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MODELING OF REACTIONS WITH DIFFUSION

MODELING OF REACTIONS WITH DIFFUSION. Semi-infinite slab reaction-diffusion model is improved to better approximate effects of chip thickness and length. Dissolved lignin and carbohydrate. Alkali Heat Sulfide. CHIP. LIQUOR. Approximation of 3-d diffusion. Equivalent-sphere model.

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MODELING OF REACTIONS WITH DIFFUSION

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  1. MODELING OF REACTIONS WITH DIFFUSION

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

  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. Sphere approximates 3-d diffusion better than slab model Average Concentration 1:1:3 chips Sphere 1:3:5 chips Infinite slab Diffusion number, Dt/L2

  5. Three-dimensional diffusion Approximation for 3-d diffusion in wood chips is used • Characteristic time ratio (L2/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. Improvement from sphere model

  7. Reaction-diffusion in a sphere

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

  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

  10. Effect of chip thickness

  11. Effect of thickness and alkali

  12. Prediction of screening rejects

  13. Estimated fiber kappa distribution

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

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

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

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