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

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

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

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

5 Kraft Pulping Kinetics H Factor/Temperature

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

7 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!

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

15 Model Performance UW model Pulping data for mill chips - Gullichsen’s data

16 Model Performance UW 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 Problem

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

20 UW: Model I Initialk=2.5*[OH - ] 0.1 Bulkk=0.47 Residualk=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 Performance UW 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 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

25 Gullichsen’s viscosity data

26 Virkola’s viscosity data

27 Virkola’s viscosity data

28 [OH - ] & [HS - ] Predictions Calculated by stoichiometry in all models as follows:

29 Model Performance UW model Gullichsen data on mill chips