[Home] [Journal papers]

CRITICAL ASSESSMENT ON MODELLING OF ELEMENTAL CHLORINE FREE BLEACHING SEQUENCE
Sandeep Jain, Grard Mortha, Nicolas Bnattar, Christophe Calais

Key words
Bleaching, ECF, Chlorine dioxide, extraction, modelling, kinetics

ABSTRACT

This paper is focused on evaluation and comparison of the different modelling approaches of the ECF bleaching process. The important parameters and tendencies were determined from the existing models and experimental data. Identification of these key governing parameters led to propose new comprehensive empirical models, which were simpler, more accurate, applicable to broader range of process conditions and easily adjustable (if required) with different kinds of wood species. Mathematical models were developed for the first chlorine dioxide (Do) and extraction (Eo) stage. The chlorine dioxide consumption with respect to kappa number decrease was found to be dependent on temperature, initial kappa number and initial chlorine dioxide charge. The initial ratio of slow and fast kappa numbers in extraction stage was found to be dependent on kappa factor in Do stage. It is now possible to separate modelling of D and E stages and also reinforcement of E stage with peroxide and oxygen could be predicted with separate models. Also more accurate correlation between K457 of D1 stage and kappa number of Eo stage was established.

1. INTRODUCTION

With increasing chemical costs, tougher environmental regulations and tighter customer demand, there is a need for an accurate and robust kinetic model that can be used for process optimization and control of bleach plant. This paper is focused on evaluation and comparison of the different modelling approaches of the ECF bleaching process. The important parameters and tendencies were determined from the existing models and experimental data. Identification of these key governing parameters led to propose new comprehensive empirical models, which were simpler, more accurate, applicable to broader range of process conditions and easily adjustable (if required) with different kinds of wood species. Mathematical models were developed for each pulp processing unit and linked together to create a generic bleaching stage in a simulator for ECF process. This paper discusses in detail, particularly, the first chlorine dioxide (Do) and extraction (Eo) stage.

A number of investigators have proposed the static as well as dynamic behaviour of various parts of the bleach plant. One approach followed was to base the modelling on the chemical reactions network in each stage. In this approach, each bleaching stage is represented by rate controlling steps and modelling each step by conventional power law kinetics. Ni, et.al.1 developed a chlorine bleaching model with three reactions in series. However, the model is still limited to predicting kappa number and chlorine concentration. Saltin, et.al.2 used a similar approach to model chlorination and caustic extraction. Gu, et.al.3 developed kinetic equations for each reaction and identified kinetic parameters from laboratory kinetic data. However, such models were shown to be exceedingly complex and not practical.

An alternative approach exists which uses neural networks to infer the needed relationships from mill operating data. Among the virtues of this method are its high degree of relevance to the particular installation on which it is based, and the fact that it does not rely on availability of laboratory derived kinetic relationships and assumptions concerning their applicability in the field. On the other hand, the predictive ability of the resulting model is limited to the ranges of the operating variables represented in the operating data used. Since it is possible that optimal operating conditions lie outside these ranges, such models will be limited in their ability to optimize the system.

A more practical approach concerns with lumping globally chemical kinetics and mass transfer and incorporating flow patterns assumptions to develop simple semi-empirical models. Most of the literature is based on this type of modelling approach. A simulation model for pulp bleaching based on multi-phase modelling and micro-scale phenomena was presented by Kuitunen and co-workers10. Extensive kinetic studies by Germgard4 show that the rate of delignification with chlorine dioxide is fifth order with respect to kappa number, which on one hand made this model extremely sensitive to initial kappa number values, on the other hand this was not a realistic representation of delignification kinetics. This is an empirical, rather than mechanistic, kinetic expression which represents a large number of simultaneous and sequential reactions between chlorine dioxide and lignin. This model was further improved by Mortha, et.al.5. The dependence of ClO2 consumption with respect to the decrease in kappa number was predicted. The variation in pH was also proposed incorporating the effect of carboxyl groups and phenolic groups present in the pulp. These models, though simpler and more accurate, presented some important drawbacks. These models combined Do with Eo stages and D1 stage with E1 stage. This rendered them unable to incorporate the addition of peroxide or oxygen in E stages. Another problem was that it uses only one single kinetic equation in each stage which makes the entire model too specific and inflexible. Also empirical fit between kappa number after DoEo stage and Kubelka-Munk, K457, parameter at the beginning of D1 stage, i.e. the relation between Kappa number (lignin content) and brightness (pulp colour), needed to be changed depending on the kind of pulp.

In recent works, it is suggested that pulp can react in two different ways to give either an easily eliminated or a slowly eliminated lignin. This approach though useful, poses problem of identifying the ratio of fast, slow and unreacting lignin. But it was possible to separate D and E stages and also reinforcement of E stage with peroxide and oxygen. Also more accurate correlation between K457 of D1 stage and kappa number of Eo stage could be developed, independent of kind of pulp. Based on this approach, Wang and co-workers6 lumped chemical kinetics and mass transfer and used kinetic expressions for CEDED sequence derived from low-consistency experiments in which the pH and bleaching agent concentrations were held constant. Earlier, Axegard and co-workers7 had used similar data to create a model of the DED partial sequence as applied to pulp prebleached in an O(C+D)E partial sequence. Both groups assumed that such expressions were applicable to the real situation, in which the consistencies are higher and the bleaching chemical concentrations change continuously as a result of consumption by pulp components. Because they incorporate kinetic expressions and flow pattern assumptions, models of this kind are, in principle, capable of simulating the dynamic behaviour of the bleach plant, a necessary feature for process control applications. However this capability comes at a price: a high degree of complexity, a large number of parameters and a demanding requirement for tuning and validation.

Figure 1.1 shows the variation in the final kappa number after Eo stage with respect to different values of initial kappa number before Do stage. It is clear that at initial Kappa number < 23, the two models by Mortha, et.al.5 and Wang, et.al.6 gave similar results. However, at initial Kappa number > 23, the former model diverged and gave higher values whereas the latter model continued to give linear variation. This suggests that the models are more sensible for higher kappa numbers than for lower kappa numbers.

bleach_1
Figure 1.1 COMPARISON OF MODELS BY WANG, et.al.6 AND MORTHA, et.al.5

Figure 3.1 also illustrates the final value of brightness after D1 stage and D2 stage respectively at different initial kappa numbers before Do Stage. It is clear that the brightness values obtained from the former model are higher than that from the latter one.

bleach_2
Figure 1.2 ClO2 CONSUMPTION VERSUS DECREASE IN KAPPA NUMBER FROM MORTHA, et.al.5 MODEL

Another major difference in the two models exists in the equation predicting ClO2 consumption versus decrease in kappa number. Figure 1.2 illustrates the final kappa number from the Mortha, et.al.5 model after DoEo stage at different ClO2 charge and at different initial kappa numbers. It is clear that the ClO2 consumption versus decrease in kappa number is non-linear, i.e. dependent on both kappa number and initial ClO2 charge. Wang, et.al.6 and Savoie, et.al.8 failed to incorporate this effect.

2. DEVELOPMENT OF NEW MODELS
 
The chlorine dioxide delignification kinetics is identified by two phases: a very fast phase (lasts for 15-20 seconds) and a slow phase (lasts for 30-60 min.). In earlier works, this was represented with the fifth order kinetics with respect to kappa number. The new models developed follow a more recent approach which divides the lignin entering the Do stage into three types: fast reacting, slow reacting and a floor level unreactive lignin. It should be noted that since lignin here is referred to Kappa number, hence it could be accepted, in broader sense, as including hexanuronic acids and other reacting species during Kappa number measurements. To make the model much simpler, accurate and easily adjustable, a preliminary study was done on the already existing models to identify the key governing parameters for the Do and Eo stage modelling.

bleach_table1
Table 2.1 BLEACHING CONDITIONS USED DURING PARAMETER STUDY

In the parameter study, effects on final kappa number were studied at different initial kappa numbers and at different ClO2 charges. The general conditions used for parameter study are shown in Table 2.1. For the Do Stage, the parameters which gave a significant variation in final result are as follows:
A: [ClO2] exponent for slow phase
B: Kappa number exponent for slow phase
C: Initial rate constant for slow phase
D: Ea, activation energy
E: DClO2/ DKappa number, ClO2 consumption versus kappa number decrease

Following figures 2.1 and 2.2 illustrate the effect on final results with 20% increase and 20% decrease in parameter values at different initial kappa numbers (15, 25, 30) and at different initial ClO2 charges (2.28%, 1.14%, 0.57%). It is observed that as kappa number decreases from 30 to 15 the effect on change in final kappa number becomes stronger except in case of parameter E where no change in intensity was observed. Again these parameters are more sensitive at lower kappa numbers and need to be carefully fixed in the low kappa number region. It is also observed that as %ClO2 charge decreases from 2.28% to 0.57% the effect on change in final kappa number diminishes for the parameters. Hence these parameters are more sensitive at higher ClO2 charge. The parameter which influenced the results more than others was the rate of ClO2 consumption with respect to decrease in kappa number (E).

bleach_2.1
Figure 2.1 EFFECT OF 20% INCREASE AND 20%  DECREASE IN PARAMETERS VALUE AT DIFFERENT KAPPA NUMBERS

bleach_2.2
Figure 2.2 EFFECT OF 20% INCREASE AND 20% DECREASE IN PARAMETERS VALUE AT DIFFERENT ClO2 CHARGES


2.1 Kinetic Model for Chlorine Dioxide Delignification (Do stage)

A kinetic model for chlorine dioxide delignification was developed based on the experimental data from Savoie, et.al.8. The model predicts kappa number, brightness and chlorine dioxide consumption after the first bleaching stage (Do). It was found that the relationship between chlorine dioxide consumption and kappa number decrease was non -linear and dependent on unbleached kappa number, initial chlorine dioxide charge and temperature.

2.1.1 Experimental conditions
Three pulp samples with different initial kappa numbers were taken. Initial kappa numbers of 29, 31 and 32.3 were selected to cover typical range of variation recorded at the mill. For each pulp, measurements were done for the kappa number, brightness and ClO2 consumption as a function of time (15 seconds, 1.33, 2.5, 4.7, 10, 15, 30, 50 and 70 min. ) at two different temperatures (40C and 50C) and at different ClO2 charges (kappa factor between 0.15 and 0.23). Sulphuric acid was added before the ClO2 injection to obtain a pH near 3 after chlorine dioxide addition. The consistency was kept at 3.1%.

Several things were observed after investigating the effect of kappa factor and temperature for the pulps at three different kappa numbers and the experimental results of kappa number, brightness and chlorine dioxide consumption as a function of time. Firstly, the chlorine dioxide delignification reaction seems to be a combination of a very fast reaction followed by a slow one. This can be related to the concept of fast and slow reacting lignin. There was an asymptote for both kappa number and brightness that is certainly linked to what is known as floor lignin. Secondly, the degree of delignification increases with increasing kappa factor and decreasing unbleached kappa number. Thirdly, the reaction was faster at higher temperature and the chlorine dioxide consumption with respect to kappa number decrease was found to be dependent on temperature, initial kappa number and initial chlorine dioxide charge.

2.1.2 Kinetics
The rate of the fast lignin removal is given by:

bleach_fig1(1)

While the rate of the slow lignin removal is:

bleach_fig2(2)

Where the reaction rate constants, kf and ks are expressed as:

bleach_fig34(3)



(4)



With [ClO2] being the concentration of chlorine dioxide expressed as active chlorine (mol/L), Kf and Ks, the content of fast and slow reacting lignin each expressed as the kappa number. The total kappa number is then:

K = Kf + Ks + K    (5)

Where, K is the floor level or unreactive lignin (during Do Stage). The initial values of the fast and slow kappa numbers Kfo and Kso are given by:

Kfo = 0.3 Ko   (6)
Kso = 0.5 Ko    (7)

Where Ko is kappa number of the unbleached pulp.

The value of activation energy for the fast kinetic phase is 68 kJ/mol. The corresponding value for the slow kinetic phase is 2 kJ/mol. The higher value of activation energy for the fast kinetic phase implies that during this phase ClO2 reacts with the free phenolic groups present in the easily extractable lignin and the rate is chemically controlled rather than diffusion controlled. On contrary, the lower value of activation energy for the slow kinetic phase implies that during this phase ClO2 needs to diffuse into the fibre matrix to react with the remaining lignin and it also represents the slow oxidation of the double bonds and non-phenolic units present in the structure of lignin by ClO2. This means that the rate in this slow phase is diffusion controlled rather than chemically controlled. This thing was not accounted in either of the models proposed by Wang, et.al.6 and Mortha, et.al.5.

The stoichiometric relationship between chlorine dioxide consumption and decrease in kappa number is given by the following equation:

bleach_fig89(8)



(9)



Where pHi is the pH initial, ICi are the carboxyl and phenolic content in the pulp (in mole per 100g of pulp), pKi are the dissociation constant of carboxyl and phenolic content, K is kappa number at time t, [H+] is hydrogen ions concentration in mol/l and DClO2 is the molar consumption of ClO2. Also li is the function of initial kappa number, initial ClO2 charge and temperature as follows:

li = f(Ko, ClO2o, T) (10)

To find an appropriate value of coefficient li, its value was varied to get the best values for different set of experimental data. Table 2.2 indicates these values for the temperature of 40C. It can be noticed that these values varied for each set of initial kappa number, but no apparent trend existed with respect to kappa number, kappa factor and even chlorine dioxide charge. Therefore, it is clear that the coefficient is now dependent on both, initial kappa number, Ko, as well as initial chlorine dioxide charge, ClO2o.Thus a factor was calculated from initial kappa number (the factor given in Mortha, et. al.5 model) and coefficient li values as follows:

Factor = li values / (-0.006337 * Ko + 0.0005023 * Ko2 (11)

The constant term of second order dependence on initial kappa number was modified from 0.0007023 to 0.0005023 in order to better fit the data. This factor was then plotted against the initial chlorine charge. Three points were excluded to avoid the duplicate values and also these points were apparently not with good experimental values.

Table 2.2 MODIFIED FITTING OF Do STAGE WITH EXPERIMENTAL DATA
Various functions were tried to fit this set of data. A second order polynomial dependence of initial chlorine dioxide charge, ClO2o, seems to fit best with a regression coefficient of 0.9926. Therefore, the coefficient li now becomes as follows:

li = (0.2092 * ClO2o - 2.0757 * ClO2o + 10.269) * (-0.006337 * Ko + 0.0005023 * Ko2) (12)

This dependency of coefficient on initial ClO2 charge better explains the similar observations in recent works9. This coefficient was found in this form for the temperature 40C. The same form of coefficient existed for 50C, 60C and 70C except that another constant factor of 0.93, 0.87 and 0.82, respectively, was needed. This established the fact that the chlorine dioxide consumption with respect
to kappa number decrease was also dependent on temperature. In order to find another function for temperature dependence, these values, 1 for 40C, 0.93 for 50C, 0.87 for 60C and 0.82 for 70C were taken into account by an exponential Arrhenius type factor. The coefficient finally becomes as follows:

li = 0.0958 * exp(734.37/T) * (0.2092 * 
   ClO2o - 2.0757 * ClO2o + 10.269) *
   (-0.006337 * Ko + 0.0005023 * Ko
(13)

bleach_table3
Table 2.3 COMPARISON OF EXPERIMENTAL DATA WITH MODEL PREDICTIONS

bleach_2.3
Figure 2.3 KAPPA NUMBER VERSUS TIME IN Do STAGE FOR T = 50C AND INITIAL KAPPA = 29


Table 2.3 compares the experiments based values of coefficient li with the predicted values of coefficient li and also compares the experimental values of final Kappa number with the model predictions. The predicted results were plotted for each set of data. Figures 2.3 – 2.8 illustrates these comparisons for two set of temperatures, 40C and 50C, and for three initial kappa numbers, 29, 31 and 32.3, for different initial kappa factor, Kf. Further, figure 2.9 compares the experimental values with the predictions from model for the final Kappa number at different ClO2 charges (or Kappa factor) applied and at different temperatures (40C, 50C, 60C, 70C).

bleach_2.4
Figure 2.4 KAPPA NUMBER VERSUS TIME IN Do STAGE FOR T = 50C AND INITIAL KAPPA = 31

bleach_2.5
Figure 2.5 KAPPA NUMBER VERSUS TIME IN Do STAGE FOR T = 50C AND INITIAL KAPPA = 32.3

bleach_2.6
Figure 2.6 KAPPA NUMBER VERSUS TIME IN Do STAGE FOR T = 40C AND INITIAL KAPPA = 29

bleach_2.7
Figure 2.7 KAPPA NUMBER VERSUS TIME IN Do STAGE FOR T = 40C AND INITIAL KAPPA = 31

bleach_2.8
Figure 2.8 KAPPA NUMBER VERSUS TIME IN Do STAGE FOR T = 40C AND INITIAL KAPPA = 32.3

bleach_2.9
Figure 2.9 FINAL KAPPA NUMBER AT DIFFERENT KAPPA FACTORS AND DIFFERENT TEMPERATURES


The model predictions were excellent and within experimental error although it slightly deviates for the 3 excluded points.

2.2 Kinetic Model for the first Extraction Stage (Eo stage)

From the parameter study for the Eo Stage, the parameters which gave significant variations in final kappa number are as follows:
A: Activation energy for fast phase
B: exponent [OH-] in initial ratio of fast to slow lignin
C: Activation energy in initial ratio of fast to slow lignin
D: Constant coefficient in initial ratio of fast to slow lignin

bleach_2.10
Figure 2.10 EFFECT OF 20% INCREASE AND 20% DECREASE IN PARAMETERS VALUE AT DIFFERENT KAPPA NUMBERS

Figures 2.10 and 2.11 illustrate the effect on final results with 20% increase and 20% decrease in parameter values at different initial kappa numbers and at different initial ClO2 charges. It is observed that as kappa number decreases from 30 to 15 and as %ClO2 charge decreases from 2.28% to 0.57% the effect on change in final kappa number is same.

bleach_2.11
Figure 2.11 EFFECT OF 20% INCREASE AND 20% DECREASE IN PARAMETERS VALUE AT DIFFERENT ClO 2 CHARGES

Hence these parameters are equally sensitive to all kappa numbers. The equation used to calculate the initial ratio of fast and slow lignin was identified most important.

The kinetic model proposed by Wang, et.al.6 was adjusted with a set of experimental data for the first alkaline extraction stage. The stoichiometric curve after stage DE exhibits a classical evolution, i.e. the kappa number decreases rapidly and linearly at low chlorine dioxide charges and the curve flattens after, showing that the oxidizing efficiency of ClO2 is significantly reduced at high charges.

2.2.1 Experimental
The experimental data used to fit the kinetics of first alkaline extraction stage was taken from recent works9. An industrial softwood kraft pulp (Aspa, Sweden) was used as a raw material. The bleaching stages were performed at 10% consistency in polyethylene bags introduced in controlled water bath. Several DE stages at varying ClO2/pulp charges (0.3 to 2.1 %odp) were carried out on the unbleached softwood pulp. The temperature was kept at 50C for Do stage for duration of 1 hour. The corresponding values for stage Eo were 60C, 70C, 80C and 2 hours respectively.

2.2.2 Kinetics
The rate of the extraction reactions is expressed as follows:

bleach_fig1415

(14)



(15)



Where [OH-] is hydroxyl ion concentration (mol/L).The rate constants of the fast and slow reactions, kEf and kEs, depend on the reaction temperature as follows:

bleach_fig17
(17)



bleach_fig118
(18)


With the ratio of initial fast and slow kappa numbers given as,

bleach_fig19
(19)



It was found that this ratio needs to be multiplied by another constant factor which was different for different initial chlorine dioxide charges used in Do stage. This means that the initial ratio calculation for fast and slow kappa numbers was also dependent on the initial chlorine dioxide charge used in Do stage. To represent this behaviour, kappa factor used in Do stage was chosen as a parameter. The constant factor required for each set of kappa factor was then determined. A second order polynomial dependence of kappa factor in Do stage seems to fit best with a regression coefficient of 0.9607. Therefore, the equation to calculate the initial ratio of slow and fast kappa numbers now becomes as follows:

bleach_fig2021
(20)


(21)


The predicted results after this modification in the equation used for calculating the initial ratio of slow and fast kappa numbers were plotted for each set of corresponding experimental data. Figure 2.12 illustrates these comparisons for Do and DoEo stages at Eo stage temperatures of 60C, 70C and 80C. The model predictions appears to be excellent and within experimental error.

bleach_2.12
Figure 2.12 COMPARISON OF EXPERIMENTAL DATA WITH PREDICTED RESULTS (Eo STAGE at 60C, 70C and 80C)

2.3 Brightness after DoEo stage

The experimental data was taken from the recent works9. Following equations are used to calculate brightness from kappa number. Kappa number is related to absorption coefficient by an empirical function and the Kubelka-Munk equation is used to convert light absorption coefficient values to brightness:


bleach_fig2223
(22)





(23)




Where, f (Kappa) is an empirical function relating kappa number and light absorption coefficient, B denotes the reflectance of the pulp sheet in the blue light region at a wavelength of 457nm, that is, brightness and S is the light scattering coefficient.

The function f is normally taken to be linear. The model used by Mortha, et.al.5 had a similar dependence between K/S and kappa number. The slope of linear equation was taken 0.06 with zero as constant value. Table 2.4 illustrates the experimental values, before fitting values and after fitting values of brightness and parameter K/S with respect to kappa number after the alkaline extraction stage.

bleach_table4
Table 2.4 BRIGHTNESS VERSUS KAPPA NUMBER FOR AN ALKALINE EXTRACTION STAGE

The K/S values were back-calculated from Kubelka-Munk equation from the experimental values of brightness. Figure 2.13 illustrates these values of K/S corresponding to experimental values of kappa number. Various functions were tried to fit this set of data. A second order polynomial dependence of kappa number seems to fit best with a regression coefficient of 0.9922. Therefore, the relation between K/S and kappa number becomes:

bleach_fig24(23)

bleach_2.13
Figure 2.13 VARIATION OF KUBELKA-MUNK PARAMETER WITH KAPPA NUMBER

The second order polynomial dependence predicts results in a wider range of kappa number. For small kappa numbers the second order term becomes negligible and the relation becomes linear with a slope of 0.0646, which is closer to the literature value of 0.06 taken by Mortha, et.al.5. This also helps in explaining that the 0.06 value was valid for only lower kappa number values. When the kappa number values are higher which means the lignin is more difficult to extract, the light absorption coefficient does not increase linearly with kappa number but the increase is slower.

bleach_2.14
Figure 2.14 COMPARISON OF EXPERIMENTAL AND FITTED MODEL BRIGHTNESS AFTER Eo STAGE

The recalculated values of K/S using the above empirical function are shown in Table 2.4. The brightness values now predicted from the new set of equations are also shown. Figure 2.14 compares the experimental data with the results predicted from the model before and after fitting. It is clear that the model (linear) before fitting did not fit well the experimental values. The new empirical model seems to fit well in the whole range of kappa number, although the relation may vary for the pulps originating from different processes and wood species. The closeness of these relations needs to be studied.

3. CONCLUSION

This paper evaluated and compared different modelling approaches of the ECF bleaching process. The important parameters and tendencies were determined from the existing models and experimental data. Identification of these key governing parameters led to propose new comprehensive empirical models, which were simpler, more accurate, applicable to broader range of process conditions and easily adjustable (if required) with different kind of wood species. Mathematical models were developed for the first chlorine dioxide (Do) and extraction (Eo) stage. It is now possible to separate modelling of Do and Eo stages and also reinforcement of Eo stage with peroxide and oxygen could be predicted with separate models which will be discussed in future publications. Also more accurate correlation between K457 of D1 stage and kappa number of Eo stage was developed.

4. ACKNOWLEDGEMENT

We would like to acknowledge the financial support from ARKEMA for the co-development of these models.

5. REFERENCES

1.Ni, Y. Kubes, G.J., and van Heiningen, A.R.P., J. Pulp Paper Sci., 21(1): J30 (1995).
2.Saltin, G.E., "Kraft Pulp Bleaching: Kinetic Models of Conventional systems and Laboratory Investigation of Chlorine Free Sequences", Ph.D. Dissertation, University of Idaho, September (1993).
3.Gu, Y.X. and Edwards, L.L., "Virtual bleach plants, Part2: Unified ClO2 and Cl2 bleaching model", Tappi Journal, Vol.2, No. 7 (2003).
4.Germgard, U. and Teder, A., CPPA Trans. Tech. Sect., 6(2): TR31 (1980).
5.Mortha, G., Lachenal, D., Chirat, C., "Modeling multistage chlorine dioxide bleaching", 11th International symposium on wood and pulping chemistry, Nice, France, Vol. III, Poster presentations, pp 447-451, 11-14 June (2001).
6.Wang, R.X., Tessier, P.J.C., Bennington, C.P.J., "Modeling and Dynamic Simulation of a Bleach Plant", AIChE Journal, 41(12), 2603-2613 (1995).
7.Axegard, P., Jansson, U. and Teder, A., "The E2 Stage Improves the Reactivity of Pulp Towards Chlorine Dioxide," J. Pulp Paper Sci., 10(1):1(1984).
8.Savoie, M., Tessier, P., "A Mathematical Model for Chlorine Dioxide Delignification", Tappi Journal, 80(6):145 (1997).
9.Bnattar, N., "Contribution la l'tude du blanchiment des ptes papetires obtenues par des procds sans soufre", Ph.D. thesis, EFPG (INPG), Grenoble, 2005
10.Kuitunen, S., Tarvo, V., Lehtimaa, T., Aittamma, J., "Fundamental modelling of pulp bleaching", 13th ISWFPC conference (APPITA), pp 257-264, 2005

[Home] [Journal papers]