

Ac The pure spectrum of EtOH is treated as background spectrum Air does not absorb

( )

noise 0, 0.1% max

c

N C E =    

( )

noise 0, 0.1% max N E =    

( )

5 x 1000

prog a

S L F E+ = = =

19/23

SLIDE 20

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems Chlorination of butanoic acid

( )

t a

Wavenumber [cm-1] Time [min] 300 1500 500

( ) ( ) ( )

v t

t V t = a a

16 300 Time [min]

( ) [ ]

kmol

r t

x

R1 R2

300 Time [min] 15

15

( ) [ ]

,

kmol

m

t x



2

, , m Cl

x

 , , m HCl

x





( )

noise 0, 3% max N t c E   =  

prog

F E+ =

300

, in

x



3

,

10

ut

x

×



Time [min]

( ) ( ) [ ]

, ,

, kg

in

ut

t t x x

 

1400

( )

T ,

ˆ

RMV m

t N W n

+

   

 

300 Time [min] 15

15

( ) [ ]

ˆ kmol

RMV t

n

( )

T , ,

rank 5 1 6

m in m

R p p N W W n     = < + + + =

   

BA MBA Cl2 HCl DBA

simulation experiment −−

simulation

experiment −−

20/23

SLIDE 21

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Gas-liquid reaction systems Chlorination of butanoic acid

ssq 159.4 147.4 11.6 8.1 line

1

r

2

BA Cl MBA

kc c c

2

BA Cl MBA

kc c c

2

BA Cl

kc c

2

Cl

kc

300 Time [min] 15

( ) [ ]

,1

kmol

r

x t

Simulation Fitting Model k Model k CI (99%) R1 M1 1.358 E : M1 PCR : M1 PLS : M1 1.335 1.353 1.353 1.310 – 1.361 1.331 – 1.374 1.331 – 1.374 R2 M2 0.100 E : M2 PCR : M2 PLS : M2 0.119 0.128 0.128 0.037 – 0.201 0.049 – 0.206 0.049 – 0.206

2 2

2 , , , , , ,

M1: , M2:

BA Cl MBA BA Cl MBA

r k c c c r k c c c = =

     

Fitting of each extent individually

PCR and PLS calibrations performed with 5 factors

R1

fitted computed −−

21/23

SLIDE 22

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Conclusions

Extent-based incremental identification

decouples each reaction from other reactions and mass transfers
allows investigating each reaction individually
leads to model reduction:

Homogeneous reaction systems: Gas-liquid reaction systems:

Extension to spectroscopic data with calibration

requires computing a minimum number of concentrations (liquid phase)

Homogeneous reaction systems: Gas-liquid reaction systems:

r requires an additional source of measurements in the liquid/gas phase

Outlook: is a calibration-free approach possible?

1 S R p → + + 1

m

S R p p → + + +

 

R R + pm

22/23

SLIDE 23

LABORATOIRE D’AUTOMATIQUE AUTOMATIC CONTROL LABORATORY

Thank you for you attention

References

S. Srinivasan, J. Billeter and D. Bonvin

Extent-based Incremental Identification of Reaction Systems using Concentration and Calorimetric Measurements Chemical Engineering Journal, in revision, 2012

N. Bhatt, M. Amrhein and D. Bonvin,

Incremental Identification of Reaction and Mass-Transfer Kinetics using the Concept of Extents Industrial & Engineering Chemistry Research, 50 (23), 12960-12974, 2011

N. Bhatt, M. Amrhein and D. Bonvin,

Extents of Reaction, Mass Transfer and Flow for Gas-Liquid Reaction Systems Industrial & Engineering Chemistry Research, 49 (17), 7704-7717, 2010

M. Amrhein, N. Bhatt, B. Srinivasan and D. Bonvin

Extents of Reaction and Flow for Homogeneous Reaction Systems with Inlet and Outlet Streams AIChE Journal, 56 (11), 2873-2886, 2010

23/23