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
1
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!
2
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
3
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
4
Delignification Kinetics Models
H Factor Model
• Provides mills with the ability to handle common
disturbance such as inconsistent digester heating
and cooking time variation.
5
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
6
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
7
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
8
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-]
9
Delignification Kinetics Models
Kerr model ~ 1970
Slopes of lines are
not a function of
EA charge
10
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
11
Delignification Kinetics Models
Gustafson 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
12
Delignification Kinetics Models
Gustafson 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
13
Delignification Kinetics Models
Gustafson 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
14
Delignification Kinetics Models
Purdue Model
2 types of lignin:
• High reactivity
• Low reactivity
Assumed to react
simultaneously
 1/ 2
dL / dt  (k1[OH ]
 1/ 2
 k2 [ HS ] )( L  L f )
Lf assumed to be zero
High reactivity E ≈ 7000 cal/mole
Ek1 ≈ 8300 cal/mole
Low reactivity
Ek2 ≈ 28,000 cal/mole
15
Delignification Kinetics Models
Purdue Model
Potential difficulties
• High reactivity lignin (initial lignin) dependent on
[OH-] and [HS-]
• No residual lignin kinetics
16
Delignification Kinetics Models
Andersson, 2003
• 3 types of lignin:
» Fast
» Medium
» slow
Lignin [%ow]
10
Assumed to react simultaneously, like
Purdue model
1
total lignin
10
0
L3 lignin
L1 lignin
10
L2 lignin
-1
0
50
100
150
200
time [min]
250
300
17
Delignification Kinetics Models
Andersson, 2003
Fast ≈ 9% on wood (all t)
dL/dt = k1+[HS-]0.06L
E ≈ 12,000 cal/mole
Medium ≈ 15% on wood (t=0)
dL/dt = k2[OH-]0.48[HS-]0.39L
E ≈ 31,000 cal/mole
Slow ≈ 1.5% on wood (t=0)
dL/dt = k3[OH-]0.2L
E ≈ 31,000 cal/mole
18
Delignification Kinetics Models
Andersson, 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*:
L*  0.49([OH  ]  0.01) 0.65 ([ HS  ]  0.01) 0.19
* (1.83  2.97 *10 (T  273.15) )
5
2
19
Delignification Kinetics Models
Andersson, 2003
Total lignin
L2,L3
Lignin [%ow]
101
L*
Increasing [OH-]
100
10-1
0
50
100
150
time [min]
200
250
300
350
20
Model Performance
Gustafson 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
21
Model Performance
Gustafson 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
22
Model Performance
Gustafson model
80
60
Predicted
40
Kappa
20
0
0
20
40
60
80
Measured Kappa
Virkola data on mill chips
23
Model Performance (Andersson)
Purdue Model
Purdue model suffers from lack of residual delignification
24
Model Performance (Andersson)
Purdue Model
Purdue model suffers from lack of residual delignification
25
Model Performance (Andersson)
Gustafson Model
Model works well until very low lignin content
26
Model Performance (Andersson)
Gustafson Model
Model handles one transition well and the other poorly
27
Model Performance (Andersson)
Andersson Model
Andersson predicts his own data well
28
Model Performance (Andersson)
Andersson Model
Model handles transition well
29