RUSAL Engineering & Technology Center, St. Petersburg, Russia:

V. O. Golubev, Head of Department of Mathematical Modeling, e-mail: vladimir.golubev2@rusal.com
D. G. Chistiakov, Senior Engineer of Department of Mathematical Modeling, e-mail: Dmitriy.Chistyakov@rusal.com

Saint-Petersburg Mining University, St. Petersburg, Russia:
V. N. Brichkin, Head of Department of Metallurgy, e-mail: Brichkin_VN@pers.spmi.ru
T. E. Litvinova, Professor of the Department of Physical Chemistry, e-mail: Litvinova_TE@pers.spmi.ru

It is shown that the development of systems and aids of mathematical modeling of alumina production at the refinery of Russia has passed a long way of evolution and it is mainly connected with creating the specialized software products and domestic mainframe computers. At the present stage, the systems and aids of domesitic mathematical modeling of technological processes is an integral part of effective functioning of alumina refinery, the specifics of the engineering plan of which makes it difficult or even excludes the possibility of a unified approach to construction of their digital twins and necessitates flexible combining the individual and universal approaches. The functionality of the models is implemented in the Windows environment with the use of SysCAD software, which makes it possible to obtain information about properties of any material flow, parameters of each technological apparatus and to solve a complex of operational and system issues. Until the present time the relevance of profound understanding of the nature of the laws, phenomena and processes occurring in the alumina production systems, as well as building the special-purpose electronic databases. This would allow one to develop and apply relevant physicalchemical model of the plants at which alumina is manufactured not only from bauxites but also from the other types of aluminiferous raw materials. At the same time, further improvement of mathematical tool is associated with the need to improve the efficiency of multithreaded calculations in design of technological systems, which being combined with an access to powerful computing resources creates the conditions for transition to a new level of solving production technological problems, including multiparametric optimization of alumina plants and others.

The work was carried with financial support of the Russian Science Foundation No. 18-19-00577 dated April 26, 2018 on providing the grant for conducting fundamental scientific and exploratory researches.

1. Perregaard J., Serensen E. L. Simulation and optimization of chemical processes: numerical and computational aspects. European Symposium on Computer Aided Process Engineering. 1992. No. 1. pp. 247–254.
2. Ramirez W. F. Computational Methods for Process Simulation. Second edition. 1997. Oxford : Reed Educationaland Professional Publishing Ltd., 1997. 461 p.
3. Elmqvist H., Otter, M., Methods for tearing systems of equations in object-oriented modeling. The ESM’94 European Simulation Multiconference : proceedings. Barcelona, 1994. pp. 326–332.
4. Alwar R. S., Raos N. R., Raos M. S. An Alternative Procedure in Dynamic Relaxation. Computers and Structures. 1975. Vol. 5. pp. 271–274.
5. Stage S. A. Comments on an Improvement to the Brent’s Method. International Journal of Experimental Algorithms. 2013. No. 4 (1). pp. 1–16.
6. Metzger D. Adaptive damping for dynamic relaxation problems with non-monotonic spectral response. International Journal for Numerical Methods in Engineering. 2003. No. 56. pp. 57–80.
7. Jeffers J., Reinders J., Sodani A. Intel Xeon Phi processor high performance programming. 2nd edition. Knights Landing Edition. San Francisco, 2016. pp. 297–314.
8. Stoykov S., Margenov S. Scalable parallel implementation of shooting method for large-scale dynamical systems. Application to bridge components. Journal of Computational and Applied Mathematics. 2015. Vol. 293. P. 223–231.
9. Blackford L. S., Choi J., Cleary A. et al. ScaLAPACK Users’ Guide. Society for Industrial and Applied Mathematics. 1997. 324 p.
10. Abramov V. Ya., Nikolaev I. V., Stelmakova G. D. Physical and chemical basis of complex processing of aluminum raw materials: alkaline methods. Moscow : Metallurgiya, 1985. 288 p.
11. Arlyuk B. I., Veprikova T. B. The dependence of the solubility of hydrargilite on the concentration of soda-alkaline solution and the temperature. Tsvetnye Metally. 1981. No. 6. pp. 59–60.
12. Rosenberg S. P., Healy S. J. A thermodynamic model for gibbsite solubility in Bayer liquors. The 4^th International Alumina Quality Workshop : collection of reports of international conference. Darwin, 1996. pp. 301–310.
13. Pál Sipos. The structure of Al(III) in strongly alkaline aluminate solutions : a review. Journal of Molecular Liquids. 2009. Vol. 146. Iss. 1, 2. pp. 1–14.

14. Alumina 3 Bayer Species Model. Available at: http://help.syscad.net/index.php/Alumina_3_Bayer_Species_Model#Density_Calculations (accessed: May 30, 2019))
15. Zelikman A. N., Voldman G. M., Belyaevskaya L. V. Theory of hydrometallurgical processes. Moscow : Metallurgiya, 1983. 423 p.
16. Abramov V. Ya., Eremin N. I. Leaching of aluminate cakes. Moscow : Metallurgiya, 1976. 208 p.
17. Djuri I., Mihajlovi I., Živkovi Ž. Kinetic modelling of different bauxite types in the Bayer leaching process. Canadian Metallurgical Quarterly. 2010. Vol. 49(3). pp. 209–218.
18. Pereira J. A., Schwaab M., Dell’Oro M. et al. The kinetics of gibbsite dissolution in NaOH. Hydrometallurgy. 2009. Vol. 96(1-2). pp. 6–13.
19. Bao L., Nguyen A.V. Developing a physically consistent model for gibbsite leaching kinetics. Hydrometallurgy. 2010. Vol. 104(1). pp. 86-98.
20. White E. T., Bateman S. H. Effect of caustic concentration on the growth rate of Al(OH)₃ particles. Light Metals 1988 : proceedings of the technical sessions presented by the TMS Aluminum Committee at the 177^th TMS annual meeting. Phoenix, 1988. pp. 157–162.
21. Brichkin V. N., Kremcheeva D. A., Matveev V. A. Quantitative seed impact on mass crystallization indicators of chemical sediments. Proceedings of the Mining Institute. 2015. Vol. 211. pp. 64–70.
22. Ramkrishna D. Population balances. London: Academic Press, 2000. 355 p.
23. Litster J. D., Smit D. J., Hounslow M. J. Adjustable discretized population balance for growth and aggregation. AIChE Journal. 1995. Vol. 41, No. 3. pp. 591–603.
24. Misra C. The precipitation of Bayer aluminiumtrihydroxide : thesis of inauguration of Dissertation … of Doctor of Philosophy. University of Queensland, 1970. 236 p.
25. Livk I., Ilievski D. A macroscopic agglomeration kernel model for gibbsite precipitation in turbulent and laminar flows. Chemical Engineering Science. 2007. Vol. 62. pp. 3787–3797.
26. Brichkin V. N., Sizyakov V. M., Oblova I. S., Fedoseev D. V. Industrial synthesis of finely-dispersed aluminum hydroxide n processing of aluminic raw materials. Tsvetnye Metally. 2018. No. 10. pp. 45–51.
27. Golubev V. O., Balde M.-B., Chistyakov D. G. Development and Utilization of Detailed Process and Technology Models at RUSAL Alumina Refineries. The 35^th International ICSOBA Conference : proceedings. Hamburg, 2017. pp. 281–288.
28. Leinewebera D. B., Bauer I., Bock H. G. An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects. Computers & Chemical Engineering. 2003. Vol. 27, Iss. 2. pp. 157–166.
29. Leinewebera D. B., Bauer I., Bock H. G. An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part II: Software aspects and applications. Computers & Chemical Engineering. 2003. Vol. 27, Iss. 2. pp. 167–174.
30. Aipeng J., Zhushu J., Jingtao H. et al. Research of Large-Scale Reduced SQP Algorithm for Chemical Process System Optimization. IFAC Proceedings Volumes. 2008. Vol. 41, Iss. 2. pp. 11034–11040.
31. Wu D., Terpenny J., Gentzsch W. Cloud-based design, engineering analysis and manufacturing: A cost-benefit analysis. Procedia Manufacturing. 2015. Vol. 1. pp. 64–76.