1. 1 MODELING OF REACTIONS WITH DIFFUSION

2. 2 Semi-infinite slab reaction-diffusion model is improved to better approximate effects of chip thickness and length Alkali Heat Sulfide Dissolved lignin and carbohydrate CHIPLIQUOR

3. 3 Approximation of 3-d diffusion Equivalent-sphere model Slab model Actual 3-dimensional diffusion in chips is better approximated by the sphere model than the slab model

4. 4 Average Concentration Diffusion number, Dt/L 2 1:3:5 chips Infinite slab 1:1:3 chips Sphere Sphere approximates 3-d diffusion better than slab model

5. 5 Three-dimensional diffusion Approximation for 3-d diffusion in wood chips is used » Characteristic time ratio (L 2 /D) for diffusion along length and thickness is from 2:3 to 1:50 » Diffusion calculation uses a sphere » Equal specific surface for chip and sphere » Sphere model improves on slab model » Complexity of 3-d modeling is avoided Approximation for 3-d diffusion in wood chips is used » Characteristic time ratio (L 2 /D) for diffusion along length and thickness is from 2:3 to 1:50 » Diffusion calculation uses a sphere » Equal specific surface for chip and sphere » Sphere model improves on slab model » Complexity of 3-d modeling is avoided

6. 6 Improvement from sphere model

7. 7 Reaction-diffusion in a sphere

8. 8 Model Variables » Alkali concentration » Temperature » Dissolved Organics » Lignin content in chip » Carbohydrate content » Alkali concentration » Temperature » Dissolved Organics » Lignin content in chip » Carbohydrate content Profile across the chip and along the digester is calculated

9. 9 Validation of sphere model Predicting data from three different sources » Thin chip pulping at varying alkali charge » Effect of chip thickness on kappa number » A priori prediction for commercial chips » Predicting screening rejects » Estimating kappa distribution for pulp Predicting data from three different sources » Thin chip pulping at varying alkali charge » Effect of chip thickness on kappa number » A priori prediction for commercial chips » Predicting screening rejects » Estimating kappa distribution for pulp

10. 10 Effect of chip thickness

11. 11 Effect of thickness and alkali

12. 12 Prediction of screening rejects

13. 13 Estimated fiber kappa distribution

14. 14 HEAT White Liquor Pre-steamed Chips Spent liquorQuench circulation Wash circ. Heating circulation Pulp BLOW WASH QUENCH COOK HEAT IMPREGNATE Dilution CONVENTIONAL KAMYR DIGESTER HEAT

15. 15 DIGEST STMIX MIXER HEATER SPLIT White liquor SteamChips Heating zone Extraction screen Heating zone Cook zone WinGEMS Flowsheet

16. 16 DIGESTER block outputs  Pulp properties  Kappa number -Maximum and minimum -Screened and total  Viscosity  Yield  Screening rejects  Residence time  Pulp properties  Kappa number -Maximum and minimum -Screened and total  Viscosity  Yield  Screening rejects  Residence time