Ind. Eng. Chem. Res. 2005, 44, 2997-3002
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Heterogeneous Kinetic Model for the Methylglucuronic and Hexenuronic Acids Reactions during Kraft Pulping of Eucalyptus globulus Joa˜ o P. F. Sima˜ o, Ana P. V. Egas, Cristina M. S. G. Baptista, and M. Grac¸ a Carvalho* GEPSI-PSE Group, Department of Chemical Engineering, University of Coimbra, Po´ lo II-Pinhal de Marrocos, 3030-290 Coimbra, Portugal
A kinetic model considering simultaneously the removal of methylglucuronic acids (GlcA), the formation of hexenuronic acids (HexA), and their degradation/dissolution is proposed. In the model, the effective alkali concentration in the entrapped liquor was used instead of that in the bulk liquor, accounting for the heterogeneous nature of wood pulping. The results are very satisfactorily explained by assuming that GlcA are composed of two subgroups: the fast GlcA, which disappear early in the cook with a low activation energy (58 kJ/mol), and the slow GlcA, which are degraded/dissolved (Ea ) 91 kJ/mol) or produce HexA, not being totally consumed. The degradation/dissolution reactions of both GlcA subgroups are second-order with respect to their content, while HexA formation (Ea ) 92 kJ/mol) and degradation (Ea ) 110 kJ/mol) are first-order with respect to slow GlcA and HexA contents, respectively. The effective alkali concentration influences the reactions that involve the slow GlcA and HexA, with a greater contribution to HexA degradation. The sulfidity is not relevant on any of these reactions. The model was experimentally validated with varying temperature, alkali, and sulfidity profiles and predicts reasonably well the GlcA and HexA contents during kraft pulping of Eucalyptus globulus. Introduction Hexenuronic acids groups (HexA) linked to wood xylans are produced by the degradation of native 4-Omethylglucuronic acids (GlcA) in alkaline media. It is well-known that the presence of these unsaturated structures in kraft pulps (especially of hardwoods) has negative effects in the bleaching process, consuming part of the chemicals such as chlorine dioxide and ozone, decreasing the brightness stability, and increasing the environmental impacts of the effluents. The HexA also react with potassium permanganate, thus contributing to the pulp κ number. Hence, the optimization of the HexA content in pulps is of major interest for the pulping industry, regarding the bleaching plant of the mill. Therefore, the development of a detailed kinetic model for the HexA reactions will provide a valuable tool enabling the optimization of the HexA content in pulps. The first part of the present investigation series1 led to the acquisition of experimental data on the effects of operating conditions on GlcA and HexA profiles during kraft pulping of Eucalyptus globulus. It was shown that the temperature and the effective alkali charge (EAC) had the strongest effect on GlcA and HexA reactions and that the degradation of HexA was only noticeable in cooks at high temperatures and/or high alkali charges, corresponding to lignin contents lower than 2% on wood. The heterogeneous nature of the wood pulping process was also demonstrated by showing the differences between the chemical concentrations in the bulk phase liquor (free liquor) and the liquor inside the wood chips (entrapped liquor). * To whom all correspondence should be addressed. Telephone: +351 239 798 700. Fax: +351 239 798 703. E-mail:
[email protected].
In the last years, some efforts have been made to evaluate the influence of pulping conditions on GlcA and particularly on HexA profiles,2-8 leading to the conclusions that the HexA reactions are mainly dependent on temperature and alkali charge. However, up to now, neither a kinetic model for the formation and the degradation of HexA nor a kinetic model contemplating simultaneously the GlcA and the HexA reactions has been put forward. Nevertheless, a few studies performed on softwood pulping presented kinetic models that considered either the formation or the degradation and dissolution of HexA. Among these, Gustavsson and AlDajani9 modeled the degradation/dissolution of HexA as a function of time, temperature, ionic charge, hydroxyl ion, and hydrogen sulfide ion concentrations, where the three last parameters were kept constant throughout the cook by using high liquid-to-wood ratios. The validity of this model for cooks with changing concentrations was not verified. The HexA formation was supposed to occur only in the heating-up period and was thus neglected in the model. Moreover, the observed decrease in HexA content might be due to a balance between HexA degradation/dissolution and some HexA formation rather than degradation/dissolution alone as assumed by these authors. On the other hand, Chai et al.4 presented a theoretical kinetic equation for the formation of HexA during the pulping of loblolly pine. Nevertheless, the estimation of its parameters and the experimental validation of results were not in the scope of their study. Unlike in softwoods pulping, in most of the hardwoods pulping the decrease in HexA content occurs only at the end of the cook. This paper proposes a kinetic model that considers simultaneously the degradation/dissolution of GlcA, the formation of HexA from GlcA, and the degradation/ dissolution of HexA during the kraft pulping process of
10.1021/ie049061m CCC: $30.25 © 2005 American Chemical Society Published on Web 03/23/2005
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Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005
Figure 1. Methylglucuronic acid content (GlcA) vs hexenuronic acid content (HexA) for different cooking temperatures (EAC ) 15 g of Na2O/100 g of odw, S ) 30%).
Figure 2. Methylglucuronic acid content (GlcA) vs hexenuronic acid content (HexA) for different effective alkali charges (T ) 165 °C, S ) 30%).
E. globulus. In this model, the influence of temperature, EAC, and hydrogen sulfide ion concentration as well as the contents of these wood components are contemplated.
GlcA content is plotted against HexA content, revealing the occurrence of reactions that consume GlcA and do not produce HexA. This finding supports an important assumption of this work: the division of the methylglucuronic acid groups into two subgroups, which will be called the fast GlcA (GlcAf) and the slow GlcA (GlcAs). During cooking, the GlcAf degrade very quickly, becoming nearly zero in the first minutes and are not converted to HexA. The GlcAs degrade more slowly, and a small amount will not be consumed, remaining at the end of the cook, a similar result to that obtained by Buchert et al.2,17 This assymptotic value can be linked to the existence of unreactive GlcA, hereafter referred to as GlcA∞. The HexA are formed from the GlcAs, linked to the xylan chain in the solid phase. It is worthwhile to notice in Figure 2 that the beginning of HexA formation depends on the EAC used in the cook and that the ratio HexA formed/GlcA consumed is higher for higher alkali charges. Furthermore, after the inflection zone, which is observed only for high delignification degrees, both HexA and GlcA contents decrease. Later, the GlcA content becomes constant while the HexA content still decreases, indicating that the formation of HexA has stopped. The multiple reactions that support the model proposed are shown in Figure 3. Mass balances to the contents of these compounds in wood chips during a batch cook lead to eqs 1-5:
Model Development To fully exploit the sensitivity of GlcA and HexA reactions to temperature (T), effective alkali charge (EAC), and sulfidity (S), a wide range of these operating parameters was used in the design of experiments, as described in our companion paper.1 Pulping is a complex reaction system involving several parallel and consecutive chemical reactions as well as mass and heat transfer phenomena. Although intrachip mass transfer limits the rate of reaction inside the wood matrix,10 so far this has not been considered in the models available. The GlcA and HexA reactions that occur in the solid matrix of the wood chips are dependent on the concentration of cooking chemicals in the entrapped liquor, which is substantially different from the chemicals concentration in the free liquor.1,11 Hence, to build a more realistic model, a heterogeneous approach was adopted by using the spatial average concentrations in the entrapped liquor, instead of those in the bulk liquor. These concentrations were effectively measured along the cook11 and not predicted by a Fick’s law diffusion model.12,13 As referred in our companion paper,1 it was assumed that all kinds of uronic acid groups, other than HexA, are 4-O-methylglucuronic acid groups (GlcA).14,15 Furthermore, the degradation of HexA by alkaline splitting from the xylan chain and the dissolution of HexA along with the xylan chain were treated in the model as one single reaction, a procedure similar to the one followed by Gustavsson and Al-Dajani.9 Therefore, from now on the term “degradation” will be used to refer to these two phenomena that lead to the HexA removal from the solid phase. The GlcA disappearance from the solid phase, related to the dissolution of xylan chains and eventually to the alkaline hydrolysis of the GlcA-xylan linkage,16 will also be called as “degradation”. Further reactions in the liquid phase were not considered in the present work. At the beginning of the cook, there is a fast decay in GlcA, which is not followed by HexA formation.1 This pattern is enlightened in Figures 1 and 2, where the
d[GlcAf] ) - r1 dt d[GlcAs] ) - r 2 - r3 dt d[HexA] ) Rr3 - r4 dt [GlcAf] + [GlcAs] ) [GlcA] fr )
[GlcAf]wood [GlcA]wood
(1) (2) (3) (4) (5)
where the compounds between brackets represent their contents in % (w/w) on wood basis (i.e., the compounds’ contents in the samples (cooked chips) multiplied by the cooking yield for each sampling time). The model
Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005 2999 Table 1. Optimal Parameter Estimates and Standard Deviations for the Kinetic Model
Figure 3. Proposed scheme for the multiple reactions involving methylglucuronic (GlcA) and hexenuronic (HexA) acids.
equations are valid for t g 0, therefore including the temperature profiles in the heating-up period and the isothermal stage.1 Since the total content of GlcA is measured but not the separate amounts of the fast and slow GlcA, the parameter fr, representing the fraction of GlcAf over the total GlcA in the native wood, was introduced. The reaction rates are identified as follows: r1 and r2 are the rates of degradation of the fast and slow GlcA, r3 is the rate of HexA formation from GlcAs, and r4 is the HexA degradation rate, with R being the stoichiometric factor for the HexA formation reaction. It is well-established13,18,19 that the carbohydrates kinetics of kraft pulping can be expressed in the form of ordinary power law kinetic equations. It was also assumed that all these reactions are dependent on temperature, wood component content, and effective alkali and hydrogen sulfide ion concentrations. This leads to eqs 6-9:
r1 ) k1e-Ea1/RTab[GlcAf]m[OH-]v[HS-]w
(6)
r2 ) k2e-Ea2/RTab([GlcAs] - [GlcA∞])n[OH-]r[HS-]x (7) r3 ) k3e-Ea3/RTab([GlcAs] - [GlcA∞])p[OH-]s[HS-]y (8) r4 ) k4e-Ea4/RTab[HexA]q[OH-]t[HS-]z
(9)
where m-z are exponents for the several concentrations involved. Results and Discussion To estimate the parameters in the kinetic model proposed in this paper, eqs 1-9 were solved using the ODRPACK package20 with the ordinary least squares criterion. The large difference in magnitude among the parameters at stake led to the re-parametrization performed on the preexponential constants and activation energies, in the form βi ) ln(ki){-Eai}/{300R}, γi ) {Eai}/{300R}, i ∈ {1, 2, 3, 4}. The stoichiometric factor R was set to 0.85, corresponding to the ratio between the molecular masses of HexA and GlcA. Therefore, the parameters to be estimated were β1-β4, γ1-γ4, the residual value [GlcA∞], the fraction fr, and the exponents m-z. Nevertheless, during the parameter estimation procedure, some preliminary conclusions have been drawn. First, in all tests, the exponents on the sulfide ion concentration in all reactions were nearly zero (
