Theoretical Model of the

Kraft Pulping Process

Quak Foo Lee

Department of Chemical and Biological Engineering

The University of British Columbia

2

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

3

Degree of Delignification

Heating rate and time Maximum temperature Cooking time at that temperature Pulping outcome

(kappa number, pulp yield, and product quality)

4

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.

5

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

6

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.

7

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.

8

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.

9

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

18

Bulk Delignification: (2.2% < Lignin < 22.5%)

dt

dLk

dt

dC

LHSOHekLOHekdt

dL

bc

Tb

Tb

4.05.0/144004.292

/172005.351 ][][][

polyethylene

19

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

33

221

7

33

221

3

101347.6

4273.2

ln

XbXbXbB

XaXaXaA

T

BA

31

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).