Model Parameters

According to Andersson, the model parameters originate from nonlinear regression

analysis of the experimental data from Lindgren and Lindstrom [33], the

investigations of Lindgren [47], and the course of the hemicelluloses components

from Matthew [83]. The initial proportions of species 2 and 3 are obtained by

means of the distribution model. The influence of [OH– ]and [HS– ]was derived

from the studies by Kondo and Sarkanen [80]and Olm and Tistad [35]for species

1, from Lindgren and Lindstrom [33]for lignin species 2 and 3, and from Lindgren

[47]for carbohydrates species 2 and 3. The model parameters listed in

Tab. 4.23 were obtained by re-fitting the experimental data using the distribution

model [7]. Since Olm and Tistad found that the proportion of lignin and carbohydrate

reactions is independent on temperature for species 1, it can be assumed

that the activation energy must be similar for both reactions (Ea = 50 kJ mol–1)

4.2 Kraft Pulping Processes 221

[35]. This low value indicates that the degradation of this species is diffusion-controlled,

and this has been considered in the model. The pre-exponential factors, A,

listed in Tab. 4.23 were derived from constant composition cooks using very high

L/W ratios (41:1). These values were adjusted by a correction factor, fc, to simulate

the conditions of industrial cooks with L/W ratios of between 3 and 5. In practical

cooks, the increasing concentration of dissolved organic substances accelerates

the reaction rates of species 2 and simultaneously retards the reaction rates of species

3; this is compared to constant composition cooks, which can be adjusted by

choosing the appropriate correction factors, less than or equal to 1 (Tab. 4.23)

[34,59]. The regression analysis revealed a rather large correction factor 6 to simulate

the course of carbohydrate species 1, CH1, but this was most likely due to the

limited experimental data points available.

The reaction rates kLj and kCHij can thus be calculated according to Eq. (125):

kLj _ kCHi _ j _ Ac _ fc _ Exp

EA

R _

443_15 _

_ _ T __ _125_

The model parameters used in the distribution model are summarized in Tab. 4.23

[7].

Tab. 4.23 Model parameters used in Eqs. (102), (109) [7].