In improvement of froth flotation of diamond-bearing raw materials, it is effective to optimize and maintain water circulation closing to ensure maximum performance of mineral dressing. To this effect, the influence of the water circulation closing quality on the concentration of neutral salts, slimes and flotation agents in the water phase, and, accordingly, on the diamond recovery was studied. The mathematical modeling of the water circulation circuit in the froth flotation cycle, using a combination of the balancing and topological methods, determined the concentration ratios of salts, slimes and flotation agents in recycling water at varied levels of the water circulation closing. The calculated results show that the increased level of the water circulation closing from 60 to 90% leads to the increase in the recycling water mineralization by 50%, in the residual concentrations of reagents by 25–40% and in the slime concentration in the water phase by 180%. The water circulation closing increased by more than 85% allows reducing consumption of agents in the froth flotation cycle of diamond-bearing materials by 5–10%. However, given such level of closing of water circulation, the diamond recovery decreases by 8%, which is governed by the impact of slimes accumulated in the recycling water. The optimal closing level of water circulation in the current single-stage clarification circuit of thickener outflows of froth flotation tailings is 75–80%. The higher level closing of water circulation needs a two-stage circuit of desliming of tailings thickening outflows or requires using control agents in desliming to reduce concentration of slimes in recycling water of froth flotation of diamond-bearing materials.

Morozov V. V., Dvoichenkova G. P., Kovalenko E. G., Timofeev A. S., Kuryanov M. V. Justification of water circulation closing in froth flotation cycle of diamond-bearing kimberlites by mathematical modeling. MIAB. Mining Inf. Anal. Bull. 2022;(12):5-19. [In Russ]. DOI: 10.25018/0236_1493_2022_12_0_5.

V.V. Morozov, Dr. Sci. (Eng.), Professor, National University of Science and Technology «MISiS», 119049, Moscow, Russia, e-mail: dchmggu@mail.ru, ORCID ID: 0000-0003-4105-944X,

G.P. Dvoychenkova^{1,2}, Dr. Sci. (Eng.), Assistant Professor, Chief Researcher; Professor, e-mail: dvoigp@mail.ru, ORCID ID: 0000-0002-0940-3880,

E.G. Kovalenko^{2}, Cand. Sci. (Eng.), Chief Engineer, Institute «Yakutniproalmaz» JSC «ALROSA» (PJSC), 678174, Mirny, Republic of Sakha (Yakutia), Russia; Assistant Professor, e-mail: kovalenkoeg@alrosa.ru,

A.S. Timofeev^{1}, Cand. Sci. (Eng.), Senior Researcher, e-mail: Timofeev_ac@mail.ru, ORCID ID: 0000-0002-3382-6007,

M.V. Kuryanov^{1}, Leading Engineer, e-mail: kmikl@yandex.ru,

^{1} Institute of Problems of Comprehensive Exploitation of Mineral Resources, Russian Academy of Sciences, 111020, Moscow, Russia,

^{2} Polytechnic Institute (branch), M.K. Ammosov North-Eastern Federal University, 678174, Mirny, Republic of Sakha (Yakutia), Russia.

G.P. Dvoychenkova, e-mail: dvoigp@mail.ru.

1. Chanturia V. A., Godun K. V., Zhelyabovsky Yu. G., Goryachev B. E. The current state of the diamond mining industry in Russia and the main diamond mining countries of the world. Gornyi Zhurnal. 2015, no. 3, pp. 55—58. [In Russ].

2. Aigistov M. R., Gerasimov E. N., Bondarenko I. F., Zyryanov I. V. Modern technologies in the extraction and processing of diamond-containing raw materials. MIAB. Mining Inf. Anal. Bull. 2022, no. 5(2), pp. 6—21. [In Russ]. DOI: 10.25018/0236_1493_2022_52_0_6.

3. Chaadaev A. S., Cherepnov A. N., Zyryanov I. V., Bondarenko I. F. Perspective directions of development of technologies for mining and processing of diamond-bearing ores in PJSC ALROSA. Gornyi Zhurnal. 2016, no. 2, pp. 56—61. [In Russ].

4. Zlobin M. N. Sostoyanie i nekotorye puti razvitiya tekhnologii obogashcheniya almazosoderzhashchikh rud na predpriyatiyakh AK «ALROSA» [Condition and some ways of development of technology of enrichment of diamond-bearing ores at the enterprises of JSC «ALROSA»], Moscow, Almazy, 2002, pp. 59—63.

5. Verkhoturova V. A. Elshin I. V., Nemarov A. A. Scientific substantiation and selection of the optimal option for restoring the hydrophobic properties of the surface of diamonds from the ore of the tube «International». Proceedings of Irkutsk State Technical University. 2014, no. 8, pp. 51—56. [In Russ].

6. Dvoychenkova G. P., Morozov V. V., Chanturia E. L., Kovalenko E. G. Choice of parameters of electrochemical conditioning of circulating water during the preparation of diamond-bearing kimberlites for foam separation. Gornye nauki i tekhnologii. 2021, no. 6(3), pp. 170—180. [In Russ].

7. Carlsson G. Topological methods for data modelling. Nature Reviews Physics. 2020, no. 2, pp. 697—708.

8. Samygin V. D., Belyaeva A. V., Severov V. V., Yagudin R. A. Application of the topological method for the calculation of flotation schemes. Gornyi Zhurnal. 2012, no. 9, pp. 96—102. [In Russ].

9. Pestryak I. V. Modeling and analysis of physicochemical processes in recirculating water conditioning. Journal of Mining Science. 2015, vol. 51, no. 4, pp. 811—818. DOI: 10.1134/ S1062739115040189.

10. Avdokhin V. M., Chernysheva E. N. Modern technologies for the enrichment of diamondbearing kimberlites. MIAB. Mining Inf. Anal. Bull. 2010, no. S1, pp. 465—477. [In Russ].

11. Morozov V. V., Pestryak I. V., Kovalenko E. G., Lezova S. P., Polivanskaya V. V. Stimulation of frother separation of diamonds by optimizing collecting agent composition and temperature conditions. MIAB. Mining Inf. Anal. Bull. 2022, no. 8, pp. 135—147. [In Russ]. DOI: 10.25018/0236_1493_2022_8_0_135.

12. Gharai M., Venugopal R. Modeling of flotation process-an overview of different approaches. Mineral Processing and Extractive Metallurgy Review. 2015, vol. 37, pp. 120—133. DOI: 10.1080/08827508.2015.1115991.

13. Zlobin M. N. Coarse-grained flotation technology for beneficiation of diamond-bearing ores. Gornyi Zhurnal. 2011, no. 1, pp. 87—89. [In Russ].

14. Pilov P. I. Scientific substantiation of the topology of technological schemes of mineral processing. MIAB. Mining Inf. Anal. Bull. 1999, no. 7, pp. 143—146. [In Russ].

15. Zhang J., Kouznetsov D., Yu M., Rylatt M. Improving the separation of diamond from gangue minerals. Minerals Engineering. 2012, vol. 36-38, pp. 168—171. DOI: 10.1016/j. mineng.2012.03.015.

16. Kovalenko E. G. Modeling and optimization of closed water circulation in the cycle of foam separation of diamond-containing kimberlites. Sbornik trudov Mezhdunarodnoy konferentsii «Sovremennye problemy kompleksnoy i glubokoy pererabotki mineral'nogo syr'ya prirodnogo i tekhnogennogo proiskhozhdeniya» (Plaksinskie chteniya-2022) [Proceedings of International Conference «Modern problems of complex and deep processing of mineral raw materials of natural and technogenic origin» (Plaksinsky Readings-2022)], Vladivostok, 2022, pp. 328—342. [In Russ].

17. Di Feo A., Mortazavi S., Langley S. The effects of water recycling on flotation at a North American concentrator. Part 1. Journal of Minerals and Materials Characterization and Engineering. 2020, vol. 8, no. 4, pp. 37—45. DOI: 10.4236/jmmce.2020.84016.