1

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 orYield

H-factor

15% EA15% EA15% EA

18% EA

20% EA

2

Emperical Kraft Pulping Models

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

Hatton Equation

Species n kappa range

Hemlock 259.3 22.57 0.41 21-49

Jack Pine 279.3 30.18 0.35 22-53

Aspen 124.7 5.03 0.76 14-31

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

3

Delignification Kinetics ModelsH Factor Model

• Uses only bulk delignification kinetics• Uses only bulk delignification kinetics

RTkedtdL /000,32/

k = Function of [HS-] and [OH-]

K*mole

cal 1.987

R =

T [=] °K

4

Delignification Kinetics ModelsH Factor Model

k0 is such that H(1 hr, 373°K) = 1k0 is such that H(1 hr, 373°K) = 1

t tRT dtekH0

)(/000,320

Relative reaction rate

5

Delignification Kinetics ModelsH Factor Model

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

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

6

Delignification Kinetics ModelsH Factor/Temperature

900

700

500

300

100Rel

ativ

e R

eact

ion

Rat

e

1 2Hours from Start

90

130

170

Tem

pera

ture

°C

H factor equalto area under thiscurve

7

Kraft Pulping KineticsH Factor/Temperature

0

5

10

15

20

25

30

0 500 1000 1500 2000 2500

H Factor

Lig

nin

(%

of

Pu

lp)

150°C

160°C

170°C

0

5

10

15

20

25

30

0 500 1000 1500 2000 2500

H Factor

Lig

nin

(%

of

Pu

lp)

150°C

160°C

170°C

8

Delignification Kinetics ModelsKerr model ~ 1970

• H factor to handle temperature

• 1st order in [OH-]

• Bulk delignification kinetics w/out [HS-] dependence

• H factor to handle temperature

• 1st order in [OH-]

• Bulk delignification kinetics w/out [HS-] dependence

LOHekdtdL RT *][*/ /000,32

9

Delignification Kinetics ModelsKerr model ~ 1970

Integrated form:Integrated form:

t tRTL

LeK

LfL

dLf

i 0

)(

000,32

)(*

H-FactorFunctional relationship between L and [OH-]

10

Delignification Kinetics ModelsKerr model ~ 1970

Slopes of lines are not a function of EA charge

11

Delignification Kinetics ModelsKerr model ~ 1970

• 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

• 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

Model can handle effect of main disturbances on pulping kinetics

12

Delignification Kinetics ModelsGustafson 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.

• 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

13

Delignification Kinetics ModelsGustafson model

• Initial» dL/dt = k1L

» E ≈ 9,500 cal/mole

• Bulk» dL/dt = (k2[OH-] + k3[OH-]0.5[HS-]0.4)L

» E ≈ 30,000 cal/mole

• Residual» dL/dt = k4[OH-]0.7L

» E ≈ 21,000 cal/mole

• Initial» dL/dt = k1L

» E ≈ 9,500 cal/mole

• Bulk» dL/dt = (k2[OH-] + k3[OH-]0.5[HS-]0.4)L

» E ≈ 30,000 cal/mole

• Residual» dL/dt = k4[OH-]0.7L

» E ≈ 21,000 cal/mole

14

Delignification Kinetics ModelsGustafson model

Another model was formulated that was of the type

dL/dt = K(L-Lf)

Where Lf = floor lignin level – set @ 0.5% on wood

• Did not result in any better prediction of pulping behavior

Another model was formulated that was of the type

dL/dt = K(L-Lf)

Where Lf = floor lignin level – set @ 0.5% on wood

• Did not result in any better prediction of pulping behavior

15

Delignification Kinetics ModelsPurdue Model

2 types of lignin:

• High reactivity

• Low reactivity

2 types of lignin:

• High reactivity

• Low reactivity

))(][][(/ 2/12

2/11 fLLHSkOHkdtdL

High reactivity E ≈ 7000 cal/mole

Low reactivityEk1 ≈ 8300 cal/mole

Ek2 ≈ 28,000 cal/mole

Lf assumed to be zero

Assumed to react simultaneously

16

Delignification Kinetics ModelsPurdue Model

Potential difficulties• High reactivity lignin (initial lignin) dependent on

[OH-] and [HS-]• No residual lignin kinetics

Potential difficulties• High reactivity lignin (initial lignin) dependent on

[OH-] and [HS-]• No residual lignin kinetics

17

Delignification Kinetics ModelsAndersson, 2003

• 3 types of lignin:» Fast

» Medium

» slow

• 3 types of lignin:» Fast

» Medium

» slow

Assumed to react simultaneously, like Purdue model

10-1

10

10

0

1

0 50 100 150 200 250 300

L1 lignin L2 lignin

L3 lignin

total lignin

Lig

nin

[%o

w]

time [min]

18

Delignification Kinetics ModelsAndersson, 2003

Fast ≈ 9% on wood (all t)

dL/dt = k1+[HS-]0.06LE ≈ 12,000 cal/mole

Medium ≈ 15% on wood (t=0)

dL/dt = k2[OH-]0.48[HS-]0.39LE ≈ 31,000 cal/mole

Slow ≈ 1.5% on wood (t=0)

dL/dt = k3[OH-]0.2LE ≈ 31,000 cal/mole

Fast ≈ 9% on wood (all t)

dL/dt = k1+[HS-]0.06LE ≈ 12,000 cal/mole

Medium ≈ 15% on wood (t=0)

dL/dt = k2[OH-]0.48[HS-]0.39LE ≈ 31,000 cal/mole

Slow ≈ 1.5% on wood (t=0)

dL/dt = k3[OH-]0.2LE ≈ 31,000 cal/mole

19

Delignification Kinetics ModelsAndersson, 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*:

))15.273(10*97.283.1(*

)01.0]([)01.0]([49.025

19.065.0*

T

HSOHL

20

Delignification Kinetics ModelsAndersson, 2003

35030025020015010050010-1

100

101

Lig

nin

[%

ow

]

time [min]

Total lignin

L2,L3

L*

Increasing [OH-]

21

Model PerformanceGustafson model

Pulping data for thin chips – Gullichsen’s data

22

Model PerformanceGustafson model

Pulping data for mill chips - Gullichsen’s data

23

Model PerformanceGustafson model

Virkola data on mill chips

24

Model Performance (Andersson)Purdue Model

Purdue model suffers from lack of residual delignification

25

Model Performance (Andersson)Purdue Model

Purdue model suffers from lack of residual delignification

26

Model Performance (Andersson)Gustafson Model

Model works well until very low lignin content

27

Model Performance (Andersson)Gustafson Model

Model handles one transition well and the other poorly

28

Model Performance (Andersson)Andersson Model

Andersson predicts his own data well

29

Model Performance (Andersson)Andersson Model

Model handles transition well