# Evaluation of Rheology Measurements Techniques for Pressure Loss in Mine Paste Backfill Transportation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Paste Backfill Preparations

_{3}content of tailing from Mine-B is higher. Also, there is no CO

_{2}and ZnO particle in Mine-A tailings. The particle size distribution (PSD) of tailings is shown in Figure 1 and Table 2. Mine-A tailings have a wider range of particle sizes than Mine-B. Mine B tailings are very fine, with 80% of the material passing 20 µm while the cumulative passing of Mine-A is only 45%. Particle sizes have a significant impact on the pressure drop across a pipe and are dependent on solid fraction and flow rate. Particles of larger size decrease the void space in the backfill, and, therefore, porosity. Coarser tailings have larger inter-particle spaces in comparison to finer tailings [40,41]. The mine-B curve has a steeper grade than Mine-A, indicating a narrower size range.

## 3. Theory and Methods

#### 3.1. Rotational Rheometer

#### 3.2. Cup and Bob Viscometer

^{−1}. The angular velocity varies from 0 to 25 rad/s with maximum torque of 0.025 Nm. Two sensors, MV DIN and SV II, were used in this test with two different types of containers. The first is a standard cup attachment and the second a cup with a height and diameter that is at least twice that of the bob [12]. The second cup is referred to as an infinite cup and aims to minimize the wall slip effects. Minor modifications were made in the shear rate calculation to account for the infinite cup. The slope of a plot between the natural log of angular velocity and shear stress at the bob was determined. This slope was used to obtain a modified shear rate, as shown in Equation (3).

#### 3.3. Vane Rheometer

#### 3.4. Slump Test

#### 3.5. Flow Loop Test

## 4. Results and Discussion

#### 4.1. Yield Stress

#### 4.2. Plastic Viscosity

#### 4.3. Statistical Analysis

## 5. Conclusions

- i.
- Slump tests overpredicted the Bingham yield stress for the finer Mine-B tailings but showed good agreement with vane for the coarser Mine-A tailings. The predictions made using the smallest 3-in mold had the least errors as statistical analyses while testing coarse paste backfill. MVDIN bob in an infinite cup showed the least errors while testing the finer Mine-B tailings.
- ii.
- FL100 vane tests showed moderate agreement with the loop test data for both sets of mine tailings. The effects of wall-slip reduced by the vane compared to smooth cylinders using MVDIN cup and bob tests were not profound in the tests. Good agreement was seen between FL100 vane and MVDIN cup and bob tests.
- iii.
- The infinite cup did not show a discernible superiority over the standard cup. However, the smaller SVII bob in the infinite cup has a better agreement for both Bingham yield stress and Bingham plastic viscosity over the MVDIN bob in the infinite cup.
- iv.
- The MVDIN standard cup had the least errors while predicting Bingham plastic viscosity for finer Mine-B tailings, as well as coarser Mine-A tailings.
- v.
- Higher particle size gives rise to a higher Bingham yield stress and viscosity.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Benzaazoua, M.; Fall, M.; Belem, T. A contribution to understanding the hardening process of cemented pastefill. Miner. Eng.
**2004**, 17, 141–152. [Google Scholar] [CrossRef] - Gharib, N.; Bharathan, B.; Amiri, L.; McGuinness, M.; Hassani, F.P.; Sasmito, A.P. Flow characteristics and wear prediction of Herschel-Bulkley non-Newtonian paste backfill in pipe elbows. Can. J. Chem. Eng.
**2017**, 95, 1181–1191. [Google Scholar] [CrossRef] - Ouattara, D.; Mbonimpa, M.; Belem, T. Rheological properties of thickened tailings and cemented paste tailings and the effects of mixture characteristics on shear behavior. In Proceedings of the 63rd Canadian Geotechnical Conference & 6th Canadian Permafrost Conference, Calgary, AB, Canada; 2010; pp. 1178–1185. [Google Scholar]
- Belem, T.; Benzaazoua, M. An overview on the use of paste backfill technology as a ground support method in cut-and-fill mines. In Proceedings of the Proceedings of the 5th International Symposium on Ground support in Mining and Underground Construction, Perth, WA, Australia, 28–30 September 2004; pp. 637–650. [CrossRef]
- Bharathan, B.; McGuinness, M.; Kuhar, S.; Kermani, M.; Sasmito, A.P.; Hassani, F.P. Friction factor model comparison for high concentration non-Newtonian mine paste backfill. Powder Technol.
**2019**, 344, 443–453. [Google Scholar] [CrossRef] - Nguyen, Q.D.; Boger, D.V. Measuring the Flow Properties of Yield Stress Fluids. Annu. Rev. Fluid Mech.
**1992**, 24, 47–88. [Google Scholar] [CrossRef] - Barnes, H.A. A Handbook of Elementary Rheology, a Handbook of Elementary Rheology; University of Wales: Aberystwyth, UK, 2000. [Google Scholar] [CrossRef]
- Kao, S.V.; Neilson, L.E.; Hill, C.T. Heology of concentrated suspensions of spheres. II. Suspensions agglomerated by an immiscible second liquid. J. Colloid Interface Sci.
**1975**, 55, 367–373. [Google Scholar] - Savage, S.B.; Mckeown, S. Shear stresses developed during rapid shear of concentrated suspensions of large spherical particles between concentric cylinders. J. Fluid Mech.
**1983**, 127, 453–472. [Google Scholar] [CrossRef] - Green, H. High-Speed Rotational Viscometer of Wide Range. Confirmation of theReiner Equation of Flow. Ind. Eng. Chem. Anal. Ed.
**1942**, 14, 576–585. [Google Scholar] [CrossRef] - Van Wazer, J.R.; Lyons, J.W.; Kim, K.Y.; Colwell, R.E. A Laboratory Handbook of Rheology; Interscience Publishers: Hoboken, NJ, USA, 1963. [Google Scholar]
- Krieger, I.M.; Maron, S.H. Direct Determination of the Flow Curves of Non-Newtonian Fluids. J. Appl. Phys.
**1952**, 23, 147. [Google Scholar] [CrossRef] - Jacobsen, R.T. The determination of the flow curve of a plastic medium in a wide gap rotational viscometer. J. Colloid Interface Sci.
**1974**, 48, 437–441. [Google Scholar] [CrossRef] - Zengeni, B.; Malloch, R.; Sittert, F.V. A comparison of 150 nb pipe loop data with rotational viscometer test methods. In Proceedings of the 4th South African Conference on Rheology, Cape Town, South Africa, 3–5 September 2012; pp. 1–4. [Google Scholar]
- Skempton, A.W. Vane Tests in the Alluvial Plain of the River Forth Near Grangemouth. Géotechnique
**1948**, 1, 111–124. [Google Scholar] [CrossRef] - Cadling, L.; Odenstad, S. The Vane Borer: An Apparatus for Determining the Shear Strength of Clay Soils Directly in the Ground. In Proceedings of the Royal Swedish Geotechnical Institute; Royal Swedish Geotechnical Institute: Stockholm, Sweden, 1950. [Google Scholar]
- Nguyen, Q.D.; Boger, D.V. Characterization of yield stress fluids with concentric cylinder viscometers. Rheol. Acta
**1987**, 26, 508–515. [Google Scholar] [CrossRef] - Saak, A.W.; Jennings, H.M.; Shah, S.P. The influence of wall slip on yield stress and viscoelastic measurements of cement paste. Cem. Concr. Res.
**2001**, 31, 205–212. [Google Scholar] [CrossRef] - Yan, J.; James, A.E. The yield surface of viscoelastic and plastic fluids in a vane viscometer. J. Nonnewton. Fluid Mech.
**1997**, 70, 237–253. [Google Scholar] [CrossRef] - Liddel, P.V.; Boger, D.V. Yield stress measurements with the vane. J. Nonnewton. Fluid Mech.
**1996**, 63, 235–261. [Google Scholar] [CrossRef] - Mizani, S.; Simms, P. Method-dependent variation of yield stress in a thickened gold tailings explained using a structure based viscosity model. Miner. Eng.
**2016**, 98, 40–48. [Google Scholar] [CrossRef] - Chandler, J.L. The stacking and solar drying process for disposai of bauxite tailings in Jamaica. In Proceedings of the International Conference of Bauxite Tailings, Jamaica Bauxite Institute, Kingston, Jamaica, 26–31 October 1986. [Google Scholar]
- Murata, J. Flow and deformation of fresh concrete. Matériaux Constr.
**1984**, 17, 117–129. [Google Scholar] [CrossRef] - Schowalter, W.R.; Christensen, G. Toward a rationalization of the slump test for fresh concrete: Comparisons of calculations and experiments. J. Rheol.
**1998**, 42, 865. [Google Scholar] [CrossRef] - Pashias, N.; Boger, D.V.; Summers, J.; Glenister, D.J. A fifty cent rheometer for yield stress measurement. J. Rheol.
**1996**, 40, 1179. [Google Scholar] [CrossRef] - Chao, S.; Xue, G.; Yilmaz, E.; Yin, Z. Assessment of rheological and sedimentation characteristics of fresh cemented tailings backfill slurry. Int. J. Min. Reclam. Environ.
**2020**, 35, 319–335. [Google Scholar] - Niu, Y.; Cheng, H.; Wu, S.; Sun, J.; Wang, J. Rheological properties of cemented paste backfill and the construction of a predictive model. Case Stud. Constr. Mater.
**2022**, 16, e01140. [Google Scholar] - Wu, A.; Ruan, Z.; Wang, J. Rheological behavior of paste in metal mines. Int. J. Miner. Metall. Mater.
**2022**, 29, 717–726. [Google Scholar] [CrossRef] - Dikonda, R.K.; Mbonipa, M.; Belem, T. Specific mixing energy of cemented paste backfill, Part II: Influence on the rheological and mechanical properties and practical applications. Minerals
**2021**, 11, 1159. [Google Scholar] [CrossRef] - Silva, M.; Hansson, M.; Silva, M.C. Rheological yield stress measurement of paste fill: New technical approaches. In Minefill 2020–2021; Hassani, F., Palarski, J., Sokola-Szewiola, V., Strozik, G., Eds.; Taylor & Francis Group: London, UK, 2021; pp. 169–182. [Google Scholar]
- Roussel, N.; Coussot, P. “Fifty-cent rheometer” for yield stress measurements: From slump to spreading flow. J. Rheol.
**2005**, 49, 705–718. [Google Scholar] [CrossRef] - Clayton, S.; Grice, T.G.; Boger, D.V. Analysis of the slump test for on-site yield stress measurement of mineral suspensions. Int. J. Miner. Process.
**2003**, 70, 3–21. [Google Scholar] [CrossRef] - Bouvet, A.; Ghorbel, E.; Bennacer, R. The mini-conical slump flow test: Analysis and numerical study. Cem. Concr. Res.
**2010**, 40, 1517–1523. [Google Scholar] [CrossRef] - Gao, J.; Fourie, A. Spread is better: An investigation of the mini-slump test. Miner. Eng.
**2015**, 71, 120–132. [Google Scholar] [CrossRef] - Gao, J.; Fourie, A. Using the flume test for yield stress measurement of thickened tailings. Miner. Eng.
**2015**, 81, 116–127. [Google Scholar] [CrossRef] - Wang, X.; Li, J.; Xiao, Z.; Xiao, W. Rheological properties of tailing paste slurry. J. Cent. South Univ. Technol.
**2004**, 11, 75–79. [Google Scholar] [CrossRef] - Senapati, P.K.; Mishra, B.K. Design considerations for hydraulic backfilling with coal combustion products (CCPs) at high solids concentrations. Powder Technol.
**2012**, 229, 119–125. [Google Scholar] [CrossRef] - Wu, D.; Yang, B.; Liu, Y. Transportability and pressure drop of fresh cemented coal gangue-fly ash backfill (CGFB) slurry in pipe loop. Powder Technol.
**2015**, 284, 218–224. [Google Scholar] [CrossRef] - Wu, D.; Baogui, Y.; Yucheng, L. Pressure drop in loop pipe flow of fresh cemented coal gangue-fly ash slurry: Experiment and simulation. Adv. Powder Technol.
**2015**, 26, 920–927. [Google Scholar] [CrossRef] - Fall, M.; Benzaazoua, M.; Ouellet, S. Experimental characterization of the influence of tailings fineness and density on the quality of cemented paste backfill. Miner. Eng.
**2005**, 18, 41–44. [Google Scholar] [CrossRef] - Yin, S.; Wu, A.; Hu, K.; Wang, Y.; Zhang, Y. The effect of solid components on the rheological and mechanical properties of cemented paste backfill. Miner. Eng.
**2012**, 35, 61–66. [Google Scholar] [CrossRef] - Malkin, A.Y.; Isayev, A.I. Rheometry experimental methods. In Rheology Concepts, Methods, and Applications, 2nd ed.; Malkin, A.Y., Isayev, A.I., Eds.; Elsevier: Oxford, UK, 2012; pp. 255–364. [Google Scholar] [CrossRef]
- SI Analytics GmbH. Visco Handbook—Theory and Application of Viscometry with Glass Capillary Viscometers; SI Analytics GmbH: Mainz, Germany, 2015. [Google Scholar]
- Steffe, J.F. Rheological Methods in Food Process Engineering; Freeman Press: East Lansing, MI, USA, 1996. [Google Scholar]
- Nguyen, Q.D.; Boger, D.V. Direct Yield Stress Measurement with the Vane Method. J. Rheol.
**1985**, 29, 335–347. [Google Scholar] [CrossRef] - Nguyen, Q.D.; Boger, D.V. Yield Stress Measurement for Concentrated Suspensions. J. Rheol.
**1983**, 27, 321. [Google Scholar] [CrossRef] - Ovarlez, G.; Mahaut, F.; Bertrand, F.; Chateau, X. Flows and heterogeneities with a vane tool: Magnetic resonance imaging measurements. J. Rheol.
**2010**, 55, 197. [Google Scholar] [CrossRef] [Green Version] - Steffe, J.F. Yield stress: Phenomena and measurement. In Advances in Food Engineering; Singh, R.P., Wirakartakusumah, A., Eds.; CRC Press: Baton Rouge, FL, USA, 1992; pp. 363–376. [Google Scholar]
- Coussot, P.; Piau, J. A large-scale field coaxial cylinder rheometer for the study of the rheology of natural coarse suspensions. J. Rheol.
**1995**, 39, 105–124. [Google Scholar] [CrossRef] - Krieger, I.M.; Dougherty, T.J. A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres. Trans. Soc. Rheol.
**1959**, 3, 137–152. [Google Scholar] [CrossRef] - Tenbergen, R.A. Paste dewatering techniques and paste plant circuit design. In Tailings and Mine Waste; A.A. Balkema Publishers: Fort Collins, CO, USA, 2000. [Google Scholar]
- Li, M.; Moerman, A. Perspectives on the scientific and engineering principles underlying flow of mineral pastes. In Proceedings of the 34th Annual Meeting of CMP, Ottawa, ON, Canada, 22–24 January 2002; pp. 573–595. [Google Scholar]
- Bentz, D.P.; Ferraris, C.F.; Galler, M.A.; Hansen, A.S.; Guynn, J.M. Influence of particle size distributions on yield stress and viscosity of cement–fly ash pastes. Cem. Concr. Res.
**2012**, 42, 404–409. [Google Scholar] [CrossRef] - Landriault, D. Paste backfill mix design for Canadian underground hard rock mining. In Proceedings of the 97th Annual General Meeting of CIM. Rock Mechanics and Strata Control Session, Halifax, NS, Canada, 14–18 May 1995; pp. 229–238. [Google Scholar]

**Figure 2.**Schematic representation of different rheometer geometries; (

**a**) cone and plate, (

**b**) concentric—cup and bob, (

**c**) parallel plate.

**Figure 5.**Schematic arrangement showing the initial and final stress distribution of the cylindrical mold slump test [25].

**Figure 6.**The flow loop test experimental apparatus (all dimensions are in mm). PD—positive displacement pump; HP—hopper; P1, P2, P3, and P4—pressure gauges; HE—heat exchanger; FM—flow meter.

**Figure 7.**Bingham yield stresses for (

**a**) Mine-A at 15 °C; (

**b**) Mine-A at 25 °C; (

**c**) Mine-A at 35 °C; (

**d**) Mine-B at 15 °C; (

**e**) Mine-B at 25 °C; and (

**f**) Mine-B at 35 °C.

**Figure 8.**Bingham plastic viscosity for (

**a**) Mine-A at 15 °C; (

**b**) Mine-A at 25 °C; (

**c**) Mine-A at 35 °C; (

**d**) Mine-B at 15 °C; (

**e**) Mine-B at 25 °C; and (

**f**) Mine-B at 35 °C.

Oxide | Mine-A | Mine-B | Oxide | Mine-A | Mine-B |
---|---|---|---|---|---|

CO_{2} | - | 0.88% | K_{2}O | 3.46% | 2.70% |

Na_{2}O | 3.32% | 1.50% | CaO | 5.67% | 6.52% |

MgO | 3.26% | 3.97% | TiO_{2} | 0.57% | 0.64% |

Al_{2}O_{3} | 18.64% | 17.67% | MnO | 0.15% | 0.13% |

SiO_{2} | 54.79% | 49.02% | Fe_{2}O_{3} | 6.75% | 9.15% |

SO_{3} | 2.83% | 7.29% | ZnO | - | 0.15% |

Parameter | Mine-A | Mine-B |
---|---|---|

d80 | 60 µm | 20 µm |

d50 | 25 µm | 10 µm |

d20 | 8 µm | 6.62 µm |

Cu | 10.1 | 3.5 |

Cc | 1.1 | 1.3 |

% <20 µm | 45% | 80% |

Specific gravity | 2.74 | 3.40 |

Test Label | Cup Type | Temperature (°C) | |||
---|---|---|---|---|---|

Standard | Infinite | 15 | 25 | 35 | |

Loop test | • | • | • | ||

MVDIN-Cup1 | • | • | • | • | |

MVDIN-Cup2 | • | • | • | • | |

MVDIN-Cup3 | • | • | • | ||

FL100-Vane1 | • | • | |||

FL100-Vane2 | • | ||||

3in-Slump1 | • | • | |||

4in-Slump1 | • | • | |||

6in-Slump1 | • | • | |||

6in-Slump2 | • |

Test Label | Cup Type | Temperature (°C) | |||
---|---|---|---|---|---|

Standard | Infinite | 15 | 25 | 35 | |

Loop test | • | • | • | ||

MVDIN-Cup1 | • | • | • | • | |

MVDIN-Cup2 | • | • | • | ||

MVDIN-Cup3 | • | • | • | ||

SVII-Cup4 | • | • | • | ||

FL100-Vane1 | • | • | • | ||

3in-Slump1 | • | • | • | ||

4in-Slump1 | • | • | • | ||

6in-Slump1 | • | • | • |

Description | MV DIN | SV II |
---|---|---|

Bob radius (Rb) | 19.36 mm | 10.10 mm |

Cup radius (Rc) | 21.00 mm | 21.00 mm |

Bob height (H) | 58.08 mm | 19.60 mm |

Description | FL 100 |
---|---|

Vane radius $({R}_{i}$) | 11.00 mm |

Standard cup radius $({R}_{o}$) | As per Equation (7) |

Vane height $(H\prime $) | 16.00 mm |

Model | Governing Expression | Interpretation |
---|---|---|

Root mean square error (RMSE) | $RMSE=\sqrt{\frac{{\sum}_{i=1}^{N}{\left({F}_{t}-{A}_{t}\right)}^{2}}{N}}$ | The smaller the errors, the better the model |

Mean absolute percent error (MAPE) | $MAPE=\frac{100}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\frac{\left|{F}_{t}-{A}_{t}\right|}{{A}_{t}}$ | The smaller the percentage error, the better the model |

Symmetric mean absolute percent error (SMAPE) | $SMAPE=\frac{200}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\frac{\left|{F}_{t}-{A}_{t}\right|}{\left|{F}_{t}+{A}_{t}\right|}$ | The smaller the percentage error, the better the model |

Akaike information criterion (AIC) | $AIC=N+Nlog\left(2\pi \right)+Nlog\left(\frac{RSS}{N}\right)+2\left(p+1\right)$ | The smaller the value, the better the model |

Bayesian information criterion (BIC) | $\begin{array}{cc}BIC=N+Nlog& \left(2\pi \right)+Nlog\left(\frac{RSS}{N}\right)\\ & +\left(logN\right)\left(p+1\right)\hfill \end{array}$ | The smaller the value, the better the model |

Rheology Test | RMSE | MAPE | SMAPE | AIC | BIC |
---|---|---|---|---|---|

Bingham yield stress | |||||

MVDIN standard cup and bob | 41.249 | 380.800 | 102.122 | 161.899 | 160.373 |

FL100 vane | 326.416 | 113.171 | 68.964 | 190.295 | 188.589 |

3in slump | 199.101 | 165.085 | 83.508 | 76.360 | 73.484 |

4in slump | 235.518 | 179.605 | 89.476 | 77.964 | 75.089 |

6in slump | 338.703 | 239.278 | 104.574 | 81.436 | 78.560 |

Bingham plastic viscosity | |||||

MVDIN Standard cup and bob | 0.256 | 240.080 | 93.455 | 25.045 | 23.520 |

Rheology Test | RMSE | MAPE | SMAPE | AIC | BIC |
---|---|---|---|---|---|

Bingham yield stress | |||||

MVDIN standard cup and bob | 53.642 | 40.862 | 54.591 | 126.916 | 125.001 |

MVDIN infinite cup and bob | 61.292 | 21.417 | 25.343 | 54.357 | 51.220 |

SVII infinite cup and bob | 56.292 | 38.419 | 48.264 | 59.088 | 56.088 |

FL100 vane | 88.563 | 100.430 | 71.147 | 102.776 | 100.467 |

3in slump | 220.953 | 150.203 | 81.409 | 116.275 | 113.967 |

4in slump | 279.756 | 179.837 | 91.663 | 119.760 | 117.451 |

6in slump | 416.296 | 240.154 | 107.715 | 125.629 | 123.320 |

Bingham plastic viscosity | |||||

MVDIN standard cup and bob | 0.083 | 23.419 | 23.537 | −2.349 | −4.264 |

MVDIN infinite cup and bob | 1.034 | 57.297 | 92.982 | 22.448 | 19.311 |

SVII infinite cup and bob | 0.500 | 68.024 | 107.564 | 17.182 | 14.045 |

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**

Ahmed, H.M.; Bharathan, B.; Kermani, M.; Hassani, F.; Hefni, M.A.; Ahmed, H.A.M.; Hassan, G.S.A.; Moustafa, E.B.; Saleem, H.A.; Sasmito, A.P.
Evaluation of Rheology Measurements Techniques for Pressure Loss in Mine Paste Backfill Transportation. *Minerals* **2022**, *12*, 678.
https://doi.org/10.3390/min12060678

**AMA Style**

Ahmed HM, Bharathan B, Kermani M, Hassani F, Hefni MA, Ahmed HAM, Hassan GSA, Moustafa EB, Saleem HA, Sasmito AP.
Evaluation of Rheology Measurements Techniques for Pressure Loss in Mine Paste Backfill Transportation. *Minerals*. 2022; 12(6):678.
https://doi.org/10.3390/min12060678

**Chicago/Turabian Style**

Ahmed, Haitham M., Bhargav Bharathan, Mehrdad Kermani, Ferri Hassani, Mohammed A. Hefni, Hussin A. M. Ahmed, Gamal S. A. Hassan, Essam B. Moustafa, Hussein A. Saleem, and Agus P. Sasmito.
2022. "Evaluation of Rheology Measurements Techniques for Pressure Loss in Mine Paste Backfill Transportation" *Minerals* 12, no. 6: 678.
https://doi.org/10.3390/min12060678