journal article·2024-11Open access

Heterarchical modelling of comminution for rotary mills: part I—particle crushing along streamlines

Mukesh Singh Bisht, François Guillard, Paul Shelley, Benjy Marks, Itai Einav

Granular Matter· Volume 26· Issue 4

Abstract

Abstract Rotary mills aim to effectively reduce the size of particles through a process called comminution. Modelling comminution in rotary mills is a challenging task due to substantial material deformation and the intricate interplay of particle kinematics of segregation, mixing, crushing, and abrasion. Existing particle-based simulations tend to provide predictions that cannot cope with the large number of particles within rotary mills, their wide range of sizes, and the physics dictating the crushing of individual particles. Similarly, there is currently no deterministic modelling means to determine the evolving population of particle sizes at any point in time and space within the mill. The aim of this two-part contribution is to address these gaps by advancing a framework for a novel stochastic comminution model for rotary mills, which has a well-defined deterministic continuum limit and can cope with arbitrarily large numbers of particles. This work describes the basic physics and structure of the new model within a heterarchical framework for ball and autogenous grinding mills. The primary focus of this Part I paper is to develop a computational model for the integration of motion of material along streamlines inside a mill. Coupled to this process is the kinetic physics dictating particle crushing. In a subsequent work, Part II, segregation and mixing will be added to this model such that realistic behaviour from the mill can be observed. Graphical Abstract
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Mineral Processing and Grinding · Minerals Flotation and Separation Techniques · Granular flow and fluidized beds

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (70)

Show source-provided references
1. Ahuja, N.: Dot pattern processing using Voronoi neighborhoods. IEEE Trans. Pattern Anal. Mach. Intell. 3, 336–343 (1982)10.1109/TPAMI.1982.4767255 ↗
2. Alaei, E.: Marks, Benjy, Einav, Itai: A hydrodynamic-plastic formulation for modelling sand using a minimal set of parameters. J. Mech. Phys. Solids 151, 104388 (2021)10.1016/j.jmps.2021.104388 ↗
3. Alizadeh, E., et al.: Characterization of mixing and size segregation in a rotating drum by a particle tracking method. AIChE J. 59(6), 1894–1905 (2013)10.1002/aic.13982 ↗
4. Andrade, J.E., Tu, X.: Multiscale framework for behavior prediction in granular media. Mech. Mater. 41(6), 652–669 (2009)10.1016/j.mechmat.2008.12.005 ↗
5. Baligh, M.M.: Strain path method. J. Geotech. Eng. 111(9), 1108–1136 (1985)10.1061/(ASCE)0733-9410(1985)111:9(1108) ↗
6. Ballantyne, G.R., Powell, M.S.: Benchmarking comminution energy consumption for the processing of copper and gold ores. Miner. Eng. 65, 109–114 (2014)10.1016/j.mineng.2014.05.017 ↗
7. Bartelt, P., McArdell, B.W.: Granulometric investigations of snow avalanches. J. Glaciol. 55(193), 829–833 (2009)10.3189/002214309790152384 ↗
8. Bisht, M.S., Das, A.: DEM study on particle shape evolution during crushing of granular materials. Int. J. Geomech. 21(7), 04021101 (2021)10.1061/(ASCE)GM.1943-5622.0002067 ↗
9. Bisht, M.S., Guillard, F., Shelley, P., Marks, B., Einav, I.: Heterarchical modelling of comminution for rotary mills: Part II---Particle crushing with segregation and mixing. https://doi.org/10.1007/s10035-024-01450-210.1007/s10035-024-01450-2 ↗
10. Brilliantov, N.V., et al.: Model for collisions in granular gases. Phys. Rev. E 53(5), 5382 (1996)10.1103/PhysRevE.53.5382 ↗
11. Bueno, Marcos, et al.: The dominance of the competent. Fifth International Autogenous and Semiautogenous Grinding Technology, University of British Columbia, Department of Mining and Mineral Process Engineering, Vancouver (2011)
12. Bueno, M.P., et al.: Multi-component AG/SAG mill model. Miner. Eng. 43, 12–21 (2013)10.1016/j.mineng.2012.06.011 ↗
13. Carmona, H.A., et al.: Fragmentation processes in impact of spheres. Phys. Rev. E 77(5), 051302 (2008)10.1103/PhysRevE.77.051302 ↗
14. Carvalho, Rodrigo, Tavares, L.: A mechanistic model of SAG mills. Proceedings of the IMPC (2014)
15. Cheong, Y.S., et al.: Modelling fragment size distribution using two-parameter Weibull equation. Int. J. Miner. Process. 74, S227–S237 (2004)10.1016/j.minpro.2004.07.012 ↗
16. Cleary, P.: Modelling comminution devices using DEM. Int. J. Numer. Anal. Methods Geomech. 25(1), 83–105 (2001)10.1002/1096-9853(200101)25:1<83::AID-NAG120>3.0.CO;2-K ↗
17. Cleary, P.W., Morrison, R.D.: Comminution mechanisms, particle shape evolution and collision energy partitioning in tumbling mills. Miner. Eng. 86, 75–95 (2016)10.1016/j.mineng.2015.12.006 ↗
18. Cleary, P.W., Morrison, R.D.: Prediction of 3D slurry flow within the grinding chamber and discharge from a pilot scale SAG mill. Miner. Eng. 39, 184–195 (2012)10.1016/j.mineng.2012.05.019 ↗
19. Cleary, P.W., Morrison, R.D., Sinnott, M.D.: Prediction of slurry grinding due to media and coarse rock interactions in a 3D pilot SAG mill using a coupled DEM+ SPH model. Miner. Eng. 159, 106614 (2020)10.1016/j.mineng.2020.106614 ↗
20. Cleary, P.W., Morrisson, R., Morrell, S.: Comparison of DEM and experiment for a scale model SAG mill. Int. J. Miner. Process. 68(1–4), 129–165 (2003)10.1016/S0301-7516(02)00065-0 ↗
21. Cunningham, Claude: The Kuz-Ram Model for production of fragmentation from blasting. Proc. first int. Symp. on Rock Fragmentation by Blasting, Lulea. (1983)
22. Da Cruz, F., et al.: Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72(2), 021309 (2005)10.1103/PhysRevE.72.021309 ↗
23. Ding, Y.L., et al.: Granular motion in rotating drums: bed turnover time and slumping–rolling transition. Powder Technol. 124(1–2), 18–27 (2002)10.1016/S0032-5910(01)00486-7 ↗
24. Ding, Y.L., et al.: Segregation of granular flow in the transverse plane of a rolling mode rotating drum. Int. J. Multiph. Flow 28(4), 635–663 (2002)10.1016/S0301-9322(01)00081-7 ↗
25. Dunning, S.A.: The grain size distribution of rock-avalanche deposits in valley-confined settings. Ital. J. Eng. Geol. Environ. 1, 117–121 (2006)
26. Einav, I., Randolph, M.F.: Combining upper bound and strain path methods for evaluating penetration resistance. Int. J. Numer. Methods Eng. 63(14), 1991–2016 (2005)10.1002/nme.1350 ↗
27. Farin, G., Hoschek, J., Kim, M.-S.: Handbook of Computer Aided Geometric Design. Elsevier, Amsterdam (2002)
28. Fuerstenau, D.W., Abouzeid, A.-Z.M.: The energy efficiency of ball milling in comminution. Int. J. Miner. Process. 67(1–4), 161–185 (2002)10.1016/S0301-7516(02)00039-X ↗
29. Gerdes, Kurt D, et al.: The US Department of Energy–Office of Environmental Management’s International Program. Waste Management 7 (2007)
30. Goldhirsch, I.: Stress, stress asymmetry and couple stress: from discrete particles to continuous fields. Granul. Matter 12(3), 239–252 (2010)10.1007/s10035-010-0181-z ↗
31. Govender, I.: Granular flows in rotating drums: a rheological perspective. Miner. Eng. 92, 168–175 (2016)10.1016/j.mineng.2016.03.021 ↗
32. Guccione, D.E., et al.: Predicting the fragmentation survival probability of brittle spheres upon impact from statistical distribution of material properties. Int. J. Rock Mech. Min. Sci. 142, 104768 (2021)10.1016/j.ijrmms.2021.104768 ↗
33. Guillard, F., Marks, B.: Frictional hyperspheres in hyperspace. Phys. Rev. E 103(5), 052901 (2021)10.1103/PhysRevE.103.052901 ↗
34. Guo, N., Zhao, J.: A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. Int. J. Numer. Methods Eng. 99(11), 789–818 (2014)10.1002/nme.4702 ↗
35. Huang, E., Marks, B., Einav, I.: Continuum homogenisation of stochastic comminution with grainsize fabric. J. Mech. Phys. Solids 138, 103897 (2020)10.1016/j.jmps.2020.103897 ↗
36. Hanley, K.J., O’Sullivan, C.: Analytical study of the accuracy of discrete element simulations. Int. J. Numer. Methods Eng. 109(1), 29–51 (2017)10.1002/nme.5275 ↗
37. Jain, N., Ottino, J.M., Lueptow, R.M.: An experimental study of the flowing granular layer in a rotating tumbler. Phys. Fluids 14(2), 572–582 (2002)10.1063/1.1431244 ↗
38. Jeswiet, J., Szekeres, A.: Energy consumption in mining comminution. Proc. CIRP 48, 140–145 (2016)10.1016/j.procir.2016.03.250 ↗
39. Kloss, C., et al.: Models, algorithms and validation for opensource DEM and CFD-DEM. Prog. Comput. Fluid Dyn. Int. J. 12(2–3), 140–152 (2012)10.1504/PCFD.2012.047457 ↗
40. Ma, G., et al.: Combined FEM/DEM modeling of triaxial compression tests for rockfills with polyhedral particles. Int. J. Geomech. 14(4), 04014014 (2014)10.1061/(ASCE)GM.1943-5622.0000372 ↗
41. Maranic, Z., et al.: A granular thermometer. Granul. Matter 23(2), 1–15 (2021)10.1007/s10035-020-01081-3 ↗
42. Marks, B., Einav, I.: A cellular automaton for segregation during granular avalanches. Granul. Matter 13, 211–214 (2011)10.1007/s10035-010-0247-y ↗
43. Marks, B., Einav, I.: A heterarchical multiscale model for granular materials with evolving grainsize distribution. Granul. Matter 19(3), 1–15 (2017)10.1007/s10035-017-0741-6 ↗
44. Marks, B., Einav, I.: A mixture of crushing and segregation: the complexity of grainsize in natural granular flows. Geophys. Res. Lett. 42(2), 274–281 (2015)10.1002/2014GL062470 ↗
45. McDowell, G.R., Amon, A.: The application of Weibull statistics to the fracture of soil particles. Soils Found. 40(5), 133–141 (2000)10.3208/sandf.40.5_133 ↗
46. Mellmann, J.: The transverse motion of solids in rotating cylinders–forms of motion and transition behavior. Powder Technol. 118(3), 251–270 (2001)10.1016/S0032-5910(00)00402-2 ↗
47. Mwansa, S., Condori, P., Powell, M.S.: Charge segregation and slurry transport in long SAG mills. Proceedings of the XXIII International Mineral Processing Congress (IMPC 2006) Promed Advertising Istanbul, Turkey.: 81–86 (2006)
48. Nakata, A.F.L., et al.: A probabilistic approach to sand particle crushing in the triaxial test. Géotechnique 49(5), 567–583 (1999)10.1680/geot.1999.49.5.567 ↗
49. Nakata, Y., et al.: One-dimensional compression behaviour of uniformly graded sand related to single particle crushing strength. Soils Found. 41(2), 39–51 (2001)10.3208/sandf.41.2_39 ↗
50. Nitka, M., et al.: Two-scale modeling of granular materials: a DEM-FEM approach. Granul. Matter 13(3), 277–281 (2011)10.1007/s10035-011-0255-6 ↗
51. Norouzi, H.R., Zarghami, R., Mostoufi, N.: Insights into the granular flow in rotating drums. Chem. Eng. Res. Des. 102, 12–25 (2015)10.1016/j.cherd.2015.06.010 ↗
52. Ouchterlony, F.: The Swebrecfunction: linking fragmentation by blasting and crushing. Min. Technol. 114(1), 29–44 (2005)10.1179/037178405X44539 ↗
53. Parker, D.J., et al.: Positron emission particle tracking-a technique for studying flow within engineering equipment. Nucl. Instrum. Methods Phys. Res., Sect. A 326(3), 592–607 (1993)10.1016/0168-9002(93)90864-E ↗
54. Phillips, C.J., Davies, T.R.H.: Determining rheological parameters of debris flow material. Geomorphology 4(2), 101–110 (1991)10.1016/0169-555X(91)90022-3 ↗
55. Pollet, N., Schneider, J.-L.M.: Dynamic disintegration processes accompanying transport of the Holocene Flims sturzstrom (Swiss Alps). Earth Planet. Sci. Lett. 221(1–4), 433–448 (2004)10.1016/S0012-821X(04)00071-8 ↗
56. Reynolds, G.K., et al.: Breakage in granulation: a review. Chem. Eng. Sci. 60(14), 3969–3992 (2005)10.1016/j.ces.2005.02.029 ↗
57. Rozenblat, Y., et al.: Impact velocity and compression force relationship-equivalence function. Powder Technol. 235, 756–763 (2013)10.1016/j.powtec.2012.11.011 ↗
58. Rozenblat, Y., et al.: Selection and breakage functions of particles under impact loads. Chem. Eng. Sci. 71, 56–66 (2012)10.1016/j.ces.2011.12.012 ↗
59. Santos, D.A., et al.: A hydrodynamic analysis of a rotating drum operating in the rolling regime. Chem. Eng. Res. Des. 94, 204–212 (2015)10.1016/j.cherd.2014.07.028 ↗
60. Tomas, J., et al.: Impact crushing of concrete for liberation and recycling. Powder Technol. 105(1–3), 39–51 (1999)10.1016/S0032-5910(99)00116-3 ↗
61. Tromans, D., Meech, J.A.: Fracture toughness and surface energies of covalent minerals: theoretical estimates. Miner. Eng. 17(1), 1–15 (2004)10.1016/j.mineng.2003.09.006 ↗
62. Tromans, D., Meech, J.A.: Fracture toughness and surface energies of minerals: theoretical estimates for oxides, sulphides, silicates and halides. Miner. Eng. 15(12), 1027–1041 (2002)10.1016/S0892-6875(02)00213-3 ↗
63. Wang, Y., et al.: A coupled FEM-DEM study on mechanical behaviors of granular soils considering particle breakage. Comput. Geotech. 160, 105529 (2023)
64. Weedon, D.M., Wilson, F.: Modelling iron ore degradation using a twin pendulum breakage device. Int. J. Miner. Process. 59(3), 195–213 (2000)10.1016/S0301-7516(99)00066-6 ↗
65. Weerasekara, N.S., et al.: The contribution of DEM to the science of comminution. Powder Technol. 248, 3–24 (2013)10.1016/j.powtec.2013.05.032 ↗
66. Weibull, W., et al.: A statistical distribution function of wide applicability. J. Appl. Mech. 18(3), 293–297 (1951)10.1115/1.4010337 ↗
67. Weinhart, T., et al.: Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids 25(7), 070605 (2013)10.1063/1.4812809 ↗
68. Yashima, S., Morohashi, S., Saito, F.: Single particle crushing under slow rate of loading. Sci. Rep. Res. Inst. Tohoku Univ. Ser. A Phys. Chem. Metall. 28, 116–133 (1979)
69. Yu, Ping, et al.: Development of a dynamic mill model structure for tumbling mills. In: XXVII International Mineral Processing Congress-IMPC 2014 Conference Proceedings, Gecamin Digital Publications Santiago, Chile, pp. 41–51 (2014)
70. Zhou, Q., Xu, W.-J., Lubbe, R.: Multi-scale mechanics of sand based on FEM-DEM coupling method. Powder Technol. 380, 394–407 (2021)10.1016/j.powtec.2020.11.006 ↗