Transcript Kraft Pulping Kinetics

Theoretical Model
of the
Kraft Pulping Process
Quak Foo Lee
Department of Chemical and Biological Engineering
The University of British Columbia
The Kraft Pulping Recipe



Uniformity of ingredients
Sufficient steaming of chips for complete air removal
Good access of liquor to all chip surfaces
WOOD
LIQUOR
HEAT
2
Degree of Delignification




Heating rate and time
Maximum temperature
Cooking time at that temperature
Pulping outcome
(kappa number, pulp yield, and product
quality)
3
Chemical Kinetics

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The reaction mechanisms form a very
complex entity in Kraft pulping.
The dissolution rates of lignin, carbohydrates
and other components vary greatly.
The diffusion of active components in the
cooking liquor (mainly OH- and HS-) through
wood cells is complicated.
The reaction occurs in an essentially
heterogeneous solid-liquid phase system
coupled with mass and heat transfer.
4
Assumptions
1.
2.
3.
4.
5.
6.
The liquor penetration rate is infinite
The chips are isothermal
The pulp chips are one-dimensional
The bulk phase is homogeneous and well
stirred
Wood is divided into lignin, carbohydrate,
and acetyl
Pulping reactions are irreversible
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Assumption 1

The liquor penetration rate is infinite


The liquor penetration is complete about the
temperature reaches 1400C during a typical kraft
cook (Hartler, 1962).
At this low temperature the delignification
reactions are still low.
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Assumption 2

The chip are isothermal


The characteristic time for heat transfer is much
less than other characteristic times of the pulping
process.
The heats of reaction of pulping reactions are
essentially zero.
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Assumption 3

The pulp chips are one-dimensional


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Chip thickness is the critical dimension.
Pulp chips have a length to thickness ratio of
about five to one.
In alkaline pulping the diffusivities in the three
primary directions are not significantly different
(Rydholm, 1965; Stone, 1957; Harter, 1962).
Therefore, chip thickness is the critical dimension.
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Assumption 4

The bulk phase is homogeneous and well
stirred


The digester is modeled as a CSTR in which the
mass transfer coefficient from the bulk phase to
the chip phase is assumed to be infinite.
These are good assumptions for modeling a
laboratory scale digester and will be relaxed when
modeling the industrial scale digester.
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Assumption 5

Wood is divided into lignin, carbohydrate, and
acetyl

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Combining the carbohydrates into one category is justified
because in softwoods the relative degradation rates of different
carbohydrates are not significantly altered by normal changes in
pulping conditions (Aurell and Hartler, 1965; Yllner et a., 1957).
The acetyl groups are considered as a separate component
(galactoglucomannans) because they consume a small, but
significant, amount of alkali in a well-characterized fashion.
The other major wood component, the extractives is assumed to
be dissolved out of the wood before pulping begins (Olm and
Tistad, 1979).
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Assumption 6

Pulping reactions are irreversible


Condensation reactions occur when the cooking
liquor lignin concentration is high and the alkali
concentration is low (Harter, 1978).
The condensation reactions occur at the end of a
cook and at the center of thick chips.
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Kraft Pulping Process
Bulk Phase
HSOH-
Chip Phase
HS-
Degradation
products
convection
convection
diffusion
diffusion
OH-
Degradation
products
Wood Components
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Kinetic Models

Single variable model: H-factor (Vroom 1957)

Three phase model (Gustafson et al. 1983)

“Two lignin” model (Gustafson et al. 1983)
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Single Variable Model: H-factor

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H-factor: combines temperature and time into
a single variable representing the extent of the
cooking (Vroom 1957).
The delignification is assumed to be one
single reaction.
t
H 
0
kT (t )
k373
t
dt   e
Rate of delignification

16113 
 43.181

T
(
t
)


dt
0
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Pulp Yield

Hatton’s (1973) model which predicts the kappa number
and yield for a variety of wood species:
Y  A  Blog H EA
n

Where Y = the total pulp yield (%)
H = H factor
EA = the applied effective alkali charge
(weight % as Na2O on wood)
A, B, n = constants which are species dependent
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Three Phase Model: Gustafson’s Model

Initial delignification: (Lignin > 22.5%)

Bulk delignification: (2.2% < Lignin < 22.5%)

Residual delignification: (Lignin < 2.2%)
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Initial Delignification:
(Lignin > 22.5%)
dL
17.58760 / T 

 kil e
L
dt polyethylene
dC
0.11 dL

 kic [OH ]
dt
dt
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Bulk Delignification:
(2.2% < Lignin < 22.5%)
dL

 kb1e 35.517200 / T [OH  ]L  kb 2 e 29.414400 / T [OH  ]0.5 [ HS  ]0.4 L
dt
polyethylene
dC
dL

 kbc
dt
dt
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Residual Delignification:
(Lignin < 2.2%)
dL

 k rl e 19.64 10804 / T [OH  ]0.7 L
dt
polyethylene
dC
dL

 k rc
dt
dt
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L = the lignin content
C = the carbohydrates content
[OH-] = the hydroxyl ion concentration
[SH-] =the hydrosulfide ion concentration
k = species related constants
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Example of Cooking
Conditions
Effective alkali conc.
Sulfidity
Heating time
Cooking time
Liquor-to-wood ratio
Cooking temperature
Lignin content
Carbohydrate content
Acetyl content
Species
25% on wood as NaOH
25%
120 min
240 min
4 L/kg
170 0C
27.3% on wood
67.7% on wood
1.3% on wood
Pinus silvestris
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Constant Fitted to Pulping
Reactions
Delignification
Reactions
Carbohydrate
Dissolution
Phase
Constant
Value
Initial
kil
1.0
kb1
0.15
kb2
1.65
Residual
krl
2.2
Initial
kic
2.53
Bulk
kbc
0.47
Residual
krc
2.19
Bulk
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Two Lignin Model

Lignin is divided into high and low reactivity
lignin, also called fast and slow lignin (Smith
and Williams 1975; Saltin 1992).
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Diffusivity
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Development of the continuous digester has been
focused o high production capacity and improved
pulp quality.
The largest continuous digester currently in
operation has a capacity of over 2000 tons/day.
The dimension of the digester increases with its
capacity.
With large dimensions, solid pressure/stress in the
chip mass tends to be high, making the chip mass
more compacted, and efficient diffusion becomes a
key issue in practice.
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Diffusion
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The diffusivities of the carbohydrate and the
lignin are zero since these species are bound in
the wood.
The diffusivity of the sulfide is unimportant
because the sulfide concentration is held
constant.
The reaction products of delignification and
carbohydrate peeling diffuse out. (But, we are
not concerned with the rate because the pulping
reactions are assumed to be irreversible.)
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Diffusivity of Alkali

Mckibbins (1960): measured the diffusivity of sodium in kraft
cooked chips.
D  3.4 102 T 1/ 2e 4870 / RT 

Gustafson (1983): corrected diffusivity with respect to pH and
lignin content.
D  5.7 102 T 1/ 2e4870 / RT [0.02L  0.13[OH ]0.55  0.58]
where D = diffusivity, cm2/min
R = gas constant (cal/mol· K)
T = temperature (K)
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Liquor Density
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Liquor density: depends on the solid concentration
and temperature.
Approximation for the density up to 50% dry solids
(Gullichsen 1999):
 25  997 649X

 1.008 0.237T / 1000 1.94(T / 1000) 2
 25
where ρ = density of black liquor (kg/m3)
T = temperature (0C)
X = dry solids concentration (kg dry solids/ kg)
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Effect of Solid Concentration and
temperature on Liquor Density
Y-axis:
X-axis:
ρ = density of black liquor (kg/m3)
X = dry solids concentration (kg dry solids/ kg)
T = temperature (0C)
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Viscosity

The viscosity of black liquor (mixture of white
liquor and dissolved solid material) depends
on several factors, particularly the
temperature and solids content.
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Viscosity

An estimate of the kinematic viscosity (Gullichsen
1999):
B
ln  A  3
T
A  2.4273 a1 X  a2 X 2  a3 X 3
B  6.1347107  b1 X  b2 X 2  b3 X 3

where ν = kinematic viscosity (mm2/s)
T =temperature (K)
ai, bi = constants
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20% Dry Solids Content
Liquor Kinematic Viscosity (mm2/s) vs. Temperature (K)
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References

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Vroom, K. E. The H factor: A means of expressing cooking times
and temperatures as a single variable, Pulp and Paper Mag.
Can. 58(3):228-231(1957).
Gustafson, R., Sleicher, C., Mckean, W., Theoretical Model of the
Kraft Pulping Process, Ind. Eng. Chem. Process Design &
Development, 22(1):87-96 (1983).
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