Post on 29-Mar-2015
Theoretical Model of the
Kraft Pulping Process
Quak Foo Lee
Department of Chemical and Biological Engineering
The University of British Columbia
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The Kraft Pulping Recipe Uniformity of ingredients Sufficient steaming of chips for complete air removal Good access of liquor to all chip surfaces
LIQUORWOOD
HEAT
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Degree of Delignification
Heating rate and time Maximum temperature Cooking time at that temperature Pulping outcome
(kappa number, pulp yield, and product quality)
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Chemical Kinetics 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.
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Assumptions
1. The liquor penetration rate is infinite
2. The chips are isothermal
3. The pulp chips are one-dimensional
4. The bulk phase is homogeneous and well stirred
5. Wood is divided into lignin, carbohydrate, and acetyl
6. 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 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 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 ProcessBulk Phase HS-
Chip Phase HS-
OH-
OH-
Wood Components
convection
diffusion
Degradationproducts
convection
diffusion
Degradationproducts
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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 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
tTt
tT dtedtk
kH
0
)(
16113181.43
0 373
)(
Rate of delignification
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Pulp Yield Hatton’s (1973) model which predicts the kappa number and
yield for a variety of wood species:
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
nEAHBAY log
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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%)
dt
dLOHk
dt
dC
Lekdt
dL
ic
Til
11.0
/87605.17
][
polyethylene
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Bulk Delignification: (2.2% < Lignin < 22.5%)
dt
dLk
dt
dC
LHSOHekLOHekdt
dL
bc
Tb
Tb
4.05.0/144004.292
/172005.351 ][][][
polyethylene
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Residual Delignification: (Lignin < 2.2%)
dt
dLk
dt
dC
LOHekdt
dL
rc
Trl
7.0/1080464.19 ][
polyethylene
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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 ConditionsEffective alkali conc. 25% on wood as NaOH
Sulfidity 25%
Heating time 120 min
Cooking time 240 min
Liquor-to-wood ratio 4 L/kg
Cooking temperature 170 0C
Lignin content 27.3% on wood
Carbohydrate content 67.7% on wood
Acetyl content 1.3% on wood
Species Pinus silvestris
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Constant Fitted to Pulping Reactions
Phase Constant Value
Delignification Reactions
Initial kil 1.0
Bulkkb1 0.15
kb2 1.65
Residual krl 2.2
Carbohydrate Dissolution
Initial kic 2.53
Bulk kbc 0.47
Residual krc 2.19
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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 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 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.
Gustafson (1983): corrected diffusivity with respect to pH and lignin content.
where D = diffusivity, cm2/min
R = gas constant (cal/mol· K)
T = temperature (K)
RTeTD /48702/12104.3
]58.0][13.002.0[107.5 55.0/48702/12 OHLeTD RT
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Liquor Density Liquor density: depends on the solid concentration
and temperature. Approximation for the density up to 50% dry solids
(Gullichsen 1999):
where ρ = density of black liquor (kg/m3) T = temperature (0C) X = dry solids concentration (kg dry solids/
kg)
2
25
25
)1000/(94.11000/237.0008.1
649997
TT
X
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Effect of Solid Concentration and temperature on Liquor Density
Y-axis: Y-axis: ρρ = density of black liquor (kg/m3) = density of black liquor (kg/m3)X-axis: X = dry solids concentration (kg dry solids/ kg) X-axis: X = dry solids concentration (kg dry solids/ kg) T = temperature (T = temperature (00C)C)
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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):
where ν = kinematic viscosity (mm2/s)
T =temperature (K)
ai, bi = constants
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221
7
33
221
3
101347.6
4273.2
ln
XbXbXbB
XaXaXaA
T
BA
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20% Dry Solids ContentLiquor Kinematic Viscosity (mm2/s) vs. Temperature (K)
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References
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).