Базова математична модель оперативного оцінювання в’язкості пульпи при подрібненні руди кульовими млинами
Journal Title: Математичне моделювання - Year 2018, Vol 1, Issue 2
Abstract
BASIC MATHEMATICAL MODEL OF OPERATIVE PULP VISCOSITY EVALUA-TION OF ORE GRINDING BALL MILL Matsui A.N., Kondratets V.A. Abstract Significant overspending of electricity, steel balls and lining when grinding ore with ball mills increases the cost of the concentrate and reduces its competitiveness and domestic iron and steel products on the international market. The lack of means for determining the viscosity of pulp in a ball mill of the first grinding stage does not allow improving these results. As this publication is aimed at solving this problem, it is an actual topic. The purpose of this publication is to develop an approach for virtual operational estimation of pulp viscosity in a ball mill operating in a closed cycle with a single-spiral classifier. The most perfect model for determining the viscosity of disperse media is G.S. Khodakov's model, which can not be used to determine the viscosity of a pulp. It is shown that, taking into account the features of the pulp in a ball mill, it is possible to make a transition to the determination of another, more convenient parameter for estimating the viscosity of the pulp. It can be effectively implemented by grinding a specific technological ore variety in the deposit. The basic mathematical model for estimating the viscosity of a pulp is reduced to determining the distance between particles of a solid with respect to its density, size, and density of the mixture. The growth of pulp density and the reduction in the particle size of solid particles leads to an increase in the undulation of the interlayers of the dispersion medium, which affects the viscosity of the mixture. The mathematical model unambiguously characterizes the relationship between the investigated parameters both in the regions of positive and conditionally negative values of the distance between solid particles. The distance between solid particles in the pulp unambiguously characterizes its viscosity when the grain size is changed under conditions of a given sparse dispersion medium. The proposed base model contains the known solid density, pulp density, which is known or can be measured, and the weighted average solid size, which makes it possible to apply it for the rapid assessment of pulp viscosity and even for parameter prediction. Since the basic model reduces to determining the distance between solid particles, it must be "adapted" to specific technological conditions and the material that is ground. The problem of finding the basic mathematical model for the operative estimation of pulp viscosity during ore grinding in ball mills with sands of a mechanical single-spiral classifier was solved for the first time. Prospects for this study consist in "adapting" the proposed basic model for rapid assessment of pulp viscosity in a ball mill with technological conditions for grinding ore and material features. References [1] Pivnjak G. G., Vajsberg L. A., Kirichenko V. I., Pilov P. I., Kirichenko V. V. Izmel'chenie. Jenergetika i tehnologija [Grinding. Energy and technology]. Moscow, 2007. 296 p. (in Russian). [2] Azaryan A. A., Krivenko Yu. Yu., Kucher V. G. Avtomatizatsiya pervoi stadii izmel'cheniya, klassifikatsii i magnitnoi separatsii – real'nyi put' povysheniya effektivnosti obogashcheniya zheleznykh rud [Automation of the first stage of grinding, classification and magnetic separation is a real way to increase the efficiency of iron ore enrichment]. Visnyk Kryvoriz'kogo nacional'nogo universytetu, 2014. no. 36, pp.276–280. (in Russian). [3] Kupin A. I. Intelektual'na identyfikacija ta keruvannja v umovah procesiv zbagachuval'noi' tehnologii' [Intellectual identification and management in the context of enrichment technology]. Kryviy Rih, 2008. 204 p. (in Ukrainian). [4] Bonch-Bruevich A. M., Bykov V. L., Chinaev P. I. Beskontaktnye elementy samonastraivayushchikhsya sistem [Noncontact elements of self-tuning systems]. Moscow, 1967. 292 p. (in Russian). [5] Skorov V. A. Obogashchenie rud [Enrichment of ores]. Moscow, 1969. 276 p. (in Russian). [6] Kondratec' V. O., Serbul O. M., Macuj A. M. Avtomatyzacija procesiv keruvannja rozridzhennjam pul'py pry podribnenni rudy barabannymy mlynamy [Automation of the processes of controlling the rarefaction of pulp when grinding ore with drum mills]. Kirovohrad, 2013. 368 p. (in Ukrainian). [7] Gatchek E. Vyazkost' zhidkostei [Viscosity of liquids]. Moscow-Leningrad, 1934. 312 p. (in Russian). [8] Rabotnov Yu. N., Rebinder P. A. Reologiya: teoriya i prilozheniya [Rheology: Theory and Applications]. Moscow, 1962. 824 p. (in Russian). [9] Reiner M. Reologiya [Rheology]. Moscow, 1965. 223 p. (in Russian). [10] Frankel N. A., and Acrivos A. “On the Viscosity of a Concentrated Suspension of Solid Spheres”. Chem. Eng. Sc., vol. 22, No. 6, pp. 847–853, 1967. [11] Fort'e A. Mekhanika suspenzii [Mechanics of suspensions]. Moscow, 1971. 264 p. (in Russian). [12] Mewis J. “Rheology of Suspensions”. Proc. 8 Con. on Rheol., vol.1, pp.149–168, 1980. [13] Graham A. L. “On the viscosity of suspensions of solid spheres”. App. Sc. Res., vol.37, pp.275–286, 1981. [14] Russel W. B. “Theoretical approaches to the rheology of concentrated dispersions”. Pow. Tech., vol.51, no. 1, pp.15–25, 1987. [15] Ur'ev N. B. Fiziko-khimicheskie osnovy tekhnologii dispersnykh sistem i materialov [Physico-chemical basis of dispersed systems and materials technology]. Moscow, 1988. – 255 p. (in Russian). [16] Patel P. D., and Russel W. B. “Mean field theory for the rheology of phase separated of flocculated dispersions”. Coll. and Surf, vol.31, pp.355–383, 1988. [17] Laskowski J. S. “Coal flotation and fine coal utilization”. Els. Sc., 384 p., 2001. [18] Khodakov G. S. Reologiya suspenzii. Teoriya fazovogo techeniya i ee eksperimental'noe obosnovanie [Rheology of suspensions. The theory of phase flow and its experimental justification]. Rossiiskii khimicheskii zhurnal, 2003. T. XLVII, no.2, pp. 33–44. (in Russian). [19] Kravtsova O. S., Kanygina O. N. Razvitie reologicheskoi modeli dlya sistemy «voda-kaolinit soderzhashchaya glina» [Development of the rheological model for the system "water-kaolinite containing clay"]. Vestnik Orenburgskogo gosudarstvennogo universiteta, 2015. no.1 (176). pp.116–119. (in Russian). [20] Andreev S. E., Perov V. A., Zverevich V. V. Droblenie, izmel'chenie i grokhochenie poleznykh iskopaemykh [Crushing, grinding and screening of minerals]. Мoscow, 1980. 415 p. (in Russian). [21] Chuyanov G. G. Obezvozhivanie, pyleulavlivanie i okhrana okruzhayushchei sredy [Dewatering, dust collection and environmental protection]. Moscow, 1987. 260 p. (in Russian). [22] Khanin A. A. Porody – kollektory nefti i gaza i ikh izuchenie [Breeds - collectors of oil and gas and their study]. Moscow, 1969. 354 p. (in Russian). [23] Kondratec' V. O., Macuj A. M. Sferychna chastynka tverdogo pevnogo rozmiru jak osnova procesu modeljuvannja rozpushennja girs'kyh porid [The spherical solid particle of a certain size as a basis for modeling the process disintegration rocks]. Matematychne modeljuvannja, 2015. no2 (33), pp. 55–59. (in Ukrainian).
Authors and Affiliations
А. М. Мацуй, В. О. Кондратець
Keywords
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- DOI 10.31319/2519-8106.2(39)2018.154232
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