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Carbohydrate Loss Models

Modeling yield prediction – A Very Difficult Modeling ProblemModeling yield prediction – A Very Difficult Modeling Problem

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Gustafson Model

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

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

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Gustafson: Model I

Initial k=2.5*[OH-]0.1

Bulk k=0.47

Residual k=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.

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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.

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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.

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Gustafson: Model II- Initial Phase

dH/dt=k1*[OH-]1.5(H-5)

dC/dt=k2*[OH-]1.5(C-32)

High reaction orders came from data generated by Genco

E ≈ 8,300 cal/mole

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Gustafson: Model II- Bulk Phase

dH/dt=k3*[OH-] (H-5.0) E ≈ 22,000 cal/mole

dC/dt=k4*[OH-](C-32) E ≈ 36,000 cal/mole

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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.

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Purdue Model

• Carbohydrates divided into cellulose, xylans and glucomannan

• All components use the form:

» dCn/dt=(k1[OH-]+k2[OH-]1/2[HS-]1/2)(Cn-Cnf)

• Carbohydrates divided into cellulose, xylans and glucomannan

• All components use the form:

» dCn/dt=(k1[OH-]+k2[OH-]1/2[HS-]1/2)(Cn-Cnf)

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Purdue Model

• Assumed to have fast and slow reaction components much like lignin

• Assumed to have fast and slow reaction components much like lignin

Cellulose/Xylan E ≈ 9000 cal/mole

Glucomannan (fast) E ≈ 17,000 cal/mole

Glucomannan (slow) E ≈ 40,000 cal/mole

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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.

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Andersson Model

• General Kinetics:• General Kinetics:

CkOHkdt

dC a *)][( 21

In practice, all carbohydrates are lumped together into CH.

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Andersson Model

• Complex model to estimate relative amount of medium and slow carbohydrate

• Complex model to estimate relative amount of medium and slow carbohydrate

CH* ≡ Carbohydrate content where CH2 & CH3 are equal

≡ 42.3 + 3.65 ( [OH-] + 0.05 )-0.54

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Andersson Model

• Activation Energies:• Activation Energies:

Fast E ≈ 12,000 cal/mole

Medium E ≈ 35,000 cal/mole

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Model PerformanceGustafson model

Virkola data on mill chips

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Model PerformanceAndersson model

Prediction of cellulose and glucomannans

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Model PerformanceAndersson model

Prediction of xylans

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Model PerformanceAndersson model

Prediction of total carbohydrates as function of [OH-]

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Model PerformanceAndersson model

Prediction of total carbohydrates as function of temperature

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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

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Prediction of pulp viscosity

dDPdt

k OH e DP

KDP

C C

n E RTn

cell na

pulp cell non cell

02

1

[ ]

[ ]

[ ] [ ] ( )[ ]

/

[ ] - Intrinsic viscosity

C - Cellulose fraction in pulp

- Degree of polymerization for celluloseDPn

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Gullichsen’s viscosity data

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Virkola’s viscosity data

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Virkola’s viscosity data

H-factor

IntrinsicViscositydm3/ kg

600

700

800

900

1000

1100

1200

0 1000 2000 3000 4000

19% E.A.22% E.A.

25% E.A.

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[OH-] & [HS-] Predictions

• Calculated by stoichiometry in all models as follows:• Calculated by stoichiometry in all models as follows:

)/,/(][

dtdCdtdLfdt

OHd

0][

dt

HSd

)/,/(][

dtdCdtdLfdt

OHd

)/(][

dtdLfdt

HSd

Gustafson

Purdue

Andersson - Stoichiometry

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Model PerformanceGustafson model

Gullichsen data on mill chips