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Fundamental continuous digester model – Doyle et al.

• Very big & complex model

• Very big & complex model

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• Lignin» High reactivity» Low reactivity

• Cellulose» High» Low

• Xylan» High» Low

• Glucomannan» High» Low

• Alkali• Sulfide

• Lignin» High reactivity» Low reactivity

• Cellulose» High» Low

• Xylan» High» Low

• Glucomannan» High» Low

• Alkali• Sulfide

Dissolved lignin

Dissolved Carbohydrates

Passive alkaliPassive sulfide

Fundamental continuous digester model – Doyle et al.

Use Purdue Pulping Kinetics

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• Transport in and out of chip modeled with an overall mass transfer coefficient• All components are assumed to diffuse in and out of chip at the same rate.

• Transport in and out of chip modeled with an overall mass transfer coefficient• All components are assumed to diffuse in and out of chip at the same rate.

Solid Entrapped Liquor Free Liquor

Tc, vc, pc, ρsiρei

Tfl, vfl, pfl, ρfl

Lo reactive ligninHi reactive ligninCelluloseAraboxylanGalactoglucoman

Active EAPassive EAActive HSPassive HSDissolved LigninDissolved Carb-ohydrate

Reaction Site

Mass Transfer

Δz

ε

η

Tc, vc, pc, ρsi ρeiTfl, vfl, pfl, ρfl

Fundamental continuous digester model – Doyle et al.

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• Digester is divided up into a series of CSTRs that chips and liquor flow into and out of.» 60 to >100 in a digester

• Model assumes no radial gradients.

• Digester is divided up into a series of CSTRs that chips and liquor flow into and out of.» 60 to >100 in a digester

• Model assumes no radial gradients.

Fundamental continuous digester model – Doyle et al.

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• Use Harkonen model to calculate chip pressure and compaction as a function of kappa number.

• Use Harkonen model to calculate the pressure drop in the chip bed.

• Mass balance - w/ kinetics• Heat Balance - w/ kinetics• Momentum balance

• Use Harkonen model to calculate chip pressure and compaction as a function of kappa number.

• Use Harkonen model to calculate the pressure drop in the chip bed.

• Mass balance - w/ kinetics• Heat Balance - w/ kinetics• Momentum balance

Dynamic model of continuous digester to predict

Fundamental continuous digester model – Doyle et al.

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Model is complex with many variables

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• Kappa, [OH-], [HS-], dissolved solids, chip density (function of extent of cooking), void fraction of bed, chip velocities, liquor velocities, temperature profiles, chips & liquor, chip porosity

• Model has been used to examine different control strategies and the effect of grade changes.

• Kappa, [OH-], [HS-], dissolved solids, chip density (function of extent of cooking), void fraction of bed, chip velocities, liquor velocities, temperature profiles, chips & liquor, chip porosity

• Model has been used to examine different control strategies and the effect of grade changes.

Fundamental continuous digester model – Doyle et al.Model predictions

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Model predictions

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Fundamental continuous digester model – Doyle et al.Model results

Comparison of predicted and measured blow line kappa number SW-HW (top) and HW-SW (bottom) transitions where solid line is nonlinear model prediction.

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Fundamental continuous digester model – Doyle et al.

• Model has been used to examine different control strategies and the effect of grade changes.

• Model has been used to examine different control strategies and the effect of grade changes.

Model applications