# Optimization of Coal Production Based on the Modeling of the Jig Operation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/h [7,41]. For these particles, the hydrodynamic conditions of jig work connected with the amount of hutch water have the biggest influence on beneficiation effects. For coarser particles, the amount of hutch water does not have such a big influence on separation efficiency, but the separation density grows significantly. For these reasons, the authors decided to check whether the influence of hydrodynamic and process conditions can be explained using mathematical modeling in narrow-size fractions and whether it is related to the quantity and quality of produced coal concentrates. Thus far, no such studies have been found in the literature on the subject.

## 2. Materials and Methodology

#### 2.1. Experiment

^{2}, operating in a mechanical preparation plant of one of the coal mines. The trials were performed with a constant number of pulsations, i.e., 26 cycles per minute. The system throughput, i.e., the feed flow rate, was varied at three levels of 200, 300, and 400 t/h. Samples of products were taken from the jig at three variable settings of the hutch water flow rate for the set jig throughput, which were 35, 50, and 70 m

^{3}/h. A schematic illustration of the studied jig separator is presented in Figure 1. At these parameters, after stabilization of the process, samples of concentrate, midllings and tailings were collected simultaneously within 3 min, following the procedures of representativeness. Subsequently, each of the separation products was subjected to densimetric and granulometric analyses. The flow and sink analysis was performed in zinc chloride solutions with densities of 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, and 2.0 t/m

^{3}, respectively. It was used to determine the accuracy of the jig’s work separation. Additionally, the samples were sieved on screens with mesh sizes of 2.0, 3.15, 5.0, 6.3, 8.0, 10.0, 12.5, 16.0, and 20.0 mm to determine the effect of variable machine operating conditions on separation efficiency. In all size fractions obtained as a result of flow-sink and granulometric analyses, the yields of the products and ash content were determined. The scheme of the performed tests is presented in Table 1.

#### 2.2. Model

^{3}/h were selected. When each test variable has the same number of variability levels, the total number of individual experiments required can be written as follows:

_{c}and A. According to the above and in relation to (2), it can be written as follows:

_{c}, A) = f (throughput, amount of hutch water)

_{c}is concentrate yield, and A denotes ash content in the concentrate.

## 3. Results

#### Multi-Factor Analysis of Variables Affecting the Effects of Coal Separation in a Jig

## 4. Discussion

#### 4.1. Modeling Results

_{c}) and ash content in the concentrate (A). The significance of each independent variable in the model was tested at a confidence level of 1 − α = 0.95. The significance coefficient R

^{2}was calculated separately for each model. Table 2 shows the calculated models for each particle size fraction and the values of R

^{2}.

^{2}coefficient. In particular, the models for ash content indicated a high degree of explanation of the dependent variable by the variables water amount and yield of concentrate. For the fine particle size fraction, a positive influence of the amount of hutch water can generally be observed. This means that as the amount of added hutch water increased, the ash content in the concentrate also increased. This trend was different for the coarse size fractions and for the 3.15–5.00 mm. In the case of jig throughput, it was clear that the relationship was usually inversely proportional, i.e., as it increased, the ash content increased. Uniform feeding is a prerequisite for the normal operation of the jig. An increase or fluctuation in the amount of feed supplied or interruptions in the supply will result in a loss of coal in the tailings and a decrease in the quality of the concentrate. On the other hand, with an incomplete load with the feed, the throughput of the jig was not fully used and particles of tailings or intergrowth entered the concentrate. An inverse relationship can be seen for the 8.0–10.0 and 10.0–12.5 mm size fractions, but the values of the coefficients for the variable t are not high. A high value of the R

^{2}coefficient proved that these observations were significant. Somewhat worse models were obtained for the amount of concentrate yield, although the parameters of the model are still statistically significant. In this case, the effect of hutch water amount and throughput on the amount of yield was generally positive, i.e., the relationships were directly proportional.

^{2}coefficient showed that the quality of most of the equations was statistically good. However, the natural variation of the feed in industrial conditions may cause some discrepancies from the results obtained during the test. However, it is worth noting that the experiments were conducted in industrial conditions—so the results can be treated as representative of an industrial practice. Anther limitation is that the preparation of coal from a certain narrow particle density-size fraction in industrial condition is very hard. However, the results may help in the appropriate preparation of the feed.

#### 4.2. Validation

_{c}and A.

## 5. Conclusions

^{2}less than 80% for the smallest particle size fraction, i.e., less than 2 mm. Lower coefficients of determination were obtained for models with a variable such as a concentrate yield, which in four cases were below 80%, proving the poorer quality of the model. Validation of the obtained model with real operating results for concentrate quality shows a high level of accuracy. This proves that the chosen approach to modeling was correct. On the other hand, the validation of the model for concentrate production, especially in the 8.0–10.0 and 10.0–12.5 mm size fractions, showed a low degree of accuracy. The analysis of the results and the developed mathematical models in narrow particle size fractions of the concentrate showed that for particles of 2.0–8.0 mm and in the size fraction 10.0–12.5 mm, at a throughput of 200 t/h and a small addition of hutch water, it is possible to obtain a very good quality concentrate, in which ash is about 6%. For these size fractions, the values of the coefficients of variable 1 (throughput) and variable 2 (hutch water) are very low. However, a similar relationship between the model in particle size fraction and concentrate yield cannot be observed.

^{2}values, but also by higher values of the coefficients of the regression equations. For the finer size fraction, the influence of both of these parameters is positive, similarly for the smallest size fraction. Only in the 8.0–10.0 and 10.0–12.5 mm size fractions is this relationship inverse, but the quality of the models for these classes is the worst, which may be the reason for the not fully correct assessment of the process. One can also pay attention to the small values of these coefficients, which, taking into account the confidence intervals, may change their sign in the model. In the case of models for ash content, their quality is very high, but the relative effect of hutch water and yield is small in terms of the value of the measured random variable. The values of the coefficients are close to zero, which means that despite the significant dependence, their influence on the ash content is relatively small.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Concentrate yield and ash contents in the concentrate as a function of particle size fraction: (

**a**) yield of concentrate—throughput 200 t/h, (

**c**) yield of concentrate—throughput 300 t/h, (

**e**) yield of concentrate—throughput 400 t/h, (

**b**) ash content—throughput 200 t/h, (

**d**) ash content—throughput 300 t/h, (

**f**) ash content—throughput 400 t/h.

**Figure 4.**Three-dimensional surfaces of the analyzed variables for all cases: (

**a**) influence of throughput and hutch water on concentrate yield, (

**b**) influence of throughput and hutch water on ash content in concentrate, (

**c**) influence of throughput and hutch water on imperfection.

Test Number | Variable 1 (Throughput t/h) | Variable 2 (Hutch Water m ^{3}/h) | Float and Sink Analysis | Size Analysis |
---|---|---|---|---|

1 | 200 | 35 | + | + |

2 | 200 | 50 | + | + |

3 | 200 | 70 | + | + |

4 | 300 | 35 | + | + |

5 | 300 | 50 | + | + |

6 | 300 | 70 | + | + |

7 | 400 | 35 | + | + |

8 | 400 | 50 | + | + |

9 | 400 | 70 | + | + |

Particle Size, mm | Concentrate Yield, γ_{c} | Ash Content in the Concentrate, A | ||
---|---|---|---|---|

Model | R^{2} | Model | R^{2} | |

<2.0 | γ_{c} = −7.38 + 0.29 hw + 0.06 t | 0.85 | A = 7.12 + 0.05 hw − 0.008 t | 0.73 |

2.0–3.15 | γ_{c} = −16.81 + 0.25 hw + 0.09 t | 0.95 | A = 5.91 + 0.02 hw − 0.005 t | 0.85 |

3.15–5.0 | γ_{c} = −17.13 + 0.32 hw + 0.08 t | 0.97 | A = 6.49 − 0.03 hw − 0.004 t | 0.83 |

5.0–6.3 | γ_{c} = 3.86 + 0.10 hw + 0.06 t | 0.71 | A = 5.19 + 0.02 hw − 0.004 t | 0.80 |

6.3–8.0 | γ_{c} = 10.37 + 0.17 hw + 0.04 t | 0.91 | A = 5.40 + 0.04 hw − 0.005 t | 0.97 |

8.0–10.0 | γ_{c} = 69.97 − 0.04 hw − 0.08 t | 0.72 | A = 1.81 + 0.02 hw + 0.02 t | 0.97 |

10.0–12.5 | γ_{c} = 78.10 − 0.15 hw-0.10 t | 0.63 | A = 1.30 + 0.03 hw + 0.01 t | 0.96 |

12.5–16.0 | γ_{c} = 17.61 + 0.05 hw + 0.06 t | 0.76 | A = 17.06 − 0.08 hw − 0.009 t | 0.98 |

16.0–20.0 | γ_{c} = 51.56 + 0.27 hw + 0.02 t | 0.97 | A = 21.83 − 0.09 hw − 0.03 t | 0.98 |

Particle Size, mm | MSE (γ_{c}) | MSE (A) |
---|---|---|

<2.0 | 9.68 | 0.66 |

2.0–3.15 | 2.33 | 0.23 |

3.15–5.0 | 1.89 | 0.38 |

5.0–6.3 | 3.03 | 0.26 |

6.3–8.0 | 2.15 | 0.16 |

8.0–10.0 | 11.85 | 0.29 |

10.0–12.5 | 16.97 | 1.57 |

12.5–16.0 | 3.49 | 0.30 |

16.0–20.0 | 1.32 | 1.35 |

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**MDPI and ACS Style**

Surowiak, A.; Niedoba, T.; Wahman, M.; Hassanzadeh, A.
Optimization of Coal Production Based on the Modeling of the Jig Operation. *Energies* **2023**, *16*, 1939.
https://doi.org/10.3390/en16041939

**AMA Style**

Surowiak A, Niedoba T, Wahman M, Hassanzadeh A.
Optimization of Coal Production Based on the Modeling of the Jig Operation. *Energies*. 2023; 16(4):1939.
https://doi.org/10.3390/en16041939

**Chicago/Turabian Style**

Surowiak, Agnieszka, Tomasz Niedoba, Mustapha Wahman, and Ahmad Hassanzadeh.
2023. "Optimization of Coal Production Based on the Modeling of the Jig Operation" *Energies* 16, no. 4: 1939.
https://doi.org/10.3390/en16041939