Source Model

Specification

Kappa

Fraction

Model parameters A

[kappa(1-q)

min–1]

EA

[kJ mol–1]

M n q

Iribarne &

Schroeder [12]

Initial 0.57 1.2 1.3 1 6.00·1011 67.0

Final 0.43 0.3 0.2 16.00·1 04 40.0

one-stage 0.7 0.7 2 3.00·106 51.0

Agarwal et. al [19] kappa 15.9 1.2 0.23 6.9 4.42·107 98.9

kappa 21.2 1.2 0.23 6.5 4.42·107 98.9

kappa 31.5 0.96 0.23 5.7 4.42·107 98.9

Nguyen &

Liang [17]

Phase

transformation

0.85 0.22 9.99·108 79.7

It should be noted that both the power-law model with the high order q and the

phase transformation model suggested by Nguyen and Liang indicate slightly too

low kappa numbers within the first 20 min reaction time. The opposite is true for

the two-stage and the power-law models, with low apparent order q, as shown in

Figs. 7.30 and 7.31. Their quality of prediction improves gradually with prolonged

reaction time if the results from oxygen delignification of the softwood pulp are

considered.

682 7Pulp Bleaching

0 20 40 60 80 100

Valchev et al. (1999) experimental data

Iribarne&Schroeder (1997): two-stage Iribarne&Schroeder (1997); one-stage

Agarwal et al. (1999) Nguyen&Liang (2002)

Kappa number

Time [min]

Fig. 7.30 Comparison of model predictions against experimental

data from oxygen delignification of beech wood

(adapted from Valchev et al. [5]).

0 20 40 60

Zou et al. experimental data

Iribarne&Schroeder (1997): two-stage Iribarne&Schroeder (1997): one-stage

Agarwal et al. (1999) Nguyen&Liang (2002)

Kappa number

Time [min]

Fig. 7.31 Comparison of model predictions against experimental

data from oxygen delignification of softwood (adapted

from Zou et al. [14]).

7.3 Oxygen Delignification 683

The development of the kappa number during oxygen delignification of a Scots

pine kraft pulp, kappa number 31.5, can be predicted sufficiently well using the

model of Agarwal et al., provided that the apparent order q is adjusted to the higher

initial kappa number (see Tab. 7.17 and Fig. 7.32). In this particular case, the

dependence on the hydroxide ion concentration has been recalculated using the

experimental results from Jarrehult and Samuelson determined at hydroxide ion

concentrations of 0.01, 0.1 and 0.5 mol L–1, respectively, while keeping all other

parameters, A, E A, and n constant [20,21]. The calculations revealed a slightly

lower exponent m (0.96 instead of 1.2) as compared to the calculations based on

the experimental data from Agarwal et al. (Tab. 7.17).

0 50 100 150 200 250

Jarrehult&Samuelson: experimental data

Agarwal et al. (1999) Nguyen&Liang (2002)

Kappa number

Time [min]

Fig. 7.32 Comparison of model predictions against experimental

data from oxygen delignification of softwood adapted

from Jarrehult and Samuelson [21]; reaction conditions:

[OH– ] = 0.1 mol L–1, [O2] = 0.00489 mol L–1; 97 °C, 0.2% consistency.

The phase transformation model using the set of model parameters determined

for a eucalypt pulp, kappa number 11.6, is however not capable of predicting the

course of kappa number degradation during oxygen delignification of a softwood

kappa-31.5, as expected (Fig. 7.32). Softwood kraft pulps and pulps with higher

initial kappa numbers are more susceptible to oxygen delignification at given conditions.

Consequently, the validity of a kinetic model is more or less limited to a

specific pulp type and grade. The simple model proposed by Agarwal et al. [19]

seems to be well-suited to predict the course of oxygen delignification of different

kinds of kraft pulps. The key contribution of this model is the utilization of a variable

apparent order q which depends on the initial kappa numbers and the frac-

684 7Pulp Bleaching

tion of easily eliminated lignin, while keeping parameters of the rate equation, A,

E A, m and n constant. The use of distribution function for the rate constants derived

for different initial kappa numbers further improves the quality of prediction.

It can be concluded that so far no kinetic model exists where the susceptibility

towards oxygen delignification is fully described. Thus, efforts must be undertaken

to develop a model which is able to describe the reactivity of the relevant pulp

components.

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