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November 2008 EVALUATING REACTION KINETIC MODELS USING WELL-DEFINED KRAFT DELIGNIFICATION DATAJohannes Bogrena*, Harald Brelida and Hans Theliandera - Presented at ISWFPC 2007
_{1} (equation 11) is used in the optimisation, the three-phase model performs somewhat better than the model using continuous distribution of reactivity.However, when all experimental data are used and R _{2} (equation 12) is used in the optimisation, the performance of the models is the opposite. It is difficult to compare the
models using different optimisation residuals. The coefficient of determination (R_{2}) describes the proportion of variability in lignin content that can be described by the model without
considering the variation in time as in R_{2}.However, when the models are compared to experimental data and figures showing the residuals at corresponding lignin values are scrutinised, it is seen that the models optimised with residual R _{2 }perform considerably better than the ones optimised with residual R_{1}. This is
mainly an effect of an even distribution of the importance of data throughout the cook. An example of this effect is shown in figure 4.5 where the performance of the model optimised
with a normal residual, R1, is poorer at low lignin contents than when residual R2 is used in the optimisation.Figure 4.5 Comparison of the continuous distribution of reactivity model when the two residuals, R
and R_{1}, are used in the optimisation: T=154ºC, OH-=0.26 mol/kg solvent, HS-=0.26 mol/kg solvent._{2}Table 4.1 Determined parameters in the three-phase model (equations 1-4): Lt=0=0.97.Table 4.2 Determined parameters in the continuous distribution of reactivity model (equations 10 and 13): Lt=0=0.97. 4.1 Interpretation of the modelsOne of the aims of this paper was to find a model that can act as a foundation for the explanation of the reaction kinetics pattern of delignification. When the values of the parameters from the fitting of the models are analysed a few rather peculiar values can be found. For example, the negative values of a _{1} and b_{1} mean that it is negative for the reaction rate of L_{1}, often called the initial phase lignin, that active cooking chemicals are
present. Furthermore, the positive value of c _{1} suggests that the removal of L_{1} is promoted by a high sodium ion concentration. Findings from studies focusing on the initial phase show that the
exponents a_{1} and b_{1} are practically zero^{12, 13}. The value of the exponents a_{1} and b_{1} is not
a result of a lignin subspecies reacting according to these kinetics, but is rather a consequence of the construction of the model. It should be noted that this type of model assumes that the three types of lignin react in parallel and not in series, resulting in compensation for the positive/negative values of the exponents in the other lignin subspecies L _{2} and L_{3}.Thus, the overall influence of chemical concentrations is low at low degrees of delignification . This gives a faulty chemical description of the reactions in the initial phase caused by the assumption of parallel reacting subspecies. The fact that other models presented in the literature, using the same assumption, have not arrived at the same conclusion can be explained by the fact that very few have considered the entire kraft cook, and instead have used data starting at a degree of delignification of approximately 75% ^{11} or have used a limited amount of data in the early part of the cook^{4}.Furthermore, the amount of lignin reacting according to third phase kinetics (L _{3}), the so called residual phase lignin, is higher than can be found in the literature6. This is primarily a
result of the model and the ensemble effects that arise when a large number of parameters are simultaneously estimated in the model. When the continuous distribution of reactivity
model is used, a more likely and straightforward description of the kinetics is obtained, and does not give rise to any obviously incorrect conclusions regarding reactions with chemicalsFigure 4.6. Distribution of the reactivity calculated from the model of continuous distribution of reactivity at
different temperatures: OH-=0.26 mol/kg solvent, HS- =0.26 mol/kg solvent.
Figure 4.7. Reactivity of the three subspecies according to the three-phase model at different temperatures: OH-=0.26 mol/kg solvent, HS-=0.26 mol/kg solvent. When the model using a time-dependent rate constant is used, the distribution of reactivity can be calculated ^{10}. The results at five different temperatures are shown in figure 4.6. At
low temperatures, the reactivity is very low; nevertheless a small part reacts very fast resulting in a very broad distribution. At higher temperatures the distribution curve is
narrower and a fairly high amount of lignin has high reactivity. The corresponding plot for the three-phase model, where the reactivities are equal to the rate constants, is shown in figure
4.7. In this case, the amount of subspecies reacting in each phase at the corresponding reactivity is shown. When the two figures are compared, it can be concluded that both
show a narrower distribution of reactivity at higher temperatures. The levels of the reactivity are also comparable in the two figures. This means that if additional phases, i.e.
lignin subspecies, are added to the threephase model (i.e. a four-phase model, a five-phase model, etc.), the plot would eventually be similar to the one in figure 4.6. However, this is
impossible since the number of parameters needed for such a model would be far too many. Therefore, the continuous distribution of reactivity model is the most suitable of these two
models for describing the reaction kinetics of delignification. The two models perform very well when fitted to well-defined experimental data. However, the physical and chemical explanation of the model using three phases becomes dubious, and is therefore not suitable for use. The number of parameters used in the models differs greatly, making it more convenient to use the model utilising continuous distribution of reactivity. Another advantage of the continuous distribution of reactivity model is the easier mathematics, since only one differential equation is used, instead of three as in the three-phase model. Consequently, the model using a continuous distribution of reactivity is recommended for modelling the reaction kinetics of delignification. 5. ACKNOWLEDGEMENTSThe authors would like to thank everyone involved at Avancell - Centre for Fibre Engineering, for fruitful cooperation. Financial support from the foundation, Södra Skogsägarnas stiftelse för forskning, utveckling och utbildning, is gratefully acknowledged. 6. REFERENCES1. Gierer, J. Chemical aspects of kraft pulping, Wood Sci. Technol., 1980, 14(4), pp. 241-266. 2. Obst, J.R. Kinetics of alkaline cleavage of ß-aryl ether bonds in lignin models: Significance to delignification, Holzforschung, 1983, 37(1), pp. 23-28. 3. Vroom, K.E. The H-factor: A means of expressing cooking times and temperatures as a single variable, Pulp Pap. Mag. Can., 1957, 38(2), pp. 228-231. 4. Chiang, V.L., Yu, J. and Eckert, R.C. Isothermal reaction kinetics of kraft delignification of Douglas fir, J. Wood Chem. Technol., 1990, 10(3), pp. 293-310. 5. Lindgren, C. and Lindström, M. The kinetics of residual delignification and factors affecting the amount of residual lignin, J. Pulp Pap. Sci., 1996, 22(8), pp. J290-J295. 6. Gustavsson, C. A., Lindgren, C. T. and Lindström, M. E. Residual phase lignin in kraft cooking related to the conditions in the cook, Nord. Pulp Pap. Res. J., 1997, 12(4), pp. 225-229. 7. Blixt, J. and Gustavsson, C. A. Temperature dependence of residual phase delignification during kraft pulping of softwood, Nord. Pulp Pap. Res. J., 2000, 15(1), pp. 12-17. 8. Montané, D., Salvadó, J., Farriol, X., Jollez, P. and Chornet, E. Phenomenological kinetics of wood delignification: Application of a timedependent rate constant and a generalized severity parameter to pulping and correlation of pulp properties. Wood Sci. Technol., 1994, 28(6), pp. 387-402. 9. Bogren J, Brelid, H and Theliander H. Reaction kinetics of kraft delignification – General considerations and experimental data, Nord. Pulp Pap. Res. J., 2007, (In press). 10. Plonka, A. Lecture Notes in Chemistry- Time-dependent reactivity of species in condensed media, Springer-Verlag, 1986. 11. Andersson, N.; Wilson, D. I. and Germgård, U. An improved kinetic model structure for softwood kraft cooking. Nord. Pulp Pap. Res. J., 2003, 18(2), pp. 200-209. 12. Kondo, R. and Sarkanen, K. V. Kinetics of lignin and hemicellulose dissolution during the initial stage of alkaline pulping, Holzforschung, 1984, 38(1) , pp. 31-36. 13. Olm, L. and Tistad, G. Kinetics of the initial stage of kraft pulping, Svensk Papperstidning, 1979, 82(15), pp. 458-464. |

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