Address: Naberezhnaya Severnoy Dviny, 17, Arkhangelsk, 163002, Russian Federation, Northern (Arctic) Federal University named after M.V.Lomonosov, office 1425

Phone: +7 (8182) 21-61-18

Lesnoy Zhurnal

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

Версия для печати

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

Complete text of the article:

Download article (pdf, 0.4MB )






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


1. Bogomolov B.D., Sapotnitskiy S.A., Sokolov O.M. et al. Processing of Sulphate and Sulphite Liquors. Moscow, Lesnaya promyshlennost’ Publ., 1989. 360 p.
2. Volkov A.D., Grigor’yev G.P. Physical Properties of Pulp Production Liquors. Moscow, Lesnaya promyshlennost’ Publ., 1970. 120 p.
3. Gorbovskiy B.G. Design and Maintenance of Evaporation Stations of Sulphate Pulp Production. Moscow, Goslesbumizdat Publ., 1953. 189 p.
4. State Standard. GOST 8.234–2013. State System for Ensuring the Uniformity of Measurements. Volumetric Glass Ware. Verification Procedure. Moscow, Standartinform Publ., 2014. 11 p.
5. Grigoray O.B., Ivanov Yu.S., Komissarenkov A.A., Smolin A.S. Processing of Black Liquors of Sulphate Production. Saint Petersburg, SPb STUPP Publ., 2012. 106 p.
6. Gur’yev A.V., Kazakov Ya.V., Komarov V.I., Khovanskiy V.V. Laboratory Course on Paper Technology. Arkhangelsk, ASTU Publ., 2001. 112 p.
7. Milovidova L.A., Komarova G.V. Production of Sulphate Pulp. Arkhangelsk, ASTU Publ., 2001. 31 p.
8. Milovidova L.A., Sevastyanova Yu.V., Komarova G.V., Dubovyy V.K. Recovery of Chemicals in the Production of Sulphate Pulp (Lime Caustization and Regeneration). Arkhangelsk, NArFU Publ., 2010. 157 p.
9. Certificate No. 411 on Metrological Certification of Measurement Procedures. Method for Determining the Mass Fraction of Solids in Black Liquor. All-Russian Scientific Research Institute of Pulp and Paper Industry, 1991. 4 p.
10. Selyanina L.I., Selyanina S.B., Kutakova N.A. Sulphate Liquor Technology. Arkhangelsk, ASTU Publ., 2002. 37 p.
11. Handbook for Paper Industry Workers. In 3 vol. Vol. 1. Moscow, Lesnaya promyshlennost’ Publ., 1964. 841 p.
12. Elkonin N.V. Study of Properties of Spent Solutions of Pulp Production by Kraft Method. Moscow, Bumazhnaya promyshlennost’ Publ., 1941, no. 2. 21 p.
13. Adams T. Sodium Salt Scaling in Black Liquor Evaporators and Concentrators. Tappi Journal, 2001, vol. 84(6), pp. 1–18.
14. Andreuccetti M.T., Leite B.S., Hallak d´Angelo J.V. Eucalyptus Black Liquor – Density, Viscosity, Solids and Sodium Sulfate Contents Revisited. O Papel, 2011, vol. 72, no. 12, pp. 52–57.
15. Bayuadri C., Verril C.L., Rousseau R.W. Stability of Sodium Sulfate Dicarbonate in Black Liquor Concentrators. TAPPI Engineering, Pulping and Environmental Conference Proceedings. TAPPI Press, 2006.
16. Bialik M.A., Theliander H., Sedin P., Verril C.L., DeMartini N. Solubility and Solid Phase Composition in Boiling-Temperature Na2CO3–Na2SO4 Solutions: A Modeling Approach. TAPPI Engineering, Pulping and Environmental Conference Proceedings. TAPPI Press, 2007, pp. 1471–1498.
17. Cardoso M., Oliveira E.D., Passos M.L.A. Kraft Black Liquor of Eucalyptus from Brazilian Mills. O Papel, 2006, vol. 67, no. 2, pp. 57–83.
18. Clay D.T. Evaporation Principles and Black Liquor Properties. TAPPI Kraft Recovery Short Course. TAPPI, 2011, pp. 3.1-1–3.1-6. Available at: (accessed 18.03.20).
19. Holmlund K., Parviainen K. Evaporation of Black Liquor. Ch. 12. Chemical Pulping. Ed. by J. Gullichsen, C.-J. Fogelholm. Helsinki, Fapet Oy, 1999, pp. B37–B93.

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


Make a Submission


Lesnoy Zhurnal (Russian Forestry Journal) was awarded the "Seal of Recognition for Active Data Provider of the Year 2024"