Mathematical modelling of selected reactions in low ...web.abo.fi/gsce/Spring_2014/Salmi.pdfMathematical modelling of selected reactions in low-temperature transformation of biomass

Mathematical modelling of selected reactions in low-temperature transformation of biomass

Tapio Salmi Åbo Akademi Turku/Åbo Finland

Millireactor technology in the transformation of biomass – hydrolysis of hemicelluloses

Polysaccharides – where?

Why reaction engineering of hemicelluloses?

Ø Hemicelluloses are rich sources of biomass-based products Ø  The key issue is the hydrolysis of hemicelluloses to sugar

monomers (homogeneous, enzymatic and heterogeneous catalysis)

Ø  The very important products of hemicellulose sugars are obtained by catalytic hydrogenation to sugar alcohols

Ø Valuable products are obtained by oxidation of the monomers to sugar acids

Extraction

H2O, T

Long chained hemicelluloses

Medium and short chained hemicelluloses

Emulsifiers, Films etc.

Platform chemicals

Further processing

Filtration

Oxidation Hydrogenation Fermentation Esterification

Aqueous reforming

Sugar acids, Sugar alcohols, Lubricants, Fuels etc.

< 10 kDa

10 kDa <

Typical hemicelluloses

Ø O-Acetylgalactoglucomannan (mostly mannose units) Ø Arabinogalactan (main chain galactose units) O-Acetyl-(4-O-methylglucurono)xylan (mostly xylose units)

Hemicellulose Monomers

Sugar alcohols

Sugar acids

Hydrolysis

O2, Cat

H2, Cat

From hemicelluloses to chemicals

A hemicellulose to hydrolysis

O-Acetylgalactoglucomannane - a branched hemicellulose (GGM)

Hydrolysed with the aid of homogeneous and heterogeneous catalysts

A hemicellulose: O-acetylgalactoglucomannan

Heterogeneous catalysts

Ø Amberlyst 15: strong sulfonic cation exchange resin

Ø Macroreticular: d=0.45-0.60 mm, pores 40-90 nm

Ø Resin composed of styrene-divinyl benzene with sulfonic acid functional group

Ø Capacity 4.7 mmoleq/g

200 µm

Heterogeneous catalysts

Ø Smopex-101

Ø Fibrous and non-porous: d=0.01 mm I=4 mm

Ø Polymer, polyethene-graft-polystyrene with sulfonic acid functional group

Ø Capacity 3.6 mmoleq/g

20 µm

Hydrolysis experiments I

Ø Batch stirred reactor

Ø Catalysts: HCI, H2SO4, CF3CO2H

Ø Reaction conditions –  pH (0.5 - 3) –  T (50 - 100°C)

Ø Analysis –  Silylation, GC-FID –  Molar weight, HPSEC-MALLS

Hydrolysis experiments II

Ø Continuous tube reactor

Ø Catalysts: HCI

Ø Reaction conditions –  pH (0.2-0.3) –  T (90-95°C)

Ø Analysis –  Silylation, GC-FID –  Molar weight, HPSEC-MALLS

Continuous tube reactor in laboratory scale

Continuous reactor system schematically

Batch reactor -HCl catalysis

0 200 400 600 800 1000 1200 1400 16000

200

400

600

800

1000

Glucose

Galactose

c

[mg/

g GG

M]

Time [min]

Mannose

Batch reactor - oligomers Molar mass distribution

0 200 400 600 800 1000 1200 1400 16000

200

400

600

800

1000

DP 2 DP 3 DP 4DP 5

c

[mg/

g GG

M]

Time [min]

DP 1

Performance of continuous reactor - monomers

Performanc eof continuous reactor - monomers

Performance of continuous reactor - oligomers

Autocatalysis detected

0 500 1000 1500 2000 2500 3000 3500 4000 45000

50

100

150

200

250

300

350

400

450 data set 1

Heterogeneous catalyst (Smopex)

Mannose

Glucose&Galactose

Heterogeneous catalysis Logarithmic plots

0,00 0,25 0,50 0,75 1,000,00

0,25

0,50

0,75

1,00

-ln(1

-cM/c0M

)

-ln(1-cGA/c0GA)

Smopex-101 Amberlyst 15

Heterogeneous catalyst

0,00 0,25 0,50 0,75 1,000,00

0,25

0,50

0,75

1,00

-ln(1

-cG/c

0G)

-ln(1-cGA/c0GA)

Smopex-101 Amberlyst 15

Hemicellulose molecule

Change of rate constant γAXdXdk =/1

0 1+

+=− γ

γXAkk

10 +=−∞ γAkk

αXkkkk )( 00 −+= ∞

)1(0αβXkk jj +=

The increase of the rate constant

(21)

β=(k∞j-k0j)/k0j is constant for all of the sugar units.

Mass balance in batch reactor

j

j

MGGA

MGGA

c

cccccccX

0000 ∑∑=

++

++=

BiWHii ccckdtdc ρ0/ =

jWW ccc ∑−= 0 iii ccc −= 00

Total conversion (X)

Mass balances...

)1(0

0

α

β ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+=∑∑

j

jii c

ckk

BiijWHj

jii ccccc

c

ckdtdc ρβ

α

))(()1(/ 000

0 −−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+= ∑∑

∑

which is solved numerically during parameter estimation

Fit of the model for autocatalysis

0 500 1000 1500 2000 2500 3000 3500 4000 45000

50

100

150

200

250

300

350

400

450 data set 1

Modelling of tube reactor

30

-  Tubular reactor - laminar flow model, liquid phase only -  Convection, both axial and radial diffusion -  Dynamic model -  Implementation in gProms (Russo & Kilpiö)

Laminar flow model

31

Mass balance

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛−⋅=2

0 1)(Rruru

AVuuu!

=⋅= ,5.10

Liquid velocity and average outlet concentration

∫

∫

⋅⋅⋅

⋅⋅⋅⋅

= R

R

i

i

drrru

drrrurzcc

0

0

2)(

2)(),(

π

π

z

r

),,(),,(1),,(

),,(),,()(),,(

2

2

,

2

2

,

rztrrrztC

rrrztCD

zrztCD

zrztCru

trztC

jiii

ir

iiz

ii

⋅+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂⋅+

∂

∂⋅+

+∂

∂⋅+

∂

∂⋅+=

∂

∂

ν

Accumulation Convection Axial diffusion

Radial diffusion Reactions

Laminar flow model

32

Mass balance

),,(),,(1),,(),,(),,()(),,(2

2

,2

2

, rztrrrztC

rrrztCD

zrztCD

zrztCru

trztC

jiii

iri

izii ⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛

∂

∂⋅+

∂

∂⋅+

∂

∂⋅+

∂

∂⋅+=

∂

∂ν

Accumulation Convection Axial diffusion Radial diffusion Reaction rate

Boundary conditions

)),(()(),(00,

0, =

=

−⋅=∂

∂⋅−

ziiz

iiz rtCCru

zrtCD 0),(

=∂

∂

=Lz

i

zrtC

Inlet: Outlet:

0),(

0

=∂

∂

=r

i

rztC 0),(

=∂

∂

=Rr

i

rztC

Centre: Wall:

GWH

GAWH

MWH

CCCkrCCCkrCCCkr

⋅⋅⋅=

⋅⋅⋅=

⋅⋅⋅=

33

22

11

Reaction rate expressions

Rate constants from continuous experiments

- good agreement with batch data

Experiment

k’’Gal [min-1]

k’’Glc [min-1]

k’’Man [min-1]

Σk’’i [min-1]

Σk’’i /10-pH

[L/mol/min] Exp I 0.00593 0.00339 0.00608 0.0154 0.031 Exp II 0.00676 0.00452 0.00717 0.0185 0.032 Exp III 0.00576 0.00688 0.01147 0.0241 0.048

Conclusions Homogeneous hydrolysis kinetics of hemicelluloses follows a very regular pattern,except an initiation period Heterogenous hydrolysis kinetics shows a remarkable autocatalytic effect A kinetic model was proposed an successully applied to explain the autocatalysis Hydrolysis can successfully be carried out in continuous mode – good agreement of rate constants compared to batch experiments Laminar flow model is good for the millireactor

Mathematical modelling of cellulose substitution

kinetics

Anhydroglucose units of cellulose C2, C3, C6

O

OH

OOH

OH

OO

OH

OH

OH

O

OH

OH

OH

OH

n

HO

1

2

3

45

6

Experimental approach Isothermal, well-controlled experiments in a slurry batch reactor Cellulose from birch was used, swelled in NaOH and let to react with monochloroacetic acid in isopropanol A lot of effort was put on the development of a new chromatographic method to reveal the detailed substitution kinetics, not only the overall degree of substitution (DS); Substituted units 2, 3, 6, 23, 26, 36 and 236 revealed

Modelling approach Incorporate as much mathematical modelling as possible Everything can be transformed to differential equations, enjoy it! Wood chemistry is not a pure empirical science

Reaction scheme Several substitution reactions

0

3

6 236

2

23

36

26 2k

6k

3k

0

33

6cc

ekδ−

⋅

0

33

2cc

ekδ−

⋅

0

66

3cc

ekδ−

⋅

0

66

2cc

ekδ−

⋅

0

22

6cc

ekδ−

⋅

( )0

2332

6cc

ekδδ +−

⋅

( )0

3663

2cc

ekδδ +−

⋅

( )0

2662

3cc

ekδδ +−

⋅

0

22

3cc

ekδ−

⋅

Substitution reactions

Cell-OH + RCOOH → RCOO-Cell + H2O M+Cell-O- + RX → Cell-OR + M+X- RX=CH3Cl R=CH3CH2Cl

CMC, ethene and propene oxides

M+Cell-O- + CH2ClCOOH → Cell-OCH2COOH + M+Cl-. Cell-OH +HO-R-O- → HO-R-O-Cell + OH- R=CH2CH2 and R=CH2CH2CH2 for ethene and propene oxides

Substitution stoichiometry

663322

PROHPROHPROH

→+

→+

→+

0060302 cccc ===

0ccc Pii =+

Substitution reactions to OH-2, OH-3 and OH-6

R is a substitution reagent and P2, P3 and P6 are product molecules.

ci unsubstituted H-groups, cPi substituted groups (i=2,3,6).

Product formation

α

α

α

RP

RP

RP

cckr

cckr

cckr

666

333

222

=

=

=

PjPPPRR cccccc ∑=++=− 6320

Formation rates

cR = concentration of the substitution reagent Reaction stoichiometry

Batch reactor

PiPi rdtdc =/

Pii ccc −= 0

PjRR ccc ∑−= 0

Mass balances of the product groups in a batch reactor

i=2,3,6.

Functional groups and DS

α))((/ 00 PjRPiiPi cccckdtdc ∑−−=

60

206262 )/(/

P

PPP cc

cckkdcdc−

−=

6/20602 )/1(1/ αcccc PP −−=

6/30603 )/1(1/ αcccc PP −−=

0/ ccDS Pj∑=6/3

066/2

0606 )/1()/1(/2 αα ccccccDS PPP −−−−+=

α3/6=k3/k6

DS analytically

tka

tka

eaeaDS ')3(

')3(

)3/(1)1(

−

−

−

−=

)'31'3(3tktkDS

+=

kiteDS −∑−= 3 )1(3 'tkeDS −−=

Second order kinetics and equal reactivities

First and pseudo-first order kinetics

Product distribution (I, II, III)

632 ''' ccccI ++=

362623 ''' ccccII ++=

236'ccIII =

Probalistic distribution

c’k, k=2,3,6,23,26,36,26

Probabilistic distribution

)/)(/1)(/1()/1)(/)(/1()/1)(/1)(/(/ 0603020603020603020 cccccccccccccccccccc PPPPPPPPPI −−+−−+−−=

)/)(/)(/1()/)(/1)(/()/1)(/)(/(/ 0603020603020603020 cccccccccccccccccccc PPPPPPPPPII −+−+−=

)/)(/)(/(/ 0603020 cccccccc PPPIII =

)/1)(/1)(/1(/' 06030200 cccccccc PPP −−−=

000 /3/2/ ccccccDS IIIIII ++=

DS for equal reactivities

300'

30

20

20

)1(/

/

)1(3/

)1(3/

xcc

xcc

xxcc

xxcc

III

II

I

−=

=

−=

−=

nnnn DSDScc −−= 3

0 )3/1()3/(/ γ

Spurlin distribution is obtained

where n=0,I,II,III. γn are obtained from Pascal’s triangle:

γn=(3n)=3!/n!/(3-n)!, n=0,,2,3.

Detailed product distribution ii rdtdc =/'

αRcckkkr 06320 ')( ++−=

αRcckkckr )')('( 263022 +−−=

αRcckkckr )')('( 362033 +−−=

αRcckkckr )')('( 632066 +−−=

αRcckckckr )'''( 236233223 −+=

αRcckckckr )'''( 263266226 −+=

αRcckckckr )'''( 362366336 −+=

αRcckckckr )'''( 236263362236 −+=

i = 0, 2,3, 6, 23,…236, R. Generation rates of different anhydroglucose units:

Kinetics and retardation

αRR cckckckckkckkckkckkkr )'''')(')(')(')(( 2362633626323622630632 +++++++++++−=

DSjj ekk ⋅−= 00

δ

0/0

ccjj

Pkkekk ⋅−∑=δ

Substitution reagent

Retardation functions

Special case

II kckcdtdcdtdcdtdcdtdc 23//// 0632 −==++

IIIII kckcdtdcdtdcdtdcdtdc 22//// 362623 −==++

IIIII kcdtdcdtdc 2//236 ==

00 3/ kcdtdc =

First order kinetics and equally reactive hydroxyl

groups

00 '3/' cddc −=θ

II ccddc 2'3/ 0−=θ

IIIII ccddc −= 2/ θ

IIIII cddc =θ/

Damköhler number, θ=kt:

Solution method

In time scale

θ300 /'

−= eccθθ 2

0 )1(3/' −−−= eecc Iθθθθθ −−−−− −=+−= eeeeecc II

220 )1(3)21(3/'

3320 )1(331/' θθθθ −−−− −=−+−= eeeecc III

)1(3 θ−−= eDS

The solution is easy:

Relative product distribution

632

02632

0

2 )'/')((''

kkkcckkk

dcdc

++

++−=

1)/'('/' 20002 −= −αcccc

)/')(1)/'(('/' 002

0002 cccccc −= −α

Relative product distribution – general approach

X=c’0/c0

The solution

XXcc )1(/' 202 −= −α

XXcc )1(/' 303 −= −α

XXcc )1(/' 606 −= −α

αi= ki/Σkj.

The solution

0632

2362332

0

23

')('''

''

ckkkckckck

dcdc

++

+−−=

31216023 /'

ααα −− −−+= XXXXcc61213

026 /'ααα −− −−+= XXXXcc61312

036 /'ααα −− −−+= XXXXcc

I, II and III

XXXXccI 3/ 6131210 −++= −−− ααα

)(23/ 6131216320

αααααα −−− ++−+++= XXXXXXXccII613121632

0 1/ αααααα −−− +++−−−−= XXXXXXXccIII

)(3 632 ααα XXXDS ++−=

Relative product distribution Equal reactivities of OH-groups

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

Degree of substitution, DS

Mol

e fra

ctio

n

unsubstitutedglucose,

x0

monosubstitutedglucose,

xI

disubstitutedglucose,

xII

trisubstitutedglucose,

xIIIk2:k3:k6 = 1:1:1

Relative product distribution Non-equal reactivities

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

Degree of substitution, DS

Mol

e fra

ctio

n

1:10:10

1:10:10

1:10:10

1:10:10

1:1:10 1:1:10

1:1:10

1:1:10k2:k3:k6

Parameter estimation

)(/ yfdtdy =

( )∑∑ −=t

titii

yyQ 2,exp,,

Experimental product distribution

High-pH AEC-PAD Monomer Distribution (mol%) DS = 0.2 DS = 0.7 Glucose (1) 76.6 34.6 6-O-CM-glucose (2) 12.4 16.8 2-O-CM-glucose (3) 4.2 18.8 3-O-CM-glucose (4) 6.8 24.4 2,6-di-O-CM-glucose (5) 0 2.4 3,6-di-O-CM-glucose (6) 0 1.6 2,3-di-O-CM-glucose (7) 0 1.5 2,3,6-tri-O-CM-glucose 0 0

5,0 5,5 6,0 6,5 7,0 7,5

40

60

80

100

D

etec

tor r

espo

nse

(nC

)

Time (min)

34

2 Fig. 2 C

line B

line A

titration and by HPAEC-PAD.

Carboxymethylation at 30oC (20 min 120 min) 2= 6-O-CM-glucose, 3=2-O-CM-glucose, 4=3-O-CM-glucose

Experimental product distribution (I)

titration and by HPAEC-PAD.

Carboxymethylation at 30oC (20 min, 120 min) 5= 2,6-di-O-CM-glucose, 6=3,6-di-O-CM-glucose, 7=2,3-di-O-CM-glucose

Experimental product distribution (II)

10 11 12 13 1444

45

46

47

48

49

50

Det

ecto

r res

pons

e (n

C)

Time (min)

Fig. 2 D5

67

line A

line B

Estimated kinetic parameters

)

0/)'/(,

0, ccDSRErefjj

Pkkja eeekk ⋅−⋅−− ∑=δδθ

.

Parameter Parameter unit Estimated parameter

value Estimated relative standard error (%)

k2,ref = k3,ref l/(mol min) 0.238 46.4 k6,ref l/(mol min) 0.326 46.5 δ2 - 2.03 52.3 δ3 - 4.42 22.6 δ6 - 6.46 23.5 Ea,2 = Ea,3 kJ/mol 140 11.5 Ea,6 kJ/mol 127 12.5 δ0 - 4.79 14.8

Degree of substitution (DS) Experiment and modelling

0 20 40 60 80 1000

0.5

1

1.5

Time / [min]

Deg

ree

of s

ubst

itutio

n, D

S

Product distribution Unsubstituted, mono-, di- and tri-

substituted units (30oC)

0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

Time / [min]

Mol

e fra

ctio

n

Product distribution Unsubstituted & I & II & III (40oC)

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Time / [min]

Mol

e fra

ctio

n

Product distribution Unsubstituted & I & II & III (60oC)

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Time / [min]

Mol

e fra

ctio

n

Detailed substitution kinetics CP2, CP3, CP6 at 60oC

0 20 40 60 80 1000

0.05

0.1

0.15

0.2

0.25

Time / [min]

Mol

e fra

ctio

n

)

Detailed substitution kinetics CP23, CP26, CP36 at 60oC

0 20 40 60 80 1000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time / [min]

Mol

e fra

ctio

n

)

Detailed substitution kinetics CP236 at 60oC

0 20 40 60 80 1000

0.02

0.04

0.06

0.08

0.1

Time / [min]

Mol

e fra

ctio

n

)

Conclusions

A new chromatographic method was developed to reveal the detailed substitution kinetics Mathematical models were developed for ideal cases and for the retardation of the reaction rate as the substitution proceeds The modelling approach was successfully appplied to the substitution of cellulose with monochloroacetic acid – the production of carboxymethyl cellulose (CMC) in a slurry batch reactor The approach is valid for starch and hemicelluloses, too

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