Detailed modeling of the kraft pulping chemistry: carbohydrate reactions

The article introduces a detailed model for carbohydrate chemistry in kraft pulping. This article is continuation to the modeling work carried out for hot water extraction and chemical pulp bleaching. The model includes galactoglucomannan, xylan, and cellulose acid – base equilibria, in addition to peeling, stopping, and alkaline hydrolysis reactions of the same carbohydrates, as well as hexenuronic acid formation and degradation reactions. The Arrhenius parameters were applied from the literature or regressed against experimental data in the present study. The model is very success-ful in predicting the experimental data of carbohydrate reactions during kraft pulping. Many features of the pulping-related model can be applied to specific fractionation chemistry considerations. The detailed knowledge on carbohydrates composition at any stage of pulping gives possibility for further development of biorefinery cases based on kraft pulping, such as biofuel and chemicals production.


| INTRODUCTION
Currently, the kraft pulping process is globally the most common pulping process. The popularity of this process can be explained by high strength properties of the pulp, relatively easy recovery of the cooking chemicals and the use of dissolved organic material for energy production. 1 On the other hand, disadvantages of kraft pulping process include the dark color of unbleached pulp, the loss of pulp yield due to carbohydrate degradation and solubilization, as well as the formation of odor compounds. 1 The main cooking chemicals in kraft pulping are sodium hydroxide and sodium sulfide in a highly alkaline aqueous solution, called white liquor. During delignification, the white liquor interacts with the wood, resulting in the formation of black liquor, which is a complex mixture of degraded lignin, carbohydrates, carboxylic acids, extractives and chemicals. 2 The carbohydrate yield loss in kraft pulping, due to degradation and dissolution of polysaccharides, is substantial and a serious drawback of the process. 1 In kraft pulping, the significant consumption of alkali takes place due to the rapid hydrolysis of acetyl groups in hemicelluloses (i.e., galactoglucomannan in softwoods and xylan in hardwoods) 3  However, these acid groups attached to the xylan backbone are relatively stable under alkaline conditions and contribute substantially to the total amount of acidic groups in kraft pulps. 5 Cellulose is a more resistant carbohydrate component against alkali in comparison with hemicelluloses, which degrade much more extensively. The overall carbohydrate degradation reactions in kraft pulping are presented in Figure 1.
In order to obtain a better understanding of alkali pulping processes, the reaction kinetics of carbohydrates and lignin degradation have been studied over the years. Different models have been developed for kraft pulping process. The first model was presented by Vroom. 6 16 is based on the idea how alkali and sodium concentration affect carbohydrates' behavior in kraft pulping. However, the model was based on experimental data from later stage of pulping, and consequently initial dissolution and primary peeling of carbohydrates could not be included. Therefore, this model was focused on alkaline hydrolysis instead of whole kraft pulping process.
Wigell 17 described glucomannan degradation in alkaline pulping by power law equation. Galactoglucomannan was described by the amount of insoluble material, degradation through alkaline hydrolysis and primary peeling. Later, Nieminen 18 presented a mathematical model where primary and secondary peeling, as well as stopping and alkaline hydrolysis reactions were included. Wigell 17 described xylan and galactoglucomannan degradation similarly in their model; however, this is not acceptable: galactoglucomannan degrades as a result of endwise degradation through primary and secondary peeling following alkaline hydrolysis, whereas xylan degradation due to endwise peeling is limited. 19,20 Components such as arabinose and glucuronic acid presented on the backbone of the xylan polysaccharide stabilize its structure. 21 Additionally, degradation products of xylan are polymers, Dissolution of xylan polymers is dependent on the porosity of cell wall. 22 After degradation of lignin and other hemicelluloses, porosity of cell wall increases and improves the dissolution of xylan. 22 Therefore, xylan degradation cannot be modeled in the same way as galactoglucomannan, which means that a more complex scheme for degradation and dissolution of xylan has to be developed. Another model dealing with kraft pulping is model by Bogren et al. 23 The model includes time-dependent rate constant and mathematical preexponent that are dependent on the degree of delignification and temperature. However, the model is challenging to use due to many adjustable "parameters." For example, in order to predict xylan removal in kraft pulping, 10 parameters are required. In general, the is a developed by Miyanishi and Shimada. 26 The model is a steadystate simulation of continuous cooking systems. The kinetic model utilized in the simulation is based on Purdue model. 10,11 The model includes, besides earlier presented components (high and slow reactive lignin, cellulose, galactoglucomannan, and xylan), also extractives. 26 They are assumed to dissolve extremely fast already in the beginning of cooking. The degradation of the other five components is modeled based on initial, bulk and residual phases of cooking. Additionally, the model is divided into three phases: wood components, as well as entrapped and free liquor. 26  Looking into all mentioned models above, it is clear that they are not taking into the consideration all chemical phenomena. By contrast, our aim is to create in-depth knowledge on the existing and possible new cooking processes. Model, presented in this work based on simulation of individual reactions and combining them together for an overall phenomenon. This is especially crucial for the development a biorefinery cases, where understanding chemistry of each wood fraction is necessary. Additionally, in order to improve prediction of the models, the amount of assumptions has to be limited. A general model with empirical kinetic equations may give a good fitting for individual cases; however, they rarely can give reliable prediction results for a wide range of experimental setups due to the fact that the equations, most often, have no physical or chemical meaning and they are just representing mathematical fitting.
In this work, the main aim is to create a detailed method for simulating chemical and physical phenomena in kraft pulping. The concept of two liquid phases was applied to take into account the ion distribution (Donnan effect) 29 and to separate the effect of mass transfer and reaction kinetics. The amount of hemicellulose reactions depends on the desired outcome. When producing dissolving pulp, the hemicelluloses should be removed almost completely (in addition to removing lignin). 51 However, when producing paper grade pulp, it is beneficial to have a relatively high hemicellulose content, because that improves the binding of the cellulosic fibers with each other in the paper. 1 During pulping (also in the case of paper grade pulp) limited removal of hemicelluloses is beneficial for better mass transfer: for example, the lignin molecules can leach out more easily from the cell wall structure, when it becomes more porous, that is, some hemicelluloses are degraded and dissolved. The present model, taking advantage of fundamental understanding of the identified reactions and can be applied to optimize the pulp production process. The current paper focuses on hemicellulose reactions in kraft pulping and Fearon et al 30 paper focuses on delignification model in kraft pulping.

| MODEL
In the present paper, carbohydrate reaction model in kraft pulping conditions is discussed. In our other recent work, 30 Table 1). The initial composition of pulping liquor as well as such parameters as temperature, pressure, and liquid-to-wood ratio, were varied depending on the experimental setup. Extremely fast mass transfer was assumed, by the fact that experimental studies with wood meal [31][32][33] were utilized for the model validation and parameter optimization. Parameter regression with Kinfit software 34 using Levenberg-Marquardt optimization algorithm was used to obtain the unknown model parameters.
The model follows time evolution of compounds presented in Table 1

| RESULTS AND DISCUSSION
Carbohydrate and lignin parameters were regressed separately, therefore carbohydrate parameters could be underestimated because of yield loss due to lignin removal and increasing fiber saturation point (FSP) were not included in the simulations. FSP is a measure of the amount of water bound to the fiber wall. 35

| Modeling of galactoglucomannan reactions
Native GGM polymers were modeled as a set of three types of units: reducing end group (GGMR), nonreducing end group (GGMNR), and units in the middle of the chain (GGMM). One end of the GGM polymer was assumed to be reducing and the other one nonreducing. The degree of polymerization of GGM in wood was assumed to be 102. 2 In alkaline conditions, the reducing end groups and the middle units of GGM undergo reversible acid-base equilibrium reactions that were added to the model ( Table 2, GE1-GE3). The pK a values for GE1 and GE2 were fitted in Kinfit software based on the work of Paananen. 32 For comparison, pK a values of 10.89 and 12.49 were reported in literature. 36 The pK a value for GE3 was compared with the pK a value of 14.28 reported for cellulose. 37 The ionization heat of glucose and mannose were reported to be 36.7 and 33.1 kJ/mol, respectively. 38 The ionized reducing end groups undergo the peeling or stopping reactions (G1-G3). 39 Activation energy for galactoglucomannan peeling reaction (G1 and G2) has been reported to be 84.6 kJ/mol. 39 The alkaline hydrolysis reaction (G4) can be encountered by intramolecular bond cleavage in the ionized middle units. 40 However, the scheme described above did not give satisfactory results in fitting between experimental and simulated results.  Of them, 4-O-methylglucuronic acid (MeGlc) side-groups were treated as individual compounds, whereas arabinose side groups were considered as leaving groups that enhance the conversion of a reducing end group in xylan into a stable metasaccharinic acid group through the stopping reaction. During pulping, a considerable amount of xylan is also dissolved as polymer and this feature was included in the model. The degree of polymerization for xylan was assumed to be 106. 2 Initially, one end was assumed to be reducing and the other end nonreducing.
As it was mentioned, XYL was modeled in the same way as GGM to encounter peeling (Table 3; X1 and X2), stopping (X3 and X4) and alkaline hydrolysis (X5) as well as reversible acid-base equilibrium reactions which were included in the model (Table 3; XE1-XE3). All kinetic parameters presented in Table 3 were regressed in Kinfit software based on Paananen 32 data. Comparison values from Chen 41 were used to prove the fitting results, of 11.69 and 12.59 for XE1 and XE2, respectively. In addition, the value for XE3 could be compared to the value of 14.28 reported for cellulose. 37 A proton ionization heat, reported by Christensen, 38 of 37.7 kJ/mol for xylose was used in the model. The formation of arabinose during peeling (X1 and X2) and alkaline hydrolysis (X5) represent the fact that, in average, every 10th xylan middle unit has an arabinose side-group. 2 The formation of  In Figure 4a effect of temperature on HexA formation and degradation is clearly shown. HexA degradation took place at temperatures higher than 139 C and proceeded faster at higher temperatures. Reversible acid-base equilibrium reactions for cellulose are presented in Table 3(CE1-CE3). For the alkaline hydrolysis, a pK a value of 14.28 has been published for cellulose. 37 Activation energy for peeling reaction has been reported to be 100.3 kJ/mol for cotton hydrocellulose 48 and 101 kJ/mol for cellulose. 49 The published activation energy for the stopping reaction are 134.8 kJ/mol and 100 kJ/mol for cotton  All reaction kinetic parameters were fitted with Kinfit software 34 for the most precise values. As it is visible from the Table 4 obtained results from the fitting are in line with published experimental values.
The list of all cellulose reactions included in the model, their stoichiometries and reaction parameters are presented in Table 4.
Cellulose peeling reactions lead to consumption of alkali and yield loss. Figure 5 presents the results for the cellulose degradation process. As can be seen from this figure, the simulation fitted the experimental data accurately.
According to all the present results current model shows a good confidence between the simulation and experimental results. The present modeling concept could be extended.

| CONCLUSIONS
In this paper, a detailed phenomenon-based model of carbohydrate  especially if current, kraft pulping, part will be combined with previously developed models (hot-water extractions, bleaching, delignification). This approach offers an exceptional opportunity to examine different theories and hypothesis on reactions mechanisms as for existing process as for new chemistry processes, by including new compounds and reaction chemistries to database and simulator.