An Empirical Mathematical Model for the Predictive Analysis of the

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An Empirical Mathematical Model for the Predictive Analysis of the Chemical Absorption of Hydroxide in Eucalyptus Wood M. M. Costa,† J. L. Gomide,‡ J. L. Colodette,‡ L. A. Lucia,*,† and P. Mutje´§ Department of Wood and Paper Science, North Carolina State UniVersity, Raleigh, North Carolina 27695-8005, Department of Forest Engineering, Pulp and Paper Laboratory, Federal UniVersity of Vic¸osa, Vic¸osa, Brazil, and Department of Chemical Engineering, Group LEPAMAP, UniVersitat de Girona, Girona, Spain

Chip steaming, heating, impregnation, and sugar acid neutralization of wood chips by an alkaline kraft liquor during the pretreatment and initial phase of pulping are critical physical-chemical phenomena for executing successful industrial kraft pulping operations. Specifically, these physical and chemical phenomena significantly affect the kraft pulping process performance in terms of chemical mass transfer that influences both delignification rate and the homogeneity of the pulp produced. Detailed fundamental knowledge about the aforementioned phenomena during the initial phase is necessary to obtain selective wood delignification and as a consequence better pulp homogeneities and yield. The present work evaluates the effect of selected critical variables on impregnation and neutralization of Eucalyptus spp wood chips. The independent variables used for this study were as follows: wood basic density (BD), 430, 490, and 550 kg/m3; effective alkali charge (EA), 5%, 9%, and 13% at 25% sulfidity; time (t), 30, 60, and 90 min; and temperature (T), 90, 110, and 130 °C. The wood chips were impregnated with the kraft liquor of specific EA and sliced into five layers, each having a thickness of 1 mm. The sodium and hydroxide ion contents in the layers were measured first by emission photometry and then by volumetric titration. These combined methods demonstrated a hydroxide ion consumption of 67%-69% from wood neutralization reactions. A nonlinear model that has a high correlation coefficient (R2 ) 96.2%) was developed that described the effects of the operational variables on the sodium hydroxide content (Y) in the chip core (Y ) -1.83 + 1.04 × t0.11 × 0.96 × T0.42 × 0.59 × EA0.69 × 0.82 × BD-0.33 + ε, where ε is the random error). A correlation matrix demonstrated that the sodium hydroxide content in the chip core is strongly influenced by the initial EA value. On the other hand, the wood density had a smaller influence. Reaction temperature and time were determined to have an intermediate influence. Neutralization reactions conducted with 40 mesh sawdust (i.e., material that has low physical limitations to impregnation, under the test conditions (60 min at 100 °C and 2% consistency) at different initial alkali concentrations) showed a consumption of 3.8% ( 0.4% of sodium hydroxide by wood weight at the point the alkali concentration tended toward zero. Therefore, it is anticipated that the amount of sodium hydroxide in the wood chip core should be 3.8% by wood weight to obtain neutralization. From an operational control point of view, this proposed empirical mathematical model may be used to predict different Eucalyptus wood chip impregnation conditions to achieve uniform and selective kraft pulping operations. Introduction Currently, eucalyptus wood is the most important renewable biomass raw materials for the Brazilian pulp and paper industry. However, optimizing the performance of the pulping process to achieve better pulp properties and yield requires examining a virtually ignored step in the process: the impregnation phase. Impregnation of the pulping process fluids (liquors) is one of the most essential steps to achieve high pulp homogeneity and yields. Generally, the dominant wood chemical pulping process (kraft) includes the process of defibering (i.e., macerating the compact wood structure by means of an aggressive chemical treatment consisting of the application of a high temperature, high sulfide, and high caustic aqueous solution (white liquor)). This treatment results in the production of individual fibers and * To whom correspondence should be addressed. Fax: 919-515-6302. E-mail address: [email protected]. † Department of Wood and Paper Science, North Carolina State University. ‡ Department of Forest Engineering, Pulp and Paper Laboratory, Federal University of Vic¸osa. § Department of Chemical Engineering, Group LEPAMAP, Universitat de Girona.

an organic residue that is called “black liquor.” The success of the pulping process hinges on the dissolution of the microscopically thin lamella, which is mainly composed of lignin and pectin.1 To ensure its efficient removal, it is necessary to have uniform kraft white liquor species (HO- and HS-) distribution, i.e., radially to the chip core. The impregnation phase attempts to achieve a homogeneous ion distribution, which includes penetration and ensuing diffusion influenced by pressure and ion concentration conditions. However, a better understanding of these phenomena during the impregnation phase is still lacking. The importance of the impregnation phase cannot be denied and is characterized by (1) liquor ion transportation to chip surface, (2) ion diffusion to the inner core, (3) chemical reactions between the ions and the wood constituents, (4) product diffusion to the exterior of chips, and (5) transportation of these products to the bulk black liquor.2 Traditionally, the kraft pulping of hardwood, such as eucalyptus wood, was realized in one vessel;the digester vessel; without an impregnation vessel. It was usually more associated with softwood raw materials. Hardwoods have, in their anatomic structure, specialized cells for liquid transport that are called vessel elements. Theses elements have a positive influence on liquor penetration. Recently, new technologies for kraft

10.1021/ie071119k CCC: $40.75  2008 American Chemical Society Published on Web 05/02/2008

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Figure 1. Leading edge of alkaline liquor penetration during the impregnation phase of a Populus tremuloides L. chip.8,10

pulping;the Compact Cooking and LoSolids processes;added an impregnation step to the traditional vapor-phase one-vessel digester to hardwood chips as well as for softwood.3 These technologies, when applied to Brazilian eucalyptus bleached pulp, have great practical implications. Hence, a more-detailed understanding of the impregnation phenomenon is necessary to optimize wood delignification with higher efficiency and yield, to provide better final pulp properties and reduce operational costs. Therefore, chip impregnation by alkaline kraft liquor is clearly an important phenomenon. Currently, the pretreatment of wood chips with a mixture of black and white liquors for impregnation is an industrial reality. Many research and industrial applications have proven that this contemporary modification provides multiple benefits, including higher pulp yield, better delignification selectivity, and reduced production cost.4–6 In the past, the impregnation phase has been considered somewhat trivial; however, recently, it has been demonstrated to be a critical step that exerts significant control over kraft pulp uniformity.7–9 The beginning of impregnation occurs in the void spaces of the wood chip, because of simple static pressure gradients, and is followed by ion diffusion to the core of the chip, based on concentration gradients. In fact, the diffusion is strongly dependent on the liquor pH; indeed, in early pulping, the ion concentrations are high, indicating that the diffusion tends to be the same in the tangential, radial, and longitudinal directions.2 In kraft pulping, alkaline impregnation has already been studied as a diffusive phenomenon, but it is mitigated, to some extent, by air in the voids.2,10,11 Air elimination from the voids is done by applying chip presteaming to ensure pulping homogeneity.12 As shown in Figure 1, impregnation occurs in all three dimensions toward the chip core until complete impregnation occurs throughout the anatomic wood structure, which is important for pulping (specifically, delignification) homogeneity.13,14 Nonhomogeneity in the lignin content of kraft pulp can result from various sources. Digesters may have temperature gradients and channel pulp liquors, which results in the uneven pulping of wood chips.15 However, another important source of variability is chip thickness, which will also lead to delignification nonhomogeneity and low product yield, even when pulped in uniform, carefully controlled, laboratory digesters.16–20 The sources of this nonuniformity include incomplete penetration of kraft pulping liquor and slow diffusion of pulping chemicals into chips to replenish those consumed by pulping reactions.19,21–23 Kraft pulping has received considerable study to address environmental issues, save energy, improve pulp quality, improve yield, and, consequently, achieve operational cost reduction. Pulping homogeneity is one of the keys factors to achieving significant operational improvement. An efficient and highly homogeneous chip impregnation phase will result in a more economically processable pulp product.24 Consequently, conditions that control ion flux to the chip core must be better

understood to improve product yields. In tandem, these conditions must also be sufficiently nonaggressive, to prevent losses in product yields that are caused by alkaline degradation of the polysaccharide components of the pulp.14,25 This work presents a empirical mathematical model that explains the wood impregnation and neutralization phenomena as based on operational variables. The sodium hydroxide content was tracked throughout the Eucalyptus chip from the surface to the core. The main operational variables analyzed in this paper that control the impregnation step are wood basic density (BD), effective alkali (EA), time, and temperature. Experimental Section Three different industrial Eucalyptus wood samples that were collected from a Brazilian mill with different basic densities (BD ) 430, 490, and 550 kg/m3) were used for the studies. This range of wood basic density fairly covers the common values of wood densities in pulp mills.26,27 However, the wood chip age (6-7 years), growth site, and seasonal variation were the same. A simplified experimental scheme is shown in Figure 2. The experimental plan shown in Figure 2 has three main components: (1) selection of chips with a thickness of 5 ( 0.2 mm, which is, in fact, the average industrial chip thickness of this Brazilian mill, whereas the width and length were not selected; (2) the impregnation phase was conducted in a stainless steel mini-cell reactor with a capacity of 0.5 L (50-g samples were evaluated under various conditions of effective alkali (EA ) 5%, 9%, and 13% by dry wood weight), time (t ) 30, 60, and 90 min), and temperature (T ) 90, 110, and 130 °C); synthetic liquors with a sulfidity of 25%, a liquor-to-wood ratio of 4:1, and 12.5, 22.2, and 32.5 g EA/L were used); and (3) from each experiment, 40% (by weight) of the initial chip mass was sliced into five pieces, each 1 mm thick, using a microtome. These pieces were designated as layers A, B, C, D, and E. The C layers from each experiment represent the chip core and subsequently were analyzed by emission photometry and titration to track the sodium and hydroxide ions, respectively. The content of NaOH in layer C was utilized as a dependent variable that is described in the empirical mathematical model by the independent variables (EA, t, T, and BD). All values were expressed in terms of the percentage of sodium hydroxide (%NaOH), according to the dry wood weight. Except where otherwise noted, standard analytical methods from TAPPI28 and SCAN29 were used. For the acetyl groups, gas chromatography (GC) procedures were used.30 The wood neutralization work was performed using 2 ( 0.001 g samples that were milled in accordance with TAPPI Standard T-257 (“Sampling and Preparing Wood for Analysis”), to obtain a sample of air-dried sawdust that would pass through a 40 mesh screen. Subsequently, 40 mesh sawdust was neutralized by alkaline solutions with different sodium hydroxide concentrations (1, 5, 10, 22.5, and 32.5 g NaOH/L) at unvarying conditions (a retention time of 60 min at 100 °C and a consistency of 2%). The sodium hydroxide consumptions for the different samples were measured by a SCAN-N 30:85 titration, using hydrochloric acid (1 M HCl) until a pH of 8.3 was achieved. Results and Discussion Wood Sawdust Neutralization. Figure 3 illustrates that the sodium hydroxide consumption of different samples that possess virtually no physical limitations to diffusion is a function of

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Figure 2. Simplified experimental design used for this work.

Figure 3. Alkaline consumption as a function of initial sodium hydroxide concentration under the tested conditions for different eucalyptus sawdust (40 mesh) samples.

Figure 4. Correlation between the sodium hydroxide content measured by photometric emission and titration methods from different layers of the chips.

the initial alkaline concentration and, to a lesser degree, the basic wood density (BD). It can be observed that a high initial alkaline concentration results in a noteworthy increase in alkaline consumption by the samples. In addition, sawdust with a high density displayed a slightly higher consumption than the other samples. However, this does not necessarily illustrate a wood density effect, rather only the possibility for increased neutralization reactions due to different wood chemistry considerations. Therefore, by theoretically eliminating the wood physical limitations, a consumption of 3.8% ( 0.4% of NaOH (by wood weight) would be expected under the tested conditions, when the initial sodium hydroxide concentration tended toward zero. The sample with the lower basic density (BD ) 430 kg/m3) interestingly had a lower acetyl group content (2.3% by wood weight) versus the samples with higher basic density (3.3% by wood weight), which suggests that there is a correlation between reactivity and the acetyl group content; this result that has been observed in the literature.26 This may possibly be one of the reasons for the increased alkaline consumption. Sodium Hydroxide Measurements. Figure 4 shows a comparison between the sodium hydroxide concentration measured by emission photometry (Na+) and titration (HO-) methods for the five different chip layers. Both results are expressed in terms of the percentage of sodium hydroxide by wood weight. It can be seen that there is good correlation between the methods used in this work. The content of sodium in the chip core describes more accurately the front end of impregnation from the ions present in the alkaline liquor. Also in Figure 4, it can be observed that there was a hydroxide ion consumption of 67%-69%, which resulted mainly from wood neutralization reactions. Despite the wood neutralization reactions and other reactions among the wood constituents and hydroxide ions, it was realized that a fraction of those ions can undergo reactions with CO2 that is present in the air during the layer microtoming. Hence, the more inert;and, therefore, stable;sodium ions measured by the photometric technique

Table 1. Correlation Matrix among Independent Variables Incorporated into the Experimental Model To Explain the Sodium Hydroxide Contents in Chip Core (Layer C) for Three Different Eucalyptus Wood Samples Operational Parameters

NaOH (% at layer C)

time (min) temperature (°C) effective alkali concentration, EA (g NaOH/L) wood basic density, BD (kg/m3)

0.2037 0.2219 0.9227 -0.0633

(where native sodium concentration values were mathematically subtracted) were the values used to build the empirical mathematical model to determine the sodium hydroxide content in the core of the Eucalyptus chips (layer C). Not surprisingly, similar results were obtained with Alamo wood.11 Experimental Mathematical Model for Chip Impregnation Phase. As mentioned previously, the main focus of this work was to evaluate the impregnation phase, based on process conditions by means of an empirical mathematical relationship. Chip thickness has been previously mentioned as the dimensional factor that restricts alkaline liquor diffusion to the chip core.1,2,18,21 Therefore, in the conceptualization of this work, the experimental mathematical models were based on the sodium hydroxide content present in layer C, which represents the chip inner layer. This experimental mathematical model attempted to describe the chip impregnation phase and its relationship to the main operation conditions. Table 1 shows a correlation among the independent variables that have been incorporated in the model. In this table, it can be noted that the initial effective alkaline concentration (EA) and wood basic density (BD) have a higher and lower impact on the model, respectively. This can probably be explained by the soaking or fiber wall swelling in the alkaline medium affecting the final wood physical properties. Therefore, for the wood samples studied in this work, which have a broad range of wood basic densities (430-550 kg/m3), there was no

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Figure 5. Observed values versus predicted values obtained by the experimental model developed, based on the operational conditions and the measured sodium hydroxide content in the chip core (layer C).

strong argument for the validity of the experimental mathematical model to explain the amount of sodium hydroxide in the inner chip (i.e., layer C). After this exploratory correlation matrix was proposed, a mathematical model was developed, as illustrated in eq 1. This model provided a good correlation coefficient (R2 ) 96.2%), which indicates that it is a reasonable attempt to adequately explain the impregnation phenomena observed in Eucalyptus wood. Y ) -1.83 + 1.04 × t0.11 × 0.96 × T0.42 × 0.59 × EA0.69 × 0.82 × BD-0.33 (1) in which Y is the percentage of sodium hydroxide by wood dry weight in layer C (%NaOH), t the impregnation reaction time (in minutes), T the impregnation reaction temperature (given in degrees Celsius), EA the initial effective alkali liquor concentration (expressed in terms of g NaOH/L), BD the wood basic density of the samples (given in units of kg/m3), and ε the random error. Figure 5 illustrates the model error, which allows an easy evaluation of the performance of the empirical mathematical model. The error indicates the difference between the observed and estimated values using the same data points from the model. Consequently, the smaller the error value, the better the model performs, in regard to explaining the phenomena of chip impregnation and neutralization, based on the operational parameters. Most of the error distribution values were (0.4%. The figure illustrates that, in the range of the values studied in this work, there was no systematic errors in the results predicted by the model. For this reason, the model shows a satisfactory performance for the prediction of the values of sodium hydroxide in the chip core (layer C), based on the main operational conditions considered in this research. Conclusions The main conclusions obtained are as follows: (1) The impregnation phase for Eucalyptus wood chips can be analyzed and thereby optimized using a highly accurate empirical mathematical model (eq 1), which displayed small error in predicting the observed values. (2) The analyses of the correlation matrix established that the initial effective alkali concentration was a stronger independent variable among those studied that significantly influences the concentration of sodium hydroxide in the chip core. On the other hand, the wood basic density, which was in the range of 430-550 kg/m3, did not show significant interactive effects, based on the impregnation model.

(3) Eucalyptus wood 40 mesh sawdust neutralization under set conditions (60 min at 100 °C and 2% consistency) and at initial alkali concentrations values close to zero showed a consumption of 3.8% ( 0.4% of NaOH among the samples tested. (4) It was noted that a hydroxide ion consumption of 67%-69%, under the conditions evaluated in this paper (EA ) 2.5, 22.2, and 32.5 g NaOH/L at a sulfidity of 25% and a wood liquor rate of 4:1; time, t ) 30, 60 and 90 min); and temperature, T ) 90, 110, and 130 °C), resulted from wood reactions during the chip impregnation step. (5) From an operational control viewpoint, based on the proposed empirical mathematical model and on Eucalyptus wood neutralization reactions, it is expected that the amount of hydroxide in the chip core should be at least 3.8% by wood weight to obtain a uniform and selective kraft pulping step. However, more work will need to be done to better clarify the relationship between operational impregnation parameters and pulping yield, as well final pulp properties. Acknowledgment The authors gratefully acknowledge the partial support of the U.S. Department of Energy (under USDOE Cooperative Agreement No. DE-FC36-01GO10626), which allowed us to organize this research. Literature Cited (1) Sjo¨stro¨m, E. Wood Chemistry: Fundamentals and Applications; Academic Press: New York, 1981; p 223. (2) Stone, J. E.; Forderrenther, C. Studies of Penetration and Diffusion into Wood. TAPPI J. 1956, 39, 679–683. (3) Gustavsson, C.; Yan, J. Yield Estimation for Compact Cooking and Kobudo Mary Pulps. Kami Pa Gikyoshi 2004, 58, 1520–1525. (4) Svedman, M.; Tikka, P.; Kovasin, K. The Role of Sulfur in Displacement Kraft Batch Cooking. In Proceedings of the 1995 Tappi Pulping Conference; TAPPI Press: Atlanta, GA, 1995; p 241. (5) Vikstrom, B.; Lindblad, M. S.; Parming, A. M.; Tormund, D. Apparent Sulfidity and Sulfide Profiles in the RDH Cooking Process. In Proceedings of the 1988 Tappi Pulping Conference; TAPPI Press: Atlanta, GA, 1988; p 669. (6) Lo¨nnberg, B.; Lindstro¨m, M.; Tikka, P.; Kovasin, K. K. Dissolution of Wood Components in Black Liquor-Started Displacement Kraft Batch Cooking. In Proceedings of the 7th International Symposium on Wood Pulping Chemistry, 1993; Vol. 1, p 362. (7) Ban, W.; Lucia, L. A. Kinetic Profiling of Green Liquor Pretreatment. Ind. Eng. Chem. Res. 2005, 44, 2948–2954. (8) Ban, W.; Wang, S.; Lucia, L. A. The Relationship of Pretreatment Pulping Parameters with Respect to Pulp Qualities: Optimization of Green Liquor Pretreatment Conditions for Improved Kraft Pulping. Pap. Puu 2004, 86, 102–108. (9) Ban, W.; Song, J.; Lucia, L. A. Insight into the Chemical Behavior of Softwood Carbohydrates during High Sulfidity Green Liquor Pretreatment. Ind. Eng. Chem. Res. 2003, 43, 1366–1372. (10) Stone, J. E.; Green, H. V. Penetration and Diffusion into Hardwoods. Pulp Pap. Mag. Can. 1958, 59, 223–232. (11) Talton, J. The Diffusion of Sodium Hydroxide in Wood at High pH as a Function of Temperature and Degree of Pulping, M.Sc. Thesis, North Carolina State University, Raleigh, NC, 1986. (12) Zanuttini, M.; Marzocchi, V.; Mocchiutti, P.; Inalbon, M. Deacetylation Consequences in Pulping Processes. Holz Roh Werkst. 2005, 63, 149– 153. (13) Malkov, S.; Tikka, P.; Gullichsen, J. Towards Complete Impregnation of Wood Chips with Aqueous Solutions. Part 4. Effects of Front-End Modifications in Displacement Batch Kraft Pulping. Pap. Puu 2002, 84, 526–530. (14) Zanuttini, M. A.; Marzocchi, V.; Citroni, M.; Mocchiutti, P. Alkali Impregnation of Hardwood. Part I: Moderate Treatment of Poplar Wood. J. Pulp Pap. Sci. 2003, 29, 313–317. (15) Tikka, P. Conditions to Extend Kraft Cooking Successfully. In Proceedings of the 1992 TAPPI Pulping Conference, Boston, 1992; pp 699-706.

3860 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 (16) Akhtaruzzaman, A.; Virkola, N. Influence of Chip Dimensions in Kraft Pulping. (5). Effect on Total Yield and Screening Rejects: Predictive Mathematical Models. Pap. Puu 1980, 62, 15–18. (17) Gullichsen, J.; Kolehmainen, H.; Sundqvist, H. On the Nonuniformity of the Kraft Cook. Pap. Puu 1992, 74, 486–490. (18) Tikka, P.; Ta¨hka¨nen, H.; Kovasin, K. Chip Thickness vs. Kraft Pulping Performance: Experiments by Multiple Hanging Baskets in Batch Digesters. TAPPI J. 1993, 76, 131–136. (19) Boyer, B.; Rudie, A. Measurement of Delignification Diversity within Kraft Pulping Processes. In Proceedings of the 1995 TAPPI Pulping Conference, Chicago, 1995; pp 765-770. (20) Malkov, S.; Tikka, P.; Gustafson, R. R.; Nuopponen, M.; Vuorinen, T. Towards Complete Impregnation of Wood Chips with Aqueous Solutions, Part 5. Pap. Puu 2003, 85, 215–220. (21) Gustafson, R.; Jimenez, G.; Mckean, W.; Chian, D. The Role of Penetration and Diffusion in Pulping Non-Uniformity of Softwood Chips. In Proceedings of the 1998 TAPPI Pulping Conference, New Orleans, 1988; pp 685-691. (22) Costanza, V.; Rossi, F. M.; Costnanza, P. Diffusion and Reaction in Isothermal Pulping Digesters. Ind. Eng. Chem. Res. 2001, 40, 3965– 3972. (23) Hultholm, T.; Lo¨nnberg, B. The Effect of Impregnation Conditions on Hydrosulfide Sorption in Kraft Cooking. In Proceedings of 7th European Workshop on Lignicellulosics and Pulp, Turku/Abo, 2002; pp 55-58.

(24) Malkov,S.StudiesonLiquidPenetrationintoSoftwoodChips;Experimental Models and Applications, Ph.D. Thesis, Department of Forest Products Technology, Helsinki University of Technology, Helsinki, Finland, 2002. (25) Kazi, K.; Gauvin, H.; Jollez, P.; Chornet, E. A Diffusion Model for the Impregnation of Lignocellulosic Materials. TAPPI J. 1997, 80, 209– 219. (26) Gomide, J.; Colodette, J. L.; Chaves de Oliveira, R.; Silva, C. M. Caracterizac¸a˜o Tecnolo´gica, para a Produc¸a˜o de Celulose, da Nova Gerac¸a˜o de Clones de Eucalyptus do Brasil. ReV. ArVore 2005, 29, 129–137. (27) Queiroz, S. C. S.; Gomide, J. L. Influeˆncia da Densidade Ba´sica da Madeira na Qualidade da Polpa Kraft de Clones Hibrı´dos de Eucalyptus grandis W. Hill ex Maiden X Eucalyptus urophylla S. T. Blake. ReV. ArVore 2004, 28, 901–909. (28) TAPPI: TAPPI Test Methods; TAPPI Press: Atlanta, GA, 19981999; p T236. (29) Scandinavian Pulp, Paper and Board Testing Committee; Stockholm, 1989. (SCAN W9.) (30) Sola´r, R.; Kacik, F.; Melcer, Y. Simple Semi-Micro Method for the Determination of O-Acetyl Groups in Wood and Related Materials. Nord. Pulp Pap. Res. J. 1987, 2, 139–141.

ReceiVed for reView August 16, 2007 ReVised manuscript receiVed February 15, 2008 Accepted February 26, 2008 IE071119K