Kinetic Model for Carbohydrate Degradation and Dissolution during

Jul 1, 2014 - ABSTRACT: The time development of the polysaccharide content in the wood residue and the black liquor during kraft pulping for softwood ...
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Kinetic Model for Carbohydrate Degradation and Dissolution during Kraft Pulping Kaarlo Nieminen,* Markus Paananen, and Herbert Sixta* Department of Forest Products Technology, Aalto University, P.O. Box 16400, 00076 Aalto, Finland S Supporting Information *

ABSTRACT: The time development of the polysaccharide content in the wood residue and the black liquor during kraft pulping for softwood is the focus of this study. The degradation process falls into two distinct categories: the chain element type and the chain fragment type. In the chain element reactions, a single element in the polymer chain can be removed, whereas in the chain fragment reaction a longer piece of the polymer is dissolved into the black liquor. The element-wise process consists of the subreactions peeling, stopping, and alkaline hydrolysis. A mathematical model considering peeling, stopping, and alkaline hydrolysis of the polymer chains as well as the dissolution of the wood components into the black liquor is presented and tested for the experimental data obtained from kraft cooking of Scots pine wood meal. As a novelty, the model distinguishes between primary peeling originating in the initial reducing end groups and secondary peeling following alkaline hydrolysis. Four series of cooking at high (1.55 M) hydroxide ion concentration were conducted at temperatures ranging from 130 to 160 °C. The reaction rates connected with the various processes were assumed to obey the Arrhenius equation, the frequency factor, and activation energy of which could be estimated while fitting the model to the data. Another series of cooking was executed at moderate (0.5 M) hydroxide ion concentration and at a temperature of 160 °C. The reaction rates associated with the different hydroxide ion concentrations were compared. Further, the effect of adding anthraquinone (AQ) to the cooking was modeled. The amounts of degradation attributed to the different subprocesses (primary peeling, secondary peeling, alkaline hydrolysis, and dissolution) were compared with each other for glucomannan, xylan, and cellulose.

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INTRODUCTION Background. Cellulose, hemicellulose, and lignin are the main chemical components in wood. Cellulose and hemicellulose are polysaccharides, the former consisting of linear chains of glucose units and the latter of slightly branched chains containing several types of sugar monomers. The degree of polymerization of cellulose in wood can attain 10 000, whereas the degree of polymerization for hemicellulose has been estimated to be 100−200.1 The hemicelluloses can further be categorized according to the sugars building them up. Galactoglucomannan (GGM) is the most common hemicellulose in softwood followed by arabinoglucoronoxylan (xylan). The constituting monosaccharaides of GGM are mannose, glucose, and galactose, whereas xylan principally consists of xylose with a contribution of arabinose and glucoronic acid.2 In the course of chemical pulping, the bulk of the lignin is eliminated from the wood or some other lignocellulosic material by treatment, at elevated temperature, in a digester containing an aqueous solution of chemicals. The resulting fibrous mass, the pulp, is a raw material for the paper, textile, food, and other industries. Kraft pulping is the dominant pulping process with 89%3 of the world production of chemical pulp. In kraft pulping, the chemicals deployed are sodium hydroxide and sodium sulfide. As an undesired side effect of the removing of lignin also part of the carbohydrates is lost. Of the polymers in this study, GGM is most susceptible to degradation of which typically 75% is removed during industrial kraft pulping, whereas the losses of xylan and cellulose constitute 38% and 10%, respectively.4 © 2014 American Chemical Society

There are several subprocesses involved in the carbohydrate polymer chain degradation.5,6 If one of the ends of the chain is a reducing end group (REG), it is susceptible to degradation (peeling reaction) in alkaline conditions. If the REG is removed by the peeling reaction, the following element in the polymer chain becomes a new REG which also can undergo peeling. Another relevant subprocess is the stopping reaction in which a reducing end group is transformed into a nonreducing one, thus preventing further peeling. Third, a nonend element in the polymer chain may be cleaved by alkaline hydrolysis. The two neighboring groups will become new end groups, but only one of them is reducing. The new REG is again the origin of a sequence of consecutive peeling reactions, which are terminated by a stopping reaction. Peeling is categorized as primary or secondary peeling depending on whether the target REG is descendent from the original ones or from one created by alkaline hydrolysis. Finally, as delignification proceeds concurrently with the shortening of the polymer chains through peeling and alkaline hydrolysis, some carbohydrate chain fragments will dissolve into the black liquor. The longer the polymer chains are the smaller the relative portion of the REG is. (If each chain had one REG and the chains were of equal length, the portion would be exactly the reciprocal of the chain length.) Therefore, the difference in chain length offers an explanation for the relative stability of Received: Revised: Accepted: Published: 11292

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and stopping reaction paces are proportional to the amount of reducing end groups, whereas the rate of alkaline hydrolysis is proportional to the amount of the remaining material. The course of peeling stopping and alkaline hydrolysis can be expressed by a system of differential equations:

cellulose as compared to hemicellulose. Softwood xylan is more stable toward peeling reactions compared to GGM because it is partially substituted with arabinose at the C-3 position of the xylose unit. Arabinose is easily cleaved off during the peeling reaction, thus forming a stable metasacharinic acid end group, which in turn stabilizes the chain against further betaelimination reactions. The degradation of carbohydrates has received less attention than delignification when it comes to kinetic models for pulping. Van Loon & Glaus7 presented a kinetic model for the degradation of cellulose in the context of radioactive waste disposal. In this model, on the basis of results by Franzon & Samuelson8 and Lai & Sarkanen,9 it was assumed that a constant amount of cellulose units was peeled off after each chain cleavage generated by alkaline hydrolysis. In this way, secondary peeling is included in the model. Pavasars et al.10 tested the model for experimental data under conditions relevant to nuclear waste depository and established a good correlation. A similar model was developed in works by Testova et al.5 and Mozdyniewicz et al.6 Unlike in the Loon & Glaus model, in that model no assumptions were made regarding how many units on average are peeled off after a chain scission; the reaction rates of peeling, stopping, and alkaline hydrolysis are estimated based on the fit of the model to the data. The works of Testova and Mozdyniewicz were in the realm of fractionation of biomass, and they also demonstrated good approximation to the experimental data on cellulose degradation. In the study of Paananen et al.,11 a model including peeling, stopping, and alkaline hydrolysis, but not secondary peeling, described the degradation of galactoglucomannan. We are not aware of any study where comparable models featuring peeling, stopping, and alkaline hydrolysis would have been fitted to data from xylan degradation. In the Purdue model12,13 glucomannan and xylan are both divided into reactive and unreactive components with just one reaction rate standing for “degradation” without specifying the nature of the degradation. Andersson14 extended this concept to a model with three subcomponents or “species” having different reaction rates. In general, there are differences in the degradation performance between the two hemicelluloses of this study. In the case of hardwood, which is rich in xylan, the kraft process provides greater yield than the sulfite process due to the resistance to alkali of xylan.15 On the other hand, for softwood pulps the sulfite process has the greater yield depending on the slower degradation of GGM and cellulose during acid conditions. In order to slow down the degradation of the carbohydrates anthraquinone (AQ) is added to the cooking. In the present study, the model of the studies of Testova and Mozdyniewicz will be exploited for the degradation of the carbohydrates in Scots pine under kraft cooking. The model will be augmented to include descriptions of (1) The effect of [OH−] level (2) The effect of AQ charge (3) The effect of temperature (4) Dissolution of carbohydrate chains into the black liquor

⎧ dR = −ksR + k h(Γ0 − P − H ) ⎪ ⎪ dt ⎪ dP ⎨ = kPR ⎪ dt ⎪ dH ⎪ = k h(Γ0 − P − H ) ⎩ dt

(1)

Here Γ0 is the initial amount of the carbohydrate in question, R is the amount of reducing end groups, P is the amount of peeled off material, and H is the amount of material that has undergone alkaline hydrolysis. Further we have the reaction rate coefficients kp for the peeling reaction, ks for the stopping reaction, and finally kh for alkaline hydrolysis. The second term on the right in the first equation of system 1 expresses that the amount of reducing end groups is increased by alkaline hydrolysis. The equation system 1 can be transformed into a second order differential equation which has an analytical solution.5,6 As a result, we obtain expressions for the quantities R, P, and H. Thus, we can calculate the amount of remaining undegraded material as the peeled off material and the material which has undergone alkaline hydrolysis subtracted from the initial material (CH = Γ0 − P − H): CH = Γ0((1/2 + μ) exp(− (K + λ)t ) + (1/2 − μ) exp((K − λ)t ))

(2)

For the sake of clarity, some entangled expressions containing the reaction rates were replaced by the new parameters κ, λ, and μ: ⎧ ⎪K = ⎪ ⎪ ⎪λ = ⎨ ⎪ ⎪ ⎪μ = ⎪ ⎩

1 (ks − k h)2 − 4k hk p 2 1 (k h − ks) 2 k h + 2ρ0 k p − ks (ks − k h)2 − 4 hk p

(3)

The initial fraction of reducing end groups R is denoted by ρ0, and it is assumed that the initial amount of both P and H is zero. The equation system 1 can also be solved analytically deploying the DSolve function of the Mathematica software. The equations in system 1 do not contain a description of the dissolution of carbohydrate chains into the black liquor. To enable modeling of the degradation, it is assumed that the peeling, stopping, and alkaline hydrolysis reactions proceed similarly regardless if the polymer is located in the wood residue or the black liquor. In this case the equations express the development of the total amount of the carbohydrate incorporating both the part in the wood residue and in the black liquor. The expression for the total remaining carbohydrate can then be fitted to the combined experimental data from wood residue and black liquor obtaining estimates for the reaction rates. Model Including Dissolution into Black Liquor. In order to model the carbohydrate development in the wood

Kinetic Model with Peeling, Stopping, and Alkaline Hydrolysis. The peeling stopping and alkaline hydrolysis reactions are modeled having pseudo-first-order kinetics. The carbohydrate material is removed either by (primary or secondary) peeling or alkaline hydrolysis. Both the peeling 11293

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Kuitunen,16 the dissociation constant value for this temperature is 2.80 × 10−12. An Empirical Model for the Anthraquinone Charge. A simple exponential model for the dependences on the AQ charge for the reaction rates for peeling, stopping, and alkaline hydrolysis is implemented:

residue only, excluding the part dissolving to the black liquor, equation system 1 is modified, adding a fourth equation representing carbohydrate dissolving into the black liquor: ⎧ dR W = −ksR W + k h(Γ0 − PW − HW − B) ⎪ ⎪ dt − kBR W ⎪ ⎪ dP ⎪ ⎪ W = kPR W ⎨ dt ⎪ ⎪ dHW = k (Γ − P − H − B) h 0 W W ⎪ dt ⎪ ⎪ d B = k (Γ − P − H − B ) ⎪ B 0 W W ⎩ dt

k = beγ AQ

In this model b is the reaction rate at zero AQ charge. Temperature Dependent Model. Temperature dependence is introduced to the model by assuming that the reaction rate coefficients follow Arrhenius’ equation:

⎛ E ⎞ k = A exp⎜ − a ⎟ ⎝ RT ⎠

(4)

Here we consider the parts of R, P, and H in the wood residue, as indicated by the suffix W. Under the assumption of equal reactions for the material in the wood residue and the black liquor the values of the reaction rates for peeling, stopping, and alkaline hydrolysis remain the same as in the system 1. The amount of material that has been dissolved into the black liquor is denoted with B and the dissolution rate with kB. There are some alterations in the original three equations as compared to the equation system 1. The dissolved material B is in equation system 4 also subtracted from the initial amount of carbohydrate to obtain the remaining material in the wood residue. A third negative term is added to the right side of the first equation to describe the dissolution of reducing end groups. The equation system 4 can also be solved analytically, but leads to a more complex expression than that emerging from the solution of equation system 1. As a matter of fact, in order to fit the model to the data it is not mandatory to have an analytical solution of the equation system. It suffices to apply a numerical solver available, e.g., in the Matlab program. Hydroxide Level Dependence. In previous studies,11 the following expressions have been deduced for the effect of the proton concentration [H+] on the reaction rate coefficients: ks = a([H+] + K 2)hp

(5)

ks = aK 2hs

(6)

kh =

KA hh [H ] + KA +

dQ = kZ dt

(11)

In this equation k is a reaction rate depending on temperature (T) through the Arrhenius equation and Z is a temperature independent quantity that may or may not be a function of Q. Converting from differentials to differences the equation at the ith time interval can be expressed as ⎛ E ⎞ ΔQ i = exp⎜ − ⎟ZiΔt ⎝ RTi ⎠

+

In eqs 5 and 6, a = K1/([H ] + K1[H ] + K1K2). The proton concentration independent reaction rates are denoted by hp, hs, and hh. Further K1, K2, and KA are equilibrium constants related to the chemical reactions. The first two constants K1 and K2 characterize the equilibrium of various neutral, mono- and diatomic groups associated with the endwise reactions. Further, KA is the acid dissociation constant characterizing the equilibrium for the hydroxyl groups of polysaccharides formed in alkaline degradation. Finally, the proton concentration is related to the alkali concentration through the dissociation constant: KW = [H+][OH−]

(10)

Here R is the universal gas constant, A is the frequency (or preexponential) factor, and Ea is the activation energy of the reaction. Isothermal Time. Each experimental cooking includes an initial heating and a final cooling stage, during which the temperature is not constant. This implies a modeling challenge since the reaction rates also change during time according to the Arrhenius equation, rendering an analytical solution of equation system 1 infeasible. A numerical solution could still be achieved, but would be time-consuming due to its repetitive use in the fitting algorithm. Consequently, in this study the concept of isothermal time, based on Arrhenius’ equation, has been adopted to allow for an analytical solution. The isothermal time can be motivated as follows: To begin with the total cooking time tcook is partitioned to a series of n consecutive time intervals of equal length Δt = tcook/n, during each of which the temperature is approximately constant. Suppose that Q is a quantity the development that can be described by a differential equation:

(7) + 2

(9)

(12)

Here ΔQi is the change in the quantity Q during the ith time interval, whereas Ti and Zi are the constant approximations of the quantities T and Z respectively during the same ith time interval. For each index value i, we define an “isothermal” time interval Δτi, during which the same amount of change would occur, at the target temperature Tc, as during the ordinary, “chronometric” time interval Δt, at the actual measured temperature. From the equal change (degradation) condition:

−kiZiΔti = −kcZiΔτi

(8)

(13)

It follows that

Despite its name, the dissociation constant is temperature dependent. Kuitunen et al. established a temperature correlation for the dissociation constant based on Gibbs energy formation data. In the present study, data for different hydroxide levels were available only at 160 °C. According to

Δτi = e E / RTc − E / RTi Δt

(14)

From these corresponding time intervals, the isothermal time is constructed in a cumulative fashion: 11294

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Figure 1. Hydroxide concentration dependent model fitted to (a) glucomannan, (b) xylan, and (c) cellulose degradation data at 160 °C. For each carbohydrate, the data values consist of the sum of the amounts in the wood residue and the black liquor. n

n

(15)

was calculated similarly as for pulp polysaccharides, according to methods available in the literature.17 The experimental part is described in more detail in the study of Paananen et al.18

EXPERIMENTAL SECTION Wood of Scots pine (Pinus sylvestris) from southern Finland was chipped and screened according to SCAN-CM 40:01. The chips were further milled with a Wiley mill to pass through a 1 mm slot screen. Subsequently, the wood meal was treated in a 10 L batch reactor at a liquor-to-wood ratio of 200:1. The high liquor-to-wood ratio endorses the model simplifying presumption of a constant level of hydroxide throughout the cooking. Experiments were conducted at temperatures ranging from 130 to 160 °C. The hydroxide ion concentration was either high (1.55 M) or conventional (0.5 M). In both cases, the sulfidity was 33%. In part of the experiments, AQ was added at levels 1, 3, and 5% on oven-dried wood. Addition of NaCl adjusted the sodium ionic strength to a constant level of 2.00 M [Na+]. Table S1 (Supporting Information) summarizes the experimental conditions of this study. For each combination of the variable levels included in the experimental plan, a series of experimental cooking with various durations was completed. Typically, one such series contained 9−12 cooking where the shortest duration at the target temperature was less than 10 min and the longest a few hours. The heating stage from room temperature to the target temperature lasted 20 min ±1 min and was approximately linear with regard to time. The cooling stage during which the pressure in the reactor dropped to atmospheric also lasted approximately 20 min. The cellulose, glucomannan, and xylan contents were measured in both the wood residue and the black liquor. The monosaccharide composition was determined by high performance anion exchange chromatography with pulsed amperometric detection (Dionex HPAEC-PAD). From the monosaccharide composition the polysaccharide composition

RESULTS AND DISCUSSION The kinetic models were fitted to the data for glucomannan, xylan, and cellulose obtained from both the solid residue and the black liquor as a function of time. Ideally, a model containing a simultaneous description of all the variables (temperature, hydroxide level, and AQ charge) having an effect on the degradation would be fitted to the entire set of available data. The drawback of this approach is that the high number of parameter values to be estimated by nonlinear regression imposes severe requirements on the selection of the initial values, in order for the fitting algorithm to return meaningful estimates. Instead, the following algorithm was adapted for modeling the carbohydrate degradation: (1) Hydroxide dependence: eqs 5−7 were inserted into eqs 2 and 3. Subsequently the resulting function for the remaining carbohydrate was fitted to the data from the cooking at the temperature 160 °C containing no added AQ with the two [OH−] levels 0.5 and 1.55 M. The fit rendered estimates for the proton concentration independent reaction rates hp, hs, and hh as well as the equilibrium constants K1, K2, and Ka at 160 °C. (2) AQ dependence: The exponential model of eq 9 was inserted into eqs 2 and 3, and two separate fits were performed for the data with temperature 160 °Cone containing the cookings of conventional (0.5 M), and the other those of high (1.55 M) hydroxide level. The reaction rates at AQ level 0% is fixed to the values obtained in the preceding hydroxide dependence step. (3) Temperature dependence: The Arrhenius expressions of eq 10 were inserted for the reaction rates in eq 2. The resulting function was fitted to the data at hydroxide level 1.55 M without added AQ and temperatures ranging from 130 to 160

t iso =

■

∑ Δτi = ∑ e E /RT − E /RT Δt c

i=1

i=1

i

■

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Figure 2. AQ-charge dependent model fitted to combined degradation data in wood residue and black liquor for (a) glucomannan, (b) xylan, and (c) cellulose at 160 °C and [OH−] = 0.5.

Figure 3. AQ-charge dependent model fitted to combined degradation data of wood residue and black liquor for (a) glucomannan, (b) xylan, and (c) cellulose at 160 °C and [OH−] = 1.55.

fitted to the mere wood residue data with estimates for the dissolving rates as a result. All the fits were performed using the FindFit function of the Mathematica software, which is a tool for nonlinear regression. The initial fraction of reducing end groups for GGM was calculated as an average (0.0075) of previously reported values.19−21 Xylan has a molar mass comparable to that of

°C, demanding that the resulting reaction rates at 160 °C coincided with those obtained in step 1. (4) Dissolution into black liquor: The values for the reaction rates affiliated with peeling, stopping, and alkaline hydrolysis obtained when fitting eq 2 to the degradation data, comprising both the wood residue and the black liquor, were inserted into the solution of equation system 4. This expression was then 11296

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Figure 4. Temperature dependent model fitted to combined degradation data of wood residue and black liquor for (a) GGM, (b) xylan, and (c) cellulose at [OH−] = 1.55 M with temperatures ranging from 130 to 160 °C.

When it comes to the reaction rate coefficients for alkaline hydrolysis, we have coefficients increasing with the hydroxide levels for all the three carbohydrates. This is manifested in the degradation data by higher degradation rate at higher alkaline levels, after the initial stage when the initial REGs have been extinguished and further peeling is dependent on the alkaline hydrolysis creating new REGs. The reason for the alkaline hydrolysis reaction rate coefficient of cellulose being lower than those of the hemicelluloses is likely to be related to the denser structure and crystallinity of the former decreasing the accessibility. Effect of AQ Charge. Increasing the AQ charge impedes the degradation of GGM due to the partial conversion of the reducing end groups to aldonic acid end groups. For the other carbohydrates, the effect of AQ on degradation is ambiguous. Inserting the simple exponential dependence on the AQ charge for the reaction rates (eq 9) into the solution of the equation system 1 allows for reasonable fits to experimental data in the case of the GGM. Figures 2 and 3 show the fits and Tables S4− S7 (Supporting Information) the estimated γ values and the reaction rates calculated from them. The value of the parameter γ depends on the reaction (peeling, stopping, or alkaline hydrolysis) and the hydroxide level (moderate or high). For GGM the parameter is always positive indicating reaction increasing with AQ charge. The parameter values are higher for the moderate hydroxide level than for the high one. As a consequence, the changes in reaction rates are bigger at the moderate hydroxide level for all three reactions. The parameter value for the stopping reaction exceeds that of the peeling reaction. From this it follows that the reaction rate coefficients of stopping grow faster than those of peeling, i.e., the peelingto-stopping ratio kp/ks decreases, when AQ is added thus being in agreement with the degradation behavior of GGM in the presence of AQ. The peeling-to-stopping ratio is crucial for the degradation, when it is dominated by primary peeling.

GGM, and for that reason it was assumed to have the same initial fraction of REGs. As for cellulose, a viscosity average degree of polymerization (DP) of 5080 has been reported.2 Assuming a polydispersity index of 3 would then give the number-average DP 1693. This further corresponds to a value 0.00059 for the initial fraction of REGs. On the basis of the effect on the goodness of the fit, the moderately higher value 0.0007 was selected for the cellulose model. Effect of the [OH−] Level. Figure 1 shows the model fitted to the carbohydrate data at 160 °C for two different hydroxide levels. It is notable that for GGM increasing the hydroxide level implies less degradation, whereas the opposite is true for xylan and cellulose. An examination of the corresponding reaction rates to some extent untangles this conduct. Table S2 (Supporting Information) contains the proton concentration independent reaction rates together with equilibrium constants for the reactions relevant to degradation. The estimated values of the equilibrium constants obtained in this study are much higher than those reported by Paananen et al.11 A partial explanation could be that the temperatures in Paananen’s work were lower (80−130 °C). The lumped reaction rates, calculated from eqs 5, 6, and 7, are displayed in Table S3 (Supporting Information). It was shown in a study by Young et al.22 that that increasing the alkali level enhances the stopping reaction. This is in accordance with our result, where the calculated reaction rate coefficient for stopping is higher at 1.55 M hydroxide level. This result in combination with the peeling rate coefficient unchanged by the hydroxide level contributes to the lower degradation for higher hydroxide level of Figure 1. In the present study, the stopping rate coefficient estimates for the other two carbohydrates also increase with the hydroxide level. The situation is however different from that of GGM in that the peeling rate coefficients increase even more, resulting in an increased peeling-to-stopping ratio kp/ks. 11297

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Figure 5. Calculated cumulative degradation amounts for primary peeling (solid lines), secondary peeling (dashed lines), and alkaline hydrolysis (dotted lines close to zero) for (a) GGM, (b) xylan, and (c) cellulose.

is exclusively a result of alkaline hydrolysis. In the present model, there is a continuous interplay between peeling stopping and alkaline hydrolysis, which maintains all three processes relevant throughout the degradation of the carbohydrates. Hence, as opposed to in the old model, the estimated values of the parameters associated with peeling and stopping are also influenced by the data from the later stages of the cooking. From the values for frequency factor and activation energy, the reaction rate coefficients at different temperatures are calculated by the Arrhenius equation. The obtained reaction rate coefficients are shown in Table S9 (Supporting Information). There is a clear difference in the rate coefficients between the two hemicelluloses GGM and xylan. GGM displays much higher values for the peeling and stopping rates, whereas, on the contrary, when it comes to alkaline hydrolysis, the reaction rates for xylan are approximately one decade higher than those of GGM. The fast initial degradation of GGM is then explained by the high peeling rate, and the quick cessation of the initial degradation phase is due to the high stopping rate. Cellulose has peeling rates comparable to those of GGM but because of the small number of initial reducing end groups the degradation of cellulose is slow. Significance of the Different Degradation Paths. A minor modification of equation system 1 allows us to calculate the portions of the carbohydrates degraded by primary and secondary peeling as well as by alkaline hydrolysis.

However, if secondary peeling is significant, the rate of alkaline hydrolysis must also be accounted for. As later will be shown, secondary peeling is more important for xylan and cellulose degradation than it is for GGM degradation. For this reason, the effect of AQ on xylan and cellulose degradation is obscured even though the peeling-to-stopping ratio decreases with added AQ also for these carbohydrates. Effect of the Temperature. Increasing the temperature accelerated the degradation of all the carbohydrates in this study. However, there are considerable differences in how the enhanced degradation manifests itself. For GGM the data show a brief and fast initial decrease, mainly independent of temperature, followed by a stage with a slower decrease which separates the data belonging to divergent temperatures. On the other hand, xylan and cellulose display degradation patterns that are more uniform in time and where the effect of temperature is evident from the start. The fits are shown in Figure 4. The fit procedure renders estimates for the activation energies and frequency factors for peeling stopping and alkaline hydrolysis. The parameter values are shown in Table S8 (Supporting Information). In the case of GGM, the activation energies obtained for peeling and stopping are surprisingly low and differ significantly from the values reported by Paananen et al. (112.5 kJ/mol for peeling and 110.6 kJ/mol for stopping). One reason for the discrepancy could be that the experimental conditions were different in Paananen’s earlier study, with temperatures ranging from 80 to 130 °C and no adjustment of the sodium ionic strength. Also, the previous model did not include a description of secondary peeling enabled by alkaline hydrolysis creating new reducing end groups. In that model, peeling and stopping proceed independently of the alkaline hydrolysis until all the reducing end groups have been eliminated by the stopping reaction and all further degradation 11298

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Figure 6. Calculated cumulative GGM degradation amounts for primary peeling (solid lines), secondary peeling (dashed lines), and alkaline hydrolysis (dotted lines close to zero) at different AQ charges at temperature 160 °C for (a) [OH−] = 0.5 M and (b) [OH−] = 1.55 M.

Figure 7. Model including dissolution fitted to wood residue degradation data for (a) GGM, (b) xylan, and (c) cellulose.

⎧ dR1 = −ksR1 ⎪ ⎪ dt ⎪ dR 2 = −ksR 2 + k h(Γ0 − P1 − P2 − H ) ⎪ ⎪ dt ⎪ dP ⎨ 1 = k pR1 ⎪ dt ⎪ dP ⎪ 2 = k pR 2 ⎪ dt ⎪ ⎪ dH = k h(Γ0 − P1 − P2 − H ) ⎩ dt

secondary peeling. For peeled off material, we have simply P1 and P2 depending on whether it is generated by primary or secondary peeling. As before H stands for the material degraded by alkaline hydrolysis, and Γ0 stands for the initial amount of the carbohydrate. The initial values of R2 and P2 are set to zero, whereas the initial values of the other functions are as in the case of equation system 1. Moreover, Table S9 (Supporting Information) shows the values of the reaction rates for peeling, stopping, and alkaline hydrolysis estimated earlier. Accordingly, those values can be inserted in equation system 16, which can be solved numerically. Figure 5 shows the numerical solution at different temperatures. The amount explicitly degraded by alkaline hydrolysis is insignificant compared to the amount degraded by peeling, but alkaline hydrolysis still makes a substantial contribution by enabling secondary peeling. Furthermore, with all three carbohydrates primary peeling is initially the most important process, but in the long run it is dominated by secondary peeling. As for the temperature, notably in the case of GGM

(16)

In equation system 16 the peeled material and the REG fraction have been split into two parts P1, P2 and R1, R2. With R1 we denote those REGs that are either original or have been formed through primary peeling, whereas R2 designates those REGs that are formed due to alkaline hydrolysis or subsequent 11299

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Figure 8. Cumulative amount of material degraded by element wise reactions (peeling, stopping, and alkaline hydrolysis)solid lines and by dissolution of longer chain fragments into the black liquor−dashed lines for (a) GGM, (b) xylan, and (c) cellulose.

peeling. Since a higher alkalinity boosts delignification, the treatment can be terminated when the cumulative effect of secondary peeling is still at a relatively low level. Hence, the overall yield loss is reduced, which is of immense practical implication. Dissolution into the Black Liquor. Part of the carbohydrates is dissolved into the black liquor as polymer fragments. When the system is solved a similar, but more complex, expression as that in eq 2 is obtained for the carbohydrates in the wood residue. When that expression is fitted to the wood residue data, with the values for the reaction rates recovered in the fit to the data including both wood residue and black liquor, an estimate for the dissolution is achieved. The data indicated the existence of two subcomponents of GGM and cellulose as well as three subcomponents of xylan, with regard to the dissolution facility. For cellulose very little of the polymer is dissolved, and it was modeled as having one component which does not dissolve. Figure 7 shows the fits to the wood residue data, and Table S10 (Supporting Information) displays the estimated frequency factors and activation energies, whereas Table S11 (Supporting Information) presents the original amounts of each subcomponent. Finally Table S12 (Supporting Information) shows the reaction rate coefficients at different temperatures calculated from the activation energies and frequency factors. We note that the amount of dissolvable cellulose is very small, and therefore the estimates of the related kinetic parameters are unreliable. It is of interest to examine how much of the degradation is due to dissolution as compared to the endwise reactions. From the solution of the equation system 4 we obtain separate expressions for material degraded by peeling, alkaline hydrolysis, and dissolution. Inserting the parameter estimates obtained by nonlinear regression renders the numerical amounts of the degradation fractions. It should be noted that

but certainly also for cellulose, the effect is clearly bigger for secondary than for primary peeling. The behavior of xylan however diverges from that of the other two carbohydrates when it comes to the response of the primary peeling to temperature. For xylan also the amount of material degraded by primary peeling is significantly increased by higher temperature. According to Sjöström15 the presence of 4-O-methylglucuronic acid groups in softwood xylan prevent the peeling of xylan chains at temperatures below 100 °C. However, this group offers only partial protection at higher temperatures. GGM was the only carbohydrate, the degradation of which responded in a pellucid way to addition of AQ. Hence, the partition of degraded material at different AQ levels was calculated exclusively for GGM. The results of the calculation are shown in Figure 6. The effect adding AQ is apparent both for primary and secondary peeling. It is however noteworthy that the actions are the opposite for the two types of peeling. While adding AQ decreases the final amount of primary peeled material it also increases the rate at which material is degraded by secondary peeling. The former can be explained by the fact that adding AQ enhances the stopping reaction more than the peeling reaction while the reason for the latter lies in the boosted reaction of alkaline hydrolysis, which is necessary for secondary peeling. The outcome for the integrated GGM degradation process is that AQ initially, while primary peeling is predominant, slows it down, and later, when the original assemblage of REGs is consumed and only secondary peeling remains, speeds it up. Figure 6 also supports the conclusion in the study of Paananen et al.18 regarding the stabilizing effect of high alkalinity on GGM with respect to lignin content. At the higher alkalinity level, the amount of material undergoing primary peeling is reduced, and a larger part of the degradation is postponed to appear through the initially slower secondary 11300

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amount of the degraded material, which was the topic of the present study, the estimates could be compared with those obtained from fitting the DP model to the data. Unfortunately, for the present data the viscosity values are interfered by the delignification and do not lead to a reliable assessment of the DP of the carbohydrates. Degrading treatments of carbohydrate substances where lignin is not present, such as cotton linters, could however offer a means for a combined fit of DP and degraded material, thus improving the estimates of the parameters. To extend the carbohydrate dissolution model to the case of wood chips, a description of diffusion of the dissolved material would have to be included. In this case, the dissolution should be modeled as a reversible process where the dissolved material can accumulate back to the wood. In the experimental procedure, screening of the milled chips allowed all wood material with a diameter less than 1 mm to pass. In retrospect, an additional screening in order to eliminate the fines should have been performed. Since the raw material was the same in all the experiments and since the maximum particle was low in order to exclude diffusion effects, we however believe that the presence of the fines is of minor importance for the results.

the dissolved material may still undergo further endwise reactions. Our categorization into endwise degraded and dissolved material does not determine the final destiny of the polysaccharides, but rather in which form they first reach the black liquor as singular chain elements or as longer chain fragments. Figure 8 shows the partition into endwise degraded and dissolved material. We observe that the two hemicelluloses of this study behave quite differentlyfor GGM the amount of endwise degraded material is during the early stage of the treatment multifold to that of dissolution, whereas for xylan the situation is the opposite. After a while the differences between the degradation modes level out, but a clear distinction when it comes to the cumulative amounts remains. Issues with the Model and Future Research. In order to keep the number of parameters to be estimated low, some a priori assumptions regarding the model were made. It seems well motivated that the rate constants of primary and secondary peeling as well as of primary and secondary stopping are the same in the model. More dubious is the assumption that the peeling, stopping, and alkaline hydrolysis rate coefficients are the same, regardless if they concern a polymer chain still in the wood residue or a fragment in the black liquor. From the experimental data, it is clear that endwise degradation still occurs in the black liquor, but to accurately estimate the reaction rates more data are needed. The activation energies obtained for peeling and stopping of the GGM polymer are strangely low. The task of determining these parameters is hampered by the initial decrease in GGM being so fast regardless of the temperature. Comparable experiments conducted at lower temperatures could throw some light on this matter. Addition of the proper amount of NaCl to the cooking liquor in each experimental run fixes the sodium ionic strength to the 2.0 M level, but as a consequence the concentration of chloride ions will vary with the hydroxide level. Those runs with the hydroxide concentration 0.5 M have a chloride anion concentration of 1.4 M, whereas for the runs with the hydroxide ion concentration 1.55 M the chloride anion concentration is 0.14 M. It has been shown that even though the chloride ions do not react with wood their presence has a retarding effect on the delignification rate in kraft cooking.23 We are not aware of any study on the effect of chloride ions on carbohydrate degradation, but if such an effect exists it would have an impact on the results for the hydroxide dependence of carbohydrate degradation. Paananen et al.18 showed that the change in degradation velocity of carbohydrates when NaCl is added follows the change in delignification velocity so that a certain lignin level corresponds to a certain carbohydrate level regardless of the amount of added NaCl. The carbohydrate dissolution model with the dissolution rate proportional to the amount of polymer in the wood is a simplification; a more rigorous model would take into account the significance of the molar mass of the polymer, with shorter chains being more likely to dissolve. For a polymer chain the degree of polymerization (DP) can be defined as the number of repeat units in the chain. The repeat unit consists of a monomer or sometimes a group of monomers. It is possible to obtain a mathematical expression for how the degree of polymerization for the degrading carbohydrates develops with time.24 On the other hand, the average degree of polymerization can be evaluated experimentally based on viscosity measurements. Since the same kinetic parameters appear in the expression for DP as for the

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CONCLUSIONS The presented kinetic model fits reasonably well to the experimental data and provides estimates of the relevant kinetic parameters. Insertion of the parameters to the model enables calculation of the effects of the various subprocesses. In consequence the following inferences can be made: (1) The endwise degradation is a composite process, where the degradation velocity cannot be concluded from the reaction rate of a single subreaction but is dependent on the interaction pattern between peeling stopping and alkaline hydrolysis. (2) Both endwise degradation and dissolution into black liquor are significant contributors to the loss of carbohydrates during Kraft pulping. (3) Even though the amount of carbohydrates degraded explicitly by alkaline hydrolysis is insignificant, the alkaline hydrolysis is still crucial in allowing secondary peeling. Without alkaline hydrolysis, the endwise degradation would feature an intense but brief initial stage, after which the reactions would cease due to the stopping of all REGs. (4) For GGM, the degradation by primary peeling is very fast for the temperatures occurring in the experiment, and no significant differences due to the four temperatures can be detected, whereas for xylan there is strong increase in primary peeled material with temperature. In this respect, cellulose lies somewhere between GGM and xylan. The xylan behavior can be explained by the temperature undermining the protection from 4-O-methylglucuronic acid groups against peeling. (5) The amount of material degraded by secondary peeling increases with temperature for all three carbohydrates. To keep the carbohydrate losses low, the temperature should not exceed 130−140 °C where the rate of alkaline hydrolysis and in turn secondary peeling substantially increases. (6) The amount of material degraded by primary peeling decreases with the addition of AQ. (7) The amount of material degraded by secondary peeling increases with the addition of AQ. (8) For GGM and cellulose, more material is degraded by the endwise reactions than by dissolution. For xylan the opposite is true. 11301

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(16) Kuitunen, S.; Kalliola, A.; Tarvo, V.; Tamminen, T.; Rovio, S.; Liitiä, T.; Ohra-aho, T.; Lehtimaa, T.; Vuorinen, T.; Alopaeus, V. Lignin Oxidation Mechanisms under Oxygen Delignification Conditions. Part 3. Reaction pathways and modelling. Holzforschung 2011, 65, 587. (17) Janson, J. Calculation of polysaccharide composition of wood and pulp. Pap. Puu 1970, 52, 323−329. (18) Paananen, M.; Liitiä, T.; Sixta, H. Further insight into carbohydrate degradation and dissolution behavior during kraft cooking under elevated alkalinity without and in the presence of Anthraquinone. Ind. Eng. Chem. Res. 2013, 52, 12777−12784. (19) Procter, A. R.; Apelt, H. M. Reactions of wood components with hydrogene sulfide. III. Efficiency of hydrogen sulfide pretreatment compared to other methods for stabilizing cellulose to alkaline degradation. Tappi 1969, 52, 1518−1522. (20) Young, R. A.; Liss, L. A kinetic study of the alkaline endwise degradation of gluco- and galactoglucomannans. Cellul. Chem. Technol. 1978, 12, 399−411. (21) Jacobs, A.; Dahlman, O. Characterisation of the molar masses of hemicelluloses from wood and pulps employing size exclusion chromathography and matrix-assisted laser desorption ionization time-of-flight mass spectrometry. Biomacromolecules 2001, 2, 894−905. (22) Young, R. A.; Sarkanen, K. V.; Johnson, P. G.; Allan, G. G. Marine plant polymers III. Kinetic analysis of the alkaline degradation of polysaccharides with specific reference to (1,3)-β-D-glucans. Carbohyd. Res. 1972, 21, 111−122. (23) Bogren, J.; Brelid, H.; Bialik, M.; Theliander, H. Impact of dissolved sodium salts on kraft cooking reactions. Holzforschung 2009, 63, 226−231. (24) Calvini, P.; Gorassini, A.; Merlani, A. L. On the kinetics of cellulose degradation: looking beyond the pseudo zero order rate equation. Cellulose 2008, 15, 193.

ASSOCIATED CONTENT

S Supporting Information *

Tables S1−S12 showing the experimental design, reaction equilibrium related constants, and parameter values obtained when fitting the models to the data. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*(K.N.) E-mail: kaarlo.nieminen@aalto.fi. *(H.S.) E-mail: herbert.sixta@aalto.fi. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Finnish Bioeconomy Cluster OY (FIBIC) is acknowledged for financial support.

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REFERENCES

(1) Jacobs, A.; Dahlman, O. Characterization of the molar masses of hemicelluloses from wood and pulps employing size exclusion chromatography and matrix-assisted laser desorption ionization timeof-flight mass spectrometry. Biomacromolecules 2001, 2, 894−905. (2) Sixta, H.; Potthast, A.; Krotschek, A. W. Chemical Pulping Processes. In Handbook of Pulp; Sixta, H., Ed.; Wiley-VCH Verlag GmbH: Weinheim, 2006; pp 109, 197. (3) FAO Yearbook of Forest Products 2011; Food and Agriculture Organization of the United Nations: Rome, Italy, 2013; pp 155, 166, 169; http://www.fao.org/docrep/018/i3252m/i3252m00.htm. (4) Sjöström, E. The behavior of wood polysaccharides during alkaline pulping processes. Tappi J. 1977, 60, 151−157. (5) Testova, L.; Nieminen, K.; Penttilä, P. A.; Serimaa, R.; Potthast, A.; Sixta, H. Cellulose degradation in alkaline media upon acid pretreatment and stabilisation. Carbohydr. Polym. 2014, 100, 185−194. (6) Mozdyniewicz, D. J.; Nieminen, K.; Sixta, H. Alkaline steeping of dissolving pulp. Part I: cellulose degradation kinetics. Cellulose 2013, 20, 1437−1451. (7) Van Loon, L. R.; Glaus, M. A. Review of the kinetics of alkaline degradation of cellulose in view of its relevance for safety assessment of radioactive waste repositories. II. J. Environ. Polym. Degrad. 1997, 5, 97−108. (8) Franzon, O.; Samuelson, O. Degradation of cellulose by alkali cooking. Svensk Papperstid 1957, 60, 872−877. (9) Lai, Y.-Z.; Sarkanen, K. V. Kinetics of alkaline hydrolysis of glycosidic bonds in cotton cellulose. Cell. Chem. Technol. 1967, 1, 517−527. (10) Pavasars, I.; Hagberg, J.; Borén, H.; Allard, B. Alkaline degradation of cellulose: mechanisms and kinetics. J. Polym. Environ. 2003, 11, 39−47. (11) Paananen, M.; Tamminen, T.; Nieminen, K.; Sixta, H. Galactoglucomannan stabilization during the initial kraft cooking of Scots pine. Holzforschung 2010, 64, 683−692. (12) Smith, C. C. Studies of the Mathematical Modelling, Simulation and Control of the Operation of a Kamyr Continuous Digester for the Kraft Process, Ph.D. Thesis, Purdue University, West Lafayette, Indiana, USA, 1974. (13) Christensen, T.; Albright, L. F.; Williams, T. J. A Kinetic Mathematical Model for the Kraft Pulping of Wood. Proceedings of Tappi Annual Meeting, 1983; Tappi Press: Atlanta, Georgia; pp 239− 246. (14) Andersson, N.; Wilson, D.; Germgård, U. An Improved Kinetic Model Structure for Softwood Kraft Cooking. Nord. Pulp Paper Res. J. 2003, 18, 200−209. (15) Sjöström, E. Wood Chemistry. Fundamentals and Applications, 2nd ed.; Academic Press: New York, 1993; p 133. 11302

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