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Empirical Kraft Pulping Models
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Transcript of Empirical Kraft Pulping Models
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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 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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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
• 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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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
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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 ModelsGustafson 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 ModelsGustafson 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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Delignification Kinetics ModelsGustafson model
Another model was formulated that was of the type
dL/dt = K(L-Lf)
Where Lf = floor lignin level – set @ 0.5% on wood
• Did not result in any better prediction of pulping behavior
Another model was formulated that was of the type
dL/dt = K(L-Lf)
Where Lf = floor lignin level – set @ 0.5% on wood
• Did not result in any better prediction of pulping behavior
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Delignification Kinetics ModelsPurdue Model
2 types of lignin:
• High reactivity
• Low reactivity
2 types of lignin:
• High reactivity
• Low reactivity
))(][][(/ 2/12
2/11 fLLHSkOHkdtdL
High reactivity E ≈ 7000 cal/mole
Low reactivityEk1 ≈ 8300 cal/mole
Ek2 ≈ 28,000 cal/mole
Lf assumed to be zero
Assumed to react simultaneously
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Delignification Kinetics ModelsPurdue Model
Potential difficulties• High reactivity lignin (initial lignin) dependent on
[OH-] and [HS-]• No residual lignin kinetics
Potential difficulties• High reactivity lignin (initial lignin) dependent on
[OH-] and [HS-]• No residual lignin kinetics
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Delignification Kinetics ModelsAndersson, 2003
• 3 types of lignin:» Fast
» Medium
» slow
• 3 types of lignin:» Fast
» Medium
» slow
Assumed to react simultaneously, like Purdue model
10-1
10
10
0
1
0 50 100 150 200 250 300
L1 lignin L2 lignin
L3 lignin
total lignin
Lig
nin
[%o
w]
time [min]
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Delignification Kinetics ModelsAndersson, 2003
Fast ≈ 9% on wood (all t)
dL/dt = k1+[HS-]0.06LE ≈ 12,000 cal/mole
Medium ≈ 15% on wood (t=0)
dL/dt = k2[OH-]0.48[HS-]0.39LE ≈ 31,000 cal/mole
Slow ≈ 1.5% on wood (t=0)
dL/dt = k3[OH-]0.2LE ≈ 31,000 cal/mole
Fast ≈ 9% on wood (all t)
dL/dt = k1+[HS-]0.06LE ≈ 12,000 cal/mole
Medium ≈ 15% on wood (t=0)
dL/dt = k2[OH-]0.48[HS-]0.39LE ≈ 31,000 cal/mole
Slow ≈ 1.5% on wood (t=0)
dL/dt = k3[OH-]0.2LE ≈ 31,000 cal/mole
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Delignification Kinetics ModelsAndersson, 2003
Model also assumes that medium can become slow lignin depending on the pulping conditions
L*≡ Lignin content where amount of medium lignin equals the amount of slow lignin
Complex formula to estimate L*:
))15.273(10*97.283.1(*
)01.0]([)01.0]([49.025
19.065.0*
T
HSOHL
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Delignification Kinetics ModelsAndersson, 2003
35030025020015010050010-1
100
101
Lig
nin
[%
ow
]
time [min]
Total lignin
L2,L3
L*
Increasing [OH-]
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Model PerformanceGustafson model
Pulping data for thin chips – Gullichsen’s data
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Model PerformanceGustafson model
Pulping data for mill chips - Gullichsen’s data
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Model PerformanceGustafson model
Virkola data on mill chips
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Model Performance (Andersson)Purdue Model
Purdue model suffers from lack of residual delignification
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Model Performance (Andersson)Purdue Model
Purdue model suffers from lack of residual delignification
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Model Performance (Andersson)Gustafson Model
Model works well until very low lignin content
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Model Performance (Andersson)Gustafson Model
Model handles one transition well and the other poorly
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Model Performance (Andersson)Andersson Model
Andersson predicts his own data well
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Model Performance (Andersson)Andersson Model
Model handles transition well