# Analysis of Energy-Saving Transport Conditions of Light-Particle Slurry

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Materials and Devices

#### 2.1. Solid and Liquid Phase Working Medium

#### 2.2. Experimental Devices

#### 2.3. Test Process and Working Conditions

#### 2.4. Error Analysis

^{3}/s. The flow pressure drop ∆P was measured using a differential pressure transmitter, and the absolute error was 0.06% Pa.

_{1,}x

_{2,}x

_{3,}…, x

_{n}represents mutually independent measured values, δ

_{N}represents the absolute error of the indirect measurement value, and δ

_{x}is the absolute error of the direct measurement value. The relative error of the indirect measurement value is δ

_{N}/N. The relative errors of flow velocity v, resistance coefficient λ, shear stress τ, and shear rate γ were 0.51%, 0.51%, 0.06%, and 0.50%, respectively.

## 3. Theory of Rheological Model

## 4. Analysis of Experimental Results and Response Surface Method

#### 4.1. Rheological Model of Light-Particle Slurry

#### 4.2. Quadratic Regression Equation of Yield Stress and Viscosity

_{v}were selected as the influencing factors, and the yield stress τ

_{0}and viscosity of the slurry μ

_{d}were taken as the response values to carry out the three factors and three levels of the Box–Behnken Design (BBD) with three factors and three levels. The BBD method is a common analysis method of the response surface method. When the factors were the same, the number of BBD tests was less. The test consisted of 13 factorial tests and 4 repeated tests. A repeat test was used to determine test error and data repeatability. The test factors and levels are shown in Table 3. The three-level factors are the values of the three variables (i.e., the experimental condition variables) taken for each influencing factor. Design Expert 8.0 software was used to design the test scheme table, as shown in Table 4. The yield stress and viscosity values in Table 4 were obtained from the experimental measurement of pressure drop and the analysis of the slurry rheological model, and the variation in its values with different working conditions were analyzed.

_{0}represented a constant term, β

_{i}was the coefficient of the x

_{i}term; x

_{i}and x

_{j}represented three independent variables: pipe diameter, particle size, and solid content; β

_{ij}was the coefficient of the interaction term.; β

_{ii}was the coefficient of the quadratic term; and ξ indicated the error item.

#### 4.3. Significance Analysis of Influencing Factors

#### 4.3.1. Yield Stress

_{v}have a significant impact on the yield stress. For the yield stress, the larger the F-value, the more significant the influence of this factor. Therefore, the main influence factor of the slurry yield stress is the pipe diameter, followed by the solid content, and finally, the particle size.

#### 4.3.2. Viscosity

#### 4.4. Analysis of Coupling Effect of Influencing Factors

^{−5}Pa and the viscosity was 0.0074 Pa·s. In addition, according to the experimental measurement results (Figure 5 and Table 4), the smaller the pipe diameter, the smaller the yield stress. The smaller the particle size, the smaller the viscosity. This is consistent with the conclusion of the best operating condition for the mixed slurry obtained by the response surface method. With experimental conditions of a pipe diameter of 17 mm, a particle size of 0.3 mm, and a solid content of 10 vol%, the measured viscosity was 0.00762 Pa·s, which is also consistent with the best operating conditions of the mixed slurry obtained using the response surface method.

## 5. Conclusions

- When the solid content, particle size, and pipe diameter were fixed, the shear stress measured in the experiment increased with increasing shear rate, and there was an intercept on the Y-axis. Therefore, the H–B model could be used for the regression analysis of the rheological properties of the light-particle mixed paste. The rheological index n of the slurry was always greater than 1, which indicated that the rheological relationship of the mixed slurry was an expansive plastic fluid with yield stress.
- The primary and secondary relationships of factors (pipe diameter, particle size, solid content) affecting the rheological parameters (yield stress and viscosity) were comprehensively analyzed using the response surface method. According to the experimental results, the response function satisfying the quadratic regression equation was obtained. The prediction deviation of the response function for yield stress and viscosity was less than 11.82%. The variance analysis of the response function showed that the influence of each factor on the yield stress is in the order of pipe diameter, solid content, and particle size. The yield stress increases with increasing pipe diameter and solid content but does not change with the particle size. The influence degree of each factor on viscosity from large to small is as follows: particle size, solid content, and pipe diameter. The viscosity increases with increasing particle size and increasing solid content and does not change significantly with the pipe diameter. When the pipe diameter is fixed, the solid content increases from 5 vol% to 10 vol%, which has little effect on viscosity. It shows that the shear thickening phenomenon is more likely to occur in the thicker dispersion system. The analysis of the sensitivity of multifactor interaction in the response surface graphs showed that the interaction of pipe diameter and solid content had the most significant impact on yield stress. The interaction of particle size and solid content had the most significant effect on viscosity.
- The response surface method is proposed as a method to determine the energy-saving transportation conditions, and the rationality of the method is verified by experiments, which provides a reference for the optimization of the design of light-particle slurry transportation.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The physical picture of polyethylene particles: (

**a**) particle size = 0.3 mm; (

**b**) particle size = 0.4 mm; and (

**c**) particle size = 0.5 mm.

**Figure 4.**Rheological curves of Newtonian fluid and four non-Newtonian fluid rheological models. (

**a**) Newtonian fluid, the Bingham model, the power-law model, and the H–B model; and (

**b**) the Casson model.

**Figure 5.**H–B model fitting curve under various working conditions when the pipe diameter was 28 mm: (

**a**) particle size = 0.3 mm; (

**b**) particle size = 0.4 mm; and (

**c**) particle size = 0.5 mm.

**Figure 6.**Comparison of actual value and predicted values of yield stress and viscosity. (

**a**) Comparison of actual value and predicted values of yield stress; and (

**b**) comparison of actual value and predicted values of viscosity.

**Figure 7.**Factors affecting yield stress. (

**a**) The relationship between yield stress and pipe diameter; and (

**b**) the relationship between yield stress and particle size.

**Figure 8.**Factors affecting viscosity. (

**a**) The relationship between viscosity and pipe diameter; and (

**b**) the relationship between viscosity and particle size.

**Figure 9.**Response surface graphs of the interaction of three factors to yield stress. (

**a**) The effect of pipe diameter and particle size on yield stress; (

**b**) The effect of pipe diameter and solid content on yield stress; and (

**c**) The effect of particle size and solid content on yield stress.

**Figure 10.**Response surface graphs for the interaction of three factors on viscosity. (

**a**) The effect of pipe diameter and particle size on viscosity; (

**b**) The effect of pipe diameter and solid content on viscosity; and (

**c**) The effect of particle size and solid content on viscosity.

Equipment Name | Product Model | Specifications | Company |
---|---|---|---|

Stirring motor | BLD09-11-0.75 | Speed: 150 r/min | Yixing Yuanjia Environmental Protection Equipment (Yixing, China) |

Circulating pump | 25GW8-22 | Speed: 2900 r/min; Rate of flow: 8 m^{3}/h; Lift: 22 m | Kaiping Danai Pump Manufacturing Co., Ltd. (Kaiping, China) |

Electromagnetic flowmeter | TBD-20Y-F4-1-A-1-16-A | Range: 0–6 m^{3}/h; Precision: ±0.5% | Dalian Measuring Machinery Co., Ltd. (Dalian, China) |

Differential pressure transmitter | 3051CD2A22B1AB415M5HR5 | Range: 0–30 kPa; Precision: ±0.06% | Emerson Electric Company (St. Louis, MO, USA) |

Thermocouple | K-type | Precision: ±0.1 °C | Shanghai No. 3 Electric Instrument Factory (Shanghai, China) |

Pressure-drop sensor | PCM300 | Range: 0–100 kPa; Precision: ±0.5% | Suzhou Xuansheng Instrument Technology Co., Ltd. (Suzhou, China) |

Name | Working Condition Parameters |
---|---|

Flow velocity: v/m·s^{−1} | 0.1~1 (Conduct an experiment every 0.1 m/s) |

Pipe diameter: D/mm | 17, 24 and 28 mm |

Solid particle size: d/mm | 0.3, 0.4 and 0.5 mm |

Solid content (IPF): C_{v}/vol% | 5, 10, 15 and 20 vol% |

Factor | Coding | Level | ||
---|---|---|---|---|

−1 | 0 | 1 | ||

Pipe diameter/mm | D | 17 | 24 | 28 |

Particle size/mm | d | 0.3 | 0.4 | 0.5 |

Solid content/vol% | C_{v} | 5 | 10 | 15 |

Test Number | Pipe Diameter D/mm | Particle Size d/mm | Solid Content C_{v} /vol% | Yield Stress τ _{0} /Pa | Viscosity μ _{d} /Pa‧s |
---|---|---|---|---|---|

1 | 28 | 0.5 | 10 | 0.31254 | 0.01390 |

2 | 28 | 0.4 | 15 | 0.50587 | 0.01340 |

3 | 24 | 0.4 | 10 | 0.27542 | 0.01109 |

4 | 24 | 0.4 | 10 | 0.27542 | 0.01109 |

5 | 24 | 0.4 | 10 | 0.27542 | 0.01109 |

6 | 17 | 0.5 | 10 | 0.15963 | 0.00916 |

7 | 24 | 0.3 | 5 | 0.11088 | 0.00872 |

8 | 24 | 0.4 | 10 | 0.27542 | 0.01109 |

9 | 28 | 0.3 | 10 | 0.27414 | 0.00701 |

10 | 28 | 0.4 | 5 | 0.15838 | 0.00987 |

11 | 17 | 0.3 | 10 | 0.06039 | 0.00762 |

12 | 24 | 0.3 | 15 | 0.30113 | 0.01135 |

13 | 17 | 0.4 | 5 | 0.00058 | 0.00738 |

14 | 24 | 0.5 | 5 | 0.26417 | 0.01133 |

15 | 24 | 0.5 | 15 | 0.38912 | 0.01886 |

16 | 17 | 0.4 | 15 | 0.17272 | 0.01006 |

17 | 24 | 0.4 | 10 | 0.27542 | 0.01109 |

Variance Source | Free. Degree | Sum of Squares | F-Value | p-Value | Significance |
---|---|---|---|---|---|

regression equation | 9 | 2.200 × 10^{−1} | 15.260 | 0.0008 | Highly significant |

D | 1 | 9.200 × 10^{−2} | 56.740 | 0.0001 | Highly significant |

d | 1 | 1.800 × 10^{−2} | 11.400 | 0.0118 | Significant |

C_{v} | 1 | 7.600 × 10^{−2} | 47.200 | 0.0002 | Highly significant |

Variance Source | Free. Degree | Sum of Squares | F-Value | p-Value | Significance |
---|---|---|---|---|---|

Model | 9 | 1.249 × 10^{−4} | 47.76 | <0.0001 | Highly significant |

D | 1 | 1.240 × 10^{−5} | 42.68 | 0.0003 | Highly significant |

d | 1 | 3.521 × 10^{−5} | 121.20 | <0.0001 | Highly significant |

C_{v} | 1 | 3.091 × 10^{−5} | 106.39 | <0.0001 | Highly significant |

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## Share and Cite

**MDPI and ACS Style**

Wang, X.; Wang, F.; Li, J.; Zhang, Y.; Zhao, L. Analysis of Energy-Saving Transport Conditions of Light-Particle Slurry. *Buildings* **2023**, *13*, 894.
https://doi.org/10.3390/buildings13040894

**AMA Style**

Wang X, Wang F, Li J, Zhang Y, Zhao L. Analysis of Energy-Saving Transport Conditions of Light-Particle Slurry. *Buildings*. 2023; 13(4):894.
https://doi.org/10.3390/buildings13040894

**Chicago/Turabian Style**

Wang, Xiaochun, Fan Wang, Jun Li, Ye Zhang, and Lianjin Zhao. 2023. "Analysis of Energy-Saving Transport Conditions of Light-Particle Slurry" *Buildings* 13, no. 4: 894.
https://doi.org/10.3390/buildings13040894