Spruce Hemicellulose for Chemicals Using Aqueous Extraction

Article pubs.acs.org/IECR

Spruce Hemicellulose for Chemicals Using Aqueous Extraction: Kinetics, Mass Transfer, and Modeling Jussi V. Rissanen,† Henrik Grénman,*,† Stefan Willför,‡ Dmitry Yu. Murzin,† and Tapio Salmi† †

Laboratory of Industrial Chemistry and Reaction Engineering, Process Chemistry Centre, Department of Chemical Engineering, Åbo Akademi University, Biskopsgatan 8, FI-20500 Åbo/Turku, Finland ‡ Laboratory of Wood and Paper Chemistry, Process Chemistry Centre, Åbo Akademi University, Porthansgatan 3, FI-20500 Åbo/Turku, Finland ABSTRACT: Pressurized hot water extraction of hemicelluloses from spruce sapwood was studied at 120−170 °C using a batchwise-operated cascade reactor, which enables precise sampling as well as very accurate and rapid temperature control. The extraction was performed under identical conditions for two different chip sizes, a 1.25−2.0-mm sieved fraction and handmade 10-mm cubic blocks, to evaluate the influence of chip size on the overall extraction kinetics. The results showed that the extraction rate increases significantly with temperature and that the pH decreases during the extraction, as a result of the liberation of acid groups. The concentration of hydronium ions in the liquid phase was observed to have a linear correlation with conversion depending, however, on the chip size, which shows that the mass transfer of the acid groups differs significantly from that of the bulky hemicelluloses. It also shows that significant amounts of acetyl groups are liberated inside the chips before the hemicelluloses enter the liquid phase, as the slopes would otherwise be identical. The extraction temperature did not influence the selectivity of dissolution significantly, which means that temperature cannot be used to influence the sugar composition of the obtained liquid phase. Mathematical modeling was performed on the overall extraction data using a simple first-order model, which corresponds to porous solid particles. An excellent fit of the model to the experimental data was obtained. The activation energy was determined to be about 120 kJ mol−1 for both chip sizes even though the reaction rates differed significantly, wheeras the pre-exponential factor was substantially lower for the larger chips. This somewhat surprising result can be explained by the fact that the diffusion inside the chips differs because of changes in viscosity and not only distance. The results contribute to the quantitative and qualitative understanding of the extraction process and shed light on the correlation of the experimental parameters used during extraction.

1. INTRODUCTION: SEPARATION OF HEMICELLULOSES In the biomass-based industry, the novel biorefinery concept has increased interest in utilizing the large resources of available biomass in new ways. Wood is one of the largest available resources being utilized industrially at present. In recent years, various carbon-neutral processes have been increasingly studied. The main components of biomass, namely, cellulose, hemicelluloses, and lignin, can be utilized for various purposes because of their different reactivities.1 Norway spruce (Picea abies), also referred to as European spruce, covers considerable parts of central and northern Europe, as well as vast areas in Russia. This wide distribution, combined with its unique properties, makes spruce one of the corner stones of the biobased industries in Europe today. Spruce is mainly utilized for the production of pulp and sawn timber. In the pulp industry, the cellulose and part of the hemicelluloses are used for pulp production, and the remaining fraction, consisting mainly of hemicelluloses and lignin, is commonly burned for energy production. The basic goal of the modern biorefinery concept is the versatile utilization of all of the different wood fractions to obtain a diversified value-added product portfolio. In addition to the further processing of the versatile hemicelluloses, the valorization of lignin and utilization of cellulose for dissolving pulp, for example, is crucial for obtaining sustainable economics in the overall process. © 2014 American Chemical Society

However, to be able to make use of the different properties of all of the main fractions, separation needs to be performed, and the separation kinetics/thermodynamics must be understood for the success of the process. The production of biofuels is a rapidly growing field. Industry already produces ethanol and some other alcohols by fermentation, and new alternative routes for fuel production are emerging at an increasing pace.2 In alcohol production, wood-based hemicelluloses are hydrolyzed to sugar monomers before the fermentation step.3−6 In addition to fermentation, the monomeric sugars obtained from the hemicelluloses can be utilized as platform molecules for the production of valueadded chemicals, for example, through oxidation, hydrogenation, and dehydrogenation to further conversion steps.7 Oligomeric hemicelluloses are desired for various applications outside the field of fuel production; for example, spruce-derived galactoglucomannan (GGM), the main hemicellulose in spruce, has the potential to be utilized in a wide assortment of products, ranging from the food industry to cosmetics, fine chemicals, and biocomposites.8−10 Received: Revised: Accepted: Published: 6341

January 17, 2014 March 20, 2014 March 21, 2014 March 21, 2014 dx.doi.org/10.1021/ie500234t | Ind. Eng. Chem. Res. 2014, 53, 6341−6350

Industrial & Engineering Chemistry Research

Article

Figure 1. Structure of water-soluble AcGGM.9

The stem wood content of O-acetyl galactoglucomannans (AcGGMs) in spruce is in the range of 15−25%. The backbone of AcGGM is constructed of β-D-(1−4)-glucopyranose and β-D(1−4)-mannopyranose units. Approximately 45% of the C-2 positions and 20% of the C-3 positions of the mannopyranose units are acetylated, whereas glucose units are nonacetylated.9 In the backbone structure, some of the mannose units, as well as some of the glucose units, are substituted at position C-6 by galactopyranose. AcGGMs (Figure 1) from spruce thermomechanical pulp (TMP) have a considerably lower number of galactose side groups at the C-6 position than AcGGMs extracted from wood, but the reason for this difference is still unclear.11 The three most abundant sugar units in sprucederived hemicellulose, in descending order, are mannose, xylose, and glucose.12 The degree of polymerization (DP) of the native hemicellulose is thought to be in the range of 100− 400.9,13 Only minor amounts of AcGGMs are easily watersoluble at room temperature, if the wood is ground and the conditions are neutral or slightly acidic. Large substituents prevent the formation of intra- and intermolecular hydrogen bonds between the different noncellulosic polysaccharide chains because of steric hindrance. The water solubility is highly related not only to the substituent level but also to the type of substituent. Even almost-complete cleavage of galactosyl groups does not affect the solubility if the number of acetyl substitutions is unchanged.9 Several different separation methods for extracting hemicelluloses from wood have been proposed. One of the most promising alternatives at the moment is pressurized hot water extraction (PHWE).9,11,14−20 PHWE has been shown to be an effective method for extraction, and water is an inexpensive and environmentally friendly solvent. Moreover, the equipment and methodology for processing large amounts of wood-related industrial water streams are well established and exist at current production plants. In general, hot water extraction without the addition of acids, bases, or enzymes leads to partial hydrolysis of hemicelluloses, as well as liberation of acetic acid and minor amounts of other compounds. The cleavage of acetyl groups from hemicelluloses is the reason for the formation of acetic acid. The pH decreases, which in turn accelerates the hydrolysis, possibly also influencing the extraction rate.21 When the conditions used are harsh and/or the “cooking time” is longer, aldehydes are formed when xylose and glucose degrade to furfural and 5hydroxymethylfurfural. Alcohols such as methanol and other light organic compounds are formed, as well. This is one of the main reasons why overall mass balances do not always hold, because, in practice, the analysis of the liquid phase does not include these light organic compounds.21 It has been reported that, if the temperature is close to or above 200 °C, the degradation of hemicellulose- and cellulose-derived crystalline

glucose starts to increase. This leads to a rise in the concentrations of degradation products, such as furfural and 5-hydroxymethylfurfural.22,23 The PHWE of softwood has not previously obtained as much attention as that of hardwood, as hardwood hemicelluloses have traditionally been more utilized in industrial production. In a previous study,14 an accelerated solvent extractor (ASE) with pure water was used in the temperature range of 100−180 °C. The yield of carbohydrates was low (3−29 mg per gram of dry wood) at or below 130 °C, but as the extraction temperature was increased to 160 °C or higher, the yields increased substantially. At prolonged extraction times exceeding 100 min, the yield started to decrease at 170 °C, and the same observation was made at 180 °C after 60 min. At higher temperatures, the pH became lower because of acetic acid formation.14 In general, the levels of noncellulosic carbohydrates started to decrease when the extraction times were too long or the temperature was too high. When the conditions were harsher, the liquid-phase concentration of cellulose-based glucose increased.14 The aim of the current work was to investigate the extraction of spruce hemicelluloses, as the fractionation of this widely available and versatile raw material has attracted far less attention than the fractionation of hardwood. In addition to temperature, extraction time, and pH, the wood chip size24 is one of the crucial factors influencing the extraction kinetics. It has been qualitatively reported in the literature that chip size influences the extraction process significantly, but quantitative data obtained under precisely controlled conditions with welldefined particles, supported by interpretation using mathematical modeling, are not widely available. Moreover, the correlation of the detachment of hemicelluloses from the wood matrix and the liberation and diffusion of acetyl groups from the chip has not been thoroughly studied. In this work, the temperature dependence of the extraction selectivity was also evaluated to determine whether, for example, temperature ramping could be utilized during extraction to increase fractionation. The information can be used to quantitatively and qualitatively assess the influence of the different parameters on the reaction kinetics. Mathematical modeling was applied to obtain a more precise quantitative assessment of the importance of the parameters and their correlations. This information can be utilized for determining guidelines for further development related to industrial production.

2. EXPERIMENTAL SECTION 2.1. Extraction Equipment and Experimental Procedure. PHWE experiments were performed with a novel cascade reactor system (Figure 2). The main advantage of this system, compared to traditional digesters, is the possibility of controlling the reaction conditions very precisely and rapidly, 6342

dx.doi.org/10.1021/ie500234t | Ind. Eng. Chem. Res. 2014, 53, 6341−6350


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Table 1. Experimental Matrix, Used for Both Chip Sizes sampling time (min) chamber

120 °C

130 °C

140 °C

150 °C

160 °C

170 °C

1 2 3 4 5

30 60 100 160 240

20 40 80 140 220

20 40 70 110 160

10 20 40 80 120

5 10 20 40 80

5 10 15 20 60

was freeze-dried in a vacuum. Calibration samples were prepared by using a methanol-based sugar monomer solution that contained a known amount of the sugar monomers to be analyzed. The calibration samples were dried under a nitrogen flow. In this particular case, 2 mL of 2 M HCl/MeOH (anhydrous) was added to the samples, which were then placed into the oven for 3 (liquid samples) or 5 (solid samples) h at 100 °C. After being allowed to cool, the samples were neutralized, and the internal standards resorcinol and sorbitol were added. The samples were dried first under a nitrogen flow and then using a vacuum desiccator. After that, the samples were derivatized using silylation reagents and allowed to stand until the following day. The derivatized samples were transferred into gas chromatography (GC) vials and analyzed on a GC system with flame ionization detection (FID).25−27 2.3. Determination of pH. The pH of the solutions was measured after the extraction at room temperature (24 °C) with a pH meter (SCHOTT Instruments, Handylab pH 12). A polymer electrode made by the same manufacturer was also used (SCHOTT Instruments, pH Electrode Blueline 28 pH, pH 0 to 14/−5 to +80 °C/Gel).

Figure 2. Simplified scheme of the recycled cascade reactor setup. The reactor units are numbered from 1 to 5.

which is the basis for reliable kinetic experiments. Moreover, the system allows the sampling of both the solid and liquid phases during the reaction. The system includes online monitoring and recording of the pressure and temperature inside each reactor chamber, which enables a detailed interpretation of the data as well as reliable modeling. Two different chip sizes of spruce sapwood were used in the experiments: a sieved 1.25−2-mm fraction and handmade 10 × 10 mm cubic blocks. The moisture contents of the wood chips were determined by freeze-drying, and the chips were stored in airtight polyethylene containers at −18 °C. A dry weight of 25 g was used in each extraction experiment, 5 g per chamber, and the chips were prewetted for 12 h in distilled water prior to the experiments. The rest of the reactor volume was filled, in bypass mode, with a predetermined amount of distilled water, and heating was turned on. A liquid-to-solid ratio of ∼180 was used to avoid the interference of thermodynamic limitations, which might occur in concentrated solutions close to the solubility limits of the compounds. After the desired temperature was achieved, hot water was allowed to flow through the reactor chambers, commencing the extraction. The reactors were then again bypassed one by one at predetermined points in time and quenched with cold water before being opened. This procedure allowed for very rapid increases and decreases in temperature. The solid and liquid phases were recovered for analysis directly after the experiment with subsequent freezing (−18 °C). More than 60 selected samples were analyzed for sugar composition, molar mass, and pH. The temperature in the experiments was between 120 and 170 °C, which has been shown to be the most relevant range for PHWE. The absolute pressure inside the reactors was between 3.7 and 10.6 bar, depending on the temperature and on whether the pressure was measured before or after the pump. The pressure in the closed system was, on average, about 1.9 bar higher than the theoretical vapor pressure of pure water at the reaction temperature, and the pressure difference over the pump was, on average, about 0.35 bar. Identical reaction times, solid and liquid loadings, and temperatures were used for both size fractions to enable direct comparisons of the results (Table 1). 2.2. Sugar Analysis. The detailed analysis of different hemicellulose-based sugars was performed by an acid methanolysis method using internal standards. At the beginning, a certain amount of liquid and/or solid sample

3. KINETIC RESULTS AND DISCUSSION 3.1. Reproducibility of the Extraction. To confirm the reproducibility of the extraction, four duplicate experiments were performed with the smaller chip size in the temperature range of 140−170 °C. Figure 3 shows the conversion of the extraction as a function of time for all experiments. As can be seen, the reproducibility is good. The R2 values, which indicate how well the data points follow the same fit, are between 0.97 and 0.99. 3.2. Effect of Temperature. The overall extraction rate was found to be strongly temperature-dependent. At the lowest

Figure 3. Conversion of the overall hemicellulose extraction as a function of time for duplicate experiments at 140−170 °C with 1.25− 2-mm chips. 6343



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temperature, 120 °C, even at relatively long extraction times (4 h), the conversion reached only about 10% for both chip sizes (1.25−2-mm and 10-mm cubic blocks), whereas at 170 °C, a conversion of about 80% was achieved within the first hour (Figures 4 and 5). The reaction rate increased gradually with

and their liquid-phase concentration remained stable after the initial stage of the extraction, whereas the concentrations of the other main sugars (mannose, xylose, glucose, and galactose) increased throughout the process. However, differences were also observed in the reaction rates of the main sugars; specifically, the release of mannose seemed to increase during the reaction. The influence of temperature on the extraction can mainly be attributed to an increase in the rates. In addition, temperature can also influence the mass transfer inside the chips, as the diffusion coefficient increases with temperature and the pore structure is opened up more at higher temperatures. Still, the sugar-specific extraction rate versus the total hemicellulose conversion was found to be independent of temperature for the main sugars, except for slight variations observed in the initial stages of the extraction for arabinose and mannose (Figure 7). The quantitative assessment of the overall extraction kinetics, including the influence of temperature, is presented in section 4.2.

Figure 4. Conversion of the overall hemicellulose extraction as a function of time at different temperatures for 1.25−2-mm chips.

Figure 5. Conversion of the overall hemicellulose extraction as a function of time at different temperatures for 10 × 10 mm cubic blocks.

temperature, but the largest influence was visible in the temperature range of 130−150 °C, which might indicate an opening of the wood pore structure. Some degradation of sugars was observed at the highest temperature, especially for the smaller chip size. This is visible in the sudden decrease in the extraction rate at 170 °C and slightly also at 160 °C (Figures 4 and 5). A variation in the extraction rates of different sugars was observed during the experiments (Figure 6). The arabinose units were extracted in the beginning of the process,

Figure 7. Ratio of different sugars in the liquid phase as a function of total conversion in the temperature range 120−170 °C.

3.3. Effect of Chip Size on Extraction Rate. A significant influence of the chip size on the overall extraction rate was observed (Figure 8). The extraction rate was considerably higher for the smaller chips (1.25−2 mm) compared to the larger ones (10 × 10 mm), at both higher and lower temperatures. The influence of the chip size on the overall extraction kinetics can be mainly attributed to internal diffusion

Figure 6. Concentration of different sugars as a function of the overall liquid-phase sugar concentration at 150 °C for 10 × 10 mm cubic blocks.

Figure 8. Conversion as a function of time for different chip sizes at 130 and 160 °C. 6344



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of the pH ≈ 3.5−4 corresponds well with the pKa values of acetic and formic acids. The pH of the solution was observed to behave differently for the different chip sizes. The decrease was significantly slower for the larger chips, as demonstrated in Figures 11 and

effects in the chips, as the large molecules cannot easily diffuse out of the wood matrix of the larger chips at the same rate as they do for the smaller chips. The chips were completely prewetted, and the temperature profiles of the chips were practically identical, so neither initial water penetration into the chips nor differences in temperature inside the chips could influence the extraction process. Water molecules are also considerably smaller than bulky hemicelluloses, which leads to the substantially faster diffusion of water. The pH might also partially explain the effect, as the pH decrease is related to the overall conversion, which leads to a lower pH for smaller chips in equal reaction times (explained in more detail in section 3.3). This influences the opening up of the wood chips, which, in turn, enhances the internal mass transfer in the porous matrix and promotes the hydrolysis of the hemicellulose. The cleavage of the larger polysaccharides leads to an increased mobility in the wood matrix and, thus, transfer to the bulk liquid. 3.4. Behavior and Influence of pH during Extraction. The pH levels decreased significantly during the reactions (Figures 9 and 10). The decrease in the pH can be mainly

Figure 11. pH as a function of time at 120 and 130 °C for different chip sizes.

Figure 9. pH as a function of time at different temperatures for 1.25− 2-mm chips.

Figure 12. pH as a function of time at 160 and 170 °C for different chip sizes.

12. However, the difference in the pH values leveled out during the course of the extraction, even though the conversions were different for the two chip sizes at the corresponding points in time. This fact leads to the conclusion that it is not only the overall conversion that accounts for the variations in pH. Similar observations were made both at lower and higher temperatures, as can be seen in Figures 11 and 12. When the hydronium-ion concentration is plotted as a function of the overall conversion, a linear correlation can be observed (Figure 13). This indicates that the pH is directly proportional to the overall conversion, which leads to the conclusion that the variations in the pH of the bulk liquid are a consequence of the extraction process itself, rather than a major factor influencing it. If the pH significantly affected the extraction rate, higher hydronium-ion concentrations would

Figure 10. pH as a function of time at different temperatures for 10mm cubic blocks.

attributed to the release of acetyl groups, which results in the formation of acetic acid in the liquid phase. The decrease in pH is strongly influenced by the temperature, as it is linked to the conversion, that is, higher temperature leads to more rapid extraction. Logically, the pH also decreases more rapidly with the smaller chips because the extraction is faster. The final value 6345



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kI = k 0Ie−Ea1/ Rθ

(2)

1 1 1 = − θ T Tmean

(3)

In eq 2, kI is the value of the rate constant at the reference temperature (Tmean). The mass balance for solid hemicellulose in the batch reactor can now be written as dcs = −k 0Ie−Ea / Rθ cs n1c H+n2 dt

The liquid-phase hemicellulose concentration (c) is calculated as c = ctot − cs (5)

Figure 13. Concentration of H3O+ as a function of the total concentration of hemicellulosic sugars.

Model eq 4 is based on ordinary differential equations (ODEs) that predict the concentrations of the compounds in the solution. The estimation of the kinetic parameters was carried out by nonlinear regression analysis using the simulation and parameter estimation software MODEST.29 The system of ODEs was solved with the backward difference method implemented in the software ODESSA,30 which is based on the LSODE code.31 All sets of experimental data containing the concentrations in the solid and liquid phases and the temperature as functions of time were merged together. The sum of residual squares, Q, given by

lead to significantly faster extraction, which, in turn, would lead to a significant decrease of the slopes in Figure 13, so that a linear correlation would not be obtained. As can also be observed in Figure 13, the slope of the linear correlation was found to depend on the chip size used in the experiments, which can be explained by the varying internal diffusion rates of different compounds, for example, acetyl groups and the significantly larger hemicelluloses. The acetyl groups are smaller, which allows them to diffuse more rapidly out of the wood matrix, compared to the bulky hemicellulose molecules. This would explain the fact that the slopes in Figure 13 are different for the two different chip sizes. The same hydronium-ion concentration (i.e., pH) is thus reached at lower overall conversion with the larger chips. In practice, this means that the release of the hydronium ions is directly proportional to the detachment and hydrolysis of the hemicelluloses inside the chips, but the internal diffusion resistance varies with chip size. Even though the hydrolysis of the hemicelluloses is known to be influenced by pH, the detachment of the molecules from the wood matrix is not.

nsets nobs(k) nydata(j , k)

Q = || cexp − cest ||2 =

∑ ∑

∑

k=1

i=1

j=1

(cexp , ijk − cest, ijk)2 (6)

where cexp and cest represent experimental and estimated concentrations, respectively, was minimized with the hybrid simplex−Levenberg−Marquardt method. 4.2. Modeling Results. The model gave a good fit to the experimental data (Figures 14 and 15). A rather high value of

4. MATHEMATICAL MODELING 4.1. Modeling Principles and Numerical Procedure. The aim was to develop a simple mathematical model for the complex overall extraction kinetics of the spruce chips (eq 1), within the range of experimental conditions used in the current work (e.g., in the temperature range of 120−170 °C). The model is based on the assumption of irreversible reactions and a porous solid particle. In addition, the internal diffusion resistance was not considered explicitly;28 that is, the diffusion was not directly applied mathematically to the model but rather was incorporated in the merged kinetic constant. Moreover, the model takes into account the temperature (T), the concentration of H3O+ (H+), and the concentration of hemicellulose in the solid phase (cs) at each point in time. The parameters n1 and n2 are the reaction orders with respect to hemicellulose and H3O+, respectively, and Ea is the apparent activation energy. A modified Arrhenius equation (eq 2), in which the reference temperature (Tmean in eq 3) is 150 °C, was used to take into account the influence of temperature on the reaction rate. The modified version was used to suppress the correlation between the activation energy and the pre-exponential factor (k0I) in the regression analysis. r = kIcs n1c H+n2

(4)

Figure 14. Fit of the model to experimental data (liquid-phase hemicellulose concentrations c) for the smaller chip size (1.25−2 mm).

about 120 kJ mol−1 was obtained for the activation energy (Ea) for both chip sizes, which can be considered a somewhat surprising result, as one would expect the internal diffusion resistance to influence the value obtained for the larger chips. First-order kinetics was obtained for the dependence of the reaction rate on the hemicellulose concentration (n1), which corresponds to a very porous solid material, as described in Salmi et al.32 and Grénman et al.12 The reaction order reflecting the dependence of the dissolution rate on the concentration of hydronium ions (i.e., pH) (n2) obtained a very low value (close

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observed in the activation energy. However, in the current case, inside the wood chips, the viscosity of the solution, containing hemicellulose as well as other compounds such as lignin, changes significantly as a function of composition and temperature. This might be the main factor explaining why the influence of the diffusion limitations mainly appears in the preexponential factor in the modeling. For processes in the liquid phase, the diffusion coefficient depends on the fluidity, that is, the reciprocal dynamic viscosity, D ∼ μ−1, which typically has an exponential temperature dependence33 μ−1 = μ0−1e−E /(RT )

Figure 15. Fit of the model to experimental data (liquid-phase hemicellulose concentrations c) for the larger chip size (10 × 10 mm).

(7)

For first-order kinetics and strong diffusion limitations in the pores of the particle, the first-order apparent rate constant (k′) is related to the intrinsic rate constant (k) as

to zero), which indicates that the dissolution rate does not correlate significantly with the liquid-phase pH. This result is in accordance with the observations shown in Figure 13, where a linear correlation of the hydronium-ion concentration and the liquid-phase hemicellulose concentration is visible. Therefore, in the final parameter estimations, n1 and n2 were fixed at 1 and 0, respectively and only k0I and Ea were determined by regression analysis. The obtained parameter values are reported in Table 2. The accuracies of the parameters are very good, as the standard errors are less than 0.5%. To check the reliability of the obtained parameters, a sensitivity analysis was performed. One of the parameters was at the value that gave the minimum of the objective function while the other was changed, and the value of the objective function was calculated. It is important that a clear minimum be found, as observing step changes or obtaining the same value for the objective function with a broad range of parameter values, for example, would show that the parameters are not well-defined, which is frequently encountered. The results in Figure 16 indicate that a clear minimum was obtained for the objective function for each parameter. To evaluate the correlation between the parameters, contour plots were made. The results in Figure 17 demonstrate that no strong correlations could be observed, as changing the value of one or both of the parameters was found to lead to nonoptimal values of the objective function, for which the minimum was found in the dark blue region in the figures. This increases the reliability of the parameter values. 4.3. Interpretation of the Modeling Results. A very interesting observation obtained from the modeling results is that the pre-exponential factor for the larger chip size was about one-half of the value obtained for the smaller ships. There are at least two possible explanations for this result, both of which probably contribute to it. The pH inside the chips is different during the course of the reaction depending on the chip size, which can definitely influence the kinetics of hemicellulose detachment from the wood matrix (Figure 13). Moreover, the classical viewpoint on how diffusion limitations influence the rate constant is based on the assumption that the viscosity of the reaction medium does not change significantly with temperature, which implies that the influence is mainly

k′ = ηeik

(8)

where

k = Ae−Ea /(RT )

(9)

The effectiveness factor for the case of strong diffusion limitations is defined by34 a ηei = φ (10) where φ is the Thiele modulus and a is the shape factor (a = 3 for the spheres, a = 2 for long cylinders). The Thiele modulus for first-order kinetics is34 kρp

φ=

Dei

Rp

(11)

where the effective diffusion coefficient can be described, for instance, with the mean transport pore model Dei = (εp/τp)Di

(12)

In eq 12 εp and τp denote the particle porosity and tortuosity, respectively. Numerous equations have been proposed in the literature for the molecular diffusion coefficient in the liquid phase, since the classical Stokes−Einstein equation.33 A characteristic feature in each case is that Di ∼ μ−1. Considering eqs 7−12, the temperature dependence of the apparent rate constant becomes k′ =

⎡ 1 (Ea + E) ⎤ β exp⎢ − ⎥ R p ⎣ 2 RT ⎦

(13)

where β=a

Aαεp ρp τpμ0

(14)

Equations 13 and 14 show that the temperature dependence of the liquid viscosity compensates for the suppression of the apparent activation energy in the case of internal diffusion

Table 2. Parameter Values Obtained from the Regression Analysis 1.25−2.00-mm chips Ea (kJ mol−1) k0I [L(n1+n2)−1/(g(n1+n2)−1 min)]

10-mm cubic blocks

estimated parameter

estimated std error (%)

estimated parameter

estimated std error (%)

122 9.57 × 10−3

0.3 0.3

120 5.55 × 10−3

0.2 0.3

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Figure 16. Sensitivity analysis of the parameters Ea and k0I for the (top) smaller and (bottom) larger chips.

Figure 17. Contour plots on the parameters Ea and k0I for the (left) smaller and (right) larger chips.

limitations. If E ≈ Ea, the same apparent activation energy is observed for both small and large particles. The results displayed in Figure 13, namely, the relation between pH and total concentration, can be explained with the aid of kinetic modeling, by considering of mass balances for solid material (s), products (p), and H3O+ ions (H+) as follows

dcs = −|νs|k1cs n1c H+n2 dt dc p dt

= +|νp|k1cs n1c H+n2

dc H + = +|ν H+|k 2cs n3 dt

Equations 15 and 16 give directly

dcs |ν | =− s dc p |νp|

(18)

By assuming that n1 = n3 = 1, as confirmed by regression analysis, eqs 16 and 17 give

(15)

dc p dc H +

=

|νp| k1 n c H+ 2 |ν H+| k 2

(19)

(16)

from which the relation between the concentrations is obtained by separation of variables and integration (cp = 0 and cH+ ≈ 0 at t = 0)

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∫0

cp

dc p =

|νp| k1 |ν H+| k 2

∫0

c H+

c H + n 2 dc H +

■

|νp| k1 c H+ |ν H+| k 2

(20)

(21)

■

that is, the total product concentration and hydronium-ion concentration are linearly related. On the other hand, if n2 = 1 (pH-dependent extraction), eq 20 gives cp =

1 |νp| k1 2 c H+ 2 |ν H+| k 2

(22)

that is c H+ =

2|ν H+| k 2 |νp| k1

cp (23)

Figure 13 confirms a linear relationship, not a square-root relationship, between the concentrations, which shows that the extraction rate is not dependent on external pH.

5. CONCLUSIONS Hemicellulose extraction from spruce sapwood using pressurized hot water was carried out in the temperature range of 120−170 °C with two wood chip sizes, a 1.25−2-mm sieved fraction and handmade 10-mm cubic chips. The extraction rate was observed to increase considerably with temperature, with the conversion after extraction ranging from about 10% to 80%. The pH decreased significantly during the extraction, reaching levels of about 3.6 at the highest temperature. The correlation between the concentration of hydronium ions and the conversion was concluded to be close to linear, with the slope depending on the chip size. The chip size influenced the overall extraction rate, which was more efficient with the smaller chips. A simple mathematical model was developed for the overall extraction kinetics, and a good fit of the model to experimental data was achieved. A first-order dependence on the hemicellulose concentration was obtained, along with a zeroth-order dependence on the liquid-phase pH. An activation energy of about 120 kJ mol−1 was obtained for both chip sizes, whereas the pre-exponential factor was significantly lower for the larger chips. The change of the viscosity inside the chips largely explains the observation that the activation energies are almost identical for the different chip sizes even though the mass-transfer limitations differ significantly. The extraction rate is dependent on simultaneous detachment from the wood matrix and hydrolysis inside the chip, as well as the changing morphology of the chips and the viscosity inside the particles, which contribute to the internal mass-transfer limitations. These factors are dependent on the surrounding conditions, such as temperature and pH, as well as the particle size.

■

ACKNOWLEDGMENTS

This work is a part of the activities of the Process Chemistry Centre (PCC), a Centre of Excellence financed by Åbo Akademi University. The authors acknowledge the Academy of Finland and the Future Biorefinery (FuBio) Joint Research 2 program financed by the Finnish Bioeconomy Cluster (FIBIC) and the Finnish Funding Agency for Technology and Innovation (Tekes) for financial support.

If n2 = 0, we obtain cp =

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NOTATION A = pre-exponential factor a = shape factor (a = 3 for spheres and cubes) c = concentration D = molecular diffusion coefficient De = effective diffusion coefficient E, Ea = activation energy k = rate constant k′ = apparent rate constant k0I = pre-exponential factor n = exponent in rate law R = gas constant Rp = characteristic dimension, particle radius t = time T = (absolute) temperature Q = sum of residual squares ∼ = proportionality factor in diffusion coefficient β = merged parameter, eq 13 εp = particle porosity ηe = effectiveness factor θ = transformed temperature μ = dynamic viscosity ν = stoichiometric coefficient ρp = density of solid particle τp = particle tortuosity

Subscripts

■

i = component index p = particle, product s = solid

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AUTHOR INFORMATION

Corresponding Author

*E-mail: Henrik.Grenman@abo.fi. Notes

The authors declare no competing financial interest. 6349



Article

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Spruce Hemicellulose for Chemicals Using Aqueous Extraction

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