K q exp calc q k exp calc

12 3051 16.3 2.20 10–9 7.17 10.4 9.6 7.44 1.10 10–9 10.4 9.7

15 1100 16.2 2.20 10–9 7.32 9.4 9.1 7.44 1.63 10–9 9.4 9.1

18 654 15.5 2.20 10–9 7.55 8.5 8.4 7.44 2.83 10–9 8.5 8.4

21 409 15.0 2.20 10–9 7.73 8.3 7.9 7.44 4.40 10–9 8.3 7.8

indicated by an increase in the rate constant, k. It may be speculated that the activation

energy for oxygen delignification is shifted to higher values when the proportion

of refractory lignin structures increases. It can be concluded that the

power-law rate equations can be successfully applied for the description of oxygen

delignification when appropriate assumptions are made [16]. This concept is characterized

by an apparent high rate order with respect to the kappa number which

can be explained in terms of a large number of parallel first-order reactions taking

place simultaneously. Easily degradable lignin structures contribute to a high rate

constant, while refractory lignin fragments account for low rate constants. The

lower rate constants are possibly due to higher activation energies.

A third category of kinetic models is based on Avrami-Erofeev’s concept of

Nuclei Growth in phase transformation processes [5,17]. The topochemical equation

of Avrami-Erofeev is predominantly used to characterize kinetics of phasetransformation

processes such as crystallization, smelting, sublimation, etc. [4].

These processes are characterized by an instantaneous formation of nuclei, followed

by growth of a new phase. The model assumes that the delignification rate

depends on the number of reactive sites formed at the beginning of the process

and the growth rate of the transformed lignin from these reactive sites. The

applicability of the topochemical equation of Avrami-Erofeev on the kinetics of

oxygen delignification was successfully verified, provided that the following

assumptions are adopted:

7.3 Oxygen Delignification 679

_ Oxygen delignification is nucleated by reactions between oxygen

and reactive lignin structures, for example, ionized phenolic hydroxyl

groups on the outside surface of the lignin phase.

_ Delignification proceeds as a topochemical reaction in such a way

that the zones of “transformed” (reacted) lignin propagate according

to a power-law with respect to time. The size, R, of the reacted

lignin zone at time t is assumed to be dependent on the diffusion

coefficient, D, and time t according to the following expression:

R _ b __ D _ t _ n _31_

where b is a constant considering the effects of temperature and lignin physical

structure on the growth, and n is an exponent which depends on the nature of

the chemical transportation in the transformed zones. If the growth of the

reacted zone follows Fick’s law of diffusion, n would be equal to 0.5 in case of a

one-dimensional system. D represents the diffusion coefficient. However, it has

been shown that Fick’s law is not applicable in a system where the chemical

concentration is dynamically affected by the reaction [18]. The value of n is

expected to be less than 1because the velocity of oxygen delignification slows

down as time proceeds.

_ The growth of a reacted zone will be interrupted by the growth of

adjacent transformed zones due to spatial limitation within the

lignin structure. Avrami proposed that the actual change of the

reacted amount of lignin, dLRA, can be calculated as the product

of the residual lignin fraction, xL, and the potential amount of

degradable lignin, dLR, according to the following expression:

dLRA _ 1 _

LRA

Ltot _ dLR _32_

where L tot represents the initial amount of residual lignin.

According to Eq. (32), the actual change of transformed lignin decreases with the

gradual increase of transformed zones.

_ Kappa number is assumed to be an appropriate indicator of the

amount of unreacted lignin. Thus, the change in kappa number

with time has been defined as follows:

_

d _

dt _ n _ b _ I _ Dn _ t _ n _1__ _ _33_

where I is the initial number of reactive sites per unit volume of lignin.

Equation (33) can be characterized as first-order reaction with a time-dependent

rate constant. If the parameters n, b, I and D are assumed to remain constant

680 7Pulp Bleaching

throughout oxygen delignification, the integral form of equation can be written

as:

_ _ _ i _ Exp _b _ I _ Dn _ tn _ _ _34_

The model parameters were determined using the results obtained from experiments

with a commercial eucalypt kraft pulp [17]. Oxygen delignification trials

were conducted to consider the effects of temperature (100–120 °C), oxygen pressure

(500–900 kPa corresponding to a dissolved oxygen concentration of 0.0046–

0.0061mol L–1) and alkali concentration (0.044–0.074 mol L–1) on the rate of

delignification. The influence of temperature on the rate of oxygen delignification

can be included in Eq. (34) if the diffusivity, D, is assumed to be dependent on the

temperature in terms of the Arrhenius equation:

_ _ _ i _ Exp _b _ I __ D 0 Exp __ E _ RT __ n

_ tn _ _ _35_

The final form of the delignification rate equation according to the concept of

phase transformation for the eucalypt kraft pulp has been given as follows [17]:

_ _ _ i _ Exp _9_99 _ 108 _ Exp _79_7 _ 103

_ _ RT __ p 0_22

oxygen __ OH _0_847_ _ t _0_32 _ __36_

Oxygen delignification is a heterogeneous, highly complex reaction comprising

a large variety of different kinds of reactions. The reactivity of the residual lignin

is predominantly determined by the wood species, the type of cooking process,

and the specific cooking conditions. Consequently, the kinetics of oxygen delignification

can only be described by empirical models. The model parameters of the

three kinetic approaches introduced are determined using results obtained from

laboratory experiments with either only one type of pulp or a very limited selection

of pulps. The two- and one-stage models of Iribarne and Schroeder [12], the powerlaw

rate equation from Agarwal et al. [19], and the topochemical reaction model derived

fromAvrami-Erofeev [17] are overlaid on the experimental data from Valchev et

al. [5] as an example for a beech kraft pulp, and the experimental data fromZou et al.

[14] and Jarrehult [20,21] as examples for a softwood kraft pulp. The relevant process

conditions of the two selected oxygen delignification trials are summarized in

Tab. 7.16, and the kinetic parameters of the selected kinetic model in Tab. 7.17.

Figures 7.30–7.32 compare the proposed models with regressed parameters given

in Tab. 7.17 and Eq. (36) to the experimental data from the researchers denoted

in Tab. 7.16. The models proposed by Agarwal et al. and Nguyen and Liang successfully

follow the data from oxygen delignification of the beech kraft pulp,

whereas the two-stage model developed by Iribarne and Schroeder for very highpressure

oxygen delignification shows increasing deviations at reaction times

longer than 50 min. Their one-stage model, however, shows a quite reasonable

prediction of the final kappa numbers for both series of oxygen delignification.

7.3 Oxygen Delignification 681

Tab. 7.16 Conditions of two series of oxygen delignification adopted from the literature.

Parameters Units Valchev et al. [5] Zou et al. [14] Jarrehult and

Samuelson [21]

Wood species beech softwood Scots pine

Pulp type kraft kraft kraft

Kappa number (t=0) 15.3 22.8 31.5

Temperature °C 100 100 97

Consistency % 10 12 0.2

[OH– ] (t=0) mol L–1 0.0556 0.0852 0.1

Pressure (t=0) kPa 608 690 700

[O2] (t=0) mol L–1 0.0043 0.0047 0.00488

Tab. 7.17 Kinetic parameters for models adopted from the

literature used for the comparative prediction of experimental data.

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