1

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.

2

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

3

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

4

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

5

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

6

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

7

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!

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 ModelsUW 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 ModelsUW 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

Model PerformanceUW model

Pulping data for thin chips – Gullichsen’s data

15

Model PerformanceUW model

Pulping data for mill chips - Gullichsen’s data

16

Model PerformanceUW model

Virkola data on mill chips

17

Model Performance (Andersson)UW Model

Model works well until very low lignin content

18

Carbohydrate Loss Models

Modeling yield prediction – A Very Difficult Modeling ProblemModeling yield prediction – A Very Difficult Modeling Problem

19

UW Model

• Two methods have been tested, but since both have the same accuracy, the simplest has been retained.

• Two methods have been tested, but since both have the same accuracy, the simplest has been retained.

20

UW: Model I

Initial k=2.5*[OH-]0.1

Bulk k=0.47

Residual k=2.19

Basic Structure: dc/dt=k*dL/dt

Some physical justification for this is given by carbohydrate-lignin linkages.

Carbohydrates lumped into a single group.

21

Gustafson: Model I

• Carbohydrate/lignin relation is assumed to be stable and not a strong function of pulping conditions.

• Selectivity of reactions assumed to be slightly dependent on OH- but independent of temperature.

• Yield/kappa relationship can be improved by using both lower pulping temperature and less alkali.

• Carbohydrate/lignin relation is assumed to be stable and not a strong function of pulping conditions.

• Selectivity of reactions assumed to be slightly dependent on OH- but independent of temperature.

• Yield/kappa relationship can be improved by using both lower pulping temperature and less alkali.

22

Model PerformanceUW model

Virkola data on mill chips

23

Prediction of pulp viscosity

Dependence of viscosity on pulping conditions was modeled

»Viscosity is a measure of degradation of cellulose chains

»Effect of temperature, alkalinity, initial DP, and time on viscosity is modeled

»Model is compared with experimental data from two sources

24

Prediction of pulp viscosity

dDPdt

k OH e DP

KDP

C C

n E RTn

cell na

pulp cell non cell

02

1

[ ]

[ ]

[ ] [ ] ( )[ ]

/

[ ] - Intrinsic viscosity

C - Cellulose fraction in pulp

- Degree of polymerization for celluloseDPn

25

Gullichsen’s viscosity data

26

Virkola’s viscosity data

27

Virkola’s viscosity data

H-factor

IntrinsicViscositydm3/ kg

600

700

800

900

1000

1100

1200

0 1000 2000 3000 4000

19% E.A.22% E.A.

25% E.A.

28

[OH-] & [HS-] Predictions

• Calculated by stoichiometry in all models as follows:• Calculated by stoichiometry in all models as follows:

)/,/(][

dtdCdtdLfdt

OHd

0][

dt

HSd

29

Model PerformanceUW model

Gullichsen data on mill chips