Eleme ve sınıflandırma ürünlerinin sözde rastgele sayı üretme rutiniyle tahmini

Predicting screening/classification products via the pseudorandom number selection routine

Screening/classification is performed for the separation of particles by their sizes. There are empirical, phenomenological, and numerical models for predicting the size distributions of screening/classification products. This paper introduces a new algorithm for the same purpose, which partially mimics phenomenological and numerical models. The algorithm iteratively selects the monosize fractions with pre-defined probabilities, then carries particle masses from the selected fractions either to the oversize or undersize product. The applicability of the algorithm was validated against the product size distributions from some industrial-scale screening/classification equipment - namely rake classifier, sieve bend (0.212 mm), vibrating screen (20 mm), and hydrocyclone - which are provided in the literature. The results show that the algorithm is predictive if each particle has a selection probability proportional to the mass of its monosize fraction and some power of its diameter. Results also suggest that vibrating screens can provide the sharpest size separation

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  • Austin, L. G., Klimpel, R. R., Luckie, P. T. 1984. Process Engineering of Size Reduction: Ball Milling. New York: AIME.
  • Camalan, M. 2021. A Computational Algorithm to Understand the Evolution of Size Distribution with Successive Breakage Events at Grinding. Environmental Sciences Proceedings, 6 (1), 7. https://doi.org/10.3390/ iecms 2021-09381.
  • Coelho, M. A. Z., Medronho, R. A. 1992. An Evaluation of the Plitt and Lynch & Rao Models for the Hydrocyclones. In L. Svarovsky and T. M. Thew (Eds.), Hydrocyclones Analysis and Applications, Southampton: Kluwer Academic Publishers, 63-72.
  • Davoodi, A., Asbjörnsson, G., Hulthén, E., Evertsson, M. 2019. Application of the Discrete Element Method to Study the Effects of Stream Characteristics on Screening Performance. Minerals, 9 (12), 788. https://doi. org/10.3390/min9120788.
  • Dong, K. J., Wang, B., Yu, A. B. 2013. Modeling of particle flow and sieving behavior on a vibrating screen: From discrete particle simulation to process performance prediction. Industrial and Engineering Chemistry Research, 52 (33), 11333–11343. https://doi.org/10.1021/ ie3034637
  • Dong, K. J., and Yu, A. B. 2012. Numerical simulation of the particle flow and sieving behaviour on sieve bend/low head screen combination. Minerals Engineering, 31, 2–9. https://doi.org/10.1016/j.mineng. 2011.10.020
  • Dündar, H. 2020. Investigating the benefits of replacing hydrocyclones with high-frequency fine screens in closed grinding circuit by simulation. Minerals Engineering, 148 (January), 106212. https://doi. org/10.1016/j.mineng.2020.106212
  • Elskamp, F., Kruggel-Emden, H. 2015. Review and benchmarking of process models for batch screening based on discrete element simulations. Advanced Powder Technology, 26 (3), 679–697. https://doi. org/10.1016/j.apt.2014.11.001
  • Frausto, J. J., Ballantyne, G. R., Runge, K., Powell, M. S., Wightman, E. M., Evans, C. L., Gonzalez, P., Gomez, S. 2021. The effect of screen versus cyclone classification on the mineral liberation properties of a polymetallic ore. Minerals Engineering, 169 (April), 106930. https://doi. org/10.1016/j.mineng.2021.106930
  • Gupta, A., Yan, D. 2016. Mineral Processing Design and Operations. Amsterdam: Elsevier.
  • Heiskanen, K. G. H. 1996. Developments in wet classifiers. International Journal of Mineral Processing, 44–45 (SPEC. ISS.), 29–42. https://doi. org/10.1016/0301-7516(95)00015-1
  • Kelly, E. G. 1991. The significance of by-pass in mineral separators. Minerals Engineering, 4 (1), 1–7. https://doi.org/10.1016/0892- 6875(91)90113-A
  • Khoshdast, H., Shojaei, V., Khoshdast, H. 2017. Combined application of computational fluid dynamics (CFD) and design of experiments
  • (DOE) to hydrodynamic simulation of a coal classifier. International Journal of Mining and Geo-Engineering, 51 (1), 9–22. https://doi. org/10.22059/ijmge.2016.218483.594634
  • King, R. P. 2012. Modeling and Simulation of Mineral Processing Systems (C. L. Schneider and E. A. King, eds.). Littleton: SME.
  • Kruggel-Emden, H., Elskamp, F. 2014. Modeling of screening processes with the discrete element method involving non-spherical particles. Chemical Engineering and Technology, 37 (5), 847–856. https://doi. org/10.1002/ceat.201300649
  • Mangadoddy, N., Vakamalla, T. R., Kumar, M., Mainza, A. 2020. Computational modelling of particle-fluid dynamics in comminution and classification: a review. Mineral Processing and Extractive Metallurgy: Transactions of the Institute of Mining and Metallurgy, 129 (2), 145–156. https://doi.org/10.1080/25726641.2019.1708657
  • Matsumoto, M., Nishimura, T. 1998. Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator. ACM Transactions on Modeling and Computer Simulation, 8 (1), 3–30. https://doi.org/10.1145/272991.272995
  • Mular, A. L. 2009. Size Separation. In M. C. Fuerstenau and K. Han (Eds.), Principles of Mineral Processing, Littleton: SME, 119–172.
  • Muñoz, D. A., Diaz, J. L., Taborda, S., Alvarez, H. 2017. Hydrocyclone Phenomenological- Based Model and Feasible Operation Region. International Journal of Mining, Materials, and Metallurgical Engineering, 3, 1–9.
  • Nageswararao, K., Wiseman, D. M., Napier-Munn, T. J. 2004. Two empirical hydrocyclone models revisited. Minerals Engineering, 17 (5), 671– 687. https://doi.org/10.1016/j.mineng.2004.01.017
  • Napier-Munn, T. J., Lynch, A. J. 1992. The modelling and computer simulation of mineral treatment processes - current status and future trends. Minerals Engineering, 5 (2), 143–167. https://doi. org/10.1016/0892-6875(92)90039-C
  • Narasimha, M., Brennan, M., Holtham, P. N. 2007. A Review of CFD Modelling for Performance Predictions of Hydrocyclone. Engineering Applications of Computational Fluid Mechanics, 1 (2), 109–125. https://doi.org/10.1080/19942060.2007.11015186
  • Olson, T. J., Turner, P. A. 2002. Hydrocyclone selection for plant design. In A. L. Mular, N. D. Halbe, and D. J. Barratt (Eds.), Mineral Processing Plant Design, Practice, and Control Proceedings, Littleton: SME, Volumes 1-2, 880–893.
  • Svarovsky, L., Svarovsky, J. 1992. A New Method of Testing Hydrocyclone Grade Efficiencies. In L. Svarovsky and T. M. Thew (Eds.), Hydrocyclones Analysis and Applications, Southampton: Kluwer Academic Publishers, 68-70.
  • Tang, Z., Yu, L., Wang, F., Li, N., Chang, L., Cui, N. 2018. Effect of particle size and shape on separation in a hydrocyclone. Water (Switzerland), 11 (1), 1–19. https://doi.org/10.3390/w11010016
  • Wills, B. A., Finch, J. A. 2016. Wills’ Mineral Processing Technology. Amsterdam: Elsevier.
  • Wong, C. K., Easton, M. C. 1980. An Efficient Method for Weighted Sampling without Replacement. SIAM Journal on Computing, 9 (1), 111–113. https://doi.org/10.1137/0209009
  • Zhao, L., Zhao, Y., Bao, C., Hou, Q., Yu, A. 2016. Laboratory-scale validation of a DEM model of screening processes with circular vibration. Powder Technology, 303, 269–277. https://doi.org/10.1016/j.powtec. 2016.09.034