Delignification Kinetics

The general structure of the model is derived from models introduced by Smith

[40], Christensen et al. [79] and later Chiang et al. [30], by Blixt and Gustavsson

[34], and later improvements of Andersson et al. [7]. The delignification is

described by three parallel reactions, assuming that the single lignin species react

simultaneously. A general rate equation can be expressed as:

dLj

dt _ _ kLj __ OH _ a __ HS _ b _ Lj _102A_

dLj

dt _ _ kj __ OH _ a __ HS _ b _ Lj _102B_

for j = lignin species 1, 2, and 3.

Equation (102) is based on the assumption that the delignification is of apparent

first order with respect to the lignin content in the wood [80]. Using this structure,

the model is only valid for kraft cooking conditions, with [HS]> 0. If pure

soda cooking must be considered (the sulfide concentration is reduced to 0),

Eq. (74) must be replaced by Eq. (103), as established by LeMon and Teder [27]:

dLj

dt _ _ k ′

j __ OH _ k ″

j __ HS _ b _ __ Lj _103_

The general solution of these first-order rate equations is displayed in Eq. (104):

Ltot __

j _1

Lj _0 _ Exp __ kLj _ t _ _104_

The sum of the three lignin species corresponds to the total amount of lignin. In

the special case of constant concentration cooks (high liquor-to-wood ratio), degradation

of the lignin species (L1, L2, and L3) can be approximated by straight lines

when plotted as a log/linear diagram (Fig. 4.30).

The sum of the three lignin species corresponds to the total amount of lignin.

The proportions of the lignin species (L1, L2, and L3) can be quantified by using

Eq. (104). A selection of literature data with regard to the single lignin weight fractions

is provided in Tab. 4.21.

212 4 Chemical Pulping Processes

0 20 40 60 80 100 120

0,1

L

lignin

L

lignin

L

lignin

total lignin

Lignin [% ow]

time [min]

Fig. 4.30 Degradation of the three lignin species of

prehydrolyzed Eucalyptus saligna during the course of a

subsequent kraft pulping under isothermal conditions

(T = 160 °C) and constant [OH– ]and [HS– ]concentrati ons [81].

Tab. 4.21 Lignin weight fractions, L1, L2, L3, selected from literature data.

Wood species I: s L0

% ow

L1/L0 L2/L0 L3/L0 Reference

Lobolly pine 200: 1 28.6 0.18 [36]

Western hemlock 10: 1 29.4 0.24 [80]

Western hemlock 75: 1 28.5 0.16 0.78 0.06 [93]

Douglas fir 50: 1 0.24 0.71 0.04 [30]

Hybrid poplar 6: 1 25.6 0.48 [82]

Poplar 0.19 0.75 0.06 [31]

Spruce 41: 1 29.5 0.31 0.64 0.05 [7]

According to Tab. 4.21, the published lignin weight fractions corresponded

quite well, except for the hybrid poplar where a very high extent of initial delignification

was reported [82]. The wood from old trees was reported to contain rather

high amounts of lignin that could easily be removed by alkali at low temperatures

at the start of the cook. The suggestion was that the hydrolytic action of acids in

the wood over a long period may have modified the wood in a manner similar to

mild pulping [75].

However, most of the models do not account for any subsequent changes in

alkali concentration as occurring in modern industrial batch and continuous cook-

4.2 Kraft Pulping Processes 213

ing processes. Lindgren and Lindstrom [14,33,47], Lindstrom [38] and Gustavsson

[56]have clearly shown that the initial amount of L3 in constant composition

cooks is not an homogeneous lignin, since reinforcing cooking conditions can

make part of it to react as L2. The amount of L3 is strongly affected by [OH]and

to some extent by [HS]and ionic strength. For spruce pulp, significant interactions

between these effects have been observed. In order to reduce the amount of

L3, it is important to have a low concentration of hydrogen sulfide in combination

with a high hydroxide concentration. Interestingly, Lindgren and Lindstrom [33]

could not detect a dependency of the initial concentration of L3 on cooking temperature,

whereas Andersson et al., using Lindgren and Lindstrom’s experimental

data, confirmed an influence of temperature on L3, since the fit improved slightly

when considering the effect of temperature [7]. Andersson et al. observed that the

amount of lignin at the intersection of the log-linear extrapolations for the species

L2 and L3 depends on the cooking conditions, [OH– ], [HS– ], and temperature.

(Ionic strength was also observed but not considered in the model.) The intersection

of the log-linear extrapolations corresponds to the lignin level of equal

amounts of L2 and L3, denoted as L*, as depicted in Fig. 4.31.

0 100 200 300 400

0.90 M [OH-]

0.44 M [OH-]

0.23 M [OH-]

0.10 M [OH-]

total lignin;

-------- L

, L

L*

Lignin on wood, %

Time [min]

Fig. 4.31 Course of total lignin, L2, L3 and L* during kraft

pulping at 170 °C and constant [HS– ]= 0.28 M and increasing

[OH]. L* shows a significant influence on [OH– ]. Experimental

data from Lindgren and Lindstrom [33]

The dependence of L* on the three major cooking parameters, temperature,

[OH– ]and [HS– ]has been evaluated by nonlinear regression analysis, assuming

no cross-coupling terms. The expression for L* is given in Eq. (105):

L * _ 0_49 ___ OH _ 0_01__0_65 ___ HS _ 0_01__0_19 _ 1_83 _ 2_91 _ 10_5_ T _ 273_15_2 _ _

_105_

214 4 Chemical Pulping Processes

The initial amounts for L1,0 and Ltot,0 are known and hence the sum of the initial

amounts for species 2 and 3 L2+3,0=Ltot,0 – L1,0. The initial values L2,0 and L3,0 depend

on cooking conditions, and can be calculated as follows using the definition of L*:

L 2_0 _ L * _ Exp kL 2 _ D t _ _ _106_

L 3_0 _ L * _ Exp kL 3 _ D t _ _ _107_

where kL2 and kL3 are the rate constants for the first-order reactions for species 2

and 3 in Eqs. (102) and (103), respectively and Dt is the time interval after which

species 2 and 3 reach the same level L*. Summing these equations yields

L 23_0 _ L * _ Exp _ kL 2 _ D t _ Exp _ kL 3 _ D t _ _106_

which can be solved numerically for Dt by any standard nonlinear equation solver

and obtaining L2,0 and L3,0 from Eqs. (106) and (107).

L2(t) and L3(t) can now be calculated from Eq. (104) as long as the reaction conditions

remain constant. If reaction parameters change at time tc, the model

assumes that the two lignin species, L2 and L3, interchange reversibly and instantaneously.

The situation is treated as if the cook starts at time tc with initial values

L2,c and L3,c exactly calculated as above from the actual total amount of species 2

and 3 L2+3,c= L2(tc)+L3(tc). If reaction conditions change continuously, the calculations

Eqs. (106–108) and Eq. (104) must be carried out for sufficient small time

steps.

The influence of ion strength of the liquor is not considered in the model. All

experimental data used for the development of the kinetic model were obtained at

comparable ion strength levels of [Na+]= 1.5 M. Lindgren and Lindstrom have

shown that reasonable variations of ion concentration around this value have only

a slight influence on the delignification kinetics [33].

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