Ind. Eng. Chem. Res. 2008, 47, 5871–5878
5871
Dimensionless Parameter Approach for Oxygen Delignification Kinetics I˙smail Dog˘an* and Gu¨niz Gu¨ru¨z Department of Chemical Engineering, Middle East Technical UniVersity, Ankara, 06531, Turkey
In this study, the kinetic analysis of oxygen delignification of Turkish southern hardwood Kraft pulp was carried out. The kinetic rate data were collected in a high pressure batch reactor at industrially significant conditions of temperature, alkali charge, and oxygen partial pressure. The mass transfer effects were examined for the system studied. After eliminating the mass transfer resistances in the delignification system, the kinetics of oxygen delignification was studied and the governing rate equations were derived. The kinetics of the carbohydrate degradation was analyzed to determine the extent of delignification without the reduction in the pulp strength below the acceptable level; which is usually taken as the removal of no more than half of the lignin in the pulp entering the oxygen stage. The kappa number, intrinsic viscosity, and reaction time were expressed in dimensionless forms to generalize the results and to make them independent of the initial values, experimental conditions, and pulping conditions prior to oxygen delignification. These dimensionless parameters were fitted to nonlinear equations. These equations can also be used for the control of the oxygen delignification towers. The same approach was also used for the reported studies in the literature which allowed the comparison with the results of this study. 1. Introduction The aim of chemical wood pulping is to remove the lignin molecules in wood without destroying the carbohydrate molecules which are cellulose and hemicelluloses. The commercial pulp production processes mainly consist of cooking and bleaching. In cooking, most of the lignin contained in the fiber walls is dissolved and the fibers in the wood are separated. The kappa number is the lignin content of the pulp. The lignin content of the pulp (in weight percent) is approximately calculated by multiplying the kappa number by 0.15.1 The kappa number is the volume of 0.1 N potassium permanganate solution consumed by 1 g of moisture free pulp. Bleaching is required to obtain the desired pulp brightness by removing the remaining 2-5% residual lignin after the cooking.1 Common bleaching chemicals are chlorine (Cl2), chlorine dioxide (ClO2), sodium hydroxide (NaOH), oxygen (O2), hydrogen peroxide (H2O2), and ozone (O3). Environmental concerns about chlorinated dioxins and other chlorinated organic material led the industry to decrease chlorine use and adopt substantial, later complete replacement with chlorine dioxide. On the other hand, more strict regulations on the bleach plant effluents led to greater utilization of oxygen delignification technology. Thus, oxygen, hydrogen peroxide, and ozone have received significant attention as the bleaching chemicals although they are less selective toward lignin degradation than chlorine based chemicals. In oxygen delignification, oxygen and alkali are used to remove the lignin from the unbleached pulp, while the carbohydrate bond in the pulp is also broken. Therefore, the intrinsic viscosity of the pulp is decreasing as the oxygen delignification continues which makes the number of cellulose chains per metric ton of pulp more meaningful (Mn). Also, the use of Mn is more suitable in kinetic studies than viscosity because in kinetics both reactants and the reaction products should be expressed in chemical units.3 Since high temperatures and alkali concentra* To whom correspondence should be addressed. Mailing address: The Scientific and Technological Research Council of Turkey, TUBITAK, Kavaklidere, Ankara, 06531, Turkey. E-mail: ismail.dogan@ tubitak.gov.tr. Fax: +90 312 467.
tions are used in the oxygen delignification systems, the resulting carbohydrate degradation causes a reduction in the pulp strength. Thus, the extent of delignification is limited to about 50% in single stage process due to carbohydrate degradation. Therefore, the oxygen delignification and carbohydrate degradation kinetics are very important in optimization and control of an oxygen delignification stage. The main advantage of oxygen delignification is the reduction in the bleach plant effluents achieved by washing the dissolved solids from the oxygen delignification stock and recycle them into the pulp mill recovery system.2 The most widely accepted oxygen delignification kinetic model was derived by Olm and Teder3 which is defined as the sum of quickly and slowly eliminated lignin in the form of first order kinetic model. The Olm and Teder3 model was later modified by taking into account the mass transfer effects.4,5 Iribarne and Schroeder6 extended the range of oxygen concentration in their experiments through the application of high oxygen pressure in the gas phase increase the delignification rates. Agarwal and co-workers7 performed a detailed investigation of the oxygen delignification kinetics for mixed southern hardwoods using mill-cooked pulp. The change in the kappa number as a function of time was fitted to a power law rate equation, following the method suggested by Schoon.8 Valchev et al.9 described the rate of oxygen delignification by a modified form of the topochemical kinetic equation of Prout-Tompkins and Nenkova et al.10 and investigated the influence of operating parameters on the effectiveness of oxygen delignification of hardwood Kraft pulp. Oxygen delignification is a complex phenomenon which shows significant variations depending upon the wood species and pulping process used. The manner in which the Kraft pulping process is executed has a significant effect on the oxygen delignification. The amount of reduced lignin remaining in the pulp, variations in the hemicellulose content and structure resulting from different pulping conditions and wood species have a significant effect on oxygen delignification.11 The aim of the present work is to derive kinetic rate equations describing delignification and carbohydrate degradation during oxygen bleaching for the eucalyptus Kraft pulp produced in the
10.1021/ie071498h CCC: $40.75 2008 American Chemical Society Published on Web 07/23/2008
5872 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 Table 1. Range of Process Variables variable
range
temperature NaOH concentration oxygen pressure reaction time amount of MgSO4 · 7H2O used
90, 100, 110 °C 0.05, 0.15, 0.25 g/L 0.5, 3.5, 6.5 bar 0, 5, 10, 30, and 60 min 10% on oven dry pulp used
southern part of Turkey. To generalize the effect of initial kappa number, intrinsic viscosity, experimental conditions, and pulping conditions prior to oxygen delignification, a dimensionless parameter approach is applied to the experimental data. To check the integrity of this approach, the same method is also applied to the reported literature data. 2. Experimental Details The Kraft eucalyptus pulp is obtained from a mill located in the southern part of Turkey. The pulp, as received, has a kappa number of 17.5 and an intrinsic viscosity of 8.5 dl/g. The experiments are performed with a 1 L pressurized reactor (Parr 4520) which is equipped with a stirrer. On the top of the reactor, three valves are used to regulate the pressure, for the introduction of gas, and for liquid sampling, respectively. In the experiments, a high-pressure 300 mL feeding tube is also used to feed NaOH solution to the system from the liquid sampling port. The temperature is measured by a thermocouple immersed inside the fluid and is controlled by a proportional integral derivative (PID) controller. The pressure of the reactor is monitored by the pressure gauge. The reactor is equipped with a turbine type impeller with a six-blade style which produces an excellent mixing over the range of stirring speeds. The experiments are performed with the aim of collecting data to study the kinetics of oxygen delignification. On the basis of this, temperature, NaOH concentration, oxygen pressure, and reaction time are chosen as the process variables. The consistency is kept constant at 0.5%. The range of process variables used in the oxygen delignification experiments are summarized in Table 1. In oxygen delignification experiments, the specified amount of unbleached pulp and MgSO4 · 7H2O are first put into the reactor. To obtain 0.5% consistency, a specified amount of boiling distilled water is transferred to the reactor. Nitrogen is bubbled through the solution in the reactor for 5 min to purge the whole system. The reactor is heated to the reaction temperature under a 40 psig nitrogen atmosphere. When the temperature reaches the set point, the NaOH solution is fed to the system with the help of nitrogen gas. Oxygen is injected to reach the desired pressure above the solution. This point is taken as the zero time for the reaction. The oxygen gas flow rate is then regulated to normal operating conditions. The oxygen pressure is continuously regulated at a constant value by an outlet flow valve located on top of the reactor. At the end of the experiment, oxygen injection is terminated, and pressure inside the reactor is released completely by opening the outlet flow valve. The reactor is opened quickly, and some of the liquid solution is taken for the tests and the rest is poured into cold water. The pulp slurry is filtered and washed thoroughly. The washed pulp is air-dried for one day and stored for the tests. The air-dried pulp is first analyzed for kappa number following the Tappi Standard T-236. The intrinsic viscosity [η] is estimated according to ASTM standard D1795. The residual alkali in the liquor from the oxygen delignification experiment is measured following Tappi Standard T-625. The determination
Figure 1. Effect of consistency on the change of kappa number (T ) 100 °C, oxygen partial pressure ) 6.5 bar, and 600 rpm).
of the kappa number and intrinsic viscosity were repeated for selected data points. 3. Results and Discussion 3.1. Mass Transfer. The controlling mechanisms in oxygen delignification systems are mass transfer of the oxygen gas into fiber, delignification reaction, and the carbohydrate degradation in the fiber. To study the reaction rate in oxygen delignification the mass transfer resistances should be eliminated. The oxygen delignification system consists of three phases, i.e., solid (fiber), liquid (aqueous alkali solution), and gas (oxygen). Hsu and Hsieh5 reported that the mass transfer resistance of oxygen in the gas phase is insignificant in comparison with the liquid phase resistance. The liquid phase resistance is high because of the low solubility of oxygen in the liquid phase. There are also interfiber and intrafiber resistances in oxygen delignification. The effect of interfiber resistances in oxygen delignification is examined by performing experiments at different consistency values and mixing rate of pulp. The change in the kappa number as a function of time at 0.5, 1, and 8% consistency values is shown in Figure 1. In these experiments, there is an initial heatup period of about 20 min (shown with dashed lines), which resulted in an initial decrease in the kappa number of around 1-2 units. It was seen from the figure that after the heating period, up to 20 min, the kappa number of the pulp at 8% consistency is higher than that of the 0.5 and 1% consistency values. There is a significant resistance for the transfer of oxygen in the experiments performed at 8% consistency. However, after 20 min the gap between the two lines is decreasing. Oxygen starts to penetrate between the fibers and the interfiber mass transfer effects are decreasing. Finally at 90 min, they reach the same kappa number. It was concluded from the figure that, in order to decrease the interfiber mass transfer limitations, the experiments should be done at lower consistencies. The NaOH concentration is kept constant in oxygen delignification experiments. Figure 2 shows the effect of consistency on NaOH concentration. While the NaOH concentration remains constant at 0.5 and 1% consistencies, it decreases with an increase in reaction time at 8% consistency. It was concluded that lower consistencies gives better control of NaOH concentration. Since NaOH concentration is kept constant and the dispersion of oxygen in the pulp is better at 0.5% consistency, oxygen delignification and carbohydrate degradation experiments are carried out at this value.
Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5873
Figure 2. Change in residual alkali concentration with respect to time (T ) 100 °C and oxygen partial pressure ) 6.5 bar).
Figure 4. Effect of refining on the change of kappa number (T ) 100 °C and oxygen partial pressure ) 6.5 bar, 0.5% pulp consistency).
By performing the Yates algorithm, Table 4 shows the importance of the variables studied in the sequence of temperature, NaOH concentration, and oxygen pressure which is followed by their interactive effects. Extensive literature on the kinetics of oxygen delignification expresses the rate equation as -ra ) -
dK )kKn dt
(1)
in which the rate coefficient, k, incorporates temperature, oxygen partial pressure, and initial sodium hydroxide concentration in the following form
[ ]
-EA [OH-]p[PO2]m (2) RT In the literature, the exponents appearing in eqs 1 and 2 take the following values:4,5,7,9,12 k ) A exp
Figure 3. Effect of mixing rate on the change of kappa number (T ) 100 °C, partial oxygen pressure ) 6.5 bar, 0.5% pulp consistency).
The liquid phase mass transfer resistance is analyzed by changing the mixing rate of the pulp. By mixing the content of the reactor more rapidly and well, it could be possible to minimize the liquid phase mass transfer restrictions. Figure 3 shows three set of experiments with different mixing speeds (500, 600, and 700 rpm) at 0.5% pulp consistency. Since mixing speed does not have an appreciable effect on the delignification curves, all experiments are performed at 600 rpm. Refining the pulp increases the fiber diameter and the surface area of the fiber. If the intrafiber mass transfer is effective in delignification, it would be expected that refining the pulp should increase the delignification rate. To investigate this effect, the refined pulp produced in the pulp and paper mill is used for a set of experiments at 0.5% pulp consistency. As can be seen from Figure 4, there is no significant effect of refining on the rate of delignification. 3.2. Rate of Oxygen Delignification. On the basis of the preliminary results, delignification experiments are performed at 0.5% consistency, eliminating interfiber mass transfer limitations and the effect of the change in alkali concentration. Kappa number data for a selected set of experiments are shown in Table 2. Statistical analysis was performed based on the Yates algorithm in order to determine the relative importance among the three variables (temperature, NaOH concentration, and oxygen pressure) studied. The algorithm, as shown in Table 3, is based on the minimum and the maximum values of the variables and the dependent variable was chosen as the kappa number change during the experiments.
0.1 e p e 2
0.1 e m e 1.3
1 e n e 7.7
(3)
In this study, the same form of the kinetic expression is used in order to correlate the experimental data. The units used in the correlation are K kappa number (mL KMnO4/g of o.d. pulp); [OH-], sodium hydroxide concentration (g/L); PO2, oxygen partial pressure (bar); t, time (min). The order of the reaction, n, is found by the integral method of analysis. Integration of eq 1 gives K1-n - K01-n ) kt, n * 1 (4) (n - 1) where K0 is the initial kappa number. Equation 4 is a linear line passing through the origin with k being the slope. The evaluation of the reaction order, n, requires a trial and error solution. The other parameters, i.e., A, EA, p, and m are determined by linear regression of the experimental data.13 Thus, the oxygen delignification rate equation is expressed as y)
-
dK -64504 ) 0.3 exp [OH-]0.74[PO2]0.32K7.9 dt RT
[
]
(5)
A relative high value of the exponent n ) 7.9 can also be due to the difficulty of separating the intarfiber diffusion from actual onsite delignification reaction. The variation of the kappa number changes with time as a function of temperature, NaOH concentration, and oxygen pressure are given in Figures 5–7, respectively. The error bars indicate the confidence intervals for the repeated kappa number determinations. There is a significant effect of temperature and
5874 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 Table 2. Change of Kappa Number with Time As a Function of Temperature, NaOH Concentration, and Oxygen Pressure Kappa Number temperature (°C) (P ) 6.5 bar, NaOH ) 0.15 g/L) time (min) 0 5 10 30 60
NaOH concentration (g/L) (T ) 100 °C, P ) 6.5 bar)
90
100
110
0.05
0.15
0.25
0.5
3.5
6.5
15.81 14.66 14.22 13.07 12.08
16.03 14.30 13.85 12.62 11.51
15.63 14.02 13.44 11.65 10.49
16.34 14.94 14.61 13.43 12.47
16.03 14.30 13.85 12.62 11.51
15.74 13.92 12.95 11.39 10.51
16.04 15.17 14.69 12.93 11.72
15.84 14.57 13.78 12.07 10.98
15.63 14.02 13.44 11.65 10.49
Table 3. Data Arranged in Yates Order temperature (°C) (variable 1) 90 110 90 110 90 110 90 110
NaOH concentration (g/L) (variable 2)
pressure (bar) (variable 3)
∆K (Ko - K)
0.05 0.05 0.25 0.25 0.05 0.05 0.25 0.25
0.5 0.5 0.5 0.5 6.5 6.5 6.5 6.5
2.37 3.55 3.59 4.87 3.24 4.55 4.16 5.99
Table 4. Ranked List of Important Factors by the Yates Algorithm identifier 1 2 3 13 12 123 23
pressure (bar) (T ) 100 °C, NaOH ) 0.15 g/L)
effect estimate 1.400 1.225 0.890 0.170 0.155 0.105 -0.045
NaOH concentration on the kappa number change. In these figures, the solid line represents the delignification rate model based on eq 5. The agreement between the experimental data and the kinetic model is tested based on root-mean-square error calculations and the values change in the range of 0.157-0.34. This model can be used for sizing oxygen delignification reactors and simulation of bleaching plants. 3.3. Rate of Carbohydrate Degradation. Two competing reactions, delignification and carbohydrate degradation, occur simultaneously during oxygen bleaching, and any kinetic study of oxygen bleaching must include the study of both delignification and carbohydrate degradation. The carbohydrate degradation is monitored by measuring the intrinsic pulp viscosity, η, (ASTM standard D1795). The carbohydrate degradation calculated as Mn (mol cellulose chains/ton pulp) data for a selected set of experiments are shown in Table 5.
Figure 5. Effect of temperature on the change of kappa number (NaOH concentration ) 0.15 g/L and oxygen partial pressure ) 6.5 bar).
A limited number of studies3,6 exists in the literature on carbohydrate degradation kinetics. In this study, the rate equation for carbohydrate degradation is represented by a two-stage zeroorder power law model in the form
[ ]
-EA1 dMn ) A1 exp [OH-]a[PO2]b(u(t) - u(t - 10)) + dt RT -EA2 [OH-]c[PO2]du(t - 10) A2 exp RT
[ ]
(6)
where u(t) is the unity function and Mn is the moles of cellulose chains per metric ton of pulp. The kinetic equation is either described by the first or second terms depending on whether reaction time is less or greater than 10 min. The relationship between the experimentally determined intrinsic viscosity, η, and Mn is given by Olm and Teder3 log Mn ) 4.35 - 1.25 log η
(7)
The parameters a, b, c, and d in eq 6 are determined by linear regression of the experimental data, and the result is given by dMn -205202 ) 33.70 exp [OH-]0.28[PO2]0.26(u(t) dt RT -14641 u(t - 10)) + 1.93 exp [OH-]0.23[PO2]0.17u(t - 10) RT (8)
[
]
[
]
The effects of temperature, NaOH concentration, and oxygen pressure on the carbohydrate degradation are shown in Figures 8, 9, and 10 respectively. The error bars indicate the confidence intervals for Mn with the repeated intrinsic viscosity determinations. As can be seen from these figures, carbohydrate degradation is strongly dependent on temperature. Therefore, the oxygen delignification towers should not be operated at high temperatures in order to preserve the pulp strength. Also, the carbohydrate degradation achieved during oxygen delignification
Figure 6. Effect of NaOH concentration on the change of kappa number (temperature ) 100 °C and oxygen partial pressure ) 6.5 bar).
Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5875 Table 5. Change of Mn (mol cellulose chains/ton pulp) with Time As a Function of Temperature, NaOH Concentration, and Oxygen Pressure Mn (mol cellulose chains/ton pulp) temperature (°C) (P ) 6.5 bar, NaOH ) 0.25 g/L) time (min) 0 5 10 30 60
NaOH concentration (g/L) (T ) 100 °C, P ) 6.5 bar)
pressure (bar) (T ) 100 °C, NaOH ) 0.25 g/L)
90
100
110
0.05
0.15
0.25
0.5
3.5
6.5
4.91 5.06 5.35 5.66 6.16
4.92 5.16 5.44 5.77 6.37
4.94 5.22 5.57 5.97 6.58
4.91 5.06 5.25 5.47 5.82
4.91 5.12 5.35 5.65 6.13
4.92 5.16 5.44 5.77 6.37
4.91 5.02 5.18 5.44 5.70
4.91 5.11 5.34 5.65 6.14
4.92 5.16 5.44 5.77 6.37
increased with increasing alkali concentration as well as with increasing oxygen partial pressure. 3.4. Dimensionless Parameters. The pulp type, pulping conditions prior to oxygen delignification, consistency, and experimental conditions have significant effects on oxygen delignification kinetics.3–7 These variables affect the initial kappa number, intrinsic viscosity, and the absolute value of these numbers with respect to time. Therefore, to generalize both the results obtained in this study and also the literature values, dimensionless variables are defined in terms of the kappa number and the reaction time. It is the first time that the dimensionless parameter approach is applied to model the kinetic analysis of oxygen delignification. The kappa number is converted to the extent of delignification as K)
|K0 - K| K0
where K0 is the initial kappa number and K is the kappa number at any time. The maximum amount of delignification achieved in this study is different for each set of experimental conditions. Literature values also show a wide variation. On the basis of eq 9, the asymptotic value of the dimensionless maximum delignification rate is determined and half of that corresponding time is chosen to define the dimensionless time as τ)
t tmax⁄2
(10)
The results obtained in terms of dimensionless approach, covering a wide range of variables, are shown in Figure 11. To fit all the data used, the different forms of equations tested13 are shown in Table 6.
(9)
Figure 7. Effect of oxygen partial pressure on the change of kappa number (T ) 100 °C and NaOH concentration ) 0.15 g/L).
Figure 8. Effect of temperature on carbohydrate degradation (NaOH concentration ) 0.25 g/L and oxygen partial pressure ) 6.5 bar).
Figure 9. Effect of NaOH concentration on carbohydrate degradation (T ) 100 °C and oxygen partial pressure ) 6.5 bar).
Figure 10. Effect of pressure on carbohydrate degradation (T ) 100 °C and NaOH concentration ) 0.25 g/L).
5876 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008
Figure 11. Extent of delignification as a function of dimensionless time (τ ) t/t0.15). Table 6. Different Dimensionless Correlations for Delignification Data dimensionless correlations
R2
Κ ) [-0.00131 + 0.5827τ0.738]/[2.7836 + τ0.738] Κ ) [0.00231 + 0.2928τ]/[1 + 0.8962τ - 0.02916τ2] Κ ) 0.31408(1 - e-0.6761τ)
0.9953 0.9947 0.9857
The R2 values are close to each other, but eq 11 is chosen for its simplicity to be used in the control of the oxygen delignification towers. It relates the kappa number change in the tower with respect to dimensionless reaction time. K ) 0.31408(1 - e-0.6761τ) (11) The same approach is also tested using the data of Agarwal et al.7 In that study, the maximum extent of delignification achieved is 0.4. Thus, the dimensionless time is calculated using the time value corresponding to the fractional delignification of 0.20 (τ ) t/t0.20). The dimensionless parameters are fitted to a nonlinear equation with a regression coefficient of 0.9874 as
eq 12. The fitted equation is drawn with a solid line in Figure 12. Also in this study, the same trend in the dimensionless parameters is seen; however at higher dimensionless time values, there is some deviation from the data. From Figures 11 and 12, it is concluded that, although the experimental conditions are different in each study, the data sets can be represented by a simple equation. K ) 0.3724(1 - e-0.7980τ) (12) The same dimensionless parameter approach is also tested using the carbohydrate degradation data in terms of Mn moles of cellulose chains per metric ton of pulp. The dimensionless carbohydrate degradation and the dimensionless time τ are defined as
Figure 12. Extent of delignification as a function of dimensionless time (τ ) t/t0.20).7
M)
|Mn0 - M| Mn0
(13)
t tmax⁄2
(14)
τ)
Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5877
Figure 13. Extent of carbohydrate degradation as a function of dimensionless time (τ ) t/t0.1). Table 7. Different Dimensionless Correlations for Carbohydrate Degradation dimensionless correlations
R2
Μ ) [-0.0004126 + 0.1462τ]/[1 + 0.4496τ - 0.01319τ2] Μ ) [-0.00103 + 0.4559τ0.92206]/[3.5446 + τ0.92206] Μ ) 0.3049(1 - e-0.3829τ)
0.9881 0.9876 0.9865
where Mn0 is the initial moles of cellulose chains per metric ton of the pulp. τ is the fraction of absolute time to the time at which half of the maximum extent of carbohydrate degradation (tmax/2) occurred. For the carbohydrate degradation data, the maximum extent of degradation occurs at around 0.2. In Figure 13, the extent of carbohydrate degradation data versus dimensionless time (τ ) t/t0.1) is presented. The data fit to a nonlinear equation as given in eq 15 which is drawn with a solid line in Figure 13. As indicated for kappa number analysis, the reason for choosing this equation from a set of similar R2 value equations shown in Table 7 is its simplicity. M ) 0.3049(1 - e-0.3829τ)
(15)
4. Conclusion In the present study, oxygen delignification and carbohydrate degradation data are collected for Turkish southern Kraft pulp. On the basis of the preliminary results obtained, it is concluded that the interfiber mass transfer resistance is insignificant at lower consistencies (at 0.5% and below) and intrafiber mass transfer resistance is negligible for the unrefined pulp that is studied. The oxygen delignification data is correlated using a general global kinetic model with integral method of analysis. The kinetic model shows good agreement with the experimental data. As a result of slowly reacting lignin molecules, the order of the kappa number (n ) 7.9) is high. In oxygen delignification systems, carbohydrate degradation is also important to preserve the strength of the pulp. In this study, the two-stage zero-order power law model is derived for the carbohydrate degradation data. This model represents the experimental data satisfactorily. There are few studies on carbohydrate degradation kinetics in the literature. Therefore,
the data obtained in this study give information on the carbohydrate degradation of hardwood eucalyptus Kraft pulp. There is a wide variation in terms of the pulp type, conditions of Kraft pulping prior to oxygen delignification, consistencies, and experimental conditions used in the previous studies.3–7 Besides, the initial kappa number and the change in the absolute value of the kappa number with respect to time are different in each study. Therefore, in order to generalize both the results of this study and that of the previous ones found in the literature, a dimensionless parameter approach is applied. The simple equation thus obtained can be used for design and control of delignification towers. It is also seen that, the dimensionless parameter approach can be applied to carbohydrate degradation data satisfactorily. Nomenclature A ) frequency factor in Arrhenius’ law Ea ) activation energy, kJ/mol K ) kappa number k ) rate constant Mn ) number of cellulose chains per ton of pulp [OH-] ) sodium hydroxide concentration, g/L PO2 ) oxygen partial pressure, bar R ) ideal gas constant, kJ/mol · K ra ) rate of reaction T ) temperature, K t ) time, min u(t) ) unity function Greek Letters η ) intrinsic viscosity, dl/g κ ) dimensionless extent of delignifcation τ ) dimensionless time M ) dimensionless carbohydrate degradation Subscripts 0 ) initial value 1,2 ) first and second part of the two stage zero order power model max/2 ) half of the maximum value Superscripts a, b, c, d, m, n, p ) exponential parameters
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Literature Cited (1) Dence, C. W.; Reeve, D. W. Pulp Bleaching Principles and Practice; Tappi Press: Atlanta, GA, 1996. (2) Smook, G A. Handbook for Pulp & Paper Technologists; Angus Wilde Publications Inc.: Vancouver, Canada, 2002. (3) Olm, L.; Teder, A. The kinetics of oxygen bleaching. Tappi J. 1979, 62 (12), 43–46. (4) Hsu, C. L.; Hsieh, J. S. Oxygen bleaching kinetics at ultra-low consistency. Tappi J. 1987, 70 (2), 107–111. (5) Hsu, C.; Hsieh, J. S. Reaction kinetics in oxygen bleaching. AIChE J. 1988, 34 (11), 116–122. (6) Iribarne, J.; Schroeder, L. R. High-Pressure oxygen delignification of kraft pulps 1. kinetics. Tappi J. 1997, 80 (10), 241–250. (7) Agarwal, S. B.; Kwon, H.B.; Genco.; J, M. Oxygen delignification of southern hardwoods. AIChE Symp. Ser. 1997, 315 (93), 26–41. (8) Schoon, N. H. Interpretation of rate equations from kinetic studies of wood pulping and bleaching. SVen. Papperstidn. 1982, R185–R193.
(9) Valchev, I.; Valcheva, E.; Christova, E. Kinetics of oxygen delignification of hardwood kraft pulp. Cellul. Chem. Technol. 1999, 33 (3-4), 303–310. (10) Nenkova, S.; Valchev, I.; Simeonova, G. Possibilities for increasing the effectiveness of oxygen delignification of hardwood kraft pulp. J. Pulp Pap. Sci. 2003, 29 (10), 324–327. (11) Zou, H.; Liukkonen, A.; Cole, B.; Genco, J.; Miller, W. Influence of kraft pulping on the kinetics of oxygen delignification. Tappi J. 2000, 83 (2), 65–71. (12) Susilo, J.; Bennington, C P.J. Modelling Oxygen-Delignification Systems. J. Pulp Pap. Sci. 2006, 32 (2), 105–109. (13) Dogan, I. Mass Transfer and Kinetics in Oxygen Delignification. Ph.D. Thesis, Middle East Technical University, Ankara, Turkey, 2004.
ReceiVed for reView November 4, 2007 ReVised manuscript receiVed May 25, 2008 Accepted May 28, 2008 IE071498H
