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1
Delignification Kinetics ModelsH Factor Model
• Provides mills with the ability to handle common disturbance such as inconsistent digester heating and cooking time variation.
• Provides mills with the ability to handle common disturbance such as inconsistent digester heating and cooking time variation.
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Delignification Kinetics ModelsH Factor/Temperature
900
700
500
300
100Rel
ativ
e R
eact
ion
Rat
e
1 2Hours from Start
90
130
170
Tem
pera
ture
°C
H factor equalto area under thiscurve
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Delignification Kinetics ModelsH Factor Model
k0 is such that H(1 hr, 373°K) = 1k0 is such that H(1 hr, 373°K) = 1
t tRT dtekH0
)(/000,320
Relative reaction rate
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Delignification Kinetics ModelsH Factor Model
• Uses only bulk delignification kinetics• Uses only bulk delignification kinetics
RTkedtdL /000,32/
k = Function of [HS-] and [OH-]
K*mole
cal 1.987
R =
T [=] °K
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Kraft Pulping KineticsH Factor/Temperature
0
5
10
15
20
25
30
0 500 1000 1500 2000 2500
H Factor
Lig
nin
(%
of
Pu
lp)
150°C
160°C
170°C
0
5
10
15
20
25
30
0 500 1000 1500 2000 2500
H Factor
Lig
nin
(%
of
Pu
lp)
150°C
160°C
170°C
6
Empirical Kraft Pulping Models
• Models developed by regression of pulping study results• Excellent for digester operators to have for quick reference
on relation between kappa and operating conditions • “Hatton” models are excellent examples of these
Kappa orYield
H-factor
15% EA15% EA15% EA
18% EA
20% EA
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Emperical Kraft Pulping Models
Kappa (or yield) = -(log(H)*EAn),, and n are parameters that must be fit to the data. Values of ,, and n for kappa prediction are shown in the table below.
Hatton Equation
Species n kappa range
Hemlock 259.3 22.57 0.41 21-49
Jack Pine 279.3 30.18 0.35 22-53
Aspen 124.7 5.03 0.76 14-31
Warning: These are empirical equations and apply only over the specified kappa range. Extrapolation out of this range is dangerous!
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Delignification Kinetics ModelsKerr model ~ 1970
• H factor to handle temperature
• 1st order in [OH-]
• Bulk delignification kinetics w/out [HS-] dependence
• H factor to handle temperature
• 1st order in [OH-]
• Bulk delignification kinetics w/out [HS-] dependence
LOHekdtdL RT *][*/ /000,32
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Delignification Kinetics ModelsKerr model ~ 1970
Integrated form:Integrated form:
t tRTL
LeK
LfL
dLf
i 0
)(
000,32
)(*
H-FactorFunctional relationship between L and [OH-]
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Delignification Kinetics ModelsKerr model ~ 1970
Slopes of lines are not a function of EA charge
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Delignification Kinetics ModelsKerr model ~ 1970
• Variations in temperature profile» Steam demand
» Digester scheduling
» Reaction exotherms
• Variations in alkali concentration» White liquor variability
» Differential consumption of alkali in initial delignification- Often caused by use of older, degraded chips
• Good kinetic model for control
• Variations in temperature profile» Steam demand
» Digester scheduling
» Reaction exotherms
• Variations in alkali concentration» White liquor variability
» Differential consumption of alkali in initial delignification- Often caused by use of older, degraded chips
• Good kinetic model for control
Model can handle effect of main disturbances on pulping kinetics
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Delignification Kinetics ModelsUW model
• Divide lignin into 3 phases, each with their own kinetics» 1 lignin, 3 kinetics
• Transition from one kinetics to another at a given lignin content that is set by the user.
• Divide lignin into 3 phases, each with their own kinetics» 1 lignin, 3 kinetics
• Transition from one kinetics to another at a given lignin content that is set by the user.
For softwood: Initial to bulk ~ 22.5% on wood
Bulk to residual ~ 2.2% on wood
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Delignification Kinetics ModelsUW model
• Initial» dL/dt = k1L
» E ≈ 9,500 cal/mole
• Bulk» dL/dt = (k2[OH-] + k3[OH-]0.5[HS-]0.4)L
» E ≈ 30,000 cal/mole
• Residual» dL/dt = k4[OH-]0.7L
» E ≈ 21,000 cal/mole
• Initial» dL/dt = k1L
» E ≈ 9,500 cal/mole
• Bulk» dL/dt = (k2[OH-] + k3[OH-]0.5[HS-]0.4)L
» E ≈ 30,000 cal/mole
• Residual» dL/dt = k4[OH-]0.7L
» E ≈ 21,000 cal/mole
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Model PerformanceUW model
Pulping data for thin chips – Gullichsen’s data
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Model PerformanceUW model
Pulping data for mill chips - Gullichsen’s data
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Model PerformanceUW model
Virkola data on mill chips
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Model Performance (Andersson)UW Model
Model works well until very low lignin content
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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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UW 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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UW: 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.
21
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.
22
Model PerformanceUW model
Virkola data on mill chips
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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
29
Model PerformanceUW model
Gullichsen data on mill chips
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