# Scale-Up of Decanter Centrifuges for the Particle Separation and Mechanical Dewatering in the Minerals Processing Industry by Means of a Numerical Process Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analytical Scale-Up Approaches

#### 2.1. $\Sigma $-Theory

#### 2.2. G-Volume Approach

#### 2.3. Leung Approach

## 3. Numerical Model and Material Characterisation

## 4. Experimental Setup

## 5. Results and Discussion

^{−1}for 1500 $\mathrm{rpm}$, 2000 $\mathrm{rpm}$, and 6000 $\mathrm{rpm}$. However, the absolute deviation of these points is less than 5 $\mathrm{wt}.\%$. This is still within the experimental measurement tolerance. Furthermore, it should be underlined that all three centrifuges, representing different scales, can be simulated with appropriate accuracy only on the basis of the material characterisation described previously.

^{−1}. The corresponding $\Sigma $-values are calculated from the geometry of the machine and the selected centrifugal acceleration according to Equation (1). This allows the scaling criterion (ratio of throughput to $\Sigma $-value, see Equation (5)) to be obtained for each experimentally measured parameter combination. The volumetric flow rate in this example is set to 3000 Lh

^{−1}for the industrial-scale decanter centrifuge. By considering the scaling criterion, the corresponding $\Sigma $-values of the industrial-scale decanter centrifuge can be calculated. It follows from these corresponding $\Sigma $-values that, on the one hand, the optimal geometry (characteristic radius and length) or, on the other hand, the optimal centrifugal acceleration and thus rotational speed can be obtained. In this case, the geometry of the industrial-scale machine is defined. Therefore, the resulting rotational speeds required for the industrial-scale apparatus are calculated. The result of the $\Sigma $-theory does not coincide with the experimental results of the industrial-scale decanter centrifuge. $\Sigma $ theory leads to higher rotational speeds than observed in the experiment, which normally means higher energy consumption. The simulation method shows very good agreement with the experimental results, as already discussed previously in this section, and provides sufficient results for scale-up. As a consequence, $\Sigma $ theory would need an empirical correction parameter to predict the correct machine behaviour in this case.

^{−1}is selected. Figure 11 illustrates the solids mass fraction of the suspension along the helical screw path of the centrifuge. The relative length of the decanter ${L}_{\mathrm{rel}}$ centrifuge describes the relative position in the cylindrical part of the decanter centrifuge. The feed enters the apparatus at the transition point between the conical and cylindrical parts, which corresponds to ${L}_{\mathrm{rel}}=0$. The centrate is drawn-off at ${L}_{\mathrm{rel}}=1$.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CFD | Computational Fluid Dynamics |

DEM | Discrete Element Method |

## References

- Stahl, W.H. Fest-Flüssig-Trennung. 2, Industrie-Zentrifugen. Maschinen-& Verfahrenstechnik; DrM Press: Maennedorf, Switzerland, 2004. [Google Scholar]
- Wakeman, R.J.; Tarleton, S. Solid/liquid Separation: Scale-Up of Industrial Equipment, 1st ed.; Elsevier: Oxford, UK, 2005; OCLC: 254305213. [Google Scholar]
- Ambler, C.M. The theory of scaling up laboratory data for the sedimentation type centrifuge. J. Biochem. Microbiol. Technol. Eng.
**1959**, 1, 185–205. [Google Scholar] [CrossRef] - Ambler, C. The evaluation of centrifuge performance. Chem. Eng. Prog.
**1952**, 48, 150–158. [Google Scholar] - Ambler, C. Theory of centrifugation. Ind. Eng. Chem.
**1961**, 53, 430–433. [Google Scholar] [CrossRef] - Leung, W.W.F. Industrial Centrifugation Technology; McGraw-Hill: New York, NY, USA, 1998. [Google Scholar]
- Zhu, M.; Hu, D.; Xu, Y.; Zhao, S. Design and computational fluid dynamics analysis of a three-phase decanter centrifuge for oil-water-solid separation. Chem. Eng. Technol.
**2020**, 43, 1005–1015. [Google Scholar] [CrossRef] - Romaní Fernández, X.; Nirschl, H. Simulation of particles and sediment behaviour in centrifugal field by coupling CFD and DEM. Chem. Eng. Sci.
**2013**, 94, 7–19. [Google Scholar] [CrossRef] - Hammerich, S.; Gleiss, M.; Stickland, A.D.; Nirschl, H. A computationally-efficient method for modelling the transient consolidation behavior of saturated compressive particulate networks. Sep. Purif. Technol.
**2019**, 220, 222–230. [Google Scholar] [CrossRef] - Stiborsky, M. Numerische Simulation der Entfeuchtung Körniger Feststoffe in Dekantierzentrifugen; Berichte aus der Verfahrenstechnik, Shaker: Aachen, Germany, 2004; OCLC: 76643773. [Google Scholar]
- Stickland, A.D. Solid-Liquid Separation in the Water and Wastewater Industries. Ph.D. Thesis, University of Melbourne, Melbourne, Australia, 2005. [Google Scholar]
- Gleiss, M.; Hammerich, S.; Kespe, M.; Nirschl, H. Development of a dynamic process model for the mechanical fluid separation in decanter centrifuges. Chem. Eng. Technol.
**2018**, 41, 19–26. [Google Scholar] [CrossRef] [Green Version] - Menesklou, P.; Nirschl, H.; Gleiss, M. Dewatering of finely dispersed calcium carbonate-water slurries in decanter centrifuges: About modelling of a dynamic simulation tool. Sep. Purif. Technol.
**2020**, 251, 117287. [Google Scholar] [CrossRef] - Records, A.; Sutherland, K. Decanter Centrifuge Handbook; Elsevier: Oxford, UK, 2001. [Google Scholar] [CrossRef]
- Loll, U.; Thomé-Kozmiensky, K.J.; Recycling-Congress, I. (Eds.) Recycling von Klärschlamm. 3: Klärschlammaufbereitung und-Behandlung; Technik, Wirtschaft, Umweltschutz; EF-Verlag für Energie- und Umwelttechnik GmbH: Berlin, Germany, 1992; OCLC: 75352531. [Google Scholar]
- Stokes, G.G. Mathematical and Physical Papers; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar] [CrossRef]
- Buscall, R.; Goodwin, J.; Ottewill, R.; Tadros, T. The settling of particles through Newtonian and non-Newtonian media. J. Colloid Interface Sci.
**1982**, 85, 78–86. [Google Scholar] [CrossRef] - Ekdawi, N.; Hunter, R.J. Sedimentation of disperse and coagulated suspensions at high particle concentrations. Colloids Surf.
**1985**, 15, 147–159. [Google Scholar] [CrossRef] - Richardson, J.F.; Zaki, W.N. The sedimentation of a suspension of uniform spheres under conditions of viscous flow. Chem. Eng. Sci.
**1954**, 3, 65–73. [Google Scholar] [CrossRef] - Leung, W.W.F. Inferring in-situ floc size, predicting solids recovery, and scaling-up using the Leung number in separating flocculated suspension in decanter centrifuges. Sep. Purif. Technol.
**2016**, 171, 69–79. [Google Scholar] [CrossRef] - Lerche, D. Dispersion stability and particle characterization by sedimentation kinetics in a centrifugal field. J. Dispers. Sci. Technol.
**2002**, 23, 699–709. [Google Scholar] [CrossRef] - Michaels, A.S.; Bolger, J.C. Settling Rates and Sediment Volumes of Flocculated Kaolin Suspensions. Ind. Eng. Chem. Fundam.
**1962**, 1, 24–33. [Google Scholar] [CrossRef] - Green, M.D.; Eberl, M.; Landman, K.A. Compressive yield stress of flocculated suspensions: Determination via experiment. AIChE J.
**1996**, 42, 2308–2318. [Google Scholar] [CrossRef] - Erk, A. Rheologische Eigenschaften Feindisperser Suspensionen in Filtern und Zentrifugen. Ph.D. Thesis, Universität Karlsruhe (TH), Karlsruhe, Germany, 2006. [Google Scholar]
- Channell, G.M.; Zukoski, C.F. Shear and compressive rheology of aggregated alumina suspensions. AIChE J.
**1997**, 43, 1700–1708. [Google Scholar] [CrossRef] - Hammerich, S.; Stickland, A.D.; Radel, B.; Gleiss, M.; Nirschl, H. Modified shear cell for characterization of the rheological behavior of particulate networks under compression. Particuology
**2020**, 51, 1–9. [Google Scholar] [CrossRef] - Alles, C.; Anlauf, H. Filtration mit kompressiblen Kuchen: Effiziente Konzeptefür eine anspruchsvolle Trennaufgabe. Chem. Ing. Tech.
**2003**, 75, 1221–1230. [Google Scholar] [CrossRef] [Green Version] - Stahl, W.; Langeloh, T. Improvement of clarification in decanting centrifuges. Chem. Ing. Tech.
**1983**, 55, 324–325. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**Overview of the required input and calculated output parameters with focus on material functions.

**Figure 3.**Hindered settling function as a function of the solids volume fraction for the two used calcium carbonate products.

**Figure 4.**Sediment consolidation function as a function of normal stress for the two used calcium carbonate products.

**Figure 6.**Solids mass fraction of the cake for three decanter centrifuge scales, volumetric flow rates, and rotational speeds: Comparison of simulation and experiment for CC1.

**Figure 7.**Solids mass fraction of the centrate for three decanter centrifuge scales, volumetric flow rates, and rotational speeds: Comparison of simulation and experiment for CC1.

**Figure 8.**Solids mass fraction of the cake for three decanter centrifuge scales, volumetric flow rates, and rotational speeds: Comparison of simulation and experiment for CC2.

**Figure 9.**Solids mass fraction of the centrate for three decanter centrifuge scales, volumetric flow rates, and rotational speeds: Comparison of simulation and experiment for CC2.

**Figure 10.**Comparison of scale-up via $\Sigma $-theory, and simulation from pilot-scale to industrial-scale for CC1.

**Figure 11.**Solids mass fraction along unrolled helix for industrial-scale decanter centrifuge with CC1 for different rotational speeds at a feed rate of 3000 Lh

^{−1}.

**Figure 12.**Particle size distribution along unrolled helix for industrial-scale decanter centrifuge with CC1 at a rotational speed of 2950 $\mathrm{rpm}$ and a feed rate of 3000 Lh

^{−1}.

**Table 1.**Overview of recommended Leung numbers and applications [6].

Le in - | Size-Cut in m | Centrifuge Type |
---|---|---|

0.5 to 5 | 1 to 10 | High-speed small throughput |

5 to 20 | 10 to 45 | Medium-speed moderate rate |

Above 20 | Above 45 | Low-speed high throughput |

Parameter | Dimension | Lab-Scale | Pilot-Scale | Industrial-Scale |
---|---|---|---|---|

Length cylinder | $\mathrm{m}$ | $0.155$ | $0.243$ | $0.746$ |

Length cone | $\mathrm{m}$ | $0.16$ | $0.174$ | $0.604$ |

Drum radius | $\mathrm{m}$ | $0.04$ | $0.075$ | $0.229$ |

Cone angle | ${}^{\circ}$ | 7 | 10 | 10 |

Pool depth | $\mathrm{m}$$\mathrm{m}$ | 12 | 14 | 64 |

Solids mass fraction inlet CC1 | $\mathrm{wt}.\%$ | $9.4$ | 35 | 35 |

Solids mass fraction inlet CC2 | $\mathrm{wt}.\%$ | $3.4$ | $20.5$ | $18.4$ |

Volumetric flow rate inlet CC1 | Lh^{−1} | 88 | 300 | 2000–3000 |

Volumetric flow rate inlet CC2 | Lh^{−1} | 33, 54 | 300 | 1000–2000 |

Parameter | Dimension | CC1 | CC2 |
---|---|---|---|

${x}_{50,3}$ | μm | $1.913$ | $1.542$ |

${a}_{1}$ | $2.243$ | $2.378$ |

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

© 2021 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Menesklou, P.; Sinn, T.; Nirschl, H.; Gleiss, M.
Scale-Up of Decanter Centrifuges for the Particle Separation and Mechanical Dewatering in the Minerals Processing Industry by Means of a Numerical Process Model. *Minerals* **2021**, *11*, 229.
https://doi.org/10.3390/min11020229

**AMA Style**

Menesklou P, Sinn T, Nirschl H, Gleiss M.
Scale-Up of Decanter Centrifuges for the Particle Separation and Mechanical Dewatering in the Minerals Processing Industry by Means of a Numerical Process Model. *Minerals*. 2021; 11(2):229.
https://doi.org/10.3390/min11020229

**Chicago/Turabian Style**

Menesklou, Philipp, Tabea Sinn, Hermann Nirschl, and Marco Gleiss.
2021. "Scale-Up of Decanter Centrifuges for the Particle Separation and Mechanical Dewatering in the Minerals Processing Industry by Means of a Numerical Process Model" *Minerals* 11, no. 2: 229.
https://doi.org/10.3390/min11020229