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 or Yield H-factor 15% EA 18% EA 20% EA

2 Emperical Kraft Pulping Models 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. Hatton Equation Species  nkappa range Hemlock Jack Pine Aspen Warning: These are empirical equations and apply only over the specified kappa range. Extrapolation out of this range is dangerous!

3 Delignification Kinetics Models H Factor Model Uses only bulk delignification kinetics k = Function of [HS - ] and [OH - ] R = T [=] °K

4 Delignification Kinetics Models H Factor Model k 0 is such that H(1 hr, 373°K) = 1 Relative reaction rate

5 Delignification Kinetics Models H Factor Model Provides mills with the ability to handle common disturbance such as inconsistent digester heating and cooking time variation.

6 Delignification Kinetics Models H Factor/Temperature Relative Reaction Rate 12 Hours from Start Temperature °C H factor equal to area under this curve

7 Kraft Pulping Kinetics H Factor/Temperature

8 Delignification Kinetics Models Kerr model ~ 1970 H factor to handle temperature 1 st order in [OH - ] Bulk delignification kinetics w/out [HS - ] dependence H factor to handle temperature 1 st order in [OH - ] Bulk delignification kinetics w/out [HS - ] dependence

9 Delignification Kinetics Models Kerr model ~ 1970 Integrated form: H-Factor Functional relationship between L and [OH - ]

10 Delignification Kinetics Models Kerr model ~ 1970 Slopes of lines are not a function of EA charge

11 Delignification Kinetics Models Kerr 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 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. 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 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 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

14 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 – 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-L f ) Where L f = floor lignin level – 0.5% on wood Did not result in any better prediction of pulping behavior

15 Delignification Kinetics Models Purdue Model 2 types of lignin: High reactivity Low reactivity 2 types of lignin: High reactivity Low reactivity High reactivityE ≈ 7000 cal/mole Low reactivity E k1 ≈ 8300 cal/mole E k2 ≈ 28,000 cal/mole L f assumed to be zero Assumed to react simultaneously

16 Delignification Kinetics Models Purdue 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 Models Andersson, types of lignin: »Fast »Medium »slow 3 types of lignin: »Fast »Medium »slow Assumed to react simultaneously, like Purdue model L 1 lignin L 2 lignin L 3 lignin total lignin Lignin [%ow] time [min]

18 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 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

19 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 * :

20 Delignification Kinetics Models Andersson, Lignin [%ow] time [min] Total lignin L 2,L 3 L*L* Increasing [OH - ]

21 Model Performance Gustafson model Pulping data for thin chips – Gullichsen’s data

22 Model Performance Gustafson model Pulping data for mill chips - Gullichsen’s data

23 Model Performance Gustafson 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