# Modelling of Red-Mud Particle-Solid Distribution in the Feeder Cup of a Thickener Using the Combined CFD-DPM Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Flocculation Zone

#### 2.2. Feeding Cup of the Thickener

#### 2.3. Creating Mesh

#### 2.4. Input Parameters

#### 2.5. Numerical Simulation

#### 2.6. Stocks Law

## 3. Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

## References

- Boikov, A.; Payor, V. The Present Issues of Control Automation for Levitation Metal Melting. Symmetry
**2022**, 14, 1968. [Google Scholar] [CrossRef] - Lebedev, A.B.; Utkov, V.A.; Khalifa, A.A. Sintered Sorbent Utilization for H2S Removal from Industrial Flue Gas in the Process of Smelter Slag Granulation. J. Min. Inst.
**2019**, 237, 292. [Google Scholar] [CrossRef] - Liu, C.; Li, H.; Shi, Y.; Xu, D. Distributed Event-Triggered Model Predictive Control of Coupled Nonlinear Systems. SIAM J. Control. Optim.
**2020**, 58, 714–734. [Google Scholar] [CrossRef] - Betancourt, R.; Bürger, S.D.; Faras, S. Modeling andcontrolling clarifier-thickeners fed by suspensions with time-dependent properties. Miner. Eng.
**2014**, 62, 91–101. [Google Scholar] [CrossRef] - Shi, Z.; Zhang, G.; Zhang, Y.; He, T.; Pei, G. Modeling of Flocculation and Sedimentation Using Population Balance Equation. J. Chem.
**2019**, 2019, 1–10. [Google Scholar] [CrossRef] - Papuga, K.; Kaszubkiewicz, J.; Kawałko, D. Do we have to use suspensions with low concentrations in determination of particle-size distribution by sedimentation methods? Powder Technol.
**2021**, 389, 507–521. [Google Scholar] [CrossRef] - Chai, T.; Jia, Y.; Li, H.; Wang, H. An intelligent switching control for a mixed separation thickener process. Control. Eng. Pract.
**2016**, 57, 61–71. [Google Scholar] [CrossRef] - Concha, F.; Sbarbaro, D.; Pereira, A.; Segovia, J.; Vergara Rojas, S. On-line instruments for measuring thickening parameters in industrial thickeners. In Proceedings of the IMPC 2014—27th International Mineral Processing Congress, Santiago, Chile, 20–24 October 2014. [Google Scholar]
- Ebrahimzadeh, M.; Soltani Goharrizi, A.; Aghajani Shahrivar, A. Modeling industrial thickener using computational fluid dynamics (CFD), a case study: Tailing thickener in the Sarcheshmeh copper mine. Int. J. Min. Sci. Technol.
**2013**, 23, 885–892. [Google Scholar] [CrossRef] - Bürger, R.; Ruiz Baier, R.; Torres, H. A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes. SIAM J. Sci. Comput.
**2012**, 34, B265–B289. [Google Scholar] [CrossRef] [Green Version] - Franks, G.; Zhou, Y. Relationship between aggregate and sediment bed properties: Influence of inter-particle adhesion. Adv. Powder Technol.
**2010**, 21, 362–373. [Google Scholar] [CrossRef] - Fawell, P.D.; Nguyen, T.V.; Solnordal, C.B.; Stephens, D.W. Enhancing Gravity Thickener Feedwell Design and Operation for Optimal Flocculation through the Application of Computational Fluid Dynamics. Miner. Process. Extr. Metall. Rev.
**2021**, 42, 496–510. [Google Scholar] [CrossRef] - Nakamura, H.; Makino, S.; Ishii, M. Continuous shear thickening and discontinuous shearthickening of concentrated monodispersed silica slurry. Adv. Powder Technol.
**2020**, 31, 1659–1664. [Google Scholar] [CrossRef] - Langlois, J.; Cipriano, A. Dynamic modeling and simulation of tailing thickener units for the development of control strategies. Miner. Eng.
**2019**, 131, 131–139. [Google Scholar] [CrossRef] - Madarász, L.; Köte, Á.; Hambalkó, B.; Csorba, K.; Kovács, V.; Lengyel, L.; Marosi, G.; Farkas, A.; Nagy, Z.K.; Domokos, A. In-line particle size measurement based on image analysis in a fully continuous granule manufacturing line for rapid process understanding and development. Int. J. Pharm.
**2021**, 612, 121280. [Google Scholar] [CrossRef] [PubMed] - O’Brien, C.S. A Mathematical Model for Colloidal Aggregation. Graduate Theses and Dissertations. 2003. Available online: https://scholarcommons.usf.edu/etd/1441 (accessed on 23 October 2022).
- Masko, O.; Bazhin, V. Monitoring of the Behavior and State of Nanoscale Particles in aGas Cleaning System of an Ore-Thermal Furnace. Symmetry
**2022**, 14, 923. [Google Scholar] [CrossRef] - Golubev, V.; Chistiakov, D.; Blednykh, I.V. Predictive Analysis of Industrial Precipitation Cycles Using Population Balance and Deep Learning Methods. In Proceedings of the 38th International ICSOBA Conference, Virtual Conference, 16–18 November 2020; pp. 205–214. [Google Scholar]
- Quezada, G.; Ayala, L.; Leiva, W.; Toro, N.; Toledo, P.; Robles, P.; Jeldres, R. Describing Mining Tailing Flocculation in Seawater by Population Balance Models: Effect of Mixing Intensity. Metals
**2020**, 10, 240. [Google Scholar] [CrossRef] [Green Version] - Quezada, G.; Jeldres, M.; Toro, N.; Robles, P.; Jeldres, R. Reducing the Magnesium Content from Seawater to Improve Tailing Flocculation: Description by Population Balance Models. Metals
**2020**, 10, 329. [Google Scholar] [CrossRef] [Green Version] - Piirainen, V.Y.; Boeva, A.A.; Nikitina, T.Y. Application of New Materials for Red Mud Immobilization. Key Eng. Mater.
**2020**, 854, 182–187. [Google Scholar] [CrossRef] - Pyagay, I.N.; Kremcheev, E.A.; Pasechnik, L.A.; Yatsenko, S.P. Carbonization processing of bauxite residue as an alternative rare metal recovery process. Tsvetnye Met.
**2020**, 10, 56–63. [Google Scholar] [CrossRef] - Kannan, P.; Banat, F.; Hasan, S.W.; Abu Haija, M. Neutralization of Bayer bauxite residue (red mud) by various brines: A review of chemistry and engineering processes. Hydrometallurgy
**2021**, 206, 105758. [Google Scholar] [CrossRef] - Russo, A.C.; da Silva Pimentel, M.A.; Hemsi, P.S. Use of continuous flocculation monitoring in the control of water treatability parameters. Eng. Sanit. Ambient.
**2020**, 25, 501–507. [Google Scholar] [CrossRef] - Grabsch, A.F.; Yahyaei, M.; Fawell, P.D. Number-sensitive particle size measurements for monitoring flocculation responses to different grinding conditions. Miner. Eng.
**2020**, 145, 106088. [Google Scholar] [CrossRef] - Liu, X.; Yin, H.; Zhao, J.; Guo, Z.; Liu, Z.; Yizhou, S. Understanding the coagulation mechanism and floc properties induced by ferrate(VI) and FeCl
_{3}: Population balance modeling. Water Sci. Technol.**2021**, 83, 2377–2388. [Google Scholar] [CrossRef] [PubMed] - Li, H.; Wu, A.-X.; Wang, H.-J.; Chen, H.; Yang, L.-H. Changes in underflow solid fraction and yield stress in paste thickeners by circulation. Int. J. Miner. Met. Mater.
**2021**, 28, 349–357. [Google Scholar] [CrossRef] - Beloglazov, I.I.; Morenov, V.A.; Leusheva, E.L.; Gudmestad, O.T. Modeling of Heavy-Oil Flow with Regard to Their Rheological Properties. Energies
**2021**, 14, 359. [Google Scholar] [CrossRef] - Aleksandrova, T.N.; Potemkin, V.A. Development of a methodology to assess the hydrocyclone process with account of the rheological properties of the mineral slurry. J. Min. Inst.
**2021**, 252, 908–916. [Google Scholar] [CrossRef] - Tabatabaee Moradi, S.S.; Nikolaev, N.I.; Nikolaeva, T.N. Development of spacer fluids and cement slurries compositions for lining of wells at high temperatures. J. Min. Inst.
**2020**, 242, 174. [Google Scholar] [CrossRef] - Ulyasheva, N.M.; Leusheva, E.L.; Galishin, R.N. Development of the drilling mud composition for directional wellbore drilling considering rheological parameters of the fluid. J. Min. Inst.
**2020**, 244, 454–461. [Google Scholar] [CrossRef] - Sizyakov, V.M.; Litvinova, T.E.; Brichkin, V.N.; Fedorov, A.T. Modern Physicochemical Equilibrium Description in Na
_{2}O–Al_{2}O_{3}–H_{2}O System and Its Analogues. J. Min. Inst.**2019**, 237, 298. [Google Scholar] [CrossRef] - Nikolaeva, N.; Aleksandrova, T.; Romashev, A. Effect of grinding on the fractional composition of polymineral laminated bituminous shales. Miner. Process. Extr. Metall. Rev.
**2018**, 39, 231–234. [Google Scholar] [CrossRef] - Wang, X.; Cui, B.; Wei, D.; Song, Z.; He, Y.; Bayly, A.E. CFD-PBM modelling of tailings flocculation in a lab-scale gravity thickener. Powder Technol.
**2022**, 396, 139–151. [Google Scholar] [CrossRef] - Zhou, T.; Li, M.; Zhou, C.Q.; Zhou, J.M. Numerical simulation and optimization of red mud separation thickener with self-dilute feed. J. Cent. South Univ.
**2014**, 21, 344–350. [Google Scholar] [CrossRef] - Owen, A.T.; Nguyen, T.V.; Fawell, P.D. The effect of flocculant solution transport and addition conditions on feedwell performance in gravity thickeners. Int. J. Miner. Process.
**2009**, 93, 115–127. [Google Scholar] [CrossRef] - Panda, S.K.; Vishnu Anand, P.; Aashranth, B.; Pandey, N.K. Disengagement of dispersed cerium oxalate from nitric-oxalic acid medium in a batch settler: Measurements and CFD simulations. Ann. Nucl. Energy
**2020**, 144, 107574. [Google Scholar] [CrossRef] - Wang, X.; Cui, B.; Wei, D.; Song, Z.; He, Y.; Bayly, A.E. Effect of feed solid concentration on tailings slurry flocculation in a thickener by a coupled CFD-PBM modelling approach. J. Environ. Chem. Eng.
**2021**, 9, 106385. [Google Scholar] [CrossRef] - Tanguay, M.; Fawell, P.; Adkins, S. Modelling the impact of two different flocculants on the performance of a thickener feedwell. Appl. Math. Model.
**2014**, 38, 4262–4276. [Google Scholar] [CrossRef] - Fedorova, E.; Pupysheva, E. Programma dlya Rascheta Granulometricheskogo Sostava Agregirovannoj Pul’py [Program for Calculating the particle-size distribution of Aggregate Slurries]. Russian Patent 2022619089, 24 October 2022. [Google Scholar]
- Duan, X.; Shi, B.; Wang, J.; Song, S.; Liu, H.; Li, X.; Chen, Y.; Liao, Q.; Gong, J.; Chen, S.; et al. Simulation of the hydrate blockage process in a water-dominated system via the CFD-DEM method. J. Nat. Gas Sci. Eng.
**2021**, 96, 104241. [Google Scholar] [CrossRef] - Boikov, A.; Payor, V.; Savelev, R.; Kolesnikov, A. Synthetic Data Generation for Steel Defect Detection and Classification Using Deep Learning. Symmetry
**2021**, 13, 1176. [Google Scholar] [CrossRef] - Kulchitskiy, A. Optical Inspection Systems for Axisymmetric Parts with Spatial 2D Resolution. Symmetry
**2021**, 13, 1218. [Google Scholar] [CrossRef]

**Figure 13.**Particle size distribution after the flocculation process (result of the population balance model). Original images.

Parameter | Size, m |
---|---|

Height, H | 0.65 |

Diameter, D | 0.4 |

Pulp flow line diameter, dp | 0.03 |

Flocculant flow line diameter, df | 0.015 |

Skirt diameter, dsk | 0.2 |

Shaft height, hsh | 0.8 |

Shaft diameter, dsh | 0.03 |

Material | Density (kg/m${}^{3}$) | Viscosity (kg/m${}^{-\mathbf{s}}$) | Mass-flow rate (kg/s) | Temperature (K) |
---|---|---|---|---|

Liquid | ||||

Pulp feed | 1044 | 0.0012 | 1.5 | 360 |

Flocculant feed | 1240 | 0.0021 | 3.29 | 330 |

Solid particles | ||||

Material | Density (kg/m${}^{3}$) | Min particle size (m) | Max particle size (m) | Temperature (K) |

Red mud | 3200 | 23E-07—32E-6 | 45E-6—65E-5 | 360 |

Particles Diameter (m) | |||||
---|---|---|---|---|---|

group | 1 | 2 | 3 | 4 | 5 |

min | 23E-07 | 36E-07 | 5E-06 | 19E-06 | 32E-06 |

max | 45E-06 | 73E-06 | 10E-05 | 37E-05 | 65E-05 |

mean | 23E-06 | 36E-06 | 5E-05 | 19E-05 | 32E-05 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Fedorova, E.; Pupysheva, E.; Morgunov, V.
Modelling of Red-Mud Particle-Solid Distribution in the Feeder Cup of a Thickener Using the Combined CFD-DPM Approach. *Symmetry* **2022**, *14*, 2314.
https://doi.org/10.3390/sym14112314

**AMA Style**

Fedorova E, Pupysheva E, Morgunov V.
Modelling of Red-Mud Particle-Solid Distribution in the Feeder Cup of a Thickener Using the Combined CFD-DPM Approach. *Symmetry*. 2022; 14(11):2314.
https://doi.org/10.3390/sym14112314

**Chicago/Turabian Style**

Fedorova, Elmira, Elena Pupysheva, and Vladimir Morgunov.
2022. "Modelling of Red-Mud Particle-Solid Distribution in the Feeder Cup of a Thickener Using the Combined CFD-DPM Approach" *Symmetry* 14, no. 11: 2314.
https://doi.org/10.3390/sym14112314