# Analysis of Energy Sustainability in Ore Slurry Pumping Transport Systems

^{1}

^{2}

^{*}

## Abstract

**:**

_{50}). The results show that all variables are statistically significant relative to the indicator I, with L having the greatest amplitude of variation in the response, increasing the energy indicator by approximately 60%. Likewise, the decrease of the D

_{50}from 300 µm to 100 µm produces an average decrease of I of 24%. Moreover, the interaction among the factors indicates that two pairs of factors are correlated, namely D

_{50}with L and D with L. Finally, a predictive model obtained a fit that satisfactorily relates with the numerical data, allowing, in a preliminary way, to identify the minimum power requirement in iron ore slurry pipeline systems.

## 1. Introduction

_{50}), while the other two are used for the topological characterization of the pumping system (the pipeline length L and diameter D). In the aforementioned studies, the energy indicator was defined as the energy needed to move 1 m

^{3}of slurry according to specific operating conditions.

_{50}, and Cv are at their lower levels, and when D is at its higher level. Regarding second-order interactions, the most significant effect can be observed between L and D. Moreover, the surface response model obtained for the three layouts fit the numerical data satisfactorily, with differences of less than 10%. Finally, the optimization of I showed that the minimum value was obtained for Cv = 5%, D

_{50}= 100 µm, L = 500 m and D varying between 227 mm and 235 mm as a function of the pumping system.

## 2. Materials and Methods

#### 2.1. Description of the Slurry Transportation Systems

#### 2.2. Characteristics of the Piping Systems

#### 2.3. Description and Rheology of the Slurry

#### Slurry Rheology

_{s}(Pa.s) is computed by Equation (1), [22],

_{l}is the dynamic viscosity of carrier fluid (water) and C

_{v}(decimal) is the volumetric concentration of solid in the slurry.

_{s}(kg/m

^{3}), can be determined by Equation (2), [21,22],

_{p}is the density of the dry solid (iron ore), ρ

_{l}is the density of the carrier fluid (water), and C

_{w}is the concentration of solids by weight in the slurry (%). For iron ore (dry), the density is 3110 kg/m

^{3}. For water, the temperature assumed to be 24 °C; therefore, physical properties are ρ = 997.42 kg/m

^{3}and μ = 0.000908 Pa.s.

_{w}(%) and the volumetric concentration C

_{v}(%), is given by Equation (3),

_{s}and S

_{p}are the specific gravity of the slurry and dry solid, respectively.

_{m}is the hydraulic gradient for slurry flow [-], I

_{f}is the hydraulic gradient for carrier flow [-], C

_{v}is the volumetric concentration of solid in slurry [decimal], S

_{p}is the specific gravity of solid [-], V

_{s}is the mean velocity of the slurry in the pipeline [m/s], V

_{50}is the value of V

_{s}when one half of solid is suspended in a carrier flow [m/s] and M is an empirical coefficient [-].

_{50}(Equation (5)) and M (Equation (6)) depend on D

_{50}.

_{85}is the 85% passing size of solid (μm) and according to Wilson-GIW model, the value of M should not exceed 1.7 nor fall below 0.25.

_{50}were considered to range between 5% and 10% and 100 µm to 300 µm, respectively.

#### 2.4. Pumps

## 3. Methodology

#### 3.1. Numerical Simulations

^{3}, expresses the specific energy consumption of the pumps, that is, how much energy is required for pumping 1 m

^{3}of slurry under specific conditions and is defined as follows:

^{3}/s), H is the head (m), ρ is the density of the slurry (kg/m

^{3}), and η is the efficiency of the pump (%).

#### 3.2. Design of Experiments

^{k}. However, a potential concern when using this type of design is the assumption of linearity of the factor’s effects, which is sometimes compensated by the knowledge of previous studies.

_{o}+ 2k + 2

^{k}. The number of central points depends heavily on the number of factors and replicas that can be performed.

_{50}, relative to the slurry’s properties. The levels, low and high, of these variables were previously defined. Moreover, to apply this CCD technique, a central value for each factor was defined as: L = 1000 m, D = 225 mm, Cv = 7.5%, and D

_{50}= 200 µm. The design selected was a CCD with axial points centered in the faces, that with four factors results in a simulation plan with 31 simulations (16 factorial points, 8 axial points, and 7 center points) recommended by the MINITAB, (see Table 1). In case of the center points, as required to obtain a response surface that can be optimized, the designs of experiments selected add center points in order to estimate the curvature in the adjusted data [28]. These 31 simulations were performed in each of the three system configurations.

## 4. Results and Discussion

_{50}, and Cv have on I for each of the slurry piping system configurations. Points in the graphs correspond to the arithmetic mean of I in each level of each factor; the average effect of each factor on the response is evidenced. As shown in Figure 4, the behaviour of the response I, due to the variation of the factors from one level to another, has the same trend regardless of the slurry piping system. Among the four variables, L has the greatest amplitude of variation between the highest and the lowest level. The minimum values of I are reached when L, Cv, and D

_{50}are at their lower levels and when D is at a higher level.

_{50}and L, as well as between D and L, for all pumping systems examined.

_{50}, L and I for the three system configurations studied. The granulometry exerts almost no influence when L is at its higher level, but its significance rises noticeably as L decreases to its lower levels.

_{50}= 100 μm (lower level), L = 500 m (lower level), and D varying between 227 mm and 235 mm as a function of the pumping system. As is well-known, this value of the diameter is not a normalized value because in the mining industry he commercial pipes has a diameter of 200 mm and 250 mm. Earlier statistical analysis established that 225 mm is the optimal value, but from a practical point-of-view, it is not possible to meet this condition. Therefore, a value of 250 mm was selected. This result is in agreement with the physical foundation of the study phenomena, as previously discussed.

## 5. Conclusions

_{50}, and Cv are at their lower levels and when D is at its higher level. Among the factors, L is the most influential factor when its value changes between its lower and higher levels. From the analysis of the main effects, the minimum values of I are reached when L, Cv, and D

_{50}are at their lower levels and when D is at its higher level. This result has a well-founded theoretical basis and can be explained from a fluid mechanics point-of-view. The interaction among variables, i.e., the second-order interactions, shows that only the relationships between L and D

_{50}and between D and L are significant for I in the three pumping systems investigated. When the effect on I is analysed regarding the interaction between L and D

_{50}, it is possible to observe that D

_{50}has different behaviour as a function of the level of L. When L is at its higher levels, the influence of D

_{50}is almost insignificant, but when L trends to lower levels, the significance of D

_{50}is appreciable.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Brazil GDP Growth Rate 2019. Available online: https://tradingeconomics.com/brazil/gdp-growth (accessed on 25 May 2019).
- Fundação Estadual do Meio Ambiente—FEAM. Available online: http://www.feam.br/ (accessed on 25 May 2019).
- Wasp, E.J. Slurry pipelines. Sci. Am.
**1983**, 249, 48–55. [Google Scholar] [CrossRef] - Jacobs, B.E. Design of Slurry Transport Systems; Elsevier Applied Science: London, UK, 1991; ISBN 978-1-85166-634-8. [Google Scholar]
- Shirakashi, M.; Yamada, S.; Kawada, Y.; Hirochi, T. Blocking of snow/water slurry flow in pipeline caused by compression-strengthening of snow column. Sustainability
**2014**, 6, 530–544. [Google Scholar] [CrossRef] - Ohlan, R.; Gopaliya, M.K.; Kaushal, D.R. Simulation of sand-water slurry flows through pipeline. Multph. Sci. Technol.
**2018**, 30, 293–318. [Google Scholar] [CrossRef] - Kumar, N.; Gopaliya, M.K.; Kaushal, D.R. Experimental investigations and CFD modeling for flow of highly concentrated iron ore slurry through horizontal pipeline. Part. Sci. Technol.
**2019**, 37, 232–250. [Google Scholar] [CrossRef] - Ihle, C.F.; Tamburrino, A.; Montserrat, S. Computational modeling for efficient long distance ore transport using pipelines. Miner. Eng.
**2014**, 63, 73–80. [Google Scholar] [CrossRef] - Ihle, C.F. The least energy and water cost condition for turbulent, homogeneous pipeline slurry transport. Int. J. Miner. Process.
**2016**, 148, 59–64. [Google Scholar] [CrossRef] - Wu, J.; Graham, L.; Wang, S.; Parthasarathy, R. Energy efficient slurry holding and transport. Miner. Eng.
**2010**, 23, 705–712. [Google Scholar] [CrossRef] - Edelin, D.; Czujko, P.-C.; Castelain, C.; Josset, C.; Fayolle, F. Experimental determination of the energy optimum for the transport of floating particles in pipes. Exp. Therm. Fluid Sci.
**2015**, 68, 634–643. [Google Scholar] [CrossRef] - De Barcelos, R.J.P.; de Araujo, E.; Vilalta, G. Influence of the iron ore properties on slurry pumping system with volumetric pumps by applying simulation and Design of experiments. In Proceedings of the Anais Do National Congress of Mechanical and Production Engineering, Novo Hamburgo, Brazil, 24–27 November 2015. [Google Scholar]
- Gava, M. Energy Analysis of Iron Ore Slurry Pumping Systems by Computational Simulation. Master’s Thesis, Federal University of São João del-Rei, São João del-Rei, Brazil, 2016. [Google Scholar]
- Tanco, M.; Viles, E.; Ilzarbe, L.; Alvarez, M.J. Implementation of Design of Experiments projects in industry. Appl. Stoch. Models Bus. Ind.
**2009**, 25, 478–505. [Google Scholar] [CrossRef] - Montgomery, D.C. Design and Analysis of Experiments, 9th ed.; Wiley: Hoboken, NJ, USA, 2017; ISBN 978-1-119-11347-8. [Google Scholar]
- Kotcioglu, I.; Cansiz, A.; Khalaji, M.N. Experimental investigation for optimization of design parameters in a rectangular duct with plate-fins heat exchanger by Taguchi method. Appl. Therm. Eng.
**2013**, 50, 604–613. [Google Scholar] [CrossRef] - Chiang, K.-T. Modeling and optimization of designing parameters for a parallel-plain fin heat sink with confined impinging jet using the response surface methodology. Appl. Therm. Eng.
**2007**, 27, 2473–2482. [Google Scholar] [CrossRef] - Larraona, G.S.; Rivas, A.; Antón, R.; Ramos, J.C.; Pastor, I.; Moshfegh, B. Computational parametric study of an impinging jet in a cross-flow configuration for electronics cooling applications. Appl. Therm. Eng.
**2013**, 52, 428–438. [Google Scholar] [CrossRef] - Bursztyn, D.; Steinberg, D.M. Comparison of designs for computer experiments. J. Stat. Plan. Inference
**2006**, 136, 1103–1119. [Google Scholar] [CrossRef] - Ferreira, M.T. Energy indicator for analysis of iron ore pumping systems via Numerical Simulation and Design of Experiments. Master’s thesis, Federal University of São João del-Rei, São João del-Rei-Minas Gerais, Brazil, 2016. [Google Scholar]
- Wilson, K.C.; Addie, G.R.; Sellgren, A.; Clif, R. Slurry Transport Using Centrifugal Pumps, 3rd ed.; Springer: New York, NY, USA, 2006; ISBN 978-0-387-23262-1. [Google Scholar]
- Chaves, A.P. Teoria e Prática do Tratamento de Minérios, 1st ed.; Signus: Rio de Janeiro, Brazil, 2009; ISBN 978-85-87803-26-9. [Google Scholar]
- Sheth, K.K.; Morrison, G.L.; Peng, W.W. Slip Factors of Centrifugal Slurry Pumps. J. Fluids Eng.
**1987**, 109, 313–318. [Google Scholar] [CrossRef] - Walker, C.I.; Robbie, P. Comparison of some laboratory wear tests and field wear in slurry pumps. Wear
**2013**, 302, 1026–1034. [Google Scholar] [CrossRef] - Kumar, S.; Gandhi, B.K.; Mohapatra, S.K. Performance characteristics of centrifugal slurry pump with multi-sized particulate bottom and fly ash mixtures. Part. Sci. Technol.
**2014**, 32, 466–476. [Google Scholar] [CrossRef] - Wills, B.A.; Finch, J.A. Wills’ Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery, 8th ed.; Butterworth-Heinemann: Montreal, QC, Canada, 2016; ISBN 978-0-08-097054-7. [Google Scholar]
- Pedrera, J.; Ortiz, J.; Vilalta, J.A. Significant variables in initial dilution process in submarine outfalls systems. Alternatives comparison. In Proceedings of the International Symposium of Outfall System, Ottawa, ON, Canada, 10–13 May 2016; pp. 324–349. [Google Scholar]
- Antony, J. Design of Experiments for Engineers and Scientists; Butterworth-Heinemann: Amsterdam, The Netherlands, 2010; ISBN 978-0-7506-4709-0. [Google Scholar]
- Box, G.E.P.; Hunter, J.S.; Hunter, W.G. Statistics for Investigators: Design, Innovation and Discovery, 2nd ed.; Reverte Editorial Sa: Barcelona, Spain, 2008; ISBN 978-84-291-5044-5. [Google Scholar]
- Hansen, E.R.; Walster, G.W. Global Optimization Using Interval Analysis, 2nd ed.; Monographs and Textbooks in Pure and Applied Mathematics; CRC Press: New York, NY, USA, 2004; ISBN 978-0-8247-4059-7. [Google Scholar]
- Myers, R.H.; Montgomery, D.C.; Anderson-Cook, C.M. Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd ed.; Wiley Series in Probability and Statistics; Wiley: Hoboken, NJ, USA, 2009; ISBN 978-0-470-17446-3. [Google Scholar]
- Murphy, T.E.; Tsui, K.-L.; Allen, J.K. A review of robust design methods for multiple responses. Res. Eng. Des.
**2005**, 15, 201–215. [Google Scholar] [CrossRef]

**Figure 3.**The scheme of a central composite design (CCD) with two variables and centered in the faces.

**Figure 5.**Main response surfaces in terms of the interacting variables for the Indicator I for the (

**a**) one-pump 1P, (

**b**) two-pump (PS), and (

**c**) two-pump uniformly-distributed (UD) configurations.

**Figure 7.**Comparison among simulations and response surface model for the Indicator I for the (

**a**) one-pump (1P), (

**b**) two-pump (PS), and (

**c**) two-pump uniformly-distributed (UD) configurations.

**Table 1.**Details of the parametric study: values of the parameters considered and their combinations in each simulation (experiment). D: diameter; L: length; Cv: volumetric concentration; D

_{50}: granulometry.

Parameter (Factor) | Values (Levels) | Exp. | Cv | D_{50} | D | L | Exp. | Cv | D_{50} | D | L | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Low (−1) | Middle (0) | High (+1) | |||||||||||

Cv | 5 | 7.5 | 10 | 1 | 0 | 0 | 0 | 0 | 17 | −1 | 1 | 1 | 1 |

D_{50} | 100 | 200 | 300 | 2 | 0 | 0 | −1 | 0 | 18 | 0 | 0 | 0 | 0 |

D | 200 | 225 | 250 | 3 | 1 | 1 | −1 | 1 | 19 | −1 | −1 | 1 | 1 |

L | 500 | 1250 | 2000 | 4 | 1 | −1 | −1 | 1 | 20 | −1 | −1 | −1 | −1 |

5 | 0 | 0 | 0 | 0 | 21 | 1 | 1 | 1 | −1 | ||||

6 | −1 | −1 | −1 | 1 | 22 | 1 | −1 | −1 | −1 | ||||

7 | 1 | −1 | 1 | −1 | 23 | −1 | 0 | 0 | 0 | ||||

8 | −1 | 1 | −1 | 1 | 24 | 0 | 0 | 0 | 0 | ||||

9 | 1 | 1 | −1 | −1 | 25 | 0 | 0 | 0 | −1 | ||||

10 | 1 | 1 | 1 | 1 | 26 | 0 | 1 | 0 | 0 | ||||

11 | −1 | 1 | −1 | −1 | 27 | 1 | 0 | 0 | 0 | ||||

12 | 0 | −1 | 0 | 0 | 28 | −1 | 1 | 1 | −1 | ||||

13 | 0 | 0 | 1 | 0 | 29 | 0 | 0 | 0 | 0 | ||||

14 | 0 | 0 | 0 | 1 | 30 | 1 | −1 | 1 | 1 | ||||

15 | 0 | 0 | 0 | 0 | 31 | −1 | −1 | 1 | −1 | ||||

16 | 0 | 0 | 0 | 0 |

**Table 2.**Optimal combination of the independent variables and verification of the results obtained by comparison of the simulation versus the predicted models.

Case | Cv (%) | D50 (µm) | D (mm) | L (m) | Desirability Function | Energy Indicator | |
---|---|---|---|---|---|---|---|

One pump (1P) | Simulation | 5 | 100 | 235 | 500 | 1.00 | 0.261 |

Model (Equation (9)) | 0.263 | ||||||

Two pumps (PS) | Simulation | 5 | 100 | 227 | 500 | 0.987 | 0.248 |

Model (Equation (10)) | 0.233 | ||||||

Two pumps (UD) | Simulation | 5 | 100 | 229 | 500 | 0.965 | 0.256 |

Model (Equation (11)) | 0.232 |

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## Share and Cite

**MDPI and ACS Style**

Masip Macía, Y.; Pedrera, J.; Castro, M.T.; Vilalta, G.
Analysis of Energy Sustainability in Ore Slurry Pumping Transport Systems. *Sustainability* **2019**, *11*, 3191.
https://doi.org/10.3390/su11113191

**AMA Style**

Masip Macía Y, Pedrera J, Castro MT, Vilalta G.
Analysis of Energy Sustainability in Ore Slurry Pumping Transport Systems. *Sustainability*. 2019; 11(11):3191.
https://doi.org/10.3390/su11113191

**Chicago/Turabian Style**

Masip Macía, Yunesky, Jacqueline Pedrera, Max Túlio Castro, and Guillermo Vilalta.
2019. "Analysis of Energy Sustainability in Ore Slurry Pumping Transport Systems" *Sustainability* 11, no. 11: 3191.
https://doi.org/10.3390/su11113191