Novel Insight into Lignin Degradation during Kraft Cooking - American

Article pubs.acs.org/IECR

Novel Insight into Lignin Degradation during Kraft Cooking Kaarlo Nieminen,*,† Susanna Kuitunen,‡ Markus Paananen,† and Herbert Sixta*,† †

School of Chemical Technology, Department of Forest Products Technology, Aalto University, Vuorimiehentie 1, FI-00076 Aalto, Finland ‡ School of Chemical Technology, Department of Biotechnology and Chemical Technology, Aalto University, Kemistintie 1, FI-00076 Aalto, Finland S Supporting Information *

ABSTRACT: In this study three different modeling approaches, with varying levels of sophistication and complexity, on modeling kraft cooking kinetics have been investigated. In the first and second approaches, isothermal conditions were used by converting the heating and cooling times into isothermal time. In the third approach, real temperature and time were used. Donnan theory, accounting for the cation exchange property of the wood fibers, was used in the second and third approaches for estimation of the cooking chemical concentrations in the fiber wall liquid, whereas in the first approach the cooking chemical concentrations in the bulk liquid phase were used. A modification of the Purdue model was used for modeling the delignification kinetics. The parameters of the Purdue model were regressed both with Matlab (commercial software) and Kinfit (in-house software). All three regressions with different modeling approaches provided very good fits to the experimental data. When Donnan theory and real temperature profiles (third approach) were employed, the estimated reaction rates for the faster reacting lignin subcomponent in the Purdue model decreased at all temperatures. On the other hand, the portion of the faster reacting component increased from 24% to 28%. In this way the third modeling approach mimics the reality in the most accurate way. Its implementation is more tedious, but the model should have more predictive capabilities. Furthermore, the effect of anthraquinone on kraft cooking kinetics was studied.

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INTRODUCTION For the production of chemical pulp, the kraft process is the most utilized technology. The aim of the process is to remove lignin and at the same time maintain a high yield of carbohydrates in the resulting pulp. The removal of lignin by kraft delignification is achieved by treating wood material in an aqueous solution of sodium hydroxide and sodium sulfide. The delignification velocity depends on the temperature as well as on the concentrations of cooking chemicals.1 The simplest model would be the following (γ is a function of the temperature and the cooking chemical concentrations, which are assumed to be constant and WL is the mass fraction of lignin): dwL = −γwL dt

degradation rate of its own. The degradation of the different subcomponents proceeds simultaneously and independently of each other. In such a model the explanation of the nonexponential nature of the lignin decay is that the decay initially is dominated by a subcomponent with a large reaction rate constant and, as the amount of that subcomponent is being degraded, its significance for the overall delignification rate is reduced and delignification proceeds at a slower rate. In other words: the Purdue model describes the remaining lignin content not by a single exponential function but as a sum of exponentials. Andersson et al.13,14 modified the Purdue model by increasing the number of lignin species from two to three and proposing some interchange of lignin between the subcomponents. Bogren et al.15 made a generalization of the Purdue model with a continuous distribution of lignin reactivity. Recently, the eucalypt wood cooking kinetics was equally well modeled with both parallel (three fractions of lignin with different reactivity) and consecutive (two delignification phases) approaches.16 The consecutive modeling approach with two delignification phases has been also applied to modeling of cooking using organic solvents.17−19 Burazin and McDonough20,21 assessed several kinetic models for delignification and carbohydrate degradation in kraftanthraquinone (kraft-AQ) cooking. For delignification, the proposed model included three parallel pathways for lignin solubilization, a pathway for lignin condensation, and a pathway

(1)

Solving eq 1 analytically gives an exponential decay for the lignin. This is not, however, in accordance with experimental data, which show the degradation rate slowing with time. Several different models have been suggested to reproduce this behavior.2 Pioneering steps in constructing a pseudo-firstprinciple theoretical framework for delignification were taken among others by Wilder and Daleski,3 Kleinert,4 LéMon and Teder,5 and Olm and Tistad.6 Based on these early works, two distinct families of degradation models emerged. The Purdue model, derived at the University of Purdue, assumes parallel reactions of the wood components,7−10 whereas the Gustafson model operates with consecutive reactions.11,12 In the Purdue model the lignin components in wood are divided into subcomponents or “species”, each with a characteristic © 2014 American Chemical Society

Received: Revised: Accepted: Published: 2614

September 3, 2013 January 3, 2014 January 22, 2014 February 7, 2014 dx.doi.org/10.1021/ie4028928 | Ind. Eng. Chem. Res. 2014, 53, 2614−2624

Industrial & Engineering Chemistry Research

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Purdue model and the Purdue−Donnan model. In experiments, the extent of Donnan effect was varied by adding sodium chloride into some of the cooks. Increasing ionic strength is known to suppress Donnan effect so that the composition of the fiber wall liquid is closer to the composition of the liquid external to the fiber wall. Furthermore, it was studied whether realistic modeling of the heating and cooling periods vs usage of isothermal time would affect on the model parameter values. Finally, the effect of anthraquinone (AQ) on the kraft delignification rate was assessed and compared to previously obtained results in the soda cooking conditions.22−24

for residual delignification pathway, in which the condensed lignin is dissolved. In Burazin’s model, one of the parallel delignification rates has a square root dependence of the AQ charge. Miranda and Pereira,17 in turn, have modeled the kinetics of AQ cooking with a consecutive approach with two delignification phases. Werthemann,22,23 as well as Abbot Bolker,24 studied soda-AQ cooking and the relation between final lignin content and AQ charge. The assumption made regarding the constant concentration of cooking chemicals and temperature (eq 1) requires some additional comment. It is true that high liquor-to-wood ratio in the cooks, typically conducted to study delignification kinetics in laboratory conditions, means that the total consumption of cooking chemicals in the degradation reactions can be neglected. There may, however, still be significant changes in the chemical concentrations during the cook in the fiber wall level (at the actual reaction site). This is due to the fact that in aqueous solution wood fibers act as cation exchangers. Cation exchange begins when uronic acids (pKa ∼ 3) and phenolic units (pKa ∼ 9−11) covalently bound to the fiber wall are dissociating resulting in an excess of bound negative charge in the fiber wall. The ion exchange behavior can be modeled using the Donnan theory.25 Towers and Scallan26 developed a mathematical model based on the Donnan theory for the estimation of the partition of cations between the fiber wall liquid and surroundings in pulp suspension. Later, the effect of ionic strength27 and temperature28 has been included into the modeling. The contribution of the Donnan effect on other phenomena such as swelling of pulp,29,30 precipitation of metal ions in the pulp mill,31 and lignin solubility during pulp bleaching32 has been studied as well. Plenty of studies discuss the Donnan effect in pulp suspension or in pulp bleaching operations, but only a few studies discuss the Donnan effect in wood or in cooking. Pu et al.33−35 studied experimentally the interactions of wood meal and alkali, and in the analysis of the experimental data, the Donnan theory was applied. To our knowledge, Donnan theory has been considered only in a few studies modeling phenomena in impregnation or kraft cooking, i.e., in the reaction kinetic model for hexenuronic acid formation and degradation,36 in modeling mass transfer during impregnation of eucalypt wood,37 and in deacetylation kinetics during alkaline impregnation.38 In an early study by Haglind et al.,39 some theoretical calculations, applying Donnan theory, were performed on the distribution of active delignifying species between the external and fiber bound water phases. They concluded that the concentration of the active species and the pH may be quite different within the fibers and in the external solution because of the Donnan effect. In short, utilization of the Donnan theory enables prediction of the concentrations of reacting ions (hydroxide and hydrogen sulfide) in the fiber wall liquid, i.e., at the actual reaction site. The hypothesis is that when modeling the ion exchange, the resulting reaction rate law is closer to the fundamental elementary reaction rate law and that the model is more predictive. The model would also be independent of factors affecting only the ion exchange as occurring through the addition of an inert salt. In this study, the Purdue model was modified by including Donnan equilibrium computations to account for the development of the hydroxide ion concentration in the fiber wall liquid. Comparisons were made between the performance of the

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SIMULATION MODEL Experimental Setup To Be Simulated. The experimental data to be modeled were obtained from two series of laboratory cooks. In both series, wood meal from Scots pine was cooked in a batch reactor at high liquor-to-wood ratio (L:W, 200:1). In the first series,40 the experiments were conducted following a full factorial plan with three temperature levels (80, 105, and 130 °C) and three levels of hydroxide ion molality (0.31, 0.93, and 1.55 M). In the second series,41 the cooks were performed at hydroxide levels of 0.5 and 1.55 M, with temperatures ranging from 130 to 160 °C (at 10 °C intervals), and in part of the cooks, AQ was added. The different chemical charges and temperatures applied are given in Table S1 (Supporting Information). At each combination of experimental conditions (chemical charges and temperature), about 10 cooks with various durations were performed. The shortest cooks lasted 1 min at the target temperature and the longest cook 400 min. The initial heating period took around 20 min, and the cooling period around 15 min. The sulfidity in all cases was 33%. Reaction Kinetics. The starting point for the delignification model used in the present study is the Purdue model with two lignin subcomponents. wL = wLF + wLS

(2)

Here wL is the total mass fraction of lignin and wLF and wLS are the fractions of the fast and slowly degrading subcomponents, respectively. The two lignin subcomponents degrade according to dwLi dt

= γiwLi

(3)

where ai bi Hγi = kimOH − (aq)m HS−(aq) ,

ki = Ai e−Eai / RT

for i = LF, LS

(4) (5)

In eq 4, mOH−(aq) and mHS−(aq) denote the molality (mol/(kg of water)) of the solute (OH− or HS−). The exponents ai and bi are dimensionless parameters, the values of which can be determined by fitting the model to the experimental data. Equation 5 is the well known Arrhenius equation, which empirically has been found to relate reaction rates to absolute temperature. Ai is the preexponential or frequency factor (1/ min), and Eai the activation energy (kJ/mol), R is the universal gas constant, and T is the temperature (K). For data containing significant variations in sodium chloride molality, eq 4 seems to be insufficient to describe the lignin degradation rate, and the expression for the slowly degrading 2615

dx.doi.org/10.1021/ie4028928 | Ind. Eng. Chem. Res. 2014, 53, 2614−2624


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much higher than the uronic acid content, the latter was not considered in the modeling. Another assumption concerns the amount of water absorbed by the solid fiber wall which corresponds to the fiber saturation point (FSP). A constant value of 0.3 kg of water/(kg of wood) was taken from Sixta et al.1 Only the chemicals, added in the experiments, and phenolic lignin units attached into the fiber wall were considered in the fiber wall liquid mass balances. The external liquid phase composition was assumed to be constant throughout the simulation due to the high L:W ratio. The reaction product, the lignin dissolved into the liquid phase during the delignification, contains a significant amount of ionizable phenolic units (even 3.1 mmol/(g of lignin)43) influencing the ionic strength and thus the extent of Donnan effect. In order to justify the assumption of excluding the mass balance of the dissolved phenolic units from the model, the liquid phase phenolic unit content was estimated to be 4 mmol/(kg of water) (=259 g of lignin/(kg of wood) × 3.1 mmol/(g of lignin) × (1/200) kg of wood/(kg of water)) with total delignification. Since the molality of the other ions is roughly a thousand times higher than the amount of the dissolved phenolic units, the assumption of excluding the dissolved phenolic unit mass balance from the model was considered to be justifiable. For the modeling of the mass balances in the fiber bound liquid phase three phenomena were considered: (1) irreversible dissolution of phenolic units from the fiber wall (IR); (2) reversible reaction equilibrium of phenolic units and water (RR); (3) mass transfer between the external liquid phase and the fiber bound liquid phase (MT). The rate for the irreversible dissolution of the phenolic units from the fiber wall is obtained from the total lignin removal rate (derived above). For simplicity and because the residual lignin structure was not analyzed, the fraction of phenolic units of the total amount of lignin was assumed to stay constant throughout the simulations.

lignin (LS) is replaced by admitting the dependence on the molality of the sodium ions: a2 b2 c2 γLS = kLSmOH − (aq)m HS−(aq)m Na +(aq)

(6)

At constant temperature and molality of the cooking chemicals, eq 3 can be solved analytically. When the solutions for both fast and slowly reacting lignin subcomponents are inserted into eq 2, the lignin content can be expressed as wL = wLFt =0se−γLFt + wLSt =0se−γLSt

(7)

wLFt=0s and wLSt=0s are the initial portions of the fast and slowly degrading lignin subcomponent. The original Purdue model9 has a slightly more complex structure with two reaction rates associated to each subcomponent. In the present study, one reaction rate per subcomponent was sufficient to model the experimental observations, whereas regression of all of the parameters in the original Purdue model led to convergence problems in the nonlinear optimization. Since the experiments were conducted at constant sulfidity (S) of 33%, the hydrogen sulfide ion molality correlates with the hydroxide ion molality, as defined by S=

2m HS−(aq) m HS−(aq) + mOH−(aq)

× 100% (8)

With S = 33%, mHS−(aq) = mOH−(aq)/5. It further turned out during the regression procedure that the degradation rate of the fast reacting lignin subcomponent is independent of the hydroxide ion (and hydrogen sulfide ion) molality in the conditions applied in this study. Inserting eq 5 into 4 and setting the exponents in the lumped reaction rate coefficient to zero for i = LF and replacing mHS−(aq) with mHS−(aq) = mOH−(aq)/ 5 in i = LS, eq 4 becomes ⎧ γ = A e−EaLF/ RT LF ⎪ LF ⎪ a+b − mOH (aq) −EaLS / RT ⎨ e γ = A LS b ⎪ LS 5 ⎪ c −EaLS / RT * mOH − (aq)e ⎩ = ALS

F dmPLOH(f),IR

= fPLOH

dt

dwL dt

(10)

The initial amount of phenolic units was obtained from the equation below:

(9)

In eq 9, we denoted c = a + b and (ALS)/(5b) = ALS * . From now on, the asterisk is dropped and the denominator, 5b is lumped into ALS. The values for the exponent (c) and Arrhenius law parameters (Ai and Eai) were obtained by fitting the model to the experimental data. Combining Donnan Theory with the Reaction Kinetics. The extent of the Donnan effect, i.e., how much the fiber wall liquid composition is different from the composition of the liquid external to the fiber wall, depends on the amount of stagnant negative charge in the fiber wall, when uronic acids and phenols ionize with increasing pH. The amount of uronic acids in Scots pine has been reported to be 0.84 mmol/(g of xylan),28 which equals 69 mmol/(kg of wood) when using the xylan content measured from wood used in the experiments. Assuming that the phenolic group mole percentage (mole fraction × 100%) of the total amount of lignin is 22.5 (the mole percentage of phenolic units is 15− 3042), and using molecular weight of a lignin unit of 180 g/mol (C10O3H12), the amount of phenolic groups in wood is around 300 mmol/(kg of wood). Since the phenolic group content is

F mPLOH(f), t = 0s

(0.225 = (180

)(259 )(0.3

mol of PLOH mol of L

= 1.08

g of L mol of L

g of L kg of wood

kg of water kg of wood

)

)

mol of PLOH kg of water

(11)

And the fraction of phenolic units of the total amount of lignin fPLOH =

F mPLOH(f), t = 0s

wL, t = 0s

= 0.04

=

(1.08 (25.9

mol of PLOH kg of water

kg of L kg of wood

)

)−%

mol ⎛⎜ (kg of water) ⎝

(

kg of L kg of wood

−%

)⎞⎠ ⎟

(12)

mFPLOH(f),IR

In eqs 10, 11 and 12, is the molality (molar amount of phenolic lignin unit per mass of water in the fiber wall) of the phenolic lignin units attached to the fiber wall, f PLOH is the 2616



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fraction of phenolic units of the total amount of lignin units, and wL is the mass fraction of lignin of the total orginal mass of wood. Furthermore, the initial amounts of the variable quantities are denoted as mFPLOH(f), t=0s and wL,t=0s. When the amount of phenolic units is decreasing, according to Le Chatelier’s principle, the reaction equilibrium is shifted to the left (Table S2, Supporting Information, eq 1). This reaction consumes hydrogen ions in the fiber bound liquid inducing the ion exchange between the fiber bound liquid and the external liquid phase. Thus another factor to be considered in the model is the ionization of water (Table S2, Supporting Information, eq 2). The equilibrium constant (Keq) is dependent on temperature (T) and is correlated to p and q (constants based on the equilibrium constant values computed in the range of 80−160 °C using Gibbs energy formation data44), as presented in eq 13. The values of p and q are given in Table S2 (Supporting Information). ⎛ q⎞ KEQ = p exp⎜ − ⎟ ⎝ T⎠

The maximum charge of a component in the simulation is +1 (zmax). Multiplying both sides of eq 20 by λzmax leads to a polynomial:

∑ ziλ z

F F F 2 F − (m Na + mHF +(aq)) − (mOH + (aq) + m HS−(aq) + mCl−(aq))λ = 0 (aq)

(22)

which is solved for λ (only positive values for lambda are acceptable since molalities are always positive): λ=

dt F − dmCl (aq)

(14)

dt F − dm HS (aq)

dt dmHF +(aq) dt

m̅ i =

+

dt

(15)

dt F − dmPLO (f)

dt

(18)

(19)

Combining eqs 18 and 19, λ is the only unknown:

∑ zi i

miF =0 λ zi

= rMT,HS−(aq)

(26)

(27)

F − = rMT,OH−(aq) + k f,EQ.2x HF2O(l) − k b,EQ.2mHF +(aq)mOH (aq)

= fPLOH

dwL F F − m F+ − k f,EQ.1mPLOH(f) + k b,EQ.1mPLO (f) H (aq) dt

F F F − m + = k f,EQ.1mPLOH(f) − k b,EQ.1mPLO (f) H (aq)

(30)

The mole fraction of water (xHF 2O(l)) is assumed to be equal to unity. Modeling the Effect of AQ on the Reaction Kinetics. The cooks with AQ addition were found to be insufficient for fully assessing the effect of the AQ concentration on the model parameters. Most of the cooks with AQ were performed at 160 °C. At that temperature the fast degrading lignin is almost completely vanished when the first measurement is done. It is therefore not possible to make a reliable estimation for the reaction rate parameters of the fast degrading lignin. Instead, the reaction rate parameters of the fast degrading lignin subcomponent were fixed to the corresponding values obtained in the regression using the first approach (isothermal conditions and the Donnan effect neglected) without AQ addition. Furthermore, it turned out that the model with only two lignin subcomponents does not always give a satisfactory fit

The liquid film composition needs to fulfill the electroneutrality condition: i

(25)

(29)

(16)

miF

∑ zimiE,film = 0

= rMT,Cl−(aq)

(28) F dmPLOH(f)

miE,film

miE,film

(24)

F F F − m + = rMT,H+(aq) + k f,EQ.1mPLOH(f) − k b,EQ.1mPLO (f) H (aq)

F − dmOH (aq)

(17) 2 The film is in Donnan equilibrium with the fiber bound liquid phase:

λ zi =

(23)

= rMT,Na+(aq)

F − + k f,EQ.2x HF2O(l) − k b,EQ.2mHF +(aq)mOH (aq)

In eq 15 i and j are an aqueous, mobile component (H (aq), Na+(aq), OH−(aq), HS−(aq), or Cl−(aq)). A linear molality profile in the film is assumed:

miE

F F F − (mOH (aq) + m HS−(aq) + mCl−(aq))

F + dm Na (aq)

+

Δmi = miE − miE,film

F F + (m Na (aq) + m H+(aq))

To summarize, λ is solved using eq 23, after which the film composition is solved from eq 18. Mass-transfer rates for individual ions are then solved using eqs 15−17. The resulting ordinary differential equations to be solved for seven components are

One-film theory has been applied for mass-transfer modeling in pulp suspensions.46 The purpose of including mass transfer into the present model is to maintain Donnan equilibrium. Thus, the value for parameter WMT (=103) was adjusted to such a high level that the Donnan equilibrium was maintained throughout the simulations. This one parameter lumps several parameters.30 rMT, i

(21)

In this specific case the resulting polynomial is of second order:

It has been suggested that the reaction between hydrogen ion H+(aq) and base is diffusion limited; i.e., the rate constant is kb,EQ = 1010 (mol/(kg of water))−1 s−1.45 Thus, the rate constant for the dissociation of an acid affords (here H2O and PLOH(f))

⎛ ⎛ ∑n z Δm ⎞⎞ j ⎟ j=1 j ⎟ = WMT⎜Δmi − m̅ izi⎜⎜ n 2 ⎟⎟ ⎜ ⎝ ∑ j = 1 zj m̅ j ⎠⎠ ⎝

miF = 0

i

(13)

k f,EQ = KEQ k b,EQ

max − zi

(20) 2617



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at prolonged delignification but tends to give too low predictions for the remaining lignin. In those cases, a third subcomponent was added to the model. Thus the kinetic model used for the fitting AQ kinetic data is:

t iso =

(31) 22,23

For soda cooks, Werthemann, as well as Abbot and Bolker,24 established a linear relationship between the reciprocal of the lignin content in pulp and the square root of the AQ charge [AQ]. (32)

In the preceding equation, L is the lignin content in pulp for a cook with added AQ, L0 is the lignin content in a corresponding cook without AQ, and t is the cooking time. The reported value of the exponent n was 1.22. Werthemann expressed the lignin content by the hypochlorite number and Abbot worked with the κ number. The above equation was used in analyzing the rate constants obtained in this study. Isothermal Time and Modeling of the Heating and Cooling Periods. In practice, it is not possible to conduct experimental cooks at a constant temperature maintained from the beginning to the end; the heating and cooling periods are always parts of the procedure. Then, according to the Arrhenius equation, the reaction rate coefficients are not constant with regard to the time and the analytical solution of the differential equations is no longer possible. One way to circumvent the mathematical difficulties caused by the temperature variation is to transform the original time into isothermal time. This enables the analytical solution of the differential equations. This concept is based on the Arrhenius equation. The total cooking time is divided into a series of short time intervals (Δt1, Δt2, Δt3, ..., Δtn). Within each of these intervals the temperature is regarded as constant. If the time interval is short enough, the change in the lignin content during the time interval is small compared to the remaining lignin, and the change in the lignin can be estimated to be ΔLj = −kjLjΔt j

kc = Ae

(34)

Parameter Regression. The set of cooks without AQ addition was used for the estimation of the activation energies and frequency factors of eq 9 by fitting the model to the experimental data. Estimates for the initial amounts of the fast and slowly degrading lignin subcomponents and hydroxide ion exponent in eq 9 were also obtained. Thus, in total six parameters were optimized. The modeling of the delignification in the experiments without AQ addition was carried out using three approaches that had different levels of simplification: (1) isothermal time, and constant hydroxide ion molality, which equals the hydroxide ion molality in the external liquid phase as given in Table S1 (Supporting Information) (method 1); (2) isothermal time and hydroxide ion molality in the fiber wall liquid estimated according to the Donnan theory (method 2); (3)

(35)

For each interval, j, a time step Δτj can be determined during which the same amount of delignification would occur at the target temperature as during the time step Δtj at the actual measured temperature:

−kjLjΔt j = −kcLjΔτj

(36)

It follows that Δτj = e(Ea/ RTc) − (Ea/ RTj)Δt j

(38)

Figure 1. Example of the temperature evolution during cooks into different target temperatures. In these cases, the heating time is around 20 min, the constant temperature period 100 min, and the cooling period 15 min. The equivalent isothermal time, taking into account the heating and cooling periods, is around 110 min.

where Tj is the temperature during the step. At the target temperature of the cook, Tc, the reaction rate is −Ea/ RTc

j

(33)

According to the Arrhenius equation the reaction rate coefficient for the time step is kj = Ae−Ea/ RTj

c

Although motivated by the Arrhenius equation, the introduction of the isothermal time is not unproblematic. The lignin subcomponents in the Purdue model have different activation energies, evoking questions about which activation energy value to use in the calculation of the isothermal time and whether it skews the analysis to make the time transformation depending on only one of the activation energies involved. In the present study, the activation energy of 110 kJ/mol, lying between the activation energy of the fast degrading and slow degrading lignin subcomponents, was used for determining the isothermal times. In order to validate the usage of isothermal time, parameter estimations were made both with the isothermal time and the original chronological time and temperature. When real temperature and time were used in the simulations (the third modeling approach), the temperature profiles during heating and cooling periods were assumed to be linear. The measured temperature profiles of each experimental setup were used for obtaining parameters that were needed to simulate the temperature profiles (Figure 1). Those parameters were durations of the heating and cooling periods in addition to the heating and cooling rates.

dwL = γLF,method1wLF + γLS1,AQ wLS1,AQ + γLS2,AQ wLS2,AQ dt

n − 1/L − 1/L0 = kAQ [AQ]1/2 mOH (aq)t

∑ Δτj = ∑ e(Ea/RT ) − (Ea/RT )Δtj

(37)

From these corresponding time steps the isothermal time is constructed in a cumulative fashion: 2618



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Figure 2. Nonlinear fits to the delignification data: (filled symbols) experimental data; (solid lines) method 1 (isothermal time and constant mOH−(aq) throughout the cook); (dashed lines) method 2 (isothermal time and mOH−(aq) estimated using the Donnan theory). Panels a−c, without NaCl; panel d, with NaCl addition.

Figure 3. Nonlinear fits to the delignification data: (open symbols ) experimental data; (+) Matlab fit; (×) Kinfit fit. Panels a−c, without NaCl; panel d, with NaCl addition.

original time and temperature, and hydroxide ion molality in the fiber wall liquid estimated according to the Donnan theory (method 3). With method 1, the analytical expression for the residual lignin content can be obtained. With methods 2 and 3, the

analytical expression cannot be derived. However, in all cases, the model equations were solved numerically using Matlab’s ode15s or Kinfit’s DDASSL47 function. In the simulations applying methods 2 and 3, initially, the fiber bound liquid phase was assumed to be in Donnan 2619



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subcomponents each one with a single activation energy. They reported an activation energy of 75 kJ/mol for the first, 124 kJ/mol for the second, and 111 kJ/mol for the third lignin subcomponent. The hydroxide and sulfide exponents in the rate law of the second lignin subcomponent were 0.28 and 0.71, respectively. Direct comparison between the parameter values obtained in this study and those reported in the literature is difficult due to the differences in the rate laws. When it comes to activation energies, the work of Andersson gives lower values than those obtained in the present study. Bogren reports a similar activation energy for the fastest degrading subcomponent, but lower for the other subcomponents. The fact that sulfidity was fixed to a constant value means that the hydroxide exponent in this study should be compared to the sum of the hydroxide and sulfide exponents reported in the other studies. Even so, it seems that exponent in the present study is around 30% higher than the sum of the exponents reported in the literature. In this study, the three methods produced parameter values that slightly differ from each other. The resulting activation energy for the fast degrading subcomponent was smaller, and for the slowly degrading subcomponent it was bigger with method 3 than with methods 1 and 2. As the reaction rates are calculated from the activation energies and frequency factors, it turns out that method 3 gives lower values for the fast degrading subcomponent regardless of the temperature and higher values for the fast degrading subcomponent. The portion of the fast degrading subcomponent is slightly higher according to method 3. The significance of the differences was tested by using the rate constants obtained at 160 °C and setting mOH−(aq) to 1 M. With method 3, 90% delignification takes 90 min, whereas 115 min with method 1 parameters and 100 min with method 2 parameters. The differences between method 1 (115 min) and method 2 (100 min) are obviously because of modeling the Donnan effect (Figure 4). In Donnan equilibrium, the molality of hydroxide ions in the fiber wall liquid is always lower than in the external liquid phase. Thus, the rate parameters obtained with method 2 need to compensate the lower hydroxide ion molality used in the rate

equilibrium with the external liquid phase. These initial equilibrium values for the molalities were obtained in the following manner: (1) The molality of phenolic units attached into the fiber wall was assumed to be 1.08 mol/(kg of water). This value was assigned to PLOH(f). The amount of PLO−(f) was set to zero. (2) The molalities of soluble ions (aq) in fiber bound liquid were assumed to be equal to molalities in the external liquid phase. (3) dwL/dt was set to zero. (4) The ordinary differential equations were solved in a time interval ranging from 0 to 200 s to attain the phase and reaction equilibrium. The two softwares, already mentioned above, were exploited for the parameter optimization. Matlab is a widely known and available commercial software, the lsqnonlin-function of which is a tool for solving nonlinear least-squares curve fitting problems. The default algorithm (“trust-region-reflective”) was selected. The other software tool was Kinfit,48 which is in-house simulation software with restricted availability. The optimization algorithm in use is Levenberg−Marquardt.49 Kinfit provides 95% confidence limits for the optimized parameters and also checks the correlation between the model parameters. With both softwares, the objective function, subject to the minimization, was the sum of absolute errors (error is the difference between the measured and simulated lignin content of pulp).

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RESULTS AND DISCUSSION Cooks without AQ. The simulated lignin profiles with three different modeling approaches are shown and compared to the experimental values in Figures 2a−d and 3a−d. With Matlab, the results from the simulations using the original time and temperature values are given only at discrete points, where the time and temperature measurement were available. Therefore this fit is shown with symbols instead of continuous lines. With Kinfit, the temperature was calculated alongside the chemical concentrations by supplementing the system of differential equations with an equation for the evolvement of the temperature. The regressed reaction kinetic parameters with the three different methods are shown in Table S3 (Supporting Information), and the reaction rate constants calculated from the activation energies and frequency factors are shown in Table S4 (Supporting Information) at different temperatures. Wisnewski et al.10 modeled softwood cooking kinetics with the original Purdue model with two rate constants per lignin subcomponent. They reported an activation energy pair {29 and 31 kJ/mol} for the first and {115 and 38 kJ/mol} for the second lignin subcomponent. For the exponent of both hydroxide and sulfide ions, they reported a value of 0.5. Andersson et al.13 modified the Purdue model to contain three lignin subcomponents with one activation energy for each subcomponent. In modeling spruce cooks, the activation energy for the first lignin subcomponent was found to be 50 kJ/mol, whereas the activation energies for both the second and the third subcomponents had the value 127 kJ/mol. The hydroxide and sulfide exponents in the rate law of the second lignin subcomponent were 0.48 and 0.39, respectively. Andersson used experimental data from cooks using wood chips with a L:W ratio of 41:1. One of the models presented by Bogren et al.,15 where the wood material was Scots pine, also had three lignin

Figure 4. Simulation of the hydroxide ion molality in the fiber wall liquid. (a) Cooks without NaCl addition. Hydroxide ion molality in the cooking liquor: (solid lines) 0.31 M; (dashed lines) 0.93 M; (dotted lines) 1.55 M. (b) Cooks with regulation of the ionic strength to a constant level of 2.0 M mNa+(aq) by adding NaCl. Hydroxide ion molality in the cooking liquor: 1.55 M. 2620



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law. The differences between method 2 (100 min) and method 3 (90 min) are caused by the more realistic temperature profile used with method 3 (Figure 5). Consequently, the selected description of the temperature has an effect on the reaction rate parameters.

Figure 6. Effect of adding sodium on (a) delignification and (b) hydroxide development: (solid lines) model without explicit sodium molality dependence; (dashed lines) model where the lumped reaction rate of the second lignin subcomponent have power law sodium molality dependence.

associated with the sodium molality is negative (Table S5, Supporting Information). Cooks with AQ Addition. From Figure 7, the effect of adding AQ in kraft cooking can be seen. The lumped reaction

Figure 5. Simulation of the Donnan λ. (a) Cooks without NaCl addition. Hydroxide ion molality in the cooking liquor: (solid lines) 0.31 M; (dashed lines) 0.93 M; (dotted lines) 1.55 M. (b) Cooks with regulation of the ionic strength to a constant level of 2.0 M mNa+(aq) by adding NaCl. Hydroxide ion molality in the cooking liquor: 1.55 M.

The differences in the results between the Matlab and Kinfit softwares are mainly insignificant. The goodness of fit as measured by the R2 value varies between 0.987 and 0.988 for the three methods indicating excellent correlation between the measured and simulated values. At present, the simple model (method 1) is a handy and easy tool for practical simulations leading to almost the same results as the more elaborated models, although some differences occur in the estimated parameters values and more pronouncedly in the reaction rates, due to whether the model relied on isothermal time and constant chemical charges or not. The differences obtained support the idea that ion exchange effect and realistic temperature profiles should be included into the kraft cooking models. Two sets of experimental data, both from cooks at 160 °C and hydroxide ion molality of 1.55 M, were different from each other only in sodium (and chloride) ion molality. The data show that the delignification rate is faster in the absence of sodium chloride, but our model predicts the opposite (Figure 6a). The reason for this is that the model gives lower values for the hydroxide molality in the fiber wall at lower sodium molality (Figure 6b) as predicted by the Donnan theory.28,50 To account for the changes in sodium and chloride molalities, the model was altered by selecting eq 6 for the reaction rate law of the slowly degrading lignin subcomponent. When the modified model was refitted using method 2 to the entire data set, the prediction for the delignification at low sodium molality is shifted into the correct direction. The R2 value of the new fit is 0.9905. The fact that adding NaCl into the cook slows the delignification is probably because the salt has influence on the solubility of lignin.51 The changes in the estimated parameter values of the modified model are rather moderate in comparison to those for method 2 (Table S3, Supporting Information). The exponent

Figure 7. Purdue model fitted to delignification data from cooks with AQ addition. Hydroxide ion molality (a) 0.5 and (b) 1.55 M.

rate constants are given in Table S6 (Supporting Information). The portion of the fast degrading lignin is still 24%, whereas the slowly degrading lignin subcomponent has been split into two fractions with portions 25% and 51% of the total lignin, respectively. The square root relationship between lignin content and AQ charge discovered by Werthemann and Abbot et al. was also tested. Lignin content was obtained using the estimated reaction rate parameters at certain isothermal times. As can be noted from Figure 8a,b, the square root relationship is valid also for kraft-AQ cooking, except at prolonged cooking times. There is a difference in the present study and in the literature in how the coefficient expressing the slope of the linear fits depends on time. Equation 32, introduced by Abbot, has a lumped coefficient 2621



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There could be several explanations for the discrepancy. First, the differences in lignin levels at hydroxide molality 1.55 M were small compared to the variability in the data, making it difficult to estimate the slope. Second, Abbot’s results were from soda delignification. In the present study, also hydrogen sulfide ions were present in the system. Third, Abbot was working with κ numbers, which depends on the total amount of oxidizable structures in pulp, while in the present study the amount of lignin is given as the weight fraction of lignin per the original amount of wood. Thus, the unit for lignin in the present study is different from that of Abbot’s study. In order to overcome this discrepancy, the yield of carbohydrates should be modeled as well. The slope s is a measure of how much adding AQ intensifies delignification. By comparing the results of Abbot and the present study, the interpretation is that the effect of AQ addition on the delignification rate when raising the hydroxide molality from 0.5 to 1.55 M is independent of the cooking time in the soda cooking, and, in the case of kraft cooking, the effect becomes more pronounced with longer cooking times.

Figure 8. (a, b) Square root relationship between the reciprocal of lignin content and AQ charge at different cooking times for mOH−(aq) = 0.5 M and mOH−(aq) = 1.55 M, respectively. n − s = kAQ mOH (aq)t

(39)

(40)

to the calculated slope coefficients gives the values α1 = 0.049, β1 = 0.015 min−1 at mOH−(aq) = 0.5 M and α1 = 0.031, β2 = 0.046 min−1 at mOH−(aq) = 1.55 M. The ratio between the slopes at different hydroxide levels is then time dependent (Figure 9): α1 (β1− β2)t n n smOH e −(aq) = 0.5M / s mOH−(aq) = 1.55M = α2 (41)

Figure 9. Exponential time dependence of the slopes (eq 40) in Figure 8

⎛ 0.5 ⎞ ⎜ ⎟ ⎝ 1.55 ⎠

ASSOCIATED CONTENT

Tables S1−S6 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.

1.22

≈ 0.25

■

S Supporting Information *

whereas eq 32 with the value n = 1.22 reported by Abbot leads to a ratio between the slopes that is constant in time: n n smOH −(aq) = 0.5M / s mOH−(aq) = 1.55M =

CONCLUSION

A simplified Purdue model containing two lignin subcomponents with different reactivity is adequate for describing the delignification in the experiments used for modeling in the present study. The delignification of the fast degrading lignin subcomponent is independent of the hydroxide ion molality within the conditions used in the experiments, whereas the reaction rate of the slowly degrading lignin subcomponent follows a power law with positive exponent with regard to the hydroxide ion molality. As sodium chloride is added into the cooks, the delignification rate slows, and it is necessary to include a negative power law dependence on the sodium ion molality into the reaction rate law for the slowly degrading lignin subcomponent. This is in agreement with the earlier results.52 The simplifying assumptions regarding constant temperature and constant hydroxide molality had some effect on the estimated parameter values and calculated reaction rates but very small influence on the goodness of the fit. Including Donnan theory into the model makes the chemical description of the course of events more realistic, avoiding the assumption of a constant concentration of chemicals in the fiber wall liquid. Likewise, replacing the isothermal time and constant temperature with the original time and temperature represents steps toward the realism in the model. Donnan theory, as well as the real temperature and time, should be building blocks in the future improved delignification models. Adding AQ to the cooking liquor increases the delignification rate. The effect of AQ addition on the rate of the fast degrading lignin subcomponent could not be assed, but the increase in the delignification rate could be accounted for by the reactions of the slowly degrading lignin subcomponent. The square root relationship between reciprocal lignin content and AQ charge earlier established for soda-AQ delignification was found to be valid also for kraft-AQ delignification.

that is linear in time, whereas the results for the kraft-AQ data show an exponential growth in time of the corresponding coefficient. Fitting the exponential model s = α e βt

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(42) 2622



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AUTHOR INFORMATION

Corresponding Authors

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*E-mail: kaarlo.nieminen@aalto.fi. *E-mail: herbert.sixta@aalto.fi. Notes

REFERENCES

(1) Sixta, H.; Potthast, A.; Krotschek, A. W. Chemical Pulping Processes. In Handbook of Pulp; Sixta, H., Ed.; Wiley-VCH Verlag GmbH: Weinheim, Germany. 2006; p 109. (2) Nieminen, K.; Sixta, H. Comparative Evaluation of Different Kinetic Models for Batch Cooking: A Review. Holzforschung 2012, 66 (7), 791−799. (3) Wilder, H. D.; Daleski, E. J. J. Delignification Rate Studies. Part II on a series on kraft pulping kinetics. Tappi 1965, 48 (5), 293−297. (4) Kleinert, T. N. Mechanisms of Alkaline Delignification. I. The Overall Reaction Pattern. Tappi 1966, 49 (2), 53−57. (5) LéMon, S.; Teder, A. Kinetics of the Delignification in Kraft Pulping I. Bulk delignification of pine. Sven. Papperstidn. 1973, 76 (11), 407−414. (6) Olm, L.; Tistad, G. Kinetics of the Initial Phase of Kraft Pulping. Sven. Papperstidn. 1979, 87 (5), 458−464. (7) 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, IN, USA, 1974 (8) Smith, C. C.; Williams,T. J. Mathematical Modelling, Simulation and Control of the Operation of Kamyr Continuous Digester for Kraft Processes, Technical Report 64; PLAIC, Purdue University: West Lafayette, IN; 1974. (9) Christensen, T.; Albright, L. F.; Williams, T. J. A Kinetic Mathematical Model for the Kraft Pulping of Wood, Tappi Annual Meeting, Atlanta, GA, USA, 1983: pp 239−246 (10) Wisnewski, P. A.; Doyle, F. J., III; Kayihan, F. Fundamental Continuous Pulp-Digester Model for Simulation and Control. AIChE J. 1997, 43 (12), 3175−3192. (11) Gustafson, R. R.; Slelcher, C. A.; McKean, W. T.; Finlayson, B. A. Theoretical Model of the Kraft Pulping Process. Ind. Eng. Chem. Process Des. Dev. 1983, 22 (1), 87−96. (12) Pu, Q.; McKean, W.; Gustafson, R. Kinetic Model of Softwood Kraft Pulping and Simulation of the RDH Process. Appita J. 1991, 44 (6), 399−404. (13) Andersson, N.; Wilson, D.; Germgård, U. An Improved Kinetic Model Structure for Softwood Kraft Cooking. Nord. Pulp Pap. Res. J. 2003, 18 (2), 200−209. (14) Lindgren, C.; Lindströ m, M. The Kinetics of Residual Delignification and Factors Affecting the Amount of Residual Lignin. J. Pulp Pap. Sci. 1996, 22 (8), 290−295. (15) Bogren, J.; Brelid, H.; Theliander, H. Assessment of Reaction Kinetic Models Describing Delignification Fitted to Well-Defined Kraft Cooking Data. Nord. Pulp Pap. Res. J. 2008, 23 (2), 210−217. (16) Lourenço, A.; Gominho, J.; Pereira, H. Modelling of sapwood and heartwood delignification kinetics of Eucalyptus globulus using consecutive and simultaneous approaches. J. Wood Sci. 2011, 57, 20− 26. (17) Miranda, I.; Pereira, H. Kinetics of ASAM and kraft pulping of Eucalypt wood (Eucalyptus globulus). Holzforschung 2002, 56, 85−90. (18) Gilarranz, M. A.; Rodríguez, F.; Santos, A.; Oliet, M.; GarciaOchoa, F.; Tijero, J. Kinetics of Eucalyptus globulus delignification in a methanol−water medium. Ind. Eng. Chem. Res. 1999, 38, 3324−3332. (19) Gilarranz, M. A.; Santos, A.; García, J.; Oliet, M.; Rodríguez, F. Kinetics. catalysis and reaction engineering. Ind. Eng. Chem. Res. 2002, 41, 1955−1959. (20) Burazin, M. A. A dynamic model of kraft-anthraquinone pulping. Ph.D. Disseration;Institute of Paper Science and Technology, Georgia Institute of Technology: Atlanta, GA, USA, 1986; [ https:// smartech.gatech.edu/handle/1853/5743]. (21) Burazin, M. A.; McDonough, T. J. Building a mechanistic model of kraft-pulping kinetics. Tappi J. 1988, 71 (3), 165−169. (22) Werthemann, D. P. The Xylophilicity/Hydrophilicity Balance of Quinoid Pulping Additives. Tappi 1981, 64 (3), 140−142.

The authors declare no competing financial interest.

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Δτ = time step in isothermal time (s) λ = Donnan separation coefficient

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

Roman Symbols

a, b, c = exponents in rate law A = frequency factor in Arrhenius law ((mol/kg)x·s−1) Ea = activation energy in Arrhenius law (J/mol) f P = fraction of phenolic units of total amount of lignin (mol/(kg of water·kg/kg·100%)) k = reaction rate coefficient ((mol/kg of water)x·s−1) kAQ = time and concentration independent coefficient in Abbot’s expression for the effect of AQ K = equilibrium constant for a reversible reaction mi = molality (moles of solute i per kg of solvent, mol/kg) r = rate (mol/(kg·s)) R = universal gas constant (8.3145 J/(K·mol)) t = time (s) tiso = isothermal time (s) T = temperature (K) Tc = target temperature (K) w = mass fraction (kg/kg·100%) WMT = parameter lumping several mass-transfer parameters (1/s) xi = mole fraction of component i z = charge of ion Abbreviations

AQ = anthraquinone aq = component dissolved in water, mobile f = component attached to fiber wall, immobile IR = irreversible reaction L = lignin LF = fast degrading lignin LS = slowly degrading lignin MT = mass transfer PLOH = phenolic lignin unit RR = reversible reaction Superscripts

F = fiber bound liquid phase E = external liquid phase E,film = liquid film interface that is in equilibrium with fiber bound liquid phase

Subscripts

b = backward evolvement of reversible reaction f = forward evolvement of reversible reaction i,j = component index p,q = constants in correlation for equilibrium constant 0 = initial value Greek Symbols

α = coefficient in exponential model β = coefficient in exponential model (s−1) γ = lumps parameters in rate law Δt = time step in normal time (s) 2623



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Novel Insight into Lignin Degradation during Kraft Cooking - American

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