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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. Figure 1.2 ClO
CONSUMPTION VERSUS DECREASE IN KAPPA NUMBER FROM MORTHA, et.al._{2} MODEL^{5}Another major difference in the two models exists in the equation predicting ClO _{2} consumption versus decrease in kappa number. Figure 1.2 illustrates the final kappa number from the Mortha, et.al. model after DoEo stage at different ClO^{5}_{2} charge and at
different initial kappa numbers. It is clear that the ClO_{2} consumption versus decrease in kappa number is non-linear, i.e. dependent on both kappa number and initial ClO_{2} charge.
Wang, et.al.6 and Savoie, et.al.8 failed to incorporate this effect.2. DEVELOPMENT OF NEW MODELSThe 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 D _{o} and E_{o} stage modelling.
Table 2.1 BLEACHING CONDITIONS USED DURING PARAMETER STUDYIn the parameter study, effects on final kappa number were studied at different initial kappa numbers and at different ClO _{2} 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: [ClO _{2}] exponent for slow phaseB: Kappa number exponent for slow phase C: Initial rate constant for slow phase D: Ea, activation energy E: DClO _{2}/ DKappa number, ClO_{2 }consumption versus kappa number decreaseFollowing 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 ClO _{2} 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 %ClO_{2} 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 ClO_{2} charge. The
parameter which influenced the results more than others was the rate of ClO_{2} consumption with respect to decrease in kappa number (E).
A kinetic model for chlorine dioxide delignification was developed based on the experimental data from Savoie, Figure 2.1 EFFECT OF 20% INCREASE AND 20% DECREASE IN PARAMETERS VALUE AT DIFFERENT
KAPPA NUMBERSFigure 2.2 EFFECT OF 20% INCREASE AND 20% DECREASE IN PARAMETERS VALUE AT DIFFERENT ClO2 CHARGES 2.1 Kinetic Model for Chlorine Dioxide Delignification (D _{o} stage)et.al.^{8}. The model predicts kappa number, brightness and
chlorine dioxide consumption after the first bleaching stage (D_{o}). 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 conditionsThree 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 ClO _{2} 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 (40°C and 50°C) and at different ClO_{2} charges (kappa factor between 0.15 and 0.23). Sulphuric acid was added before the ClO_{2} 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 KineticsThe rate of the fast lignin removal is given by: (1) While the rate of the slow lignin removal is: (2) Where the reaction rate constants, kf and ks are expressed as: (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 = K _{f} + K_{s} + 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: K _{fo} = 0.3 K_{o} (6)K _{so} = 0.5 K_{o } (7)Where K _{o} 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 ClO _{2} 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 ClO_{2} 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 ClO_{2}. 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: (8) (9) Where pHi is the pH initial, ICare the carboxyl and phenolic content in the pulp (in mole
per 100g of pulp),_{i} pK 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:_{i}li = f(K _{o}, ClO^{2o}, 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 40°C. 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 = l values / (-0.006337 * K_{i}_{o} + 0.0005023 * K_{o}^{2} (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 * ClO ^{2o}² - 2.0757 * ClO^{2o} + 10.269) * (-0.006337 * K_{o} + 0.0005023 * K_{o}^{2}) (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 40°C. The same form of coefficient existed for 50°C, 60°C and 70°C 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 40°C, 0.93 for 50°C, 0.87 for 60°C and 0.82 for 70°C 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 * ClO ^{2o}² - 2.0757 * ClO^{2o} + 10.269) * (-0.006337 * K _{o} + 0.0005023 * K_{o}²) (13)
Table 2.3 COMPARISON OF EXPERIMENTAL DATA WITH MODEL PREDICTIONSFigure 2.3 KAPPA NUMBER VERSUS TIME IN D
STAGE FOR T = 50°C AND INITIAL KAPPA = 29_{o}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, 40°C and 50°C, 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 ClO _{2} charges (or Kappa factor) applied and
at different temperatures (40°C, 50°C, 60°C, 70°C).Figure 2.4 KAPPA NUMBER VERSUS TIME IN D
STAGE FOR T = 50°C AND INITIAL KAPPA = 31_{o}Figure 2.5 KAPPA NUMBER VERSUS TIME IN D STAGE FOR T = 50°C AND INITIAL KAPPA = 32.3_{o}Figure 2.6 KAPPA NUMBER VERSUS TIME IN D STAGE FOR T = 40°C AND INITIAL KAPPA = 29_{o}Figure 2.7 KAPPA NUMBER VERSUS TIME IN D
STAGE FOR T = 40°C AND INITIAL KAPPA = 31_{o}Figure 2.8 KAPPA NUMBER VERSUS TIME IN D STAGE FOR T = 40°C AND INITIAL KAPPA = 32.3_{o}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 (E stage)_{o}From the parameter study for the E _{o} 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 Figure 2.10 EFFECT OF 20% INCREASE AND 20% DECREASE IN PARAMETERS VALUE AT DIFFERENT KAPPA NUMBERSFigures 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. Figure 2.11 EFFECT OF 20% INCREASE AND 20% DECREASE IN PARAMETERS VALUE AT DIFFERENT ClO
CHARGES_{2}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 ClO_{2} is significantly reduced at high charges.2.2.1 ExperimentalThe experimental data used to fit the kinetics of first alkaline extraction stage was taken from recent works ^{9}. 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 ClO_{2}/pulp charges (0.3
to 2.1 %odp) were carried out on the unbleached softwood pulp. The temperature was kept at 50°C for Do stage for duration of 1 hour. The corresponding values for stage Eo were 60°C, 70°C, 80°C and 2 hours respectively. 2.2.2 KineticsThe rate of the extraction reactions is expressed as follows: (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: (17) (18) With the ratio of initial fast and slow kappa numbers given as, (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: (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 60°C, 70°C and 80°C. The model predictions appears to be excellent and within experimental error. Figure 2.12 COMPARISON OF EXPERIMENTAL DATA WITH PREDICTED RESULTS (Eo STAGE at 60°C, 70°C and 80°C)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: (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. 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: (23) Figure 2.13 VARIATION OF KUBELKA-MUNK PARAMETER WITH KAPPA NUMBERThe 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.Figure 2.14 COMPARISON OF EXPERIMENTAL AND FITTED MODEL BRIGHTNESS AFTER Eo STAGEThe 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. CONCLUSIONThis 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 (D _{o}) and extraction (E_{o}) stage. It is now possible to separate modelling of Do and E_{o} stages and also reinforcement of E_{o} 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 D_{1} stage and kappa number of E_{o} stage was developed.
4. ACKNOWLEDGEMENTWe would like to acknowledge the financial support from ARKEMA for the co-development of these models. 5. REFERENCES1.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 ClO _{2} 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 E _{2} 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.Bénattar, N., "Contribution à la l'étude du blanchiment des pâtes papetières obtenues par des procédés 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 |

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