7078
Ind. Eng. Chem. Res. 2005, 44, 7078-7085
Kinetic Model for Kraft Pulping Process Ling Yang† and Shijie Liu*,†,‡ Department of Chemical and Materials Engineering, University of Alberta, Edmonton T6G 2G6, Canada, and Alberta Research Council, 250 Karl Clark Road, Edmonton, Alberta T6N 1E4, Canada
A new mechanism is proposed for the heterogeneous delignification reaction during the Kraft pulping process. The mechanism consists of three key kinetic steps: (1) adsorption of hydroxide and hydrosulfide ions on lignin; (2) surface reaction on the solid surface to produce degraded lignin products; and (3) desorption of degradation products from the solid surface. The most important step for the delignification process is the surface reaction, rather than the reactions occurring in the liquid phase. A kinetic model has, thus, been developed based on the proposed mechanism. The derived kinetic model shows that the mechanism can be employed to predict the pulping behavior under a variety of conditions with good accuracy. Introduction Kraft pulping is a process in which lignin is removed in the presence of sodium hydroxide and sodium sulfide, and it still plays an important role in the pulping process worldwide today. Therefore, modeling the Kraft pulping process is essential and significant for the optimization of the process conditions. In the last half century, many studies on the kinetics and transport behavior of the Kraft pulping process have been conducted, and the models with various complexities describing the delignification kinetics have been developed for control and design purposes.1-7 In the previous works, the kinetics of the Kraft pulping process is mostly divided into three stages, that is, the initial, bulk, and residual stages. The models currently used in the open literature can be expressed as follows
dL ) (k1[OH-]a + k2[OH-]b[HS-]c)Ld dt
(1)
where L is the concentration of lignin in wood, [OH-] is the alkali concentration in the cooking liquor, [HS-] is the hydrosulfide concentration in the cooking liquor, and k1 and k2 are the rate constants. Different values of parameters a, b, and c were found for each stage during the delignification process. The transition points between the stages depend on the lignin content and the cooking conditions and are determined empirically by plotting carbohydrate content versus lignin content. Although this stepwise approach has been widely employed, there are still some issues that need to be resolved. It is generally accepted that the delignification rate is first order in the residual lignin of wood, that is, d ) 1, but Li et al.8 found an apparent second-order reaction kinetics in kappa number. These authors attributed this different behavior to the wide range of kappa numbers used in their work, and the first-order reaction kinetics in kappa number cannot explain the * Corresponding author. E-mail:
[email protected]. Present address: Faculty of Paper Science and Engineering, SUNY Environmental Science and Forestry, 1 Forest Drive, Syracuse, NY 13210. † University of Alberta. ‡ Alberta Research Council.
transition point from the late bulk phase to the early residual delignification phase. Smith and Williams9 proposed that lignin is composed of two classes. Each class of lignin possesses a different reactivity in 70% and 30%, respectively, and is degraded by two different reactions: with hydroxide ion alone and with a combination of hydroxide and hydrosulfide ions. This reaction scheme is shown below OH-
L1 98 Ld OH-,HS-
L1 98 Ld OH-
L2 98 Ld OH-,HS-
L2 98 Ld
(2) (3) (4) (5)
where L1 and L2 are the two fractions of lignin with a different reactivity in the wood and Ld is the fraction of dissoluble lignin. Gilarranz et al.10 and Oliet et al.11 carried out the investigation into organosolv pulping. They treated the lignin as three classes, initial, bulk, and residual, and delignification was described as the consecutive dissolution of these three lignin species. The kinetic models developed in their works are similar to each other. The difference is that, in Gilarranz et al.,10 the reactions of bulk lignin are reversible, whereas in Oliet et al.,11 the reactions are irreversible. Although efforts have been directed at modeling the Kraft process, most of the investigators assumed that Kraft pulping is a pseudo-homogeneous process and neglected the heterogeneous nature of the process. The objective of this study is to examine the delignification during the Kraft pulping process from a chemical reaction engineering science perspective. In particular, the chemical reaction mechanism takes into account the heterogeneous nature of Kraft pulping. Lignin reacts in parallel with sodium hydroxide and sodium sulfide.9 To avoid too many parameters and to reduce the complexity of the kinetic model involved, we treat lignin or lignin segments as one class with the same reactivity. Two delignification reactions take place during cooking: (1) lignin reacts with sodium hydroxide alone and (2) lignin reacts with the combination of sodium hydroxide and sodium sulfide. In addition, the developed
10.1021/ie050301n CCC: $30.25 © 2005 American Chemical Society Published on Web 08/02/2005
Ind. Eng. Chem. Res., Vol. 44, No. 18, 2005 7079
heterogeneous pulping model is based on a lumped parameter approximation, in which the chemical species in wood are lumped, for example, to lignin and carbohydrates, without referring to a specific chemical compound, removing the complexity of the detailed chemistry involved. Reaction Mechanism In view of the heterogeneous nature of Kraft pulping, the delignification may be considered to occur in a stepwise manner, as follows: 1. Transport of hydroxide and hydrosulfide ions from the bulk liquor to the exterior surface of the chip; 2. Diffusion of the chemical ions to the interior of the chip; 3. Chemisorptions occur on the interior surface; 4. Surface reaction between the chemical ions and lignin; 5. Desorption of the dissoluble lignin degradation products; 6. Diffusion of the dissoluble lignin degradation products to the chip exterior; 7. Transport of the dissoluble lignin degradation products in the bulk liquor. Under normal conditions, transport steps 1 and 7 are probably unimportant but the diffusion steps of 2 and 6 may play a significant role unless the effective thickness of the chips is less than the critical thickness (2-3 mm).12-13 Under such conditions, these transport steps reach a negligible extent to the overall observed pulping rate. The chemical reactions involved are said to be the rate-controlling steps, which means the overall reaction rate is dependent on steps of 3-5 directly, provided that the chips with the thickness of 2-3 mm or less are cooked. In this paper, we are interested in the intrinsic kinetics, i.e., steps 3-5, only. According to these considerations, hydroxide and hydrosulfide ions are present on the solid surface through adsorption from the bulk liquid phase, and delignification reactions take place on the solid surface. Assuming the lignin segments in wood are of identical reactivity, we propose a simplistic mechanism: k1
OH- + R - L 79 8 R - L‚OHk -1
k2
HS- + R - L 79 8 R - L‚HSk -2
k3
R - L‚OH- 98 R - Ls1k4
HS-‚R - L‚OH- 98 R - Ls22R-
k5 8 Ls1- 79 k-5 k6
R+
Ls1-
8 R + Ls22R - Ls22- 79 k -6
(6)
(7)
(8)
(9)
(10)
(11)
where R - L denotes the native lignin segments connected with the fibers, on which hydroxide and hydrosulfide can be adsorbed, denoted by R - L‚OHand R - L‚HS-; R - Ls1- and R - Ls22- denote two kinds
of undesorbed reaction products of lignin; and Ls- and Ls2- denote the dissolved lignin degradation products. Equation 6 represents the adsorption of hydroxide ion onto the lignin surface, and eq 7 represents the adsorption of hydrosulfide ion onto the lignin surface. The active sites for adsorption are assumed to be the sites on lignin. We assume that one active site or lignin segment for adsorption can absorb one hydroxide ion and/or one hydrosulfide ion. The adsorptions of hydroxide and hydrosulfide ions are, therefore, not competitive. Equations 8 and 9 are the surface-reaction steps, where the delignification reactions occur in which the lignin is converted into dissoluble degraded lignin products. Considering the process of soda pulping, in which the delignification reaction takes place without the addition of hydrosulfide ion, eq 8 may occur. Moreover, we assume that the other delignification reaction takes place on the active sites occupied by both hydroxide and hydrosulfide ions simultaneously. Thus, two kinds of delignification reactions proceed by following different reaction paths. Equations 10 and 11 are the desorption of the dissoluble lignin fragments formed. Adsorption Isotherm It is assumed that the adsorption and desorption reactions occur at much faster rates than those of surface reactions on the lignin surface. Therefore, one can assume that the adsorption steps are always in equilibrium. The adsorption process can be represented as the elementary reversible reactions shown by eqs 6 and 7. Thus, at the time scale of the surface reaction, the equilibrium of adsorption of hydroxide and hydrosulfide ions is given by
k1[OH-]Cv1 - k-1CR-L‚OH- ) 0
(12)
k2[HS-]Cv2 - k-2CR-L‚HS- ) 0
(13)
where Cv1 (mol/(kg of oven dry wood)) and Cv2 (mol/(kg of oven dry wood)) denote the vacant surface concentration of the active sites that have not been occupied by hydroxide and hydrosulfide ions, respectively. CR-L‚OH(mol/(kg of oven dry wood)) and CR-L‚HS- (mol/(kg of oven dry wood)) denote the surface concentration of the active sites occupied by hydroxide and hydrosulfide ions, respectively. The rate constants, k1 (L‚mol-1‚min-1) and k2 (L‚mol-1‚min-1), are the adsorption rate constants of hydroxide and hydrosulfide ions, respectively, and k-1 (min-1) and k-2 (min-1) are the desorption rate constants of hydroxide and hydrosulfide ions, respectively. Equation 12 can be reduced to
CR-L‚OH- )
k1 [OH-]Cv1 ) K1[OH-]Cv1 k-1
(14)
where K1 (mol‚L-1) is the adsorption (equilibrium) constant of hydroxide on the active site. One may expect that the total available active sites would be shared by three portions, the vacant sites, the coverage of hydroxide, and the coverage of hydrosulfide, if the two adsorptions are competitive. However, hydroxide adsorption is not competitive to the hydrosulfide adsorption; although both adsorptions occur on the same type of active sites, both adsorptions can occur on one single site simultaneously. As the total number of active sites available is finite, a site concentration balance
7080
Ind. Eng. Chem. Res., Vol. 44, No. 18, 2005
leads to
Ct ) Cv1 + CR-L‚OH-
(15)
where Ct (mol/(kg of oven dry wood)) is the total surface concentration of the active sites on the wood cell surface. Combining eqs 14 with 15 gives the following
Cv1 )
Ct 1 + K1[OH-]
CR-L‚OH- )
K1[OH-]Ct 1 + K1[OH-]
(16)
Ct 1 + K2[HS-]
CR-L‚HS- )
K2[HS-]Ct 1 + K2[HS-]
CHS-‚R-L‚OH- )
k2 [HS-]Cv3 ) K2[HS-]Cv3 (24) k-2
where Cv3 (mol/(kg of oven dry wood)) is the concentration of the hydroxide-adsorbed active sites not occupied by hydrosulfide ion. The site concentration balance leads to
CR-L‚OH- ) Cv3 + CHS-‚R-L‚OH-
(17)
CHS-‚R-L‚OH- )
K2[HS-]CR-L‚OH1 + K2[HS-]
(1 + K1[OH-])(1 + K2[HS-])
(19)
rs )
k3K1[OH-]Ct 1 + K1[OH-]
+
k4K1K2[OH-][HS-]Ct (1 + K1[OH-])(1 + K2[HS-]) (27)
where k3 (min-1) and k4 (min-1) are the rate constants of the reactions depicted by eqs 8 and 9, respectively. The active site concentration Ct is proportional to the percentage of lignin in the wood, i.e.,
Ct ) k0L
On the basis of the reactions depicted by eq 8, we can obtain the delignification rate by the action of the hydroxide ion
(20)
(21)
where r3 and r4 are the intrinsic rates of delignification for eqs 8 and 9 as they are written. The overall rate of delignification is
rs ) r3 + r4 ) k3CR-L‚OH- + k4CHS-‚R-L‚OH- (22) where rs ((mol of active sites)/(min‚kg of oven dry wood)) is the surface reaction rate expressed by the active site concentration. CHS-‚R-L‚OH- (mol/(kg of oven dry wood)) is the concentration of the active sites occupied by both hydroxide and hydrosulfide ions simultaneously. CHS-‚ R-L‚OH- can be derived by the adsorption of hydrosulfide ion onto the hydroxide-adsorbed active sites or the adsorption of hydroxide onto the hydrosulfide-adsorbed active sites; both adsorptions will give the same result. Here, we use the adsorption of hydrosulfide onto the active sites preoccupied by hydroxide as an illustrative instance. k2
-2
(23)
(28)
where k0 (mol/(kg of lignin)) is the proportional constant between the lignin content and the active site (i.e., reactive lignin segment) concentration and L ((kg of lignin)/(kg of dry wood)) is the content (percentage) of lignin in the wood. Substituting eq 28 into eq 27 we obtain
and the rate of delignification is depicted by eq 9
8 HS-‚R - L‚OHHS- + R - L‚OH- 79 k
(26)
Substituting eq 26 into eq 22, we obtain
Reaction Rates
r4 ) k4CHS-‚R-L‚OH-
)
K1K2[OH-][HS-]Ct
(18)
where K2 (mol‚L-1) is the adsorption (equilibrium) constant of hydrosulfide on the active site. Therefore, the amounts or concentrations of the hydroxide and hydrosulfide ions on the surfaces of the wood cells are directly related to their respective bulk concentrations in the liquid phase.
r3 ) k3CR-L‚OH-
(25)
Combining eq 25 with eqs 17 and 24, we obtain
which is typical of the Langmuir isotherm. For the adsorption of hydrosulfide ion, the adsorption isotherm can be derived in a similar fashion as that for the adsorption of hydroxide
Cv2 )
The concentration of the active sites occupied by both hydroxide and hydrosulfide ions can be derived from the adsorption equilibrium
- rL )
k0k3K1[OH-]L 1 + K1[OH-]
+
k0k4K1K2[OH-][HS-]L (1 + K1[OH-])(1 + K2[HS-]) (29)
where -rL ((mol of lignin)/min/(kg of wood)) is the delignification rate expressed by the lignin content. In a commercial Kraft pulping process, the typical liquor-to-wood ratio is about 3-5:1 L/kg, so the concentrations of hydroxide and hydrosulfide ions decrease during the cooking process. Only under the condition of a high liquor-to-wood ratio can the concentrations of hydroxide and hydrosulfide ions be assumed as constant. Therefore, when a typical liquor-to-wood ratio is employed, a model should be necessary to incorporate the consumption of chemicals while lignin and carbohydrates are removed. As described by other investigations,14 the chemicals are consumed mainly in four reactions: hydrolysis of acetyl side groups associated with hemicelluloses polymers, neutralization of the acid products in the wood, peeling reactions of the carbohydrate, and formation of lignin degradation products. Thus, it is difficult to determine the amounts of chemicals consumed by the delignification reaction alone. Kleinert2 assumed that the carbohydrate reaction rate
Ind. Eng. Chem. Res., Vol. 44, No. 18, 2005 7081
is a linear function of the delignification rate, and the constant of proportionality is independent of pulping conditions. To estimate the alkali reaction rate, Gustafson et al.3 assumed that the alkali consumption could be expressed as a linear function of the acetyl, lignin, and carbohydrate degradation rates. In this study, the factors f1 and f2 are introduced into the consumption rate to include the chemicals consumed by other components in the wood, for example, carbohydrate. The consumption rates of hydroxide and hydrosulfide ions are expressed as
- rOH- ) f1(-rL) ) f1
(
k0k3K1[OH-]L 1 + K1[OH-]
+
-
-
k0k4K1K2[OH ][HS ]L
)
(1 + K1[OH-])(1 + K2[HS-])
(30)
- rHS- ) f2‚r4 ) f2 (1 + K1[OH-])(1 + K2[HS-]) (31) One should note that, under batch pulping conditions, the mass balance of the whole system leads to, for lignin:
dL dt
(32)
For hydroxide ion in the system, hydroxide ion is distributed in the bulk of the liquor and on the surface of the lignin by adsorption effect, so the mass balance of [OH-] is obtained as follows
-
d([OH-]VL + CR-L‚OH-W) ) -rOH-W dt
(33)
For [HS-], the case is the same as that for hydroxide ion, so the mass balance is
-
d([HS-]VL + CR-L‚HS-W) ) -rHS-W dt
(34)
where W (kg of oven dry wood) denotes the mass of dry wood and VL (L) denotes the volume of liquid. So we obtain
-
k3K1[OH-]L dL 1 + ) (-rL) ) dt k0 1 + K1[OH-] k4K1K2[OH-][HS-]L (1 + K1[OH-])(1 + K2[HS-])
(35)
-
-
d[OH ] ) dt 1 k0K1L
VL + W (1 + K [OH-])2 1
(
f1 -
K1[OH-] 1 + K1[OH-]
)
d[HS-] ) dt 1 k0K2L
VL + W (1 + K [HS-])2 2
[
f2r4 -
K2[HS-]
]
(-rL) (37)
1 + K2[HS-]
When eqs 35-37 are solved simultaneously, the dynamic (or kinetic) behavior of the delignification can be predicted during the Kraft pulping process; then the lignin and the concentrations of chemicals can be predicted, too. Analysis and Discussion
k0k4K1K2[OH-][HS-]L
- rL ) -k0
-
(-rL) (36)
The parameters (K1, K2, k3, k4, f1, f2, and k0) in the kinetic model can be estimated by minimizing the variance associated with the model prediction and the experimental data15 simultaneously. In this work, the data of Santos et al.7 and Wilder and Daleski1 will be used to compare with the model prediction. The cooking conditions used by Santos et al. and Wilder and Daleski are given in Tables 1 and 2, respectively. In the work of Santos et al.,7 two sets of isotherm runs were performed. One set of experiments was carried out at a low liquor-to-wood ratio of 5, in which the concentrations of hydroxide and hydrosulfide ions decreased during the cook. The other was carried out at a high liquor-to-wood ratio (50:1 L/kg), in which the concentrations of chemicals were treated as constant throughout the cook. Data from the two sets of runs have been selected to model the kinetics of delignification during the Kraft pulping process. Because a comprehensive set of data could not be procured in the open literature, only data at 140, 150, and 160 °C in the experiment of Santos et al. are employed to compare with the kinetic model of delignification. If the same cook material, such as Eucalyptus globules in the work of Santos et al., was cooked under different cooking condition, the parameters in the kinetic model are only a function of temperature, and they are independent of the liquid-to-wood ratio. Therefore, whether a high liquor-to-wood ratio or a low liquorto-wood ratio is employed in the work of Santos et al.,7 the parameters obtained are the same for these two conditions. To obtain such parameters suitable for both low and high liquor-to-wood ratios, we combine the two sets of experimental data under low and high liquorto-wood ratios to minimize them at the same time. Considering that the real initial concentrations of hydroxide and hydrosulfide ions are lower than that before the mixing of the liquor with chips because of adsorption effects, the mass balance were made at the initial time (t ) 0)
VL[OH-]0 ) VL[OH-]0 + CR-L‚OH-W0
(38)
VL[HS-]0 ) VL[HS-]0 + CR-L‚HS-W0
(39)
where [OH-]0 and [HS-]0 are the concentrations of hydroxide and hydrosulfide in the liquor before mixing with chips. In the work of Santos et al.,7 [OH-]0 ) 1.2 mol‚L-1 and [HS-]0 ) 0.18 mol‚L-1. [OH-]0 and [HS-]0 are the initial concentrations of hydroxide and hydrosulfide in the liquor when the reactions start. W0 is the initial mass of dry wood. The parameters estimated are shown in Table 3. Figures 1-3 compare the model
7082
Ind. Eng. Chem. Res., Vol. 44, No. 18, 2005
Table 1. Cooking Conditions Used by Santos et al.7 species chip size lignin content cellulose content pentosans content extractives and ash moisture cooking temperature liquor-to-wood ratio [OH-] [HS-]
Eucalyptus globules 3 mm × 5 mm × 20 mm 22.1% on dry wood 50.4% on dry wood 23.2% on dry wood 1.9% on dry wood 41.2% on dry wood 100-180 °C 5:1 L/kg, 50:1 L/kg 1.2 M 0.18 M
Table 2. Cooking Conditions Used by Wilder and Daleski1 species chip size lignin content cooking temperature liquor-to-wood ratio active alkali concentration sulfidity
loblolly pine 1 mm × 1/4 in. × 2 in. 29.1% on wood 142, 150, 160, 171 °C 200:1 L/kg 60 g/L as NaOH 40%
Figure 3. Hydrosulfide ion consumption at different temperatures with a low liquor-to-wood ratio (5:1) vs time.
Table 3. Kinetic Parameters Estimated from the Experimental Data of Santos et al.7 T, °C K1, M-1 K2, M-1 160 150 140
5.63 8.42 10.6
1.00 1.45 1.62
k3, min-1
k4, min-1
f1
f2
0.043 0.0571 2.17 4.78 0.0208 0.0179 1.93 4.30 0.00872 0.0075 1.65 3.90
k0, mol/kg 9.48 10.1 11.8
Figure 4. Calculated vs experimental lignin content under a low liquor-to-wood ratio.7
Figure 1. Lignin removal at different temperatures with a low liquor-to-wood ratio (5:1). The symbols are experimental data of Santos et al.7
Figure 5. Calculated vs experimental hydroxide concentration under a low liquor-to-wood ratio.7
Figure 2. Effective alkali consumption at different temperatures with a low liquor-to-wood ratio (5:1) vs time.
predictions with the experimental data under a low liquor-to-wood ratio. As can be seen from Figures 1-3, for all of the lignin test cases, the data fit rather well. But for the hydrosulfide ions, the results at the low temperature are not as affirmative as those for lignin; at a higher temperature, such as at 160 °C, the fits are quite reasonable.
Higher deviations occur for the model predictions of hydrosulfide ion at the low temperature (140 °C). The one reason for this behavior may be caused by experimental error. As can be seen from Figure 3, the difference between the data of 140 °C and 150 °C is very small, although the reaction takes place at the different temperature. The other reason may be attributed to the assumption made for the model that the consumption of hydroxide and hydrosulfide ions by other components in the wood is proportional to that by lignin. This assumption for hydrosulfide consumption may be somewhat weak at the low temperature. That means that the introduction of the proportionality constant to explain the consumption of hydrosulfide by other components in the wood chips may result in the error. The calculated versus experimental lignin content and chemical concentrations under a low liquor-to-wood ratio are shown in Figures 4-6.
Ind. Eng. Chem. Res., Vol. 44, No. 18, 2005 7083
Figure 6. Calculated vs experimental hydrosulfide concentration under a low liquor-to-wood ratio.7
Figure 7. Lignin removal rate at different temperatures with a high liquor-to-wood ratio (50:1). The symbols are the experimental data of Santos et al.7
Table 4. Proportionality Factors F1 and F2 F1 F2
140 °C
150 °C
160 °C
0.274 0.071
0.331 0.073
0.397 0.093
In the work of Santos et al., the proportionality factor between the consumption rate of hydroxide and the delignification rate is 1.67 and 0.3 for initial and bulk delignification, respectively, and the proportionality factor between the consumption rate of hydrosulfide and the delignification rate is 0.44 and 0.042 for initial and bulk delignification, respectively. To make a comparison among the proportionality factors f1 and f2 with those in Santos’s work, eqs 36 and 37 are rearranged into a fashion similar to that in Santos’s work.
-
d[OH-] ) dt L0k0 k0K1L
VL + W (1 + K [OH-])2 1
(
-
-
[
(
f1 -
K1[OH-] 1 + K1[OH-]
) (
2
f2 -
k3(1 + K2[HS ] K2k4[HS-]
×
)
d(1 - XL) d(1 - XL) ) F1 (40) dt dt
L0 k 0 d[HS-] × ) k0K2L dt VL + W (1 + K [HS-])2
1+
)
Figure 8. Effective alkali consumption at different temperatures with a high liquor-to-wood ratio (50:1) vs time.
-
K2[HS-] -
]
1 + K2[HS ]
(
(
F2 -
-
)
d(1 - XL) ) dt
)
d(1 - XL) (41) dt
Seen from the above equations, F1 and F2 are a function of the parameters, such as the rate constant, and the proportionality factor f as well as the concentrations of hydroxide and hydrosulfide ions. During the pulping process at the low liquor-to-wood ratio, the chemical concentrations undergo changes. That is, F1 and F2 are not constant in our work. Although F1 and F2 change with cooking time, the results show that their changes are minimal. Therefore, the average values of F1 and F2 are shown in Table 4. Compared with the value of the proportionality factors in the work of Santos,7 F1 and F2 are not constant
Figure 9. Hydrosulfide consumption at different temperatures with a high liquor-to-wood ratio (50:1) vs time.
as the temperature is varied. As can be seen from Table 4, the values of F1 and F2 in our work are between the values of initial and bulk delignification in Santos et al.7 Figures 7-9 compare the model predictions with the experimental data under a high liquor-to-wood ratio.7 As can be seen from Figure 7, good agreement was achieved between the model prediction and the experimental data in all three cases. It is also found from Figures 8 and 9 that, under a high liquor-to-wood ratio of 50, the concentrations of hydroxide and hydrosulfide decrease slightly during cooking. Wilder and Daleski1 carried out the experimental study on the delignification kinetics of loblolly pine. In their work, a high liquor-to-wood ratio (200:1) was employed to keep the concentration of liquor composition constant, and thin wood shavings were used for digestion to eliminate the effect of liquor penetration and diffusion. Figure 10 shows a comparison made
7084
Ind. Eng. Chem. Res., Vol. 44, No. 18, 2005 Table 5. Calculation of Activation Energy and Frequency Factors ∆H or Ea (kJ/mol) ln A correlation coefficient, R2
eq 6
eq 7
eq 8
eq 9
-46.96 -11.28 0.97
-35.73 -9.88 0.90
118.76 29.85 0.99
151.21 39.07 0.99
be obtained by the slope of the straight lines; the calculations of responding parameters are shown in Table 5. Conclusion Figure 10. Lignin removal rate at a high liquor-to-wood ratio (200:1). The symbols are the experimental data of Wilder and Daleski.1
Figure 11. Plot of ln k versus the reciprocal of temperature.
between the experimental data and the model prediction. As can be seen in Figure 10, the line fits the experimental data very well. Heats of Adsorption and Activation Energy According to the Arrhenius law, the rate constant k conforms to the following equation -Ea/RT
k)Ae
(42)
where Ea is the activation energy for the irreversible reaction under consideration (eqs 8 and 9). For a reversible reaction (eqs 6 and 7), it denotes the heat of adsorption. T is the absolute temperature. Taking natural logs of both sides gives
ln k ) ln A -
Ea RT
(43)
If a straight line is obtained based on the model prediction when plotting ln k versus (1/T), the kinetic model developed in this work is validated. Figure 11 shows the relationship between the rate constant (or equilibrium constant) and the reciprocal of temperature. It can be seen from Figure 11 that the natural log of the rate constant is linear with the reciprocal of temperature. The equilibrium constant of adsorption reactions (eqs 6 and 7) increases as temperature decreases; this behavior can be explained by the fact that the chemical adsorptions are exothermic. As the temperature of the system decreases, adsorption equilibrium moves to the production side, so the equilibrium constant increases. The activation energy (based on k3 and k4) or the heat of adsorption (based on K1 and K2) can
A new mechanism has been proposed for the heterogeneous delignification reaction of the Kraft pulping process. The proposed kinetics of delignification consist of three steps: (1) adsorption of hydroxide and hydrosulfide ions on the active sites on the lignin surface, (2) chemical reactions in which insoluble lignin is reacted with hydroxide and hydrosulfide ions in parallel to produce dissoluble degradation products, and (3) desorption of the dissoluble degradation products formed on the lignin surface. In our case, the active sites for adsorption of hydroxide and hydrosulfide ions are the sites on the lignin; the adsorption of hydroxide and hydrosulfide ions follows the noncompetitive mechanism of Langmuir adsorption. The kinetic parameters have been estimated by fitting the model prediction with the experimental data of cooking in the literature, in which the pulping rates were kinetically controlled. The model shows good agreement with the experimental data. In the present study, only the delignification reaction was considered. Degradation of carbohydrates is included by introducing the proportionality factors especially, in which chemicals are consumed. Such treatment results in a deviation of hydrosulfide consumption at the low temperature. Acknowledgment The authors are indebted to Alberta Pacific Forest Industries, Inc. for financial support. Literature Cited (1) Wilder, H. D.; Daleski, E. J., Jr. Delignification Rate Studies, Part 2 of a Series on Kraft Pulping Kinetics. Tappi J. 1965, 48 (5), 293. (2) Kleinert, T. N. Mechanisms of Alkaline Delignification. 1. The Overall Reaction Pattern. Tappi J. 1966, 49 (2), 53. (3) Gustafson, R. R.; Slelcher, C. A.; Mckean, W. T.; Finlayson, B. A. Theoretical Model of the Kraft Pulping Process. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 87. (4) Juvekar, P.; Ransdell, J.; Cole, B.; Genco, J. Kraft Pulping Kinetics of Eastern White Cedar. AIChE Symp. Ser. 1995, 307 (91), 1. (5) Mirams, S.; Ngugen, K. L. Kinetics of Kraft Pulping of Eucalyptus Globulus, AICHE Symp. Ser. 1996, 311 (92), 1 (6) Giudici, R.; Park, S. Kinetic Model for Kraft Pulping of Hardwood. Ind. Eng. Chem. Res. 1996, 35, 856. (7) Santos, A.; Rodriguez, F.; Gilarranz, M. A.; Moreno, D.; Garcia-Ochoa, F. Kinetic Modeling of Kraft Delignification of Eucalyptus Globules. Ind. Eng. Chem. Res. 1997, 36, 4114. (8) Li, Z.; Li, J.; Kubes, G. J. Kinetics of Delignification and Cellulose Degradation During Kraft Pulping With Polysulphide and Anthraquinone. J. Pulp Pap. Sci. 2002, 28 (7), 234. (9) Smith, C. C.; Williams, T. J. Mathematical Modelling, Simulation and Control of the Operation of a Kamyr Continuous Digestor for the Kraft Process. Ph.D. Thesis, Purdue University, West Lafayette, IN, 1974. (10) Gilarranz, M. A.; Rodriguez, F.; Santos, A.; Oliet, M.; Garcia-Ochoa, F.; Tijero, J. Kinetics of Eucalyptus globules delig-
Ind. Eng. Chem. Res., Vol. 44, No. 18, 2005 7085 nification in a methanol-water medium. Ind. Eng. Chem. Res. 1999, 38, 3324. (11) Oliet, M.; Rodriguez, F.; Santos, A.; Gilarranz, M. A.; Garcia-Ochoa, F.; Tijero, J. Organosolv delignification of Eucalyptus globules: Kinetics study of autocatalyzed ethanol pulping. Ind. Eng. Chem. Res. 2000, 39, 34. (12) Wilder, H. D.; Daleski, E. J., Jr. Kraft pulping kinetics. I. Literature review and research program. Tappi J. 1964, 47 (5), 270. (13) Hatton, J. V.; Keays, J. L. Effect of Chip Geometry and Moisture on Yield and Quality of Kraft Pulps from Western Hemlock and Black Spruce. Pulp Pap. Can. 1973, 74 (1), 79.
(14) Sjo¨sto¨m, E. Wood Chemistry. Fundamentals and Applications; Academic: New York, 1981. (15) Liu, S. Parametric Estimation and Error Structure. Dyn. Cont., Discrete Impulsive Syst., Ser. B: Appl. Algorithms 2004, 11 (1), 1.
Received for review March 2, 2005 Revised manuscript received June 17, 2005 Accepted June 27, 2005 IE050301N
