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

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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.
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

k Function of HS- and OH-
R
T K
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Delignification Kinetics ModelsH Factor Model
Relative reaction rate

• k0 is such that H(1 hr, 373K) 1

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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.

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Delignification Kinetics ModelsH
Factor/Temperature
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Kraft Pulping KineticsH Factor/Temperature
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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

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Delignification Kinetics ModelsKerr model 1970

• Integrated form

H-Factor
Functional 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
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 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.

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 (k2OH- k3OH-0.5HS-0.4)L
• E 30,000 cal/mole
• Residual
• dL/dt k4OH-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 _at_ 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

Assumed to react simultaneously
Lf assumed to be zero
High reactivity E 7000 cal/mole
Low reactivity Ek1 8300 cal/mole
Low reactivity Ek2 28,000 cal/mole
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Delignification Kinetics ModelsPurdue Model

• 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

Assumed to react simultaneously, like Purdue model
1
10
total lignin
Lignin ow
0
10
L3 lignin
L1 lignin
L2 lignin
-1
10
0
50
100
150
200
250
300
time min
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Delignification Kinetics ModelsAndersson, 2003

• Fast 9 on wood (all t)
• dL/dt k1HS-0.06L
• E 12,000 cal/mole
• Medium 15 on wood (t0)
• dL/dt k2OH-0.48HS-0.39L
• E 31,000 cal/mole
• Slow 1.5 on wood (t0)
• dL/dt k3OH-0.2L
• E 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
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Delignification Kinetics ModelsAndersson, 2003
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Model PerformanceGustafson model
Pulping data for thin chips Gullichsens data
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Model PerformanceGustafson model
Pulping data for mill chips - Gullichsens 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