Optimization the cellulose production process from flax fibre with the formalization of the optimality criteria

Abstract

Flax fibre is an environmentally friendly, pure vegetable material with high durability. During the long flax fibres production, the short fibres, which have limited using, are formed. One of the ways of short flax fibre using is the cellulose with various purposes production because the short fibre is a valuable raw material. The problem of vegetable raw materials rational using is relevant.

The previous results showed the possibility of obtaining cellulose from flax materials. Flax raw materials, in comparison with wood, has a higher content of cellulose and lower content of lignin and in its properties is approaching to the cotton.

The soda boiling of flax cellulose from short flax fibre with preliminary aqueous hydrolysis is carried out in the research. The alkali consumption for boiling is 20% of the mass of dry raw materials with anthraquinonoid catalyst.

An attempt to solve such a problem was carried out with the participation of the authors. The quality of the boiling process was controlled by the indexes: cellulose output (Y₁, %), lignin content (Y₂, %), α-cellulose content (Y₃, %), celluloses viscosity (Y₄, mPas/s). The second order regression models that describe the dependence of the process quality indexes was built.

The aim of the research is solution the multi-criteria optimization problem of the flax celluloses soda boiling with the previous aqueous hydrolysis process. Optimality criteria are given in the linguistic expressions form: cellulose output – “as high as possible”; α-cellulose content – “above 90%”; the content of lignin – “less than 2.5%”; the viscosity – “about 20 mPas/s”. Therefore, for optimization problem solution the linguistically defined optimality criteria must be formalized.

For the formalization of the optimality criteria, we use the methods of the fuzzy set theory. The optimality criteria are considered as fuzzy sets and the membership functions are built for these sets. We suggest using S-shaped membership functions for the indexes Y₁ and Y₂, Z-shaped functions for index Y₃ and U-shaped function for index Y₄. In order to facilitate the optimization problem solution, we consider expedient to use sigmoidal type of membership functions for indexes form Y₁ to Y₃, and bell-shared type for index Y₄.

The upper and lower limits of the membership functions’ universe are the worst values of quality indexes obtained in the experiment and the best theoretically possible values of these indexes. Because the both sigmoidal and bell-shared membership functions generate not strictly normal, but subnormal fuzzy sets, we suggest the maximum deviation of 0.01. Based on the above considerations, we established the numerical values for the membership functions’ parameters.

The Bellman-Zade optimality principle is used to find the optimal solution. According to this principle, the solution is considered the optimal one, for which the lowest of the membership functions has the maximum value. The optimum values of technological parameters for obtaining linseed cellulose are established, namely: the duration of aqueous pre-hydrolysis is 2 hours 12 minutes, the temperature of preliminary hydrolysis is 154 ^OC, the duration of sodium hydroxide is 3 hours, and the boiling temperature is 166 ^OC with the hydro-module is 6:1. As can be seen from the results, the content of lignin and the content of α-cellulose limit for the found optimum value. Our optimal results are in good agreement with solutions obtained by other methods.

Thus, the proposed approach allows obtaining the high quality cellulose. Linseed cellulose can be used after bleaching for the cellulose nitrates or carboxymethyl-cellulose production.