Kinetics of Eucalyptus globulus Delignification in a Methanol−Water

3324

Ind. Eng. Chem. Res. 1999, 38, 3324-3332

Kinetics of Eucalyptus globulus Delignification in a Methanol-Water Medium Miguel A. Gilarranz, Francisco Rodrı´guez,* Aurora Santos, Mercedes Oliet, Fe´ lix Garcı´a-Ochoa, and Julio Tijero Departamento de Ingenierı´a Quı´mica, Facultad de Quı´mica, Universidad Complutense, 28040 Madrid, Spain

The kinetics of Eucalyptus globulus delignification in methanol-water pulping has been studied. A total of 17 isothermal runs at a liquor-to-wood ratio of 50 L kg-1 were carried out to develop the kinetic model describing the system. In a first series of experiments, eight models were considered to study the influence of temperature on the delignification rate. The most suitable model, which was discriminated according to statistical criteria, describes delignification as the consecutive dissolution of three lignin species: initial, bulk, and residual lignin, their content in wood being 10, 69, and 21%, respectively. Initial and residual delignification were considered as irreversible reactions and bulk delignification as reversible. The influence of hydrogen ion concentration was taken into account by means of a general power-law expression. The model proposed was validated by reproducing the experimental data from four runs carried out under nonisothermal conditions and a liquor-to-wood ratio of 7 L kg-1, which are closer to industrial operating conditions. Introduction The pioneering studies of Kleinert1-3 on organosolv pulping generated a great interest in delignification with organic solvents. In the last years, some organosolv processes such as Organocell,4 ASAM,5 ALCELL,6 and MILOX7 have been developed at pilot plant and industrial scale. However, more research is needed to achieve fully competing processes and a better understanding of organosolv pulping. Organosolv processes will not solve all the problems of existing processes, but they could complement the production from certain raw materials and could provide some advantages such as easy bleachability, lesser odorous emissions, and lower mill size.8 Information about organosolv pulping can be found reviewed elsewhere.9 Among the variety of solvents employed in organosolv pulping, methanol meets some interesting characteristics. Thus, it has a low cost when compared to other pulping solvents and its volatility enables easy recovery by distillation. Besides, the methanol generated during the pulping can compensate the losses.10 So far, the scope of methanol has been the alkaline organosolv pulping,8 although it was shown that pulps with low lignin content and acceptable viscosity can be obtained by the methanol acidic pulping.11 The studies on the kinetics of delignification in methanol-water can provide a better understanding of delignification in this medium and can be a valuable tool for process control and optimization. The aim of this work is the proposal of a kinetic model for acidautocatalyzed pulping of Eucalyptus globulus wood in a methanol-water medium. In a first series of experiments, several models are proposed to study the influence of cooking temperature. Once the most suitable model according to statistical criteria, i.e., lower value of sum-of-squares residuals, is discriminated, the influ* To whom correspondence should be addressed. Phone: 3491-3944246. Fax: 34-91-3944243. E-mail: [email protected]. ucm.es.

ence of hydrogen ion concentration on the rate constant is established. Finally, the developed model is validated by reproducing experimental data obtained under nonisothermal conditions. Delignification Kinetics Wood delignification was found to take place according to several mechanisms.12 At the beginning, delignification is rapid, but after certain portions of lignin have been removed from wood the delignification proceeds at a slower rate. Thus, for the sake of simplicity, it can be divided into three stages: initial, bulk, and residual. In the bulk stage most of the lignin is removed. It has been observed that in organosolv-autocatalyzed pulping the transition from the bulk to residual period takes place when 80-85% of the total lignin has been dissolved, whereas in acid-catalyzed systems the amount of lignin removed at this transition point is higher.13 The residual stage is the slowest, since at this point the most reticulated fraction of lignin is removed. The dissolution of lignin is usually described by means of the following differential equation:12

dL ) -kL ) -k0e-E/(RT)L dt

(1)

The studies on delignification usually employ two different approaches. In the first of them, it is assumed that wood only contains one type of lignin. In this case, the different phases observed in delignification correspond to changes in the mechanism that controls the reaction rate of the overall process.14,15 The activation energy obtained with this assumption varies between 66.5 and 78.2 kJ mol-1. In the second hypothesis, the lignin in wood is supposed to be composed of several species (usually initial, bulk, and residual lignin) dissolving at different rates.3,16-23 The most usual approach is to assume that the different lignin species react consecutively according to the first-order kinetic model expressed by eq 1. The ranges reported for the activation

10.1021/ie990161f CCC: $18.00 © 1999 American Chemical Society Published on Web 07/30/1999

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3325

energy of bulk and residual organosolv delignification are 26-140 and 56-64 kJ mol-1, respectively. There is no data available for the initial stage. The value of the rate constant, k, is affected by the chemical concentrations in the pulping liquor. In the case of organosolv acid pulping, the increase in the hydrogen ion concentration leads to a rise in the value of the rate constant.15 In the approaches proposed to take into account the influence of hydrogen ion concentration on the rate constant, a first-order dependence is usually assumed by comparison with other acidcatalyzed reactions.13,15,23 Tirtowidjojo et al.13 observed important deviations with respect to the behavior expected. It was stated that these deviations were caused by neutralization of sulfuric acid by wood ash and protein components. The value of the parameters obtained for the kinetic models can differ notably depending on the experimental conditions. Thus, Va´zquez et al.15 observed that in the acetic acid pulping of Eucalyptus globulus catalyzed with hydrochloric acid, the activation energy determined was 78.2 kJ mol-1 when the hydrochloric acid concentration was lower than 0.007 N. However, when this concentration was raised, the activation energy dropped. A minimum value of 66.5 kJ mol-1 was obtained for a hydrochloric acid concentration of 0.027 N. These changes can be caused by increased lignin condensation and redeposition. Parajo´ et al.14 calculated the value of the rate constant for lignin redeposition and found that the interaction between the cooking temperature and the hydrogen ion concentration has an influence on lignin redeposition. The value of the rate constant at 115 °C varied between 0.83 × 10-3 and 10-3 min-1 in the 0.15-0.45 N hydrochloric acid concentration range, while at 130 °C, in the same concentration range, the rate constant increased from 1.2 × 10-3 to 6.7 × 10-3 min-1. Experimental Section Analysis. UV spectrophotometry was used to determine lignin concentration in pulping black liquors. A sample of 20 µL of black liquor was placed in a glass tube containing 1 mL of acetone. The content of the tube was evaporated to dryness in a vacuum oven at 60 °C for 12 h, which enabled furfural removal. The evaporation residue was dissolved in pH 12 buffer solution and its absorbency was measured. A sample of lignin precipitated from the black liquor by dilution with acidified water was purified and employed as the standard. At the end of the cooking run, the lignin concentration determined by black liquor analysis was compared to the theoretical concentration, which was determined from the difference between wood initial lignin content and pulp lignin content (TAPPI test method T222). Differences lower than 5% were observed in all cases. Materials. The cooking experiments were carried out with Eucalyptus globulus chips selected by hand (approximately 3 × 20 × 30 mm3). The chemical composition of the wood was as follows: 21.9% lignin (TAPPI test method T222), 47.2% cellulose (TAPPI T203), 23.4% pentosans (TAPPI T223), 2.5% extractives (TAPPI T204), and 0.3% ash (TAPPI T211). All values above are given as a percent of the dry wood weight. Experimental Setup and Procedure. The cooking runs were carried out in a stainless steel autoclave of 4 L (Autoclave Engineers, Erie, PA). The detailed experi-

Table 1. Experimental Conditions for Cooking Runs run

temperature (°C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

110 120 130 140 150 160 170 180 190 200 130 130 130 180 180 180 180 185 190 195 200

isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal isothermal nonisothermal nonisothermal nonisothermal nonisothermal

liquor-to-wood ratio (L kg-1)

[H+] (M)

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7

2.4 × 10-4 2.4 × 10-4 2.4 × 10-4 2.4 × 10-4 2.4 × 10-4 2.4 × 10-4 2.4 × 10-4 2.4 × 10-4 2.4 × 10-4 2.4 × 10-4 2.4 × 10-3 1.6 × 10-3 1.5 × 10-5 2.3 × 10-3 7.9 × 10-4 1.0 × 10-5 6.8 × 10-7 autocatalyzed autocatalyzed autocatalyzed autocatalyzed

mental setup was described in a previous work.12 The chips were impregnated in water and placed into the autoclave and the white liquor (50% methanol, w/w) was introduced into an auxiliary pressure vessel. Both vessels were purged with nitrogen. The temperature in the autoclave was raised to 100 °C, whereas the temperature in the auxiliary vessel was raised to a value that, after mixing with the chips, allowed us to reach rapidly the desired cooking temperature. Then, the white liquor was fed to the autoclave from the auxiliary vessel. The moment that the system reached the desired temperature was stated as the zero reaction time. Black liquor samples were collected throughout the experiment. The conditions for all the experiments are shown in Table 1. In the isothermal runs (1-17) the liquor-towood ratio was 50 L kg-1 (on oven-dried wood basis) and the hydrogen ion concentration was maintained constant throughout the run. The data obtained in these runs were used to determine the influence of both cooking temperature (1-10) and hydrogen ion concentration (11-17) on the delignification rate. The value of hydrogen ion concentration in runs 1-10 was 2.4 × 10-4 M, which is the final average concentration in the autocatalyzed runs. In runs 1-10, 13, 16, and 17 the white liquors were buffered with acetic acid/sodium acetate buffer solution. The runs 11, 12, 14, and 15 were catalyzed with sulfuric acid. In the runs performed under nonisothermal conditions (18-21) the ramp of temperature was 3 °C min-1. They were performed at a liquor-to-wood ratio of 7 L kg-1 and the liquor was composed exclusively by methanol and water (autocatalyzed cooking). These runs were carried out to validate the kinetic model proposed. Experimental Results and Discussion Figure 1 shows the 1-XL vs time plot, where XL is the lignin conversion obtained from the wood lignin content and lignin concentration in the black liquor. From these figures a linear relationship between the logarithm of 1-XL and the reaction time can be observed. Therefore, the delignification rate can be assumed to be first-order with respect to the lignin content in wood. The plot of data from runs at 120 and 130 °C shows two different slopes. The higher slopes can be observed

3326 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999

Figure 2. Experimental data for runs 3, 8 and 11-17. Liquorto-wood ratio ) 50 L kg-1. (a) T ) 130 °C; [H+] ) (1.5 × 10-5) (2.4 × 10-3). (b) T ) 180 °C; [H+] ) (6.8 10-7) - (2.3 × 10-3).

Figure 1. Experimental data for runs 1-5. Liquor-to-wood ratio ) 50 L kg-1, [H+] ) 2.4 × 10-4. (a) T ) 110-130 °C; (b) T ) 140150 °C; (c) T ) 160-200 °C.

for a lignin conversion lower than 10%. From this point the delignification slows down. The first region is identified as the initial stage of delignification, whereas the second corresponds to the bulk stage. In the plots for runs at 140 and 150 °C the difference between the slope for XL < 0.1 and for XL > 0.1 is not significant since the delignification rate in the initial and bulk stages is similar. This phenomenon has also been observed in the kraft delignification of Eucalyptus

globulus at moderate temperatures.12 The percentage of the total lignin removed in the initial stage (10%) is lower than that in kraft delignification, where 20-25% of lignin is removed.12,24-26 In the case of the runs at high temperature (160-200 °C), the faster stage observed corresponds to bulk delignification, whereas the slower second is attributed to the residual stage. The transition point between the two phases observed in each experiment varies slightly with the cooking temperature. The value for lignin conversion at this point is 77 and 83% at 170 and 200 °C, respectively. A mean value of 79% can be calculated for the lignin conversion at the transition point. The percentage of the total lignin to be removed in the residual stage (21%) is considerably higher than that for delignification in methanol-water with strong acids13 and that for kraft delignification.12,25,26 This is one of the reasons for the usually higher lignin content of pulps obtained in autocatalyzed pulping. The data obtained in the experiments with variable hydrogen ion concentration (runs 11-17) are plotted in Figure 2. This figure shows a strong influence of hydrogen ion concentration on the lignin dissolution rate for all stages of delignification, as was previously reported by other authors.13-15 In most of the runs shown, two stages can be appreciated. The deviations

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3327

are found for run 13, carried out at 130 °C and very high pH, and for run 17, carried out at 180 °C and very low pH. Both of them are the extreme conditions. Kinetic Models Proposed

number of data available for each delignification stage does not allow reliable data fitting to models with a large number of parameters. The reaction rate expressions corresponding to the reaction schemes shown above are as follows:

Several reaction schemes have been considered for the kinetic model proposal: k1

LN 98 LD k1

} LD LN {\ k e

k1

ke

k1

k2

LN 98 LD {\} LR } LR LN 98 LD {\ k -2

Model I Model II Model III

(4)

Model IV

(5)

)

dt

kr

dXL

ki

ei

kb

LNb {\ } LD k eb

dt

)

∑

ej

Li0 ) 0.1L0; Lb0 ) 0.69L0; Lr0 ) 0.21L0

)

)

[

Lj0

]

XLj

∑ kj (1 - XLj) - k j)i,b,r L

Model VII

(16)

0.1 < XL < 0.79, j ) b XL > 0.79, j ) r

XL < 0.1, j ) i; 0.1 < XL < 0.7,

In models I-IV it was assumed that native lignin in wood consists of a single species. Model I, where the reaction is considered as the irreversible dissolution of lignin, is the simplest of those reported in the literature. Model II has a similar reaction scheme, but the reaction is assumed to be reversible. Models III and IV were developed from the reaction scheme proposed by Parajo´ et al.14 but, unlike the original scheme, it was supposed that the redeposition of dissolved lignin is a reversible reaction. Otherwise, the model would calculate a very high lignin content for pulps obtained in runs at high temperature, which was not the trend observed in this study. In models V-VIII lignin is assumed to be composed of three different species. As was mentioned above, the percentage of each type of lignin is 10% initial, 69% bulk, and 21% residual. The three species of lignin can dissolve simultaneously (models V and VI) or consecutively (models VII and VIII). The reaction schemes of models V and VII are similar to that of model I, whereas models VI and VIII are analogous to model II. A model similar to III and IV was not employed because the low

(12)

XL < 0.1, j ) i

XL < 0.1, j ) i; 0.1 < XL < 0.7, j ) b; XL > 0.7, j ) r Model VII (8)

Model VIII (9)

Model III

∑

dXL ) kj(1 - XL) dt

j ) b; XL > 0.7, j ) r

(11)

dt 0 ej Li0 ) 0.1L0; Lb0 ) 0.69L0; Lr0 ) 0.21L0 Model VI (15)

er

kj

Lj0 dXLj 0

kr

} LD LNj {\ k

Lj0 dXLj

∑ j)i,b,r L

LNr {\ } k kj

Model II

Lj0 kj(1 - XLj) j)i,b,r L0 dt j)i,b,r L0 Li0 ) 0.1L0; Lb0 ) 0.69L0; Lr0 ) 0.21L0 Model V (14)

Model VI (7)

LNj 98 LD

)]

(10)

dXL ) (k1 - k2)e-k1t + k-2 - (k2 + k-2)XL dt Model IV (13)

LNr 98 LNi {\ } k

(

dXL ) k1[1 - XL(1 + ke)] dt

dXL Li0 ) 0.1L0; Lb0 ) 0.69L0; Lr0 ) 0.21L0 Model V (6)

Model I

dXL 1 ) k1 1 - XL 1 + dt ke

(3)

ki

LNb 98 LD

[

(2)

LNi 98 kb

dXL ) k1(1 - XL) dt

[

]

dXL XL ) kj (1 - XL) dt kej

Model VIII (17)

XL < 0.1, j ) i 0.1 < XL < 0.79, j ) b XL > 0.79, j ) r Influence of Temperature From the reaction schemes proposed in eqs 2-9, the integration of their corresponding rate expressions (eqs 10-17) yield the following equations to describe delignification as a function of cooking time and temperature:

XL ) 1 - (1 - XL0) exp(-k1t) XL ) 1 -

1 ke

[(

(

) )

Model I (18)

1 1 ke ke -k1(1 + ke)t exp Model II (19) ke (1 - XL0) 1 +

(

)]

3328 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999

XL )

1 - [1 - XL0(1 + ke)] exp[-k1t(1 + ke)] 1 + ke Model III (20)

{

(1 - XL0)(k1 - k-2) [exp[(-k1 + k2 + (-k1 + k2 + k-2) k-2 k-2)t] - 1] + [exp[(k2 + k-2)t] - 1] (k2 + k-2) exp[(k2 + k-2)t] Model IV (21)

XL ) XL0 +

}/

XL ) 1 -

∑

exp(-kjt)

j)i,b,r L0

Model V (22)

∑

(

( )

j)i,b,r

1+

1

L0j

L0j + e-kjt(1+1/kej) L0kej L0

)

kej

Model VI (23)

Li0 ) 0.1L0; Lb0 ) 0.69L0; Lr0 ) 0.21L0 XL ) 1 - (1 - XLpj) exp[-kj(t - tpj)]

Model VII (24)

0.1 < XL < 0.79, j ) b XL > 0.79, j ) r

[

(

XL )

confidence interval includes the zero value

I, eq 18 II, eq 19 III, eq 20 IV, eq 21 V, eq 22 VI, eq 23 VII, eq 24

1.074 0.589 0.587 0.568 0.879 0.677 0.006i 0.430b 0.010r 0.005i 0.210b 0.009r

no no no yes yes yes no no no no no yes

1 kej

)] [

(

exp -kj(t - tpj) 1 +

residual delignification because model VIII does not fulfill the statistical criteria. According to the above commented results, to study the influence of temperature on the delignification rate, model VII has been selected for the initial and residual stages and model VIII for the bulk stage. Influence of Hydrogen Ion Concentration

XL < 0.1, j ) i

1 + 1 - Xpj 1 -

SQRa

a The superscripts i, b, and r represent the dissolution of initial, bulk, and residual lignin, respectively.

Li0 ) 0.1L0; Lb0 ) 0.69L0; Lr0 ) 0.21L0 XL ) 1 -

model

VIII, eq 25

Lj0

1

Table 2. Sum of Square Residuals (SQR) Obtained by Experimental Data Fitting (Runs 1-10) to Models I-VIII

1 kej

)]

1 1+ kej Model VIII (25) XL < 0.1, j ) i 0.1 < XL < 0.79, j ) b XL > 0.79, j ) r

To determine the value of the parameters of eqs 1825, nonlinear regression27 was applied to the experimental data obtained in runs 1-10. The temperature was taken as a variable and the hydrogen ion concentration was maintained as a constant. The results obtained are summarized in Table 2. On one hand, models I, II, III, VII, and the initial and bulk delignification in model VIII fulfill the statistical criteria since the confidence intervals for their parameters do not include the zero value. On the other hand, models IV, V, VI, and residual delignification in model VIII do not fulfill the statistical criteria. The models VII and VIII show the lower values of the sum of square residuals (SQR). They assume delignification as the result of the consecutive dissolution of three different types of lignin. Model VIII has a slightly lower SQR value for initial delignification; however, model VII is more suitable for this stage because of its higher simplicity. The fitting of bulk delignification data to model VIII results in a significantly lower value of SQR than when model VII is employed. Model VII has been selected for the

As was shown in Figure 2, the hydrogen ion concentration has a strong influence on the delignification rate. Three models were selected to express the influence of this variable on the delignification rate constant. The expression for these models are as follows:

kj ) k0j[H+]

(26)

kj ) k0j[H+]mj

(27)

kj )

kA0j[H+]aj 1 + kB0j[H+]dj

(28)

The models in eqs 26 and 28 assume a power-law function on the hydrogen ion concentration. A first-order dependence is supposed in eq 26, as in other previous works,13,15,23 whereas in eq 27 the reaction order is calculated by the fitting of experimental data. Equation 28 corresponds to a hyperbolic model; this model was only employed for bulk delignification, where the number of data available is enough to fit a large number of parameters. In bulk delignification it has been assumed that the hydrogen ion concentration has an influence on the delignification constant, but not on the equilibrium constant. The data fitting was carried out by nonlinear regression of the results obtained in experiments 11-17 (Table 3). The first-order power-law model (eq 26) exhibits a very high SQR value. Therefore, in the pulping system studied, the assumption of a first-order dependence of delignification on the hydrogen ion concentration would lead to important deviations. The general potential model (eq 27) is the most suitable, judging by the value of the SQR and the simplicity of the model. The value of the parameters determined for the hyperbolic model, eq 28, shows that the term “1” in the denominator is negligible compared to the term “kBOj[H+]dj”. Thus, this model can be simplified to a potential model. Prior to data reproduction, the parameters of the models were recalculated. Nonlinear regression coupled to a Runge-Kutta fourth-order algorithm was applied

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3329 Table 3. Influence of Hydrogen Ion Concentration: Parameters Values Calculated by Experimental Data Fitting (Runs 3, 8, 11-17) to the Kinetic Models in Equations 26-28 lignin species

dependence on temperature

dependence on [H+]

parameter Ln k0i Ln k0b Ln k0r Ln k0i mi Ln k0b mb Ln k0r mr Ln kA0b EAb/R ab Ln kB0b EBb/R db

initial bulk residual initial

model VII, eq 24 model VIII, eq 25 model VII, eq 24 model VII, eq 24

eq 26 eq 26 eq 26 eq 27

bulk

model VIII, eq 25

eq 27

residual

model VII, eq 24

eq 27

bulk

model VIII, eq 25

eq 28

SQR 29.41 ( 0.23 30.75 ( 0.14 11.54 ( 0.064 24.76 ( 0.15 0.33 ( 0.015 25.06 ( 0.086 0.23 ( 0.0080 11.37 ( 0.44 0.98 ( 0.062 54.68 ( 136740 10645 ( 2.35 × 108 1.21 ( 943.0 32.76 ( 36750 -223.3 ( 2.35 × 108 0.986 ( 944.0

0.062 8.46 0.013 0.003 0.382 0.013 0.384

Table 4. Parameters Values Recalculated by Experimental Data Fitting (Runs 1-17) to the Kinetic Model Proposed (equations 24, 25, and 27a) dependence on T

dependence on [H+]

initial

model VII, eq 24

eq 27

bulk

model VIII, eq 25

eq 27

residual

model VII, eq 24

eq 27

lignin species

a

parameters Ln k0i mi Ei/R Ln k0b mb Eb/R Ln k0eb Eeb/R Ln k0r mr Er/R

22.89 ( 1.69 0.293 ( 0.048 11197 ( 595 23.98 ( 0.48 0.214 ( 0.0059 11834 ( 208 -32.59 ( 0.57 -16120 ( 306 11.36 ( 1.11 0.97 ( 0.035 3824 ( 472

SQR: 1.327.

to fit the data obtained in runs 1-17. The final parameter values are summarized in Table 4. The suitability of the model can be observed from the reproduction of experimental data corresponding to runs 1 to 10, which is shown in Figure 3. In Figure 4 it can be seen that the agreement between calculated and experimental data is acceptable for most of the data in runs 1-17. The final expression of the model is as follows:

dXL 93.1 + 0.29 [H ] (1 - XL) ) 8.73 × 109 exp dt RT XL < 0.1; initial (29)

(

)

[

dXL 98.4 + 0.21 ) 2.59 × 1010 exp [H ] (1 - XL) dt RT

(

)

XL

]

134.0 RT 0.1 < XL < 0.79; bulk (30)

(

1.42 × 1014 exp -

)

dXL 31.8 + 0.97 ) 8.58 × 104 exp [H ] (1 - XL) dt RT XL > 0.79; residual (31)

(

)

The activation energy obtained for initial delignification (93.1 kJ mol-1) is significantly higher than the values reported for kraft initial delignification12 (4080 kJ mol-1). In kraft delignification the rate of the initial stage is controlled by the diffusion of reactants into wood. The low viscosity of alcohol-based liquors, which enables easy diffusion, can be the reason for the

higher initial activation energy found in the current study. The value of the bulk delignification activation energy (98.4 kJ mol-1) is within the range reported for organosolv pulping systems. However, it is lower than that for kraft delignification12,28 (105-150 kJ mol-1). With regard to the residual stage, the activation energy obtained (31.8 kJ mol-1) is remarkably lower than those in other organosolv systems and kraft pulping.20,21,28 The kinetic order for the hydrogen ion concentration has a value of 0.29, 0.21, and 0.97 for the initial, bulk, and residual stage of delignification, respectively. Except for residual delignification, these values are far from unity, which is the value assumed in other works.13,15,23 Validation of the Model The usual industrial pulping is nonisothermal, since the procedure includes a heating time to reach the programmed operating temperature. Therefore, to validate the kinetic model, nonisothermal runs (18-21) were carried out. These runs were performed in an autocatalyzed pulping medium, where the hydrogen ion concentration increases as the pulping proceeds as a result of the release of organic acids from wood. Since the model includes the hydrogen ion concentration as a variable, an external relationship between [H+] and XL must be developed to reproduce the value of [H+]. In Figure 5 the pH of the black liquor is plotted vs lignin conversion for runs 18-21. It can be seen that there is a stoichiometric relationship between the amount of acid released by wood and the lignin conversion. Besides, this relationship does not depend on the cooking temperature. Up to a lignin conversion of 6%, the pH of the black liquor drops dramatically. From this point the acidification rate of the cooking medium slows

3330 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999

Figure 5. Black liquor pH vs lignin conversion for runs 18-21.

tion of the hydrogen ion concentration and, therefore, to reproduce the experimental data obtained in runs 18-21 (Figure 6). The suitability of the model obtained (eqs 29-31) to reproduce delignification data from nonisothermal runs can be observed. Carbohydrate Reaction

Figure 3. Reproduction of experimental data from runs 1-10 by the model proposed in eqs 29-31.

Experimental data obtained in runs 1-21 and data from a previous work on methanol pulping of Eucalyptus globulus11 were used to study the relationship between lignin conversion and carbohydrate conversion. These data correspond to the conversion attained at the end of the cooking run and they are plotted in Figure 7. Two different stages can be observed, the transition between them taking place at a lignin conversion value of 35%. For lignin conversion values lower than 35%, about 25% of the total carbohydrate in wood dissolves. In this stage the ratio XC/XL is higher; therefore, the carbohydrate reaction rate, referred to as the delignification rate, is also higher. This fact can be attributed to the dissolution of hemicellulose. In the second stage (XL > 0.35) the lower carbohydrate dissolution rate can be interpreted as the dissolution of cellulose, whose reactivity is lower. These stages have been previously described in the kraft delignification of Eucalyptus globulus.12 In the work cited, the ratio XC/XL for the first stage is lower than that in the current work, whereas it has a similar value for the second stage. Conclusions

Figure 4. Calculated vs experimental lignin conversion (runs 1-17) for the model proposed in eqs 29-31.

down. The pH of the black liquor remains nearly constant from a lignin conversion of about 40%. Data were fitted to the expressions shown in Figure 5. These expressions were used to establish the varia-

A kinetic model has been developed to describe delignification in a methanol-water medium employing experimental data from isothermal runs at a liquor-towood ratio of 50 L kg-1. The expression selected to take into account the influence of temperature has been discriminated among eight different kinetic models. It describes delignification as a reaction scheme formed by the consecutive dissolution of three different species of lignin: initial, bulk, and residual lignin, whose content in wood are 10, 69, and 21%, respectively; the reactions of the initial and residual lignin are irreversible, whereas bulk delignification is a reversible reac-

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3331

Figure 6. Reproduction of experimental data from runs 18-21 by the model proposed in eqs 29-31.

the initial, bulk, and residual delignification being 0.29, 0.21, and 0.97, respectively. The kinetic model obtained satisfactorily reproduces the trend of experimental data from runs carried out under nonisothermal conditions and a liquor-to-wood ratio of 7 L kg-1. To achieve this reproduction, the relationship between lignin conversion and the hydrogen ion concentration of the black liquor was established. The hydrogen ion concentration drops dramatically when the lignin conversion is lower than 6% and it remains at a constant value from a lignin conversion of 40%. Besides, it was found that this relationship does not depend on the pulping temperature. Acknowledgment

Figure 7. Carbohydrate conversion vs lignin conversion for runs 1-21 and from a previous work.11

tion. The activation energies calculated have values of 93.1, 98.4, and 31.8 kJ mol-1 for initial, residual, and bulk delignification, respectively. These values are within the range reported in the literature, except in the case of residual delignification, whose activation energy is rather low. The influence of hydrogen ion concentration on the rate constant has been considered by means of a power-law model, the kinetic orders for

The authors are grateful to the Comisio´n Interministerial de Ciencia y Tecnologı´a for financial support (project AMB94-0012-C02-01). Nomenclature a ) kinetic order for H+ in eq 28 d ) kinetic order for H+ in eq 28 E ) activation energy (kJ mol-1) H+ ) hydrogen ion (mol L-1) k ) kinetic constant ke ) equilibrium constant k0 ) frequency factor L ) lignin content (% in wood, g L-1)

3332 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 m ) kinetic order for H+ in eq 27 R ) gas constant (kJ mol-1 K-1) SQR ) sum of squares residuals: ∑[(1 - XL)exp - (1 XL)calc]2 t ) time (min) T ) temperature (°C, K) XC ) carbohydrate conversion (CD/C0) XL ) lignin conversion (LD/L0) XLj ) lignin conversion for j species: LjD/Lj0 Subscripts b ) related to bulk lignin D ) related to dissolved matter i ) related to initial lignin N ) related to native lignin pj ) related to the first date of the j stage of delignification r ) related to residual lignin R ) related to redepositated lignin 0 ) value at initial time

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Received for review March 1, 1999 Revised manuscript received May 14, 1999 Accepted May 27, 1999 IE990161F