Kinetics of Delignification

In the literature, three categories of mathematical models have been introduced to

describe the kinetics of oxygen delignification:

_ Two-stage model comprising two parallel rate equations.

_ One-stage model or power-law rate equation.

_ Nuclei growth concept according to Avrami-Erofeev [4]. Topochemical

delignification model according to the modified equation

of Prout-Thomson [5].

The first category of models considers the rapid initial rate and a considerable

slow-down as the reactions proceed. Mathematically, this can be described as a

two-phase model expressed by two-parallel equations, each first order on lignin.

According to Macleod and Li, the rapid-reacting lignin can be assigned to a dissolved

kraft lignin which is trapped in the fiber wall due to a drop in the pH during

conventional brownstock washing [6]. The kraft lignin is leached to the liquid

phase as soon as the conditions of high pH and high temperature are re-established

during a subsequent oxygen delignification.

The apparent kinetic expression of the two-stage model is displayed in Eq. (24):

_

d _ f

dt _ kf __ OH _ mf __ O 2 nf __ qf

f

_

d _ s

dt _ ks __ OH _ ms __ O 2 ns __ qs

s

_24_

where q f and q s = 1, and m and n are the exponents for dependencies of hydroxide

and dissolved oxygen concentrations, respectively. According to the basic assumptions

of this model, the kappa number, j, consists of two differently reacting lignin

fractions, k f the fast- and k s the slow-reacting lignin expressed as kappa numbers,

respectively. Some authors have also suggested the presence of a nonreacting

lignin fraction (floor kappa number level) denoted as refractory kappa number,

jb, originally proposed for a kinetic delignification model for chlorination

[2,7,8]. Myers and Edwards [2] proposed that 10% of the incoming kappa number

(unbleached) can be attributed to the refractory kappa number, regardless of the

chemical and physical nature of the residual lignin. This assumption is derived

simply from the results of fitting the model using a nonlinear least-square technique,

and is not really based on a measurable chemical reactivity of a certain residual

lignin fraction. Similar conclusions can also be drawn for the “fast” and

“slowly” eliminated lignin fraction. Their fractions vary in a rather broad range, as

can be seen in Tab. 7.13.

Vincent et al. reported that the rate equations for oxygen delignification established

by Myers and Edwards are inadequate for predicting results for eucalypt

pulp [13]. These authors concluded that, under more extreme conditions, the residual

lignin present in the eucalypt pulp is more resistant as compared to that in

a softwood pulp (which was the dominating pulp source in the Myers and

Edwards study [2]). Thus, Vincent et al. determined alternative rate equations,

672 7Pulp Bleaching

Tab. 7.13 Coefficients of the apparent kinetic expressions for

alkaline oxygen delignification according to a two-stage model.

Overview of literature data [1,2,9–12].

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