Distribution Law of the Temperature Inversion Layer in a Deep Open-Pit Mine.

Using the methods of field experiment, numerical simulation, and theoretical analysis, a deep concave open-pit mine (DCOM) geometric model is established. Ansys Fluent software is used to simulate the change in the temperature field at night in the DCOM over time and analyze the probability of the spatial distribution of the temperature inversion layer. The results show that the location inside the stope close to the southwest edge is more likely to present temperature inversion, and the location close to the northeast edge is the least likely to have temperature inversion, and the height range where temperature inversion is likely to occur is 100-0 m. The simulated results reveal a greater probability of temperature inversion at the closed circle (+80 m), which is consistent with that obtained by field observation. Through multiple nonlinear regression analysis, a prediction model of the spatial distribution probability of the temperature inversion layer is established, which provides a theoretical basis for the prediction and control of atmospheric pollution in the DCOMs.

Introduction

During the blasting, perforation, crushing, loading, and transportation of the deep concave open-pit mine (DCOM), a large amount of dust and other toxic and harmful gases will be generated. If these pollutants are not effectively eliminated, they will accumulate inside the open pit. Pollutants can endanger the health of miners and the safe production of enterprises, causing economic losses.[1−3] The open-pit stope will show a “concave” structure as the mining depth increases. When the wind is calm or there is a breeze, the special topographical structure will make it easier to form an inversion layer inside the stope under the thermal action dominated by solar radiation. Due to the existence of the temperature inversion layer, the warm and light air is above the cold and heavy air, forming very stable air stratification. Stratification can hinder the air quality and energy exchange between the upper and lower layers and inhibit the diffusion of dust. At the same time, it keeps dust in the stope for a long time, causing air pollution and endangering human health.[4,5]

There are only a few studies on the temperature field and temperature inversion layer of DCOMs at home and abroad, mainly in the 1970s and 1990s. Wang,[6] Lu et al.,[7] and Jin[8] all found the temperature inversion which affects the diffusion of pollutants and makes the stope air pollution more serious after the low-altitude temperature observation of the DCOM. Setenko et al.[9] believed that the cause of temperature stratification in the Mulongtao open-pit mine was that the cold air from the surface entered the open-pit mine. In recent years, Tukkaraja[10] and Bhowmick[11] used the computational fluid dynamics (CFD) technology to simulate the diffusion of pollutants and dust in open-pit mines. They found that the dust cannot diffuse outside the pit due to the existence of the inversion layer. Pagès and Miró[12] used the vertical-weighted regression method to analyze the inversion temperature of the complex terrain. In our previous work, we studied the changes in the thickness, intensity distribution probability, and duration of the inversion layer inside the DCOM stope through field measurements.[13] We also analyzed the influence of rock wall temperature and solar radiation on the internal temperature field of the DCOM based on the field test results.[14] An empirical formula for the temperature change of the internal rock wall of the DCOM was established.

Some scholars got the evolution model of the inversion height or the inversion time change using different methods. Zhao[15] used the numerical integration of the Nieuwstadt equation to predict the time change of the temperature inversion layer based on the initial potential temperature profile, ground potential temperature, and geostrophic wind speed. Based on the formation and evolution of the planetary boundary layer at night and day and using the thermal energy equation to construct the prediction equation of the height of the inversion layer, some research groups got the evolution model of the night inversion height.[16−18] The model could simply estimate the height of ground inversion at night. Someone applied similar profiles to the integration of the stable boundary layer of the temperature equation, obtained the rate equation for the height of the temperature inversion layer, and derived an analytical solution.[19,20] According to the evolution model of night inversion height proposed by Anfossi et al.,[17] Tomasi[21] verified that the radiosonde was used to obtain the inversion height data of a certain valley under calm wind conditions. Zong put forward a new sunny night off-ground temperature inversion distribution prediction model.[22] Zhu used mathematical statistics to establish the discriminant equation of mountain inversion and the linear and nonlinear regression equation of the height of the inversion layer top.[23] Tongyu et al. used linear regression methods to obtain short-term forecasts of the intensity of the inversion layer based on the actual sounding data at 7 o’clock a day in Harbin for 10 years.[24]

There are few studies on the prediction of inversion layers at home and abroad, and they are basically concentrated on the prediction of inversion layer strength. There are still deficiencies in the research on the prediction model of the spatial distribution probability in the inversion layer. Therefore, this paper uses a DCOM as an experimental mine. Through field testing, numerical simulation, and theoretical analysis, a probabilistic prediction model for the spatial distribution of the inversion layer of the DCOM is established. The research results provide theoretical basis and technical parameters for the prediction and forecast of air pollution in DCOMs. It is of great significance for the formation and dissipation of pollutants in open-pit mines, optimizing the working environment of open-pit mines, ensuring safe production, and improving production efficiency.

Results and Discussion

Field Experiment

The experimental mine is located at 118°32′–118°36′ east longitude and 40°06′–40°09′ north latitude. The geological structure belongs to the Yanshan subsidence zone, and the lithology is dominated by gneiss. The whole mining area is trending from the southwest to the northeast; the long-axis distance from the southwest to the northeast is 3395 m, and the longest distance from the southeast to the northwest longitudinal axis is 1318 m. The height of the closed circle on the surface of the mine is +80 m above sea level, and the deepest depth of the pit bottom is −210 m. Combined with the actual topography and direction of the wind in the stope of the mining area, four measuring points are set near the dust source of the working face (as shown in Figure ) without affecting the on-site operation and ensuring the safety of the testers. The continuous changes in air temperature, relative humidity, and wind speed at a certain measuring point in the mining area were tested. The instrument used in the experiment is the Taiwan Hengxin AZ9671 wind speed temperature and humidity recorder.

Figure 1

Measuring point distribution (photograph: courtesy of “Google Earth” Copyright 2020.).

Numerical Simulation of an Open-Pit Temperature Field

Geometric Model Establishment

According to the mining plan of the open-pit mine, Auto CAD software was used to establish sections of different heights that intersect the plan. After importing the contour map of the stope by connecting the intersection points into Ansys Spaceclaim, an air layer with a length of 4000 m, a width of 2000 m, and a height of 400 m was established above the stope. By simplifying the hillside surrounding the central stope, the solid geometric model of the open-pit mine was then established, as shown in Figure a,b.

Figure 2

(a,b) are the solid geometric models of the open-pit mine at different viewing angles; (c) southwest boundary of the air layer; (d) southeast boundary of the air layer; (e) northwest boundary of the air layer; (f) northeast boundary surface of the air layer; and (g) top boundary surface of the air layer.

The wind direction from the mine was generally southwest, and the wind direction was stable. Flows with low wind speeds were considered incompressible and stable. Therefore, the southwest boundary surface of the air layer was used as the entrance boundary of the mine model, and the boundary surfaces of the other air layers were used as the exit boundary. The southwest, northeast, northwest, southeast, and top boundary surfaces are shown in Figure c–g, respectively.

Reliability Analysis of Numerical Simulation Results

The reliability of the numerical simulation of the internal temperature field of the open-pit mine was verified by comparing the results of numerical simulation and field observation. Taking the same measuring point as the comparison object and under the same boundary conditions, the temperature data of numerical simulation and field observation at different times were analyzed and compared. The temperature change with time at the same measuring point is shown in Figure , which illustrates that the numerical-simulated temperatures are basically consistent with those of the field test over the whole measured time range. However, the two sets of data still had certain differences due to that the temperature field was affected by various external conditions during the field observation and that there was a certain difference in the numerical simulation for the model establishment, mesh division, and boundary condition setting compared with the actual situation. In general, the comparative analysis of temperature changes shows that it is feasible to use Ansys Fluent software to simulate the temperature field distribution in the open-pit mine stope.

Figure 3

Comparison of the numerical simulation results with the measured values at each time.

Analysis Method of Numerical Simulation Results

The central area of the open-pit mine was cut along the long axis of five equidistant sections (with a spacing of 70 m) and denoted as M, a = 1, 2, 3, 4, and 5 (Figure a). A total of 25 equidistant sections along the short-axis direction (spacing 50 m) were taken, denoted as N, b = 1, 2, 3, 4, ..., and 25 (Figure b). The long-axis section and the short-axis section intersect (as shown in Figure c), and the line of intersection is denoted as LM. As shown in Figure d, the yellow line segments (a total of 125) show the model analysis profile.

Figure 4

(a) Five equidistant sections on the major axis; (b) 25 equidistant sections on the minor axis; (c) converging into a line; (d) 125 analysis profiles; (e) analysis profile side view; and (f) schematic diagrams of nine analysis profile positions.

The as-drawn analysis profile was divided into 25 areas, which are marked as a–y areas and each area contains five contours. At the same time, the vertical height is divided into seven distance sections, namely, 400–100, 100–50, 50–0, 0 to −50, −50 to −100, −100 to −150, and −150 to −250 m, which is helpful to analyze the distribution and changes of the temperature inversion layer on the vertical height in each area, as shown in Figure e.

Temperature Change with Time at the Vertical Height

Ansys Fluent was used to simulate the mine temperature field from 17:00 to 5:00 on the next day. Ansys CFD-Post was used to extract the hourly temperature changes of 125 analysis profiles. Due to the large number of profiles, only the temperature changes on the analysis profiles in the central area of nine stopes are analyzed, namely, the profiles LM, LM, LM, LM, LM, LM, LM, LM, and LM, whose locations are shown in Figure f. Temperature variations for different time intervals as a function of height for these profiles are illustrated in Figures , S1, and S2 (see the Supporting Information).

Figure 5

Temperature variation for different time intervals as a function of height for the profiles (a) LM, (b) LM, and (c) LM.

In general, the spatial distribution of the temperature inversion layer in the open-pit mine stope was relatively random, but there were still rules to follow. The average temperature in the stope was relatively high from 17:00 to 21:00, and the temperature inversion layer was distributed in a wide range, with a greater probability of occurrence. The temperature on the profile after 21:00 fluctuated greatly with the decrease in the average temperature. Thus, the distribution of the inversion layer was more random, and the probability of occurrence of the inversion layer was small. The profiles close to the rock wall and the height of 100 to −50 m, that is, near the closed circle of the stope, were more likely to present temperature inversion layers.

Probability Distribution of the Inversion Layer in the Open-Pit Mine

In order to analyze the probability distribution of the inversion layer in the entire open-pit mine, the probabilities of the inversion layer in each analysis area were calculated according to the evaluation index T of the inversion layer probability, which can be expressed aswhere K is the total number of inversion layers in the area and N is the number of temperature measurement points in the area.

According to Tables S1–S13 (in the Supporting Information), the locations with a higher probability of occurrence of the inversion layer at 17:00 were mostly concentrated at 100–0 m and the bottom of the pit, and the locations with a lower probability were mostly concentrated at −50 to −150 m. Although the occurrence probability of the temperature inversion layer became dispersive from 19:00 to 22:00, it was much greater in the range of 100–0 m than that in other heights. From 23:00 to 5:00, the probability of occurrence of temperature inversion began to gradually concentrate in the range of 100–0 m, while the probability at the bottom of the pit was gradually decreased or even disappeared. The inside of the stope near the southwestern slope was more likely to display temperature inversion, but it was least likely to occur near the northeast slope. The location where temperature inversion was likely to occur was at 100–0 m. This was basically consistent with the results obtained by field observations that a greater probability of temperature inversion was at +80 m.

Prediction of the Spatial Distribution Probability of the Inversion Layer in the Deep Open-Pit Mine

In order to further analyze the spatial distribution of the inversion layer of the open-pit mine, the probability of the inversion layer in the area of the same open-pit height from 17:00 to 5:00 o’clock (the next day) was added, and the change in the total probability was analyzed. Since it divides seven different height regions, as shown in Section , there will be seven probability curves with time, as shown in Figure a. In addition, the average temperature of these seven different altitude areas and the average temperature difference of adjacent areas as a function of time were counted, as shown in Figure b,c.

Figure 6

(a,b) Change in the inversion probability and average temperature over time in seven different height areas from 17:00 to 5:00 and (c) change in the average temperature difference of adjacent areas over time.

As shown in Figure a, the total inversion probability in the height range of 400–100 m is basically unchanged over time. There is a maximum probability of 55% at 18:00 and a minimum probability of 38% at 22:00. In the height range of 100–50 and 50–0 m, the total inversion probability has a similar trend with time. The inversion probability fluctuates three times with the passage of time and continues to increase after reaching the lowest probability at 3:00. In the range from 0 to −50 m, the probability decreases after reaching 55% at 20:00, reaching the lowest of 37% at 2:00, and the probability of the inversion layer at 4:00 and 5:00 started to rise again, eventually reaching 70%. In the range from −50 to −100 m, the probability of inversion temperature is generally low, below 50%. The total inversion probability at 17:00 is the lowest, that is, 13%, and then, it increases first and then decreases to the total inversion temperature at 1:00. The probability reaches 20%, and the total temperature inversion probability starts to rise after 2:00, reaching a maximum of 45% at 5:00. In the height range of −100 to −150 and −150 to −250 m, the total temperature inversion probability has a similar trend with time and generally decreases with the passage of time, and the probability reaches the minimum at 5:00.

As shown in Figure b, the change trend of the average temperature over time in the seven altitude ranges is basically the same. The average temperature is highest at 17:00, and the average temperature gradually decreases with time and reaches the minimum at 5:00. Figure c shows the change in the difference of the average temperature between two adjacent height ranges over time. By comparing Figure a, it can be seen that the two change trends are basically the same. It is found that the total temperature inversion probability from −100 to −150 m and below −150 m varies with time and the trend of the average temperature is similar. The total temperature inversion probability of other heights changes with time and the corresponding change trends of the average temperature difference between adjacent areas are similar. Therefore, a theoretical formula for the occurrence probability of the inversion layer, the average temperature, and the average temperature difference between adjacent areas was established aswhere T is the probability of the inversion layer in the area, t̅ is the average temperature in the area, Δt̅ is the average temperature difference between adjacent areas, and A, B, and C are three coefficients.

According to eq , the total inversion probability in seven different height areas from 17:00 to 5:00 was fitted with the average temperature and the average temperature difference of adjacent areas. The calculation formulas for total inversion probability at seven heights are obtained, and the values of the coefficients A, B, and C are shown in Table .

Table 1

Formula Coefficient Values under Different Vertical Height Ranges

vertical height range/m	A	B	C
400–100	0.01	0.41	0.38
100–50	0.02	0.32	0.49
50–0	0.01	0.87	0.55
0 to −50	–0.01	0.67	0.54
–50 to −100	–0.02	0.79	0.52
–100 to −150	0.06	–0.41	–0.16
–150 to −250	0.1	–0.53	–0.41

In order to verify the accuracy of the fitting formula, the fitting result is compared with the occurrence probability of temperature inversion, as shown in Figure . Figure a–g illustrates the comparison results within the height range of 400–100, 100–50, 50–0, 0 to −50, −50 to −100, −100 to −150, and −150 to −250 m, respectively. The results show that the fitting formula is basically accurate and can well reflect the relationship between the average temperature and the occurrence probability of the temperature inversion layer. The occurrence probability of the temperature inversion layer within the height range of 400–100 m is less than 55%, and the occurrence probability is 35–45% when the average temperature is 2–8 °C. The occurrence probability of the temperature inversion layer increases with the increase in the average temperature, which can reach up to 50%. The probability of occurrence of temperature inversion at 100–50 m is above 50%. When the average temperature is 5 °C, the probability of occurrence of the inversion layer is the lowest, and then, it increases with the increase in average temperature, up to more than 70%. When the height is 50–0 m, the probability of occurrence of the inversion layer is about 60%. When the average temperature is 5 °C, there is a minimum probability of 40%, and then, it gradually increases to more than 70% with the increase in the average temperature. The probability of occurrence of inversion from 0 to −50 m is about 50%. When the average temperature is 5 °C, the probability decreases to the lowest value of 30% and then gradually increases with the increase in the average temperature. When the average temperature is 9 °C, the probability is close to 60%. With further increasing the temperature, the occurrence probability of the temperature inversion layer gradually decreases to 40%. In the range from −50 to −100 m, the probability of temperature inversion is basically the same as that from 0 to −50 m. The probability is the lowest at 5 °C, reaching 50% at 9 °C, and then gradually decreases with increasing temperature. In the height range from −100 to −150 and −150 to −250 m, the occurrence probability of the inversion layer basically increases with the increase in the average temperature, and the occurrence probability ranges from 20 to 60% and from 10 to 80%, respectively. In summary, in seven different height ranges, the occurrence probability of the inversion layer is basically consistent with the fitted value. The occurrence probability of the temperature inversion layer is related to the average temperature and the average temperature difference between adjacent areas. The fitted formula has certain accuracy. Substituting the values of the coefficients A, B, and C in eq for the different height ranges in Table , one can get formula

Figure 7

Comparison of the fitted values with the actual occurrence probability of the inversion layer in seven different height regions: (a) height range of 400–100 m; (b) height range of 100–50 m; (c) height range of 50–0 m; (d) height range from 0 to −50 m; (e) height range from −50 to −100 m; (f) height range from −100 to −150 m; and (g) height range from −150 to −250 m.

If the average temperature within a certain altitude range and the average temperature difference within the adjacent altitude range are known, the occurrence probability of the temperature inversion layer within this range can be calculated according to eq . Based on this conclusion, the spatial distribution of the inversion layer of the open-pit mine can be accurately grasped.

Conclusions

Based on the field observation, numerical simulation, and theoretical analysis of the open-pit temperature field, the spatial distribution law of the temperature inversion layer is analyzed. The specific conclusions are as follows.

The parameters and boundary conditions are set reasonably during the numerical simulation process, and they can continue to be applied to the numerical simulation of the deep open-pit mine temperature field and concentration field.

The location inside the stope close to the southwest edge is more likely to present a temperature inversion, and the height range that is prone to temperature inversion is 100–0 m. The results are consistent with the results obtained by field observation that the probability of temperature inversion at the closed circle (+80 m) is much greater.

Based on nonlinear regression analysis, the calculation formulas among the occurrence probability of the inversion layer and the average temperature and the average temperature difference between adjacent areas in seven different height ranges are obtained. The formulas can calculate the occurrence probability of the inversion layer in this range and accurately predict the spatial position of the inversion layer.