# Temperature Prediction Model in the Main Ventilation System of an Underground Mine
## 3 Methods
### Data Processing and Analysis  
The equipment to record and collect data was calibrated regularly to avoid inaccurate measurements [36]. The effective temperature was transformed into daily average values, resulting in a total of 1155 daily records. Figure 1 shows the temperatures measured in each node, corresponding to the fixed control points representing the ventilation conditions of the intake. As can be seen in Figure 1, there was a higher dispersion in the initial nodes due to the influence of outside conditions, which were quite variable depending on the season of the year. According to [PERSON] et al. [37], variations in temperature in an underground mine are caused by several intrinsic and extrinsic characteristics, as shown in Equation (2). \[\Delta T_{total}=\Delta T_{ac}+\Delta T_{rp}+\Delta T_{\alpha}+\Delta T_{de}+ \Delta T_{hm}+\Delta T_{w} \tag{2}\]  
where \(\Delta T_{ac}\) represents autocompression (\({}^{\circ}\)C), \(\Delta T_{rp}\) represents thermal rock properties (\({}^{\circ}\)C), \(\Delta T_{\alpha}\) represents heat emission from electrical equipment (\({}^{\circ}\)C), \(\Delta T_{de}\) represents heat emission from diesel equipment (\({}^{\circ}\)C), \(\Delta T_{hm}\) represents human metabolism (\({}^{\circ}\)C), and \(\Delta T_{w}\) represents thermal water (\({}^{\circ}\)C). The underground atmospheric temperature, at any location inside the mine, can be expressed as a function of the underground initial temperature, eliminating the autocompression factor from Equation (2), since the temperature at the bottom of the shaft is taken into account, thereby obtaining Equation (3). \[t_{2}=t_{1}+\Delta T_{total} \tag{3}\]  
where \(t_{2}\) is the underground atmospheric temperature (\({}^{\circ}\)C), and \(t_{1}\) is the underground initial temperature (\({}^{\circ}\)C). The intake drifts from the case study had very steady conditions in terms of equipment usage, working force, and thermal rock properties, due to them being opened for a long time. It was also considered that the thermal water had no influence, due to the intrinsic characteristics of the type of  
Figure 1: Effective temperature measurements in each node (**left**) and as a function of distance (**right**). mineral extracted in the case study. The physicochemical properties of the air conditions were not considered either. Therefore, the more developed form of Equation (3), with simplifications, can be written as Equation (4). \[t_{2}=t_{1}+\Delta T_{intake} \tag{4}\]  
where \(\Delta T_{intake}\) depends on the dry and wet temperatures expressed as equivalent temperature (\({}^{\circ}\)C). However, the airflow is not steady throughout the main ventilation circuit, with some leakages existing along the intake and/or return, especially in U-shaped circuits as considered in this study, as well as airflow splits to different extracting panels. In this case, the cross-section did not have a substantial variation along the intake drift. Therefore, the heat contribution was similar along the intake drifts and the airflow was mainly reduced due to its distribution to the workplace. Distance was also very important to consider because of the interaction between the air and heat sources along the drifts. Equation (5) describes the factors influencing temperature variation along a drift. \[t_{2}=F(C,\ D,\ \Delta T_{intake}), \tag{5}\]  
where C is the airflow (m\({}^{3}\)/s), and D is the distance (m). A mathematical model is a simplified representation of reality with predictive variables (x\({}_{1}\), x\({}_{2}\),..., x\({}_{n}\)) and target variables that need to be estimated [38]. The model presented herein was based on the variables detailed in the previous paragraph, with the aim of forecasting the temperature using in situ measurements of temperature and airflow along the ventilation circuit, taking into account seven preset control points (see Figure 2).