Energy (EA)

m n q [kJ mol–1]

Olm & Teder [1]

Fast

Slow

Softwood

Softwood

29.5

29.5

n.s.

n.s.

0.1

0.3

0.1

0.2

Hsu & Hsie [9,10]

Fast

Slow

Southern Pine

Southern Pine

29.5

29.5

n.s.

n.s.

0.78

0.7

0.35

0.74

3.07

3.07

Myers & Edwards [2]

Fast

Slow

Softwood, Hardwood

Softwood, Hardwood

11–128

12–128

0.225

0.675

0.875

0.43

0.43

Iribarne & Schroeder [12]

Fast

Slow

Pinus taeda

Pinus taeda

20.5–58

20.3–59

0.57

0.43

1.2

0,3

1.3

0,2

a. On concentrations or pressure as given in the reference

n.s. = not separated.

based on Myers and Edward’s two-stage pseudo first-order model, that fit the

experimental results reasonably well.

A two-stage kinetic model enables a better description of the initial, rapid

delignification reaction as compared to a single-stage model. Furthermore, prediction

of the outlet kappa number is more reliable in case of varying initial kappa

numbers, since the rate equations are mainly first order on lignin (an exception

was the model proposed by Hsu and Hsie [10]). Both models, however, can be

considered as pure empirical models.

More recently, it was shown that the kappa number degradation during oxygen

delignification can be fitted to a power-law rate equation of apparent order q with

sufficient precision using the single-stage approach [3,14]:

_

d _

dt _ k _ _ q _25_

with j, the kappa number and k, the rate constant of oxygen delignification

according to Eq. (26):

7.3 Oxygen Delignification 673

k _ A _ Exp _

EA

RT ___ OH _ m __ O 2 n _26_

where A is the pre-exponential factor, E A is the activation energy (in kJ mol–1),

[OH– ] is the molar hydroxide ion concentration, and [O2] is the dissolved molar

oxygen concentration. Integration of Eq. (25) and implying constant conditions of

dissolved oxygen and hydroxide ion concentrations leads to the following expression

for the calculation of the kappa number as a function of time:

_ _ _ _1_ q _ _0 __ q _ 1__ k _ t _

1_ q _27_

where j0 is the initial unbleached kappa number. The parameters of the apparent

kinetic expression, A, E A, m, and n can be calculated by a using nonlinear leastsquares

technique.

It is well known that the application of a power-law representation of the rate

equation yields a high reaction order q on lignin [2,3]. Using a single rate equation,

the course of slow lignin degradation during the final stage of oxygen

delignification can be described mathematically by a high order on lignin. The

slower the final delignification rate, the higher the order on lignin. According to

Axegard et al., refractory lignin structures and mass transfer limitations could

account for the slow rate in the residual phase of oxygen delignification [15]. In

analogy to the kinetic description of polymer degradation in petrochemical processing,

Schoon suggested that a power-law applies when the oxygen delignification

reactions are performed by an infinite number of parallel first-order reactions

[16]. Schoon further derived a frequency function f (k) which provides a correlation

between the observed order q and the distribution of the rate constants. The derived

expression for the function f (k) is given in Eq. (28):

f _ k __

p

q _1 k

2_ q

q _1

C 1

_ q _1_

Exp __ p _ k _ _28_

where C[1/(q – 1)] represents the gamma function evaluated at 1/(q – 1).

The value of the parameter p is a function of the apparent rate order q, the reaction

rate coefficient k and the initial kappa number, j0, and can be determined

according to the following expression:

p _ _ q _ 1__ k _ _ q _1

_ 0 _1

_29_

The frequency function f (k) of the rate constant distribution as determined by

Eqs. (28) and (29) is defined as the fraction of the rate constants having values

between k and k + d k.

The distribution function F (a,b) is expressed as the fraction of the rate constants

with the limits of integration between k = a and k = b, according to Eq. (30):

674 7Pulp Bleaching

F _ a _ b ___

b

a

f _ k _ dk _30_

Oxygen delignification can be understood as a sum of an infinite number of

parallel first-order reactions where the rate constants can be displayed as a distribution

function. High rate constants indicate the presence of easily removable lignin.

The concept of Schoon’s distribution function is exemplified by two hardwood

kraft pulps of different initial kappa numbers, one with a low kappa number of

13.2 (pulp A) and the other with a high kappa number of 47.9 (pulp B).

The kinetic parameters necessary to calculate the frequency distribution functions

are included in Tab. 7.14. It is assumed that oxygen delignification exhibits

the same value of the rate constant, k q, equal to 9.62. 10–9 kappa (q – 1) min–1 for

both pulps if a hydroxide ion concentration of 0.0852 mol L–1 and a dissolved oxygen

concentration of 0.0055 mol g–1 is considered (derived from an alkali charge

of 2.5% on o.d. pulp at 12% consistency and an oxygen pressure of 800 kPa at a

reaction temperature of 100 °C). The main difference between the two pulps is

expressed in the different apparent reaction order q of 7.08 for pulp A and 5.15 for

pulp B.

1E-9 1E-7 1E-5 1E-3 0.1

0.0

0.1

0.2

0.3

Kappa number = 13.2 Kappa number = 47.9

F(a,b) fraction

rate constant "k"

Fig. 7.28 Distribution function for the rate constants

for oxygen delignification at 100 °C,

0.085 mol [OH– ]; mol/l L–1, 0.0055 mol O2 L–1

for two hardwood kraft pulps, kappa number

13.2 (pulp B) and 47.9 (pulp A), respectively.

The parameter p and the frequency

functions f (k) are determined by Eqs. (29) and

(28) using rate constant, k, in the range 10–10 to

10 kappa (q – 1).min–1 in intervals of one order of

magnitude (e.g., 10–10–10–9, 10–9–10–8,...).

The integral in Eq. (30) is solved numerically.

7.3 Oxygen Delignification 675

The different apparent reaction orders and initial kappa numbers are responsible

for the change of the frequency functions f (k) in relation to the rate constants.

The change from a reaction order of 7.08 for the low-kappa number pulp A to 5.15

for the high-kappa number pulp B results in a shift of the distribution function to

higher rate constants. It can be seen from Fig. 7.28 that pulp B, with the higher

starting kappa number, has a greater fraction of easily removable lignin compounds

as compared to pulp A. This leads to the conclusion that the reactivity of

the lignin moieties is expressed in the magnitude of the apparent reaction order q.

Delignification kinetics of high-kappa number pulps predict a lower rate order as

compared to low-kappa number pulps, which means that the extent of oxygen

delignification increases with rising initial kappa numbers of hardwood kraft

pulps. When cooking is terminated at a high kappa number, the resulting pulp

contains a greater fraction of highly reactive lignin moieties as compared to a pulp

derived from prolonged cooking, provided that the other cooking conditions

remain constant.

Experimental data from the literature have been fitted to the power-law rate

equation to demonstrate the suitability of this approach. The corresponding

results are summarized in Tab. 7.14.

Apart from the results taken from Iribarne and Schroeder [12], all the laboratory

oxygen delignification data were derived from a constant initial kappa number. The

kappa number after oxygen delignification was calculated (Kappa_calc after 30 min),

assuming an initial kappa number of 25 and applying the parameters of the powerlaw

rate expression given in Tab. 7.14 to evaluate the applicability of the kinetic

model. The following typical reaction conditions were used for the calculations:

reaction time 30 min, temperature 100 °C, 0.085 mol L–1 initial hydroxide ion concentration

(alkali charge of 2.5% at 12% consistency) and 0.0055 mol L–1 dissolved

oxygen concentration (oxygen pressure 800 kPa, 100 °C, 0.085 mol OH L–1).

Table 7.14 illustrates that the calculated kappa numbers after oxygen delignification

are reliable only for those references where the kappa number of the

unbleached pulp used for the oxygen delignification trials was in the range of the

assumed kappa number 25. The parameters derived from oxygen delignification

of low (13.2) and high (47.9) initial kappa numbers yield either too low or too high

final kappa numbers. Iribarne and Schroeder demonstrated that applying the

power-law rate equation for a variety of initial kappa numbers (20.3–58), the

apparent order decreases significantly [12]. The kappa number of oxygen delignified

pulps can be predicted for a broad range of initial kappa numbers. However,

the precision is lower as compared to the results when applying the parameters

obtained from the given initial kappa number. Using the power-law rate equation,

a better approach would be to adjust the apparent order q, as demonstrated by

Agarwal et al. [3]. Since the rate (k) constant is independent of the initial

unbleached kappa number, it can also be applied to evaluate the apparent rate

order q which best fit the experimental data with different initial kappa numbers.

As seen from Tab. 7.14, the values determined for q decrease with increasing

unbleached kappa number. The experimental and calculated kappa numbers

throughout oxygen delignification are shown in Fig. 7.29.

676 7Pulp Bleaching

7.3 Oxygen Delignification 677

Tab. 7.14 Parameters of the power-law rate equation

for oxygen delignification according to Eqs. (25), (26)

and (27). Recalculated from Refs. [3,10,12].

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