Empirical Models

Delignification

H-Factor concept

Process control in practical pulping is mainly based on empirical models due to

their simplicity and ease of implementation. One of the earliest kinetic models

was developed by Vroom and this, even today, is widely used for control purposes

[13]. This model is called the H- factor, and expresses the cooking time and temperature

as a single variable in batch reactors. It is defined as:

H _

t

t 0

kL _ dt _76_

where kL is the relative reaction rate of pulping (dimensionless). The rate at 100 °C

is chosen as unity, and all other temperatures are related to this rate. An Arrhe-

4.2 Kraft Pulping Processes 189

nius-type equation is used to express the temperature dependence of the reaction

rate. At a temperature T, it is expressed as

Ln _ kL _ T ___ Ln _ A __

EA _ L

R _

T _77_

The reference reaction rate at 100 °C is simplified to

Ln kL _100_ C _ __ Ln _ A __

EA _ L

R _

373_15 _78_

The relative reaction rates at any other temperature can be expressed by the following

equation:

Ln

kL __ T _

k 100_ C _

EA _ L

R _ 373_15 _

EA _ L

R _ T _79_

The activation energy values E A for bulk delignification published in the literature

range from 117 kJ mol–1 [14]for birch to 150 kJ mol–1 [15]for pine. Assuming an

activation energy of 134 kJ mol–1, according to Vroom the H-factor can be

expressed as

H _

t

t 0

kL __ T _

k 100_ C _ dt _

t

t 0

Exp _ 43_19 _

T _ __ dt _80_

The H-factor is designated as the area under the curve of k vs. time in hours. As

an example, the H-factor for 1-h isothermal cooking at 170 °C equals a value of

925. The H-factor was developed to predict the temperature or cooking time

needed to achieve a given Kappa number. This means that the result is only valid

when the relationship between the H-factor and the Kappa number is known, provided

that the other cooking conditions such as effective alkali concentration,

liquor-to-wood-ratio, etc. are kept constant. In this case, the prediction of kappa

number is of sufficient precision. Figure 4.24 shows as an example the course of

kappa number and yield as a function of H-factor for softwood kraft cooking.

Depending on the charge of effective alkali and the sulfidity of the cooking

liquor, H-factors in the range of 1000 to 1500 are needed for a complete kraft cook

[17].

A number of simple models for the relationship between two or three process

variables have been developed. Hatton describes a model to predict yield and

kappa number based on the H-factor and the charge of effective alkali for a variety

of wood species with an equation of the form [18]:

Y _ _ _ a _ b __ LogH __ EA _ n _ _81_

190 4 Chemical Pulping Processes

800 1000 1200 1400 1600

Yield [% on wood]

Kappa number

Kappa number

H factor

Yield

Fig. 4.24 Course of kappa number and yield as a function of

the H-factor. Spruce/pine = 1:1; liquor-to-wood-ratio = 3.8:1;

maximum temperature = 170 °C; EA-charge = 19% on wood;

sulfidity 38% [16].

where Y is the yield, k the kappa number, a and b are adjustable parameters, H is

the H-factor, and EA is the effective alkali charge based on wood.

The integration of additional process parameters into the model structure certainly

improves the precision of kappa number prediction. For example, the

model of Bailey et al. uses five variables in a 20-term polynomial to predict kappa

number [19]. Despite the high complexity, the reliability of these models is limited

to the specific cooking plant investigated.

Control of kraft pulping by monitoring of hydroxy carboxylic acids

A prerequisite for reliable H-factor control is that the cooking conditions are precisely

known and kept strictly constant, since the prediction of the cooking time

needed to reach the target kappa number is based only on temperature measurements.

Typical industrial conditions, however, include uncontrollable variations in

the moisture content and the quality of chips, the concentration of the active cooking

chemicals, and the temperature measurements. Alternatively, it was suggested

to correlate the progress of delignification with the carbohydrate degradation taken

place during cooking. The majority of carbohydrates in kraft pulping are

degraded to hydroxy carbonic acids according to the peeling reaction (see Section

4.2.4.2.1). The formation of these short-chain acids is directed by temperature and

effective alkali concentration. Detailed investigations have shown that adequate

information with regard to the extent of delignification can be obtained simply by

analyzing the key hydroxy monocarboxylic acids as their trimethylsilyl derivatives

by gas-liquid chromatography [20]. Kraft pulping of pine can be reliably controlled

by following the concentration ratio comprising the sum of 3,4-dideoxypentanoic

4.2 Kraft Pulping Processes 191

acid (A) and anhydroglucoisosaccharinic acid (B) divided by the concentration of

2-hydroxybutanoic acid (C). This procedure is also advantageous because it avoids

the difficulty of measuring the absolute concentrations.

0 30 60 90 120 150

A+B

C

Kappa number

0 20 40 60 80 100

Xylosisosaccharinic acid

á-Glucoisosaccharinic acid

Ratio of birch-to-pine [%]

Fig. 4.25 (A) Acid concentration ratio versus

kappa number of pine kraft pulping according

to [21]. EA-charge 18–24% on wood, sulfidity

35%. A = 3,4 dideoxypentonic acid;

B = anhydroglucoisosaccharinic acid;

C = 2-hydroxybutanoic acid. (B) Ratio of the

concentrations of xyloisosaccharinic acid to

a-glucoisosaccharinic acid as a function of the

wood composition consisting of birch and pine

(according to [21]).

192 4 Chemical Pulping Processes

4.2 Kraft Pulping Processes 193

Figure 4.25A shows the concentration ratio in relation to the course of kappa

numbers. Based on this relationship, it was possible to determine the end point of

the cook with an accuracy corresponding to ± 2 kappa number units. However,

the described method for the determination of the ratio of hydroxy monocarboxylic

acids is still too time-consuming to be used for process control under

industrial conditions.

The fragmentation pattern of the carbohydrates under alkaline cooking conditions

is different for softwoods and hardwoods. Thus, the proportion of, for example

hardwood in a wood composition consisting of a mixture of hardwood and

softwood, can be detected by using this method. Among different possibilities, the

ratio of xyloisosaccharinic acid to a-glucoisosaccharinic acid determines the composition

of the softwood and hardwood chip mixtures as seen in Fig. 4.25B, which

shows clearly that the composition of the chip mixtures can be reliably determined

on the basis of the analysis of the hydroxy monocarboxylic acids.

Carbohydrate degradation

The selectivity of kraft pulping is determined by the ratio of polysaccharide degradation

and lignin removal. For the production of dissolving pulp, the most important

control parameter is the average degree of polymerization, determined as

intrinsic viscosity. A kinetic model for the degradation of pulp polysaccharides

(cellulose and hemicelluloses) can be derived by assuming the initial number of

molecules to be M0 and the initial total number of monomer units as N0, then the

initial total number of bonds is n0, where [22]

n 0 _ N 0 _ M 0 _ N 0 _ 1 _

DPn _0 _ _ _82_

where DPn,0 is the initial degree of number average polymerization= N0/M0.

Similarly, the number of bonds in the polymer substrate remaining at time t

can be described as:

nt _ Nt _ Mt _ N 0 _ 1 _

DPn _ t _ _ _83_

where Mt is the number of polymer molecules at time t, DPn,t is the degree of

number average polymerization at time t = Nt/Mt, and nt is the number of intermonomer

bonds per molecule at time t.

For first-order kinetics of bond scission, the rate is proportional to the number

of unbroken bonds in the polymer and the hydroxide ion concentration:

_

dn

dt _ k ′ C __ OH _ _ n _84_

In the case of constant hydroxide ion concentration the equation simplifies to:

Ln

nt

n 0 _ __ _ k ′ C __ OH _ a _ t _ _ kC _ t _85_

where kc is the rate constant of the first-order reaction.

Substituting for nt and n0

Ln 1 _

DPn _ t _ __ Ln 1 _

DPn _0 _ __ _ kC _ t _86_

If DPt and DP0 are large, which is valid in the case of pulp polysaccharides, this

simplifies to a zero-order reaction:

DPn _ t _

DPn _0 _ __ CS _ kC _ t _87_

where CS is the number of chain scissions per anhydroglucose unit and kC is a

reaction rate for cellulose degradation; assuming DPn,0 = 1500 and DPn,t = 1000,

the number of chain scissions calculates to 0.33 mmol AHG–1.

It must be taken into account that this approach is strictly applicable only if the

polymer is linear, monodisperse, and there is no loss of monomer units during

scission. Although the pulp carbohydrates are by no means monodisperse and

there is also some loss of monomers during scission due to peeling reactions, the

model is applicable to predict the degree of average polymer weight with sufficient

precision. In a certain range of the degree of polymerization it can be assumed

that the polydispersity remains constant during the degradation reaction.

The rate of cellulose chain scission is also strongly dependent on the hydroxide

ion concentration, as expressed by Eq. (85). The value of a can be obtained as the

slope of a plot of ln(kC) against ln([OH]). Kubes et al. studied the effect of hydroxide

ion concentration for both kraft and Soda-AQ pulping of black spruce [23]. Figure

4.26 illustrates the effect of [OH]on the rate of cellulose chain scissions at a

cooking temperature of 170 °C.

According to Fig. 4.26, Soda-AQ cooking displays a more pronounced effect on

the rate of cellulose chain scissions as compared to kraft cooking. The corresponding

values for the power constant in Eq. (85) have been determined to be 2.63 for

Soda-AQ and 1.77 and for kraft pulping, respectively. In the case of kraft pulping,

Eq. (87) can thus be modified to

DPn _ t _

DPn _0 _ __ CS _ k ′ C _ OH _ _ 1_77_ t _88_

The temperature dependence can be described by the Arrhenius equation according

to the following expression

k ′ C _ A _ Exp _

EA _ C

R _

T _ _ _89_

where E A,C can be calculated from the slope of the graph of ln kC versus 1/T.

194 4 Chemical Pulping Processes

-0,8 -0,4 0,0 0,4 0,8

-14

-13

-12

-11

-10

Kraft

SODA-AQ

ln(k

CS

)

ln[OH-]

Fig. 4.26 Effect of hydroxide concentration on

the rate of cellulose chain scissions in the

course of kraft and Soda-AQ cooking of black

spruce at 170 °C as a plot of ln(kC) against

ln([OH]) with liquor-to-wood ratio amounts to

0.5–2.6 mol L–1; The Tappi Standard Viscosity

Method T-230 (0.5% cuene) was converted by

the equation IV[mL g–1]= 1.103.[8.76.log(V) –

2.86]to the intrinsic viscosity (IV = SCAN-CM-

15:88) which again was converted to DPv by the

appropriate equations included in the SCAN

Method CM 88.

Kubes et al. obtained an activation energy of 179 ± 4 kJmol–1 for the chain scissions

in both Soda-AQ and kraft pulping. This result reveals that additives such as sulfide

for kraft and anthraquinone for Soda-AQ pulping do not affect pulp viscosity. This

observation was confirmed quite recently, showing that the activation energies for cellulose

degradation were not influenced by the addition of AQ and PS, either alone

or in combination, and were in the range of 170–190 kJ mol–1 [24,25].

Finally, Eq. (90) represents the complete rate equation for cellulose chain scissions

of Soda-AQ and kraft pulping combining the expressions for temperature

and hydroxide ion concentration dependences:

SODA _ AQ _

DPn _ t _

DPn _0 _ __ 2_80 _ 1015 _ Exp _ _

_ T ___ OH _ 2_63_ t

KRAFT _

DPn _ t _

DPn _0 _ __ 4_35 _ 1015 _ Exp _ _

T _ ___ OH _ 1_77_ t

_90_

Following Vroom’s approach, Kubes et al. have derived the G-factor model for viscosity

loss as a means for expressing the effect of cooking time and temperature

in a single variable [8,23]. Analogous to the H-factor concept, the reaction rate constant

for cellulose degradation, kC, can be related to the rate at 100 °C which is chosen

as unity. Thus, the relative reaction rates at any other temperature can be

expressed by the following equation:

4.2 Kraft Pulping Processes 195

Ln

kC __ T _

kC _100_ C _

EA _ C

R _ 373_15 _

EA _ C

R _ T _91_

Inserting the activation energy for viscosity loss, 179 kJ mol–1, leads to the following

expression for the G-factor:

G _

t

t 0

Exp _ 57_70 _

T _ __ dt _92_

At a constant hydroxide ion concentration, the G-factor can be related to the chain

scission according to Eq. (93):

DPn _ t _

DPn _0 _ __ G _93_

In industrial pulping the hydroxide ion concentration varies as a function of time.

Fleming and Kubes recognized a linear correlation between the cellulose chain

scissions and the product from residual alkali concentration and G-factor.

Figure 4.27 shows a plot of ([OH–

res]· G) against the reciprocal viscosity average

degree of polymerization, 1/Pv, for both hardwood (birch and aspen) and softwood

kraft pulping.

0 3000 6000 9000 12000

2,0x10-4

3,0x10-4

4,0x10-4

5,0x10-4

6,0x10-4

7,0x10-4

Hardwoods: birch and aspen

Softwood; spruce

1/DP

v

[OH

resid

-]*G-factor [mol/l]

Fig. 4.27 Reciprocal viscosity average degree of polymerization

against ([OH–

res]· G-factor) for kraft pulping of birch,

aspen and spruce at 30% sulfidity and a liquor-to-wood-ratio

of 5:1 (according to [26]).

196 4 Chemical Pulping Processes

The results confirmed a linear relationship between 1/DPv and the product

from [OHresid]and G-factor, with different slopes for hardwoods and softwood. The

reason for the more intense cellulose degradation in the case of hardwood pulps

might be due to the lower amount of residual lignin being a measure of protection

against polysaccharide degradation. The intercept on the ordinate corresponds to

a viscosity average degree of polymerizations of 5315 for hardwood and 5080 for

softwood which in turn correspond to intrinsic viscosities of 1550 and 1495 mL g–1,

respectively.

Pulping selectivity: As a consequence of its high activation energy, viscosity loss

accelerates more rapidly than delignification as temperature increases. The ratio

of kL to kC can be used to represent the pulping selectivity. The values of this ratio

against the cooking temperatures have been calculated on the basis of kraft pulping

of black spruce at constant alkali concentration (Tab. 4.18).

Tab. 4.18 Pulping selectivity denoted as the ratio of kL to kc.

Kraft cooking of black spruce wood [OH]= 1.1 mol L–1,

liquor-to-wood ratio = 24:1; sulfidity = 30% according to [25]

Li et al. (2002).

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