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Determination of the Mathematical Dependence of the Black Liquor Density on the Dry Matter Content (High Yield Softwood Pulp)

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Yu.V. Sevastyanova, Е.А. Toptunov, N.V. Shcherbak, P.V. Solntsev

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A modern evaporator station is an energy-saving production of evaporated liquor with high dry matter content for ensuring the minimum SO2 emissions from the soda recovery boiler. Such stations are equipped with Falling Film devices and consist of 5–7 stages. The necessity to improve and create new black liquor concentrators is driven by the increased attention to environmental issues and the wish to produce liquor with a higher calorific value. The physical properties of black liquor depend on its composition and have a significant impact on the selection and design of evaporators. The main properties considered in the evaporation and combustion processes are density, viscosity, surface tension, heating value and boiling temperature. One of the most important characteristics of the liquor evaporation is its viscosity, since it determines the ability of the liquor to pump and affects the design features. Another equally important characteristic is density. With its help, the dry matter content and evaporation process in the main stages of the liquor regeneration are regulated. The study was carried out to determine the mathematical dependence of the black liquor density on the dry matter content for high yield softwood pulp. The study objectives were the following: analyze the effect of the dry matter temperature and concentration on the density of black liquor obtained from cooking high yield softwood pulp according to the technological flow of production; develop a mathematical model of dependence of the black liquor density of high yield sulphate softwood pulp on the concentration and temperature; conduct the TAPPI comparative testing of the results of mathematical and correlation dependences. A mathematical dependence of the black liquor density on the temperature and dry matter content required for immediate technological calculations of chemical regeneration departments in sulphate production of semi-finished products for cardboard was obtained. The following equation of mathematical dependence based on the conducted research, regression analysis, and mathematical processing of the results was obtained: ρ = 0.974 + 0.0071x – 0.0002t – 0.000007xt – 0.00000045t2 – 0.0000045x2 (where ρ – density, g/cm3; x – dry matter content, %; t – temperature, °C). It allows calculating with the highest accuracy the density of black liquor obtained from cooking high yield softwood sulphate pulp. Comparative testing of the results of the developed mathematical dependence and correlation dependence (published by TAPPI) of black liquor density on the dry matter content was carried out. A high level of comparability of the proposed mathematical equations was found.


Yuliya V. Sevastyanova1, Candidate of Engineering, Assoc. Prof.; ResearcherID: ABE-4746-2020, ORCID:
Evgeniy А. Toptunov1, Engineer of the Innovative Facilities Engineering and Innovation Center «Advanced Northern Bioresources Processing Technologies»; ResearcherID: ABE-4069-2020, ORCID:
Natalia V. Shcherbak1, Candidate of Engineering, Assoc. Prof.;
ResearcherID: ABE-4156-2020, ORCID:
Pavel V. Solntsev2, Head of the CHPP-2 of Cardboard Production;
ResearcherID: ABE-4402-2020, ORCID:


1Northern (Arctic) Federal University named after M.V. Lomonosov, Naberezhnaya Severnoy Dviny, 17, Arkhangelsk, 163002, Russian Federation; e-mail:,
2Arkhaneglsk Pulp and Paper Mill, ul. Mel’nikova, 1, Novodvinsk, Arkhangelsk region, 164900, Russian Federation


high yield sulphate pulp, chemical recovery, black liquor physical properties, dry matter content, black liquor density, evaporation, mathematical model

For citation

Sevastyanova Yu.V., Toptunov Е.А., Shcherbak N.V., Solntsev P.V. Determination of the Mathematical Dependence of the Black Liquor Density on the Dry Matter Content (High Yield Softwood Pulp). Lesnoy Zhurnal [Russian Forestry Journal], 2021, no. 1, pp. 192–200. DOI: 10.37482/0536-1036-2021-1-192-200


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Determination of the Mathematical Dependence of the Black Liquor Density on the Dry Matter Content (High Yield Softwood Pulp)


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