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