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Delignification Kinetics Models
H Factor Model
• Provides mills with the ability to handle common
disturbance such as inconsistent digester heating
and cooking time variation.
1
170
900
700
130
500
300
H factor equal
to area under this
curve
90
100
Temperature °C
Relative Reaction Rate
Delignification Kinetics Models
H Factor/Temperature
1
2
Hours from Start
2
Delignification Kinetics Models
H Factor Model
t
H  k0  e
0
32, 000/ RT ( t )
dt
Relative reaction
rate
k0 is such that H(1 hr, 373°K) = 1
3
Delignification Kinetics Models
H Factor Model
• Uses only bulk delignification kinetics
dL / dt  ke32,000 / RT
k = Function of [HS-] and [OH-]
R=
1.987
cal
mole * K
T [=] °K
4
Kraft Pulping Kinetics
H Factor/Temperature
Lignin (% of Pulp)
30
25
150°C
160°C
170°C
20
15
10
5
0
0
500
1000
1500
2000
2500
H Factor
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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 or
Yield
15% EA
18% EA
20% EA
H-factor
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Emperical Kraft Pulping Models
Hatton Equation
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.


n
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
Species
kappa range
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 Models
Kerr model ~ 1970
dL / dt  k * e
32, 000 / RT

[OH ] * L
• H factor to handle temperature
• 1st order in [OH-]
• Bulk delignification kinetics w/out [HS-]
dependence
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Delignification Kinetics Models
Kerr model ~ 1970
Integrated form:

Lf
Li
t
dL
 K e
0
L * f ( L)
32, 000
RT ( t )
H-Factor
Functional
relationship between L
and [OH-]
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Delignification Kinetics Models
Kerr model ~ 1970
Slopes of lines are
not a function of
EA charge
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Delignification Kinetics Models
Kerr model ~ 1970
Model can handle effect of main disturbances on pulping kinetics
• 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
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Delignification Kinetics Models
UW 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.
For softwood: Initial to bulk ~ 22.5% on wood
Bulk to residual ~ 2.2% on wood
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Delignification Kinetics Models
UW 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
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Model Performance
UW model
50
40
1.5 mm chips
Screened 30
Kappa 20
10
0
15
20
25
30
% Active Alkali on wood
Pulping data for thin chips – Gullichsen’s data
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Model Performance
UW model
60
50
Mill chips
40
Total
30
Kappa
20
10
0
15
20
25
30
% Alkali charge
Pulping data for mill chips - Gullichsen’s data
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Model Performance
UW model
80
60
Predicted
40
Kappa
20
0
0
20
40
60
80
Measured Kappa
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 Problem
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UW Model
• Two methods have been tested, but since both
have the same accuracy, the simplest has been
retained.
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UW: Model I
Basic Structure: dc/dt=k*dL/dt
Initial k=2.5*[OH-]0.1
Bulk k=0.47
Residual k=2.19
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.
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Model Performance
UW 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
dDPn
E /RT
2
  k0 [OH ] e
DPn
dt
[ ]cell  KDPna
[ ]pulp  C[ ]cell  ( 1  C )[ ]non cell
[ ] - Intrinsic viscosity
C - Cellulose fraction in pulp
DPn - Degree of polymerization for cellulose
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Gullichsen’s viscosity data
1300
1200
1.5 mm chips
1100
Intrinsic 1000
Viscosity
dm3/kg 900
800
700
600
12
16
20
24
28
% A.A. on wood
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Virkola’s viscosity data
1200
1100
1000
Predicted
900
Viscosity
800
700
600
600
800
1000
1200
Measured Viscosity, dm3/kg
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Virkola’s viscosity data
1200
22% E.A.
1100
Intrinsic 1000
Viscosity 900
dm3/kg 800
19% E.A.
25% E.A.
700
600
0
1000
2000
3000
4000
H-factor
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[OH-] & [HS-] Predictions
• Calculated by stoichiometry in all models as follows:
d [OH  ]
 f (dL / dt, dC / dt)
dt
d [ HS  ]
0
dt
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Model Performance
UW model
0.8
0.6
Residual
0.4
[OH]
0.2
0
12
14
16
18
20
22
24
26
28
30
Initial Active Alkali on wood
Gullichsen data on mill chips
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