1. 1 Carbohydrate Loss Models Modeling yield prediction – A Very Difficult Modeling Problem

2. 2 Gustafson Model Two methods have been tested, but since both have the same accuracy, the simplest has been retained.

3. 3 Gustafson: 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.

4. 4 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.

5. 5 Gustafson: Model II Divide the carbohydrates into cellulose and hemicellulose. For each of those divide the pulping into initial and bulk pulping. The transitions are defined by the lignin content. Divide the carbohydrates into cellulose and hemicellulose. For each of those divide the pulping into initial and bulk pulping. The transitions are defined by the lignin content.

6. 6 Gustafson: Model II- Initial Phase dH/dt=k 1 *[OH - ] 1.5(H-5) dC/dt=k 2 *[OH - ] 1.5(C- 32) High reaction orders came from data generated by Genco E ≈ 8,300 cal/mole

7. 7 Gustafson: Model II- Bulk Phase dH/dt=k 3 *[OH - ] (H-5.0)E ≈ 22,000 cal/mole dC/dt=k 4 *[OH - ](C-32)E ≈ 36,000 cal/mole

8. 8 Gustafson: Model II Application Applied the model to predict pulping behavior of RDH and SuperBatch (displacement batch) digesters. Model could predict, but was unstable at extremes, especially high alkaline conditions. Applied the model to predict pulping behavior of RDH and SuperBatch (displacement batch) digesters. Model could predict, but was unstable at extremes, especially high alkaline conditions.

9. 9 Purdue Model Carbohydrates divided into cellulose, xylans and glucomannan All components use the form: »dC n /dt=(k 1 [OH - ]+k 2 [OH - ] 1/2 [HS - ] 1/2 )(C n -C nf ) Carbohydrates divided into cellulose, xylans and glucomannan All components use the form: »dC n /dt=(k 1 [OH - ]+k 2 [OH - ] 1/2 [HS - ] 1/2 )(C n -C nf )

10. 10 Purdue Model Assumed to have fast and slow reaction components much like lignin Cellulose/XylanE ≈ 9000 cal/mole Glucomannan (fast)E ≈ 17,000 cal/mole Glucomannan (slow)E ≈ 40,000 cal/mole

11. 11 Andersson Model Carbohydrates split into: »Cellulose »Glucomannan »Xylan Fast, medium and slow components are assumed for each carbohydrate phase. Carbohydrates split into: »Cellulose »Glucomannan »Xylan Fast, medium and slow components are assumed for each carbohydrate phase.

12. 12 Andersson Model General Kinetics: In practice, all carbohydrates are lumped together into CH.

13. 13 Andersson Model Complex model to estimate relative amount of medium and slow carbohydrate CH * ≡ Carbohydrate content where CH 2 & CH 3 are equal ≡ 42.3 + 3.65 ( [OH - ] + 0.05 ) -0.54

14. 14 Andersson Model Activation Energies: FastE ≈ 12,000 cal/mole MediumE ≈ 35,000 cal/mole

15. 15 Model Performance Gustafson model Virkola data on mill chips

16. 16 Model Performance Andersson model Prediction of cellulose and glucomannans

17. 17 Model Performance Andersson model Prediction of xylans

18. 18 Model Performance Andersson model Prediction of total carbohydrates as function of [OH-]

19. 19 Model Performance Andersson model Prediction of total carbohydrates as function of temperature

20. 20 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

21. 21 Prediction of pulp viscosity

22. 22 Gullichsen’s viscosity data

23. 23 Virkola’s viscosity data

24. 24 Virkola’s viscosity data

25. 25 [OH - ] & [HS - ] Predictions Calculated by stoichiometry in all models as follows: Gustafson Purdue Andersson - Stoichiometry

26. 26 Model Performance Gustafson model Gullichsen data on mill chips