Empirical Kraft Pulping Models

• Models developed by regression of pulping study results • Excellent for digester operators to have for quick reference on relation between kappa and operating conditions • “Hatton” models are excellent examples of these Kappa or Yield 18% EA 20% EA H-factor 1

Emperical Kraft Pulping Models

Hatton Equation Kappa (or yield) =   (log(H)*EA n )  ,  , and n are parameters that must be fit to the data. Values of  ,  , and n for kappa prediction are shown in the table below.

Species Hemlock Jack Pine Aspen  259.3

279.3

124.7

 22.57

30.18

5.03

n 0.41

0.35

0.76

kappa range 21-49 22-53 14-31

Warning: These are empirical equations and apply only over the specified kappa range. Extrapolation out of this range is dangerous

! 2

Delignification Kinetics Models H Factor Model

• Uses only bulk delignification kinetics

dL

/

dt



ke

 32 , 000 /

RT

k = Function of [HS ] and [OH ] R = cal 1.987

mole *  K T [=] °K 3

Delignification Kinetics Models H Factor Model

H



k

0  0

t e

 32 , 000 /

RT

(

t

)

dt

Relative reaction rate k 0 is such that H(1 hr, 373°K) = 1 4

Delignification Kinetics Models H Factor Model

• Provides mills with the ability to handle common disturbance such as inconsistent digester heating and cooking time variation.

5

Delignification Kinetics Models H Factor/Temperature

170 900 700 500 300 100 H factor equal to area under this curve 130 90 1 2 Hours from Start 6

Kraft Pulping Kinetics H Factor/Temperature 30 25 20 15 10 5 0 0 150°C 160°C 170°C 500 1000 1500 H Factor 2000 2500

7

Delignification Kinetics Models Kerr model ~ 1970

dL

/

dt



k

*

e

 32 , 000 /

RT

[

OH

 ] *

L

• • • H factor to handle temperature 1 st order in [OH ] Bulk delignification kinetics w/out [HS ] dependence 8

Delignification Kinetics Models Kerr model ~ 1970

Integrated form: 

L i L f dL L

*

f

(

L

) 

K

 0

t e

 32 , 000

RT

(

t

) Functional H-Factor relationship between L and [OH ] 9

Delignification Kinetics Models Kerr model ~ 1970

Slopes of lines are not a function of EA charge 10

Delignification Kinetics Models Kerr model ~ 1970

Model can handle effect of main disturbances on pulping kinetics • • • Variations in temperature profile » » » Steam demand Digester scheduling Reaction exotherms Variations in alkali concentration » White liquor variability » Differential consumption of alkali in initial delignification Often caused by use of older, degraded chips Good kinetic model for control 11

Delignification Kinetics Models Gustafson model

• • Divide lignin into 3 phases, each with their own kinetics » 1 lignin, 3 kinetics Transition from one kinetics to another at a given lignin content that is set by the user.

For softwood: Initial to bulk ~ 22.5% on wood Bulk to residual ~ 2.2% on wood 12

Delignification Kinetics Models Gustafson model

• • • Initial » dL/dt = k 1 L » E ≈ 9,500 cal/mole Bulk » » dL/dt = (k 2 [OH ] + k 3 [OH ] 0.5

[HS ] 0.4

)L E ≈ 30,000 cal/mole Residual » » dL/dt = k 4 [OH ] 0.7

L E ≈ 21,000 cal/mole 13

Delignification Kinetics Models Gustafson model

Another model was formulated that was of the type dL/dt = K(L-L f ) Where L f = floor lignin level – set @ 0.5% on wood • Did not result in any better prediction of pulping behavior 14

Delignification Kinetics Models Purdue Model

2 types of lignin: • High reactivity Assumed to react •

dL

Low reactivity /

dt

 simultaneously (

k

1 [

OH

 ] 1 / 2 

k

2 [

HS

 ] 1 / 2 )(

L



L f

) L f assumed to be zero High reactivity E ≈ 7000 cal/mole Low reactivity E k1 ≈ 8300 cal/mole E k2 ≈ 28,000 cal/mole 15

Delignification Kinetics Models Purdue Model

• •

Potential difficulties

High reactivity lignin (initial lignin) dependent on [OH ] and [HS ] No residual lignin kinetics 16

Delignification Kinetics Models Andersson, 2003

• 3 types of lignin: » » » Fast Medium slow Assumed to react simultaneously, like Purdue model 10 1 total lignin 10 0 10 -1 0 L 1 lignin 50 L 3 lignin L 2 lignin 100 150 time [min] 200 250 300 17

Delignification Kinetics Models Andersson, 2003

Fast ≈ 9% on wood (all t) dL/dt = k 1 +[HS ] 0.06

L E ≈ 12,000 cal/mole Medium ≈ 15% on wood (t=0) dL/dt = k 2 [OH ] 0.48

[HS ] 0.39

L E ≈ 31,000 cal/mole Slow ≈ 1.5% on wood (t=0) dL/dt = k 3 [OH ] 0.2

L E ≈ 31,000 cal/mole 18

Delignification Kinetics Models Andersson, 2003

Model also assumes that medium can become slow lignin depending on the pulping conditions L*≡ Lignin content where amount of medium lignin equals the amount of slow lignin Complex formula to estimate L * :

L

*  0 .

49 ([

OH

 ]  0 .

01 )  0 .

65 ([

HS

 ]  0 .

01 )  0 .

19 * ( 1 .

83  2 .

97 * 10 5 (

T

 273 .

15 ) 2 ) 19

10 1

Delignification Kinetics Models Andersson, 2003

Total lignin L 2 ,L 3 L * Increasing [OH ] 10 0 10 -1 0 50 100 150 time [min] 200 250 300 350 20

Model Performance Gustafson model

50 40 Screened Kappa 30 20 10 0 15 1.5 mm chips 20 25 % Active Alkali on wood Pulping data for thin chips –

Gullichsen’s data

30 21

Model Performance Gustafson model

60 50 40 Total Kappa 30 20 10 0 15 20 % Alkali charge 25 Pulping data for mill chips -

Gullichsen’s data

Mill chips 30 22

Model Performance Gustafson model

80 60 Predicted Kappa 40 20 0 0 20 40 Measured Kappa 60 Virkola data on mill chips 80 23

Model Performance (Andersson) Purdue Model

Purdue model suffers from lack of residual delignification 24

Model Performance (Andersson) Purdue Model

Purdue model suffers from lack of residual delignification 25

Model Performance (Andersson) Gustafson Model

Model works well until very low lignin content 26

Model Performance (Andersson) Gustafson Model

Model handles one transition well and the other poorly 27

Model Performance (Andersson) Andersson Model

Andersson predicts his own data well 28

Model Performance (Andersson) Andersson Model

Model handles transition well 29