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Simulation Of Mine Water Inflow: Case Study Of The Štavalj Coal Mine (Southwestern Serbia)

Simulation Of Mine Water Inflow: Case Study Of The Štavalj Coal Mine (Southwestern Serbia) Arch. Min. Sci., Vol. 60 (2015), No 4, p. 955­969 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.1515/amsc-2015-0063 BRANKO MILADINOVI*, VESNA RISTI VAKANJAC**, DRAGOMIR BUKUMIROVI***, VESELIN DRAGISI**, BORIS VAKANJAC**** SIMULATION OF MINE WATER INFLOW: CASE STUDY OF THE STAVALJ COAL MINE (SOUTHWESTERN SERBIA) SYMULACJA WPLYWU WÓD KOPALNIACH DO WYROBISKA. STUDIUM PRZYPADKU: KOPALNIA WGLA STAVALJ (POLUDNIOWO-ZACHODNIA SERBIA) The inflow of mine water to mining operations is often caused by random events such as precipitation. Consequently, the mine water inflow regime can be defined as a function of random events applying the theory of random processes. Regression models of the multiple linear correlation type have been used to simulate the inflow of mine water into mining operations, produce short-range predictions and facilitate rapid response inside the mine. The significance of such models lies in the ability to simulate and predict the consequences (mine water inflow), caused by events of a random nature (meteorological parameters: precipitation and air temperature). The presented prognostic models have been calibrated for mine water inflow to the Stavalj Coal Mine in southwestern Serbia. Mathematical dependencies were defined based on daily mine water inflow rates recorded during the period from 2003 to 2011, which can be used to generate short-range (1-7 day) predictions of mean daily mine water inflow rates to the Stavalj Coal Mine. A strong correlation (coefficient of correlation r = 0.93, Sig. = 0.00) was derived for the one-day forecast. The coefficients of correlation for predictions of mean daily mine water inflow rates related to time periods of two, three...seven days gradually declined to 0.63 (7-day mean daily inflow rate). Keywords: mine water, coal, simulation, short-range prediction Przedostawanie si wody do wyrobisk górniczych spowodowane jest czynnikami losowymi, na przyklad opadami. Dlatego te doplyw wód kopalniach zdefiniowa mona jako funkcj czynników losowych, z zastosowaniem teorii procesów losowych. Symulacje doplywu wód kopalniach do wyrobiska prowadzono z wykorzystaniem modelu regresji typu wielokrotnych korelacji liniowych, na tej podstawie opracowano prognozy krótkoterminowe, tym * ** *** **** GEOLOGICAL SURVEY OF SERBIA, BELGRADE, SERBIA, E-MAIL: BRANKO.MILADINOVIC@GZS.GOV.RS FACULTY OF MINING AND GEOLOGY, UNIVERSITY OF BELGRADE, SERBIA STAVALJ COAL MINE, SJENICA, SERBIA FACULTY OF APPLIED ECOLOGY, SINGIDUNUM UNIVERSITY, BELGRADE, SERBIA samym umoliwiajc podjecie szybkich dziala w kopalni. Znaczenie modeli takich polega na ich przydatnoci do symulacji i przewidywania skutków doplywu wód kopalnianych, spowodowanego czynnikami losowymi (parametry meteorologiczne: opady i temperatura powietrza). Zaproponowany model skalibrowany zostal na przykladzie badanego doplywu wód kopalnianych do kopalni Stavalj w poludniowo-zachodniej Serbii. Matematyczne zalenoci zdefiniowano w oparciu o dobowe natenia przeplywu wód kopalniach zarejestrowane w okresie od 2003 do 2011 roku, które wykorzysta mona do opracowania krótkoterminowych prognoz (obejmujcych 1-7 dni) redniego natenia przeplywu wody do kopalni wgla Stavalj. Stwierdzono wysoki poziom korelacji dla prognozy jednodniowej (wspólczynnik korelacji r = 0.93). Wartoci wspólczynnika korelacji otrzymywane dla kolejnych dni stopniowo malaly, do 0.63 dla prognozy siedmiodniowej. Slowa kluczowe: wody kopalniane, wgiel, symulacje, prognozy krótkoterminowe 1. Introduction Assessments of the conditions leading to the hydration of hard and subbituminous (black lignite) coal deposits in Serbia suggest that mine water inflow to underground mining operations is an inherent characteristic of all natural and anthropogenic processes that take place at a coal mining site. The main feature of these processes is their random nature in space and time, such that their outcome (mine water inflow) also has the characteristics of a random process. Given that the causes of mine water inflow are random events such as precipitation, the mine water inflow regime can be defined as a function of such a process applying the theory of random processes. The present research specifically assesses mine water inflow to the Stavalj Coal Mine. The Stavalj Coal Mine is one of the most prospective underground black lignite mining sites in Serbia (Fig. 1). Geological reserves of 240 million tons have been detected over only 20% of its surface area. However, it is also the wettest coal mine in Serbia. It was flooded on a number of occasions and measured mine water inflow rates as high as 200 l/s at certain coal extraction stages (Lukovi, 1970). Fig. 1. Satellite image of the Stavalj Coal Mine Correlation theories of random processes were used to simulate and produce short-range predictions of mine water inflow to this particular mine. Based on daily mine water inflow, precipitation and temperature data recorded during the period from 2003 to 2011, mathematical dependencies suitable for inflow rate estimation as a function of meteorological conditions were defined. Multiple linear correlation functions were used to establish the mathematical dependencies. A prognostic function defined in this way can be used for short-range predictions of mine water inflow to mining operations for time periods of one to seven days or more. 2. Mine water inflow simulation methods Regression models were used to simulate mine water inflow to mining operations, particularly the multiple linear regression model. The multiple linear regression model is commonly used to simulate or predict certain variables (Kresi, 2010). If an event is a function of two or more independent occurrences, then we speak of multiple linear regression. If the regression analysis is aimed to test multiple correlations, the number of observations N should be N > 50 + 8 m, where N ­ number of observations and m ­ number of independent variables (Tabachnick et al., 2007; Soldi-Aleksi, 2011). The significance of this type of model lies in the ability to predict the outcome of an event based on our knowledge about other occurrences. A correlation is in fact established between the dependent variable Y and independent variables X1, X2, ... Xk, to simulate or predict the independent variable over a certain time period (Prohaska, 2006). This dependency is expressed by the following regression model: Yi o 1 x1,i x 2 ,i ... x n ,i ei (1) where: Yi xi i ei -- -- -- -- dependent variable of the i-th order; independent variable of the i-th order; unknown coefficients of multiple regression and random error. Applying the least square method, the unknown coefficients of multiple regression were computed and Equation (1) became: ~ y a b1 x1 b2 x2 ... bn xn where: ~ -- analytical value of dependent variable; y a, b1, b2,...,bn -- computed numerical values of multiple regression coefficients. 3. Analysis of mine water inflow regime Opening of the mine and the initial stages of mining at the Stavalj Coal Mine caused intensive drainage of groundwater from a fractured aquifer formed in Miocene sediments overlying the coal seam (Fig. 2). Mine water inflow to the mining operations largely came from the faults intersected by mining (Markovi et al., 1996). Large surfaces excavated over time and caving of the coal seam roof enhanced surface water infiltration and enabled hydraulic linking of groundwaters from various faults (Zeremski et al., 1975). While coal was being extracted from a relatively shallow section of the mine, mine water inflow fluctuated to a large extent during the year, depending on the precipitation regime (Lukovi, 1970). The ratio of minimum to maximum mean monthly mine water inflow rates was 1:3. Under present mining conditions, where mining operations have reached a depth of 260 m from the ground surface, the mine water inflow rates are more uniform (Q = 51-77 l/s), but they still depend on the precipitation regime (Bukumirovi, 2002). The inflow interferes with coal extraction and necessitates considerable expenditures for ongoing maintenance of the drainage system. The pumping capacity has been designed for the current inflow rates. Inflow predictions are extremely important for safety reasons, to ensure appropriate sizing of the mine drains and handling of the maximum expected inflow rates. Fig. 2. Hydrogeological map of the extended area of the Stavalj Coal Mine, including characteristic section I-I' al ­ alluvium, intergranular aquifer; Pl ­ Pliocene gravel, sand and clay, hydrogeological complex; M2,3 ­ Miocene marl, marly limestone, clay and coal, hydrogeological complex; T2,3 ­ Middle and Upper Triassic limestones, karst aquifer; C ­ Carboniferous schists, non hydrated rocks The duration of minimal inflow rates is also very significant for coal mines. Such intervals are suitable for brief shutdowns of the drainage system to service electrical installations and piping, undertake pump maintenance or replacement, connect new drains, clean pipes from sediments that reduce their conveyance capacity, and the like. To assess the groundwater regime and simulate groundwater inflow (Risti-Vakanjac et al., 2012), it was necessary to first define the surface area of the terrain where inflow to the mining operations was formed directly from precipitation or indirectly by infiltration of a portion of the precipitation (Risti, 2007; Risti-Vakanjac et al., 2013). Based on available data (Cokorilo et al., 2011; Cokorilo, 2012), the mean annual evaporation rate (E) in the extended area of the Stavalj Coal Mine from 2003 to 2011 was 450 mm. In the same area, the mean long-term precipitation total (P) from 2003 to 2011 was 807.6 mm. Based on these data, the runoff layer (h) was: P E 807.6 450 357.6 mm The size of the drainage area (F) can be computed from the runoff layer (h) and mean annual groundwater inflow to the mining operations (Q), using the equation: h Q t F (2) where t is the time period in seconds. It follows from Equation (2) that the drainage area is: F Q t h 0.069 m 3 /s 31.536 10 6 s 0.357 m 6.0951 10 6 m 2 6.1 km 2 Table 1 shows the water balance parameters, where F is the size of the drainage area, P is the mean annual precipitation total, E is the mean annual evaporation rate, h is the runoff layer, Qav is the average annual groundwater inflow rate to the mine, q is the specific runoff, W is the water volume and j is the runoff coefficient. TABLE 1 Summary of groundwater balance parameters of the aquifer that discharges into the pit of the Stavalj Coal Mine F (km2) P (mm) E (mm) h (mm) Qav (m3/s) q (l/s/km2) W (106 m3) 4. Multiple linear regression results For multiple linear regression purposes, first an auto-correlation analysis of groundwater inflow to the mining operations (Fig. 3) and a cross-correlation analysis of precipitation and water inflow were undertaken for a time step of up to 100 days (Kresi, 2010), Figure 4. Fig. 3. Auto-correlation analysis of mine water inflow to the mining operations Fig. 4. Cross-correlation function of precipitation in the drainage area and mine water inflow to mining operations Figure 3 suggests that the effect of the groundwater inflow rate rapidly decreased with timestep increase. The auto-correlation coefficient stagnated for time steps of 25 to 28 days, while the correlation coefficients increased after 69 and 93 days (two peaks in the auto-correlogram), as a result of snowmelt following a long and cold winter (after 2-3 months). This was corroborated by the cross-correlogram. Even though the coefficients of correlation between daily precipitation and daily groundwater inflow to the mine were low for different time steps (up to 100 days), the cross-correlogram exhibited distinct peaks after 1, 24, 56 and 84 days, indicating higher groundwater inflow rates caused by snowmelt. Keeping this in mind and for the purpose of simulating mine water inflow using daily precipitation totals and mean daily temperatures, the predicted mean daily inflow to the Stavalj Coal Mine was derived applying multiple linear regression as follows: Qin flow ,i where: Qin flow P T a, b1, b2, b3, b4, b5 -- -- -- -- a b1 Pi b3 Pi b4 Pi b5 Ti (3) mean daily water inflow to the Stavalj Coal Mine on the i-th day; daily precipitation totals on days i­1, i­24, i­56 and i­84; mean daily air temperature on day i­1; dimensionless parameters defined by the least square method. The dimensionless parameters were obtained applying multiple linear regression and their values were: Qin flow,i 66.766 0.0354 Pi 0.0025 Pi 0.0094 Pi 0.0172 Pi 0.271 Ti (4) Analysis of the impact of predictor (Equation 4) on the variable (mine water inflow), are shown in Table 2. TABLE 2 Analysis of the impact of predictor (Equation 4) on the variable (mine water inflow) Dependent variable Independent variable Standardized Coefficients Sig. Mine water inflow at the moment i Precipitation at the moment i ­1 Precipitation at th moment i ­24 Precipitatin at the moment i ­56 Precipitation at themoment i ­84 Air temperature at the momentu i 0.019 ­0.011 ­0.019 0.003 0.491 F = 202.20; Sig. = 0.00; r = 0.49; Sig. = 0.00; Adjusted R² = 0.23 There is explained 23% of the variance in the dependent variable (R² = 0.23) by the regression model. The coefficient of correlation is r = 0.49; Sig. = 0.00. The model is statistically significant (F = 202.20; Sig. = 0.00). Precipitation at the moment i­1 ( = 0.019; Sig. = 0.039) and the air temperature at the moment i­1 ( = 0.491; Sig. = 0.000), impact on the mine water inflow at the moment i (Table 2). Figure 5 shows recorded groundwater inflow rates to the Stavalj Coal Mine and those computed from Equation (4). Fig. 5. Real and computed groundwater inflow rates to the Stavalj Coal Mine applying multiple linear correlation (Equation 4) A new dependency was established in order to ensure the best possible simulation of daily groundwater inflow rates. In addition to precipitation and temperature, an independent variable ­ groundwater inflow for a one-day time step ­ was introduced as: Qin flow,i a b1 Qin flow,i b4 Pi b3 Pi b5 Pi b6 Ti (5) where: Qin flow P T a, b1, b2, b3, b4, b5, b6 -- -- -- -- mean daily water inflow to the Stavalj Coal Mine on days i and i­1; daily precipitation totals on days i­1, i­24, i­56 and i­84; mean daily air temperature on the i-th day; dimensionless parameters defined by the least square method. Here, too, the dimensionless parameters were derived applying multiple linear regression and the values were: Qin flow,i 6.319 0.9048 Qin flow,i 0.00175 Pi 0.0087 Pi 0.00156 Pi 0.00527 Pi 0.02648 Ti (6) Analysis of the impact of the predictor (Equation 6) on the variable (mine water inflow), are shown in Table 3. TABLE 3 Analysis of the impact of the predictor (Equation 6) on the variable (mine water inflow) Dependent variable Independent variables Standardized Coefficients Sig. Mine water inflow at the moment i Mine water inflow i ­1 Precipitation at the moment i ­1 Precipitation at the moment i ­24 Precipitation at the moment i ­56 Precipitation at the moment i ­84 Air temperature at the moment i F = 353.4; Sig. = 0.00; r = 0.93; Sig. = 0.00; Adjusted R² = 0.86 There is explained 83% of the variance in the dependent variable (R² = 0.86) by the regression model. The coefficient of correlation is as high as r = 0.93; Sig. = 0.00. The model is statistically significant (F = 353.4; Sig. = 0.00). The mine water inflow at the moment i­1 ( = 0.908; Sig. = 0.000), the precipitation at the moment i­1 ( = 0.018; Sig. = 0.048) and the air temperature at the moment i ( = 0.047; Sig. = 0.000) impact the mine water inflow at the moment i (Table 3). Figure 6 shows recorded groundwater inflow rates to the Stavalj Coal Mine and those computed applying Equation 6, for the entire study period. In this way a strong correlation between computed and recorded groundwater flow rates was established. It can be used to predict in the short term (for the next day) the expected mine water inflow rate to the mining operations in the event of heavy rainfall. Fig. 6. Real and computed groundwater inflow rates to the Stavalj Coal Mine applying multiple linear correlation (Equation 6) Multiple linear regression was also used to predict mean weekly inflow rates, as follows: Qin flow, j a b1 Qin flow, j b2 Pj b3 T j (7) where: Qin flow Pj ­1 Tj ­1 a, b1, b2, b3 -- -- -- -- mean weekly inflow rate to the Stavalj Coal Mine, j-th week; weekly (7-day) precipitation total for week j­1; mean weekly air temperature for week j­1; dimensionless parameters defined by the least square method. After the dimensionless parameters were computed, Equation (7) became: Qin flow, j 27.798 0.5828 Qin flow, j 0.0041 Pj 0.1171 T j (8) Analysis of the impact of the predictor (Equation 8) on the variable (mean weekly mine water inflow), are shown in Table 4. There is explained 54% of the variance in the dependent variable (R² = 0.54) by the regression model. The coefficient of correlation is r = 0.73; Sig. = 0.00. The model is statistically significant (F = 179.1; Sig. = 0.00). The mean weekly mine water inflow related to the previous week j­1 ( = 0.590; Sig. = 0.000) and mean weekly temperatures of the previous week ( = 0.219; Sig. = 0.000) affect the mean weekly mine water inflow (Table 4). Statistical significance for both variables is at the 0.01 level. Likewise, total precipitation for the previous week affects the mean weekly mine water inflow ( = 0.180; Sig. = 0.049) (Table 4). This significance is at the very threshold limit value of statistical significance (0.05), but it also exceeds it, thus the impact has been confirmed. TABLE 4 Analysis of the impact of the predictor (Equation 8) on the variable (mean weekly mine water inflow) Dependent variable Independent variables Standardized Coefficients Sig. Mean weekly (7 days) mine water inflow Mean weekly, but related to the previous week (j ­1), mine water inflow Total precipitation for the previous week (j ­1) Mean weekly temperatures of the previous week (j ­1) F = 179.1; Sig. = 0.00; r = 0.73; Sig. = 0.00; Adjusted R² = 0.54 Figure 7 shows recorded mean weekly groundwater inflow rates to the Stavalj Coal Mine and those calculated from Equation (8), for the entire study period. Equation (8) can be used to predict mean weekly inflow rates to the Stavalj Coal Mine, or to predict in the short term (7 days) the expected average mine water inflow to the mining operations in the event of heavy rainfall. Fig. 7. Real and computed mean weekly groundwater inflow rates to the Stavalj Coal Mine applying multiple linear correlation (Equations 8) 5. Discussion The application of proposed multiple regression models required for the simulation of daily rates of mine water inflow (Equations 4 and 6) as well as the statistical analysis of the impact of the predictor on the analysed variable (Tables 2 and 3) have indicated that precipitation, temperatures and mine water inflows recorded for previous days justify statistically the formation of the proposed regression equation. However , it is statistically proved that previous precipitation recorded for 24, 56, and 84 days is not statistically justified to be used in the contemplated regression equations (Tables 2 and 3). In this case, for the above reasaons, the following regression dependence was used for simulation requirements of mine water inflow daily rates of the Stavalj Mine: Qin flow,i a b1 Qin flow,i b3 Ti (9) where: Qin flow P T a, b1, b2, b3 -- -- -- -- mean daily water inflow to the Stavalj Coal Mine on days i and i­1; daily precipitation totals on days i­1; mean daily air temperature on the i-th day; dimensionless parameters defined by the least square method. After the dimensionless parameters were computed, Equations (9) became: Qin flow,i 6.20522 0.90681 Qin flow,i 0.00736 Pi 0.02617 Ti (10) Analysis of the impact of the predictor (Equation 10) on the variable (mean daily mine water inflow), are shown in Table 5. TABLE 5 Analysis of the impact of the predictor (Equation 10) on the variable (mean daily mine water inflow) Dependent variable Independent variables Standardized Coefficients Sig. Mine water in flow at the moment i Mine water inflow at the moment i­1 Precipitation at the moment i­1 Air temperature at the moment i­1 F = 10615.4; Sig. = 0.00; r = 0.93; Sig. = 0.00; Adjusted R² = 0.86 The regression model explains 86% of the variance in the dependent variable (R² = 0.86). The coefficient of correlation is as high as r = 0.93; Sig. = 0.00. The model is statistically significant (F = 10615.4; Sig. = 0.00). The mine water inflow at the moment i­1 ( = 0.909; Sig. = 0.000), the precipitation at the moment i­1 ( = 0.018; Sig. = 0.048) and the air temperature at the moment i ( = 0.047; Sig. = 0.000) affect the mine water inflow at the moment i (Table 5). To determine mean daily inflow rates that can be expected in the next two, three, four,... seven days, correlations were established like in Equation (9), where the series of independent variables (precipitation, temperature and water inflow) reflected the time step for which the prediction was made (i­1, i­3, ... i­7). For example, a time step of two days was used for the independent variables to predict mean daily inflow rates, that is: Qin flow,i a b1 Qin flow,i b3 Ti (11) The same principle was applied to establish the correlations needed to predict mean daily inflow rates to the mining operations in the next 3, 4, 5, 6, and 7 days. The dimensionless parameters were determined applying the above-described procedure. The coefficients of correlation between recorded and computed daily inflow rates are shown in Table 6. TABLE 6 Coefficients of correlation between computed and recorded daily inflow rates to the mining operations for different prognostic time intervals as well as anaysis of predictor impact on variable (mean daily mine water inflow) Time interval 1 day Adjusted R² 0.86 F 10615.4** Coefficient of 0.932** correlation (r) Qi­n () 0.909** Ti­n () 0.047** Pi­n () 0.019* 2 days 0.75 4851.9** 0.867** 0.819** 0.091** 0.025** 3 days 0.64 2943.7** 0.805** 0.728** 0.139** 0.017* 4 days 0.56 2085.3** 0.753** 0.645** 0.185** 0.014 5 days 0.49 1590.4** 0.707** 0.573** 0.220** 0.012 6 days 0.44 1262.2** 0.665** 0.505** 0.251** 0.011 7 days 0.39 1046.7** 0.629** 0.450** 0.273** / * Statistical significance at the level of 0.05 ** Statistical significance at the level of 0.01 The multiple linear correlation method applied to simulate and generate short-range (one to seven day) predictions of mine water inflow rates to the Stavalj Coal Mine yielded good results. Analyses presented in Table 6 indicate that mine water inflows, precipitation and temperatures registered in time intervals of one, two or three days can be used for the prognosis of the mine water inflow up to 3 days in advance. After the third day precipitation loses statistical significance thus for the requirements of the simulation of mine water inflow for time intervals (4, 5, 6, and 7 days) only mine water inflows and temperatures can be used. The coefficients of correlation were from 0.63 to 0.93 (Equation 9 and 10 and Table 6). A common feature of the simulations and derived prognostic equations was that the computed values were generally higher than recorded values in the winter months, and vice-versa in the summer months (Figure 8). The apparent differences were a result of snowfall and the temperature regime in the Stavalj Coal Mine area (alt. 1040 m), where the long-term mean air temperature was 6.4oC (1960-2011), and the mean monthly temperatures in December, January and February were almost always sub-zero. For this period, the model considered snowfall at the time of occurrence, and not from the time snowmelt and infiltration into the underground began. For the duration of snow cover on frigid days, the computed inflow rates were higher than recorded rates, by up to 18% (Figure 8, black circles). When there was infiltration due to snowmelt, the computed inflow rates were up to 15% lower (Figure 8, red circle), compared to measured rates. These differences are numerically represented in Table 7. 80 groundwater inflow in the mine Q (l/s) 50 May-05 Jun-05 Aug-05 Sep-05 Mar-05 Apr-05 Oct-05 Jul-05 Nov-05 Dec-05 Feb-05 Jan-05 Qinflow,measured Qinflow,calculated Fig. 8. Real and computed groundwater inflow rates to the Stavalj Coal Mine applying multiple linear correlation (Equation 10), year 2005 Due to a lack of data, the model did not take into account the temporal redistribution of precipitation occurring in the form of snow and remaining on the ground surface as snow cover. TABLE 7 Mean monthly and absolute maximum and minimum monthly departures from computed inflow rates, relative to recorded rates (%), derived for the year 2005 using Equation (10) Month Jan Av ­0.2 Max 6.8 Min ­7.3 Feb 0.2 4.9 ­12.9 Mar ­0.8 15.5 ­18.0 Apr 0.0 7.8 ­9.0 May 0.1 4.0 ­4.2 June 0.2 3.0 ­2.7 July 0.0 5.1 ­1.6 Aug ­0.1 5.3 ­4.2 Sep ­0.3 3.9 ­5.7 Oct 0.5 4.2 ­1.4 Nov ­0.9 3.1 ­12.6 Dec ­0.4 8.2 ­4.1 Distinct differences between seasonal inflow rates to the mine (Fig. 9) corroborated the above findings. These differences were more pronounced in the coldest years, like 2003, 2005 and 2008 (Fig. 9). In 2011, which was the warmest year with very little snow, the differences between seasonal inflow rates were virtually negligible as the groundwater inflow to the Stavalj Coal Mine was rather uniform throughout the year (Fig. 9). Fig. 9. Mean seasonal mine water inflow rates to the Stavalj Coal Mine 6. Conclusion Regression models are commonly used to simulate or predict dependent variables. Multiple linear regression was applied in the present research to simulate and produce short-range predictions of groundwater inflow rates to the Stavalj Coal Mine. To establish correlations, the independent variables used included daily precipitation totals, temperatures and daily groundwater inflows for time steps of i = 1, 2, 3..., or for the time periods for which the mine water inflow prediction was generated. For short-range predictions of one day (i = 1), applying the theory of multiple linear regression, the equation Qin flow,i 6.20522 0.90681 Qin flow,i 0.00736 Pi 0.02617 Ti produced very good results; the coefficient of correlation between recorded and computed inflow rates was 0.93. The same principle was applied to derive the dependencies needed to predict inflow rates to the mining operations in the next 2, 3, ... 7 days. As the prognostic time interval grew, the coefficient of correlation between computed and recorded values decreased, such that for the prognostic time interval of 7 days r = 0.63, which was still a strong enough correlation. However, although the correlation coefficients are satisfactory, the impact of precipitation loses statistical significance for short-range predictions exceeding three days ,thus, for these prognoses, there may be used only mine water inflows and mean daily temperatures with lengthening of time interval, for which short range predictions (4, 5, 6, and 7 days) are made. It should be noted in closing that had snow data been available, the coefficients of correlation would have been much higher (i.e. the derived dependencies would have simulated groundwater inflow rates to the mining operations much better). In fact, the applied models did not take into account the time interval during which water was stored in the snow cover on the ground surface, or the period of snowmelt following an air temperature increase. Acknowledgment We express our gratitude to the Stavalj Coal Mine for making available mine water inflow monitoring data. We also thank the National Hydrometeorological Service for providing access to meteorological data, as well as Project 47003 funded by the Ministry of Education and Science. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Mining Sciences de Gruyter

Simulation Of Mine Water Inflow: Case Study Of The Štavalj Coal Mine (Southwestern Serbia)

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Arch. Min. Sci., Vol. 60 (2015), No 4, p. 955­969 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.1515/amsc-2015-0063 BRANKO MILADINOVI*, VESNA RISTI VAKANJAC**, DRAGOMIR BUKUMIROVI***, VESELIN DRAGISI**, BORIS VAKANJAC**** SIMULATION OF MINE WATER INFLOW: CASE STUDY OF THE STAVALJ COAL MINE (SOUTHWESTERN SERBIA) SYMULACJA WPLYWU WÓD KOPALNIACH DO WYROBISKA. STUDIUM PRZYPADKU: KOPALNIA WGLA STAVALJ (POLUDNIOWO-ZACHODNIA SERBIA) The inflow of mine water to mining operations is often caused by random events such as precipitation. Consequently, the mine water inflow regime can be defined as a function of random events applying the theory of random processes. Regression models of the multiple linear correlation type have been used to simulate the inflow of mine water into mining operations, produce short-range predictions and facilitate rapid response inside the mine. The significance of such models lies in the ability to simulate and predict the consequences (mine water inflow), caused by events of a random nature (meteorological parameters: precipitation and air temperature). The presented prognostic models have been calibrated for mine water inflow to the Stavalj Coal Mine in southwestern Serbia. Mathematical dependencies were defined based on daily mine water inflow rates recorded during the period from 2003 to 2011, which can be used to generate short-range (1-7 day) predictions of mean daily mine water inflow rates to the Stavalj Coal Mine. A strong correlation (coefficient of correlation r = 0.93, Sig. = 0.00) was derived for the one-day forecast. The coefficients of correlation for predictions of mean daily mine water inflow rates related to time periods of two, three...seven days gradually declined to 0.63 (7-day mean daily inflow rate). Keywords: mine water, coal, simulation, short-range prediction Przedostawanie si wody do wyrobisk górniczych spowodowane jest czynnikami losowymi, na przyklad opadami. Dlatego te doplyw wód kopalniach zdefiniowa mona jako funkcj czynników losowych, z zastosowaniem teorii procesów losowych. Symulacje doplywu wód kopalniach do wyrobiska prowadzono z wykorzystaniem modelu regresji typu wielokrotnych korelacji liniowych, na tej podstawie opracowano prognozy krótkoterminowe, tym * ** *** **** GEOLOGICAL SURVEY OF SERBIA, BELGRADE, SERBIA, E-MAIL: BRANKO.MILADINOVIC@GZS.GOV.RS FACULTY OF MINING AND GEOLOGY, UNIVERSITY OF BELGRADE, SERBIA STAVALJ COAL MINE, SJENICA, SERBIA FACULTY OF APPLIED ECOLOGY, SINGIDUNUM UNIVERSITY, BELGRADE, SERBIA samym umoliwiajc podjecie szybkich dziala w kopalni. Znaczenie modeli takich polega na ich przydatnoci do symulacji i przewidywania skutków doplywu wód kopalnianych, spowodowanego czynnikami losowymi (parametry meteorologiczne: opady i temperatura powietrza). Zaproponowany model skalibrowany zostal na przykladzie badanego doplywu wód kopalnianych do kopalni Stavalj w poludniowo-zachodniej Serbii. Matematyczne zalenoci zdefiniowano w oparciu o dobowe natenia przeplywu wód kopalniach zarejestrowane w okresie od 2003 do 2011 roku, które wykorzysta mona do opracowania krótkoterminowych prognoz (obejmujcych 1-7 dni) redniego natenia przeplywu wody do kopalni wgla Stavalj. Stwierdzono wysoki poziom korelacji dla prognozy jednodniowej (wspólczynnik korelacji r = 0.93). Wartoci wspólczynnika korelacji otrzymywane dla kolejnych dni stopniowo malaly, do 0.63 dla prognozy siedmiodniowej. Slowa kluczowe: wody kopalniane, wgiel, symulacje, prognozy krótkoterminowe 1. Introduction Assessments of the conditions leading to the hydration of hard and subbituminous (black lignite) coal deposits in Serbia suggest that mine water inflow to underground mining operations is an inherent characteristic of all natural and anthropogenic processes that take place at a coal mining site. The main feature of these processes is their random nature in space and time, such that their outcome (mine water inflow) also has the characteristics of a random process. Given that the causes of mine water inflow are random events such as precipitation, the mine water inflow regime can be defined as a function of such a process applying the theory of random processes. The present research specifically assesses mine water inflow to the Stavalj Coal Mine. The Stavalj Coal Mine is one of the most prospective underground black lignite mining sites in Serbia (Fig. 1). Geological reserves of 240 million tons have been detected over only 20% of its surface area. However, it is also the wettest coal mine in Serbia. It was flooded on a number of occasions and measured mine water inflow rates as high as 200 l/s at certain coal extraction stages (Lukovi, 1970). Fig. 1. Satellite image of the Stavalj Coal Mine Correlation theories of random processes were used to simulate and produce short-range predictions of mine water inflow to this particular mine. Based on daily mine water inflow, precipitation and temperature data recorded during the period from 2003 to 2011, mathematical dependencies suitable for inflow rate estimation as a function of meteorological conditions were defined. Multiple linear correlation functions were used to establish the mathematical dependencies. A prognostic function defined in this way can be used for short-range predictions of mine water inflow to mining operations for time periods of one to seven days or more. 2. Mine water inflow simulation methods Regression models were used to simulate mine water inflow to mining operations, particularly the multiple linear regression model. The multiple linear regression model is commonly used to simulate or predict certain variables (Kresi, 2010). If an event is a function of two or more independent occurrences, then we speak of multiple linear regression. If the regression analysis is aimed to test multiple correlations, the number of observations N should be N > 50 + 8 m, where N ­ number of observations and m ­ number of independent variables (Tabachnick et al., 2007; Soldi-Aleksi, 2011). The significance of this type of model lies in the ability to predict the outcome of an event based on our knowledge about other occurrences. A correlation is in fact established between the dependent variable Y and independent variables X1, X2, ... Xk, to simulate or predict the independent variable over a certain time period (Prohaska, 2006). This dependency is expressed by the following regression model: Yi o 1 x1,i x 2 ,i ... x n ,i ei (1) where: Yi xi i ei -- -- -- -- dependent variable of the i-th order; independent variable of the i-th order; unknown coefficients of multiple regression and random error. Applying the least square method, the unknown coefficients of multiple regression were computed and Equation (1) became: ~ y a b1 x1 b2 x2 ... bn xn where: ~ -- analytical value of dependent variable; y a, b1, b2,...,bn -- computed numerical values of multiple regression coefficients. 3. Analysis of mine water inflow regime Opening of the mine and the initial stages of mining at the Stavalj Coal Mine caused intensive drainage of groundwater from a fractured aquifer formed in Miocene sediments overlying the coal seam (Fig. 2). Mine water inflow to the mining operations largely came from the faults intersected by mining (Markovi et al., 1996). Large surfaces excavated over time and caving of the coal seam roof enhanced surface water infiltration and enabled hydraulic linking of groundwaters from various faults (Zeremski et al., 1975). While coal was being extracted from a relatively shallow section of the mine, mine water inflow fluctuated to a large extent during the year, depending on the precipitation regime (Lukovi, 1970). The ratio of minimum to maximum mean monthly mine water inflow rates was 1:3. Under present mining conditions, where mining operations have reached a depth of 260 m from the ground surface, the mine water inflow rates are more uniform (Q = 51-77 l/s), but they still depend on the precipitation regime (Bukumirovi, 2002). The inflow interferes with coal extraction and necessitates considerable expenditures for ongoing maintenance of the drainage system. The pumping capacity has been designed for the current inflow rates. Inflow predictions are extremely important for safety reasons, to ensure appropriate sizing of the mine drains and handling of the maximum expected inflow rates. Fig. 2. Hydrogeological map of the extended area of the Stavalj Coal Mine, including characteristic section I-I' al ­ alluvium, intergranular aquifer; Pl ­ Pliocene gravel, sand and clay, hydrogeological complex; M2,3 ­ Miocene marl, marly limestone, clay and coal, hydrogeological complex; T2,3 ­ Middle and Upper Triassic limestones, karst aquifer; C ­ Carboniferous schists, non hydrated rocks The duration of minimal inflow rates is also very significant for coal mines. Such intervals are suitable for brief shutdowns of the drainage system to service electrical installations and piping, undertake pump maintenance or replacement, connect new drains, clean pipes from sediments that reduce their conveyance capacity, and the like. To assess the groundwater regime and simulate groundwater inflow (Risti-Vakanjac et al., 2012), it was necessary to first define the surface area of the terrain where inflow to the mining operations was formed directly from precipitation or indirectly by infiltration of a portion of the precipitation (Risti, 2007; Risti-Vakanjac et al., 2013). Based on available data (Cokorilo et al., 2011; Cokorilo, 2012), the mean annual evaporation rate (E) in the extended area of the Stavalj Coal Mine from 2003 to 2011 was 450 mm. In the same area, the mean long-term precipitation total (P) from 2003 to 2011 was 807.6 mm. Based on these data, the runoff layer (h) was: P E 807.6 450 357.6 mm The size of the drainage area (F) can be computed from the runoff layer (h) and mean annual groundwater inflow to the mining operations (Q), using the equation: h Q t F (2) where t is the time period in seconds. It follows from Equation (2) that the drainage area is: F Q t h 0.069 m 3 /s 31.536 10 6 s 0.357 m 6.0951 10 6 m 2 6.1 km 2 Table 1 shows the water balance parameters, where F is the size of the drainage area, P is the mean annual precipitation total, E is the mean annual evaporation rate, h is the runoff layer, Qav is the average annual groundwater inflow rate to the mine, q is the specific runoff, W is the water volume and j is the runoff coefficient. TABLE 1 Summary of groundwater balance parameters of the aquifer that discharges into the pit of the Stavalj Coal Mine F (km2) P (mm) E (mm) h (mm) Qav (m3/s) q (l/s/km2) W (106 m3) 4. Multiple linear regression results For multiple linear regression purposes, first an auto-correlation analysis of groundwater inflow to the mining operations (Fig. 3) and a cross-correlation analysis of precipitation and water inflow were undertaken for a time step of up to 100 days (Kresi, 2010), Figure 4. Fig. 3. Auto-correlation analysis of mine water inflow to the mining operations Fig. 4. Cross-correlation function of precipitation in the drainage area and mine water inflow to mining operations Figure 3 suggests that the effect of the groundwater inflow rate rapidly decreased with timestep increase. The auto-correlation coefficient stagnated for time steps of 25 to 28 days, while the correlation coefficients increased after 69 and 93 days (two peaks in the auto-correlogram), as a result of snowmelt following a long and cold winter (after 2-3 months). This was corroborated by the cross-correlogram. Even though the coefficients of correlation between daily precipitation and daily groundwater inflow to the mine were low for different time steps (up to 100 days), the cross-correlogram exhibited distinct peaks after 1, 24, 56 and 84 days, indicating higher groundwater inflow rates caused by snowmelt. Keeping this in mind and for the purpose of simulating mine water inflow using daily precipitation totals and mean daily temperatures, the predicted mean daily inflow to the Stavalj Coal Mine was derived applying multiple linear regression as follows: Qin flow ,i where: Qin flow P T a, b1, b2, b3, b4, b5 -- -- -- -- a b1 Pi b3 Pi b4 Pi b5 Ti (3) mean daily water inflow to the Stavalj Coal Mine on the i-th day; daily precipitation totals on days i­1, i­24, i­56 and i­84; mean daily air temperature on day i­1; dimensionless parameters defined by the least square method. The dimensionless parameters were obtained applying multiple linear regression and their values were: Qin flow,i 66.766 0.0354 Pi 0.0025 Pi 0.0094 Pi 0.0172 Pi 0.271 Ti (4) Analysis of the impact of predictor (Equation 4) on the variable (mine water inflow), are shown in Table 2. TABLE 2 Analysis of the impact of predictor (Equation 4) on the variable (mine water inflow) Dependent variable Independent variable Standardized Coefficients Sig. Mine water inflow at the moment i Precipitation at the moment i ­1 Precipitation at th moment i ­24 Precipitatin at the moment i ­56 Precipitation at themoment i ­84 Air temperature at the momentu i 0.019 ­0.011 ­0.019 0.003 0.491 F = 202.20; Sig. = 0.00; r = 0.49; Sig. = 0.00; Adjusted R² = 0.23 There is explained 23% of the variance in the dependent variable (R² = 0.23) by the regression model. The coefficient of correlation is r = 0.49; Sig. = 0.00. The model is statistically significant (F = 202.20; Sig. = 0.00). Precipitation at the moment i­1 ( = 0.019; Sig. = 0.039) and the air temperature at the moment i­1 ( = 0.491; Sig. = 0.000), impact on the mine water inflow at the moment i (Table 2). Figure 5 shows recorded groundwater inflow rates to the Stavalj Coal Mine and those computed from Equation (4). Fig. 5. Real and computed groundwater inflow rates to the Stavalj Coal Mine applying multiple linear correlation (Equation 4) A new dependency was established in order to ensure the best possible simulation of daily groundwater inflow rates. In addition to precipitation and temperature, an independent variable ­ groundwater inflow for a one-day time step ­ was introduced as: Qin flow,i a b1 Qin flow,i b4 Pi b3 Pi b5 Pi b6 Ti (5) where: Qin flow P T a, b1, b2, b3, b4, b5, b6 -- -- -- -- mean daily water inflow to the Stavalj Coal Mine on days i and i­1; daily precipitation totals on days i­1, i­24, i­56 and i­84; mean daily air temperature on the i-th day; dimensionless parameters defined by the least square method. Here, too, the dimensionless parameters were derived applying multiple linear regression and the values were: Qin flow,i 6.319 0.9048 Qin flow,i 0.00175 Pi 0.0087 Pi 0.00156 Pi 0.00527 Pi 0.02648 Ti (6) Analysis of the impact of the predictor (Equation 6) on the variable (mine water inflow), are shown in Table 3. TABLE 3 Analysis of the impact of the predictor (Equation 6) on the variable (mine water inflow) Dependent variable Independent variables Standardized Coefficients Sig. Mine water inflow at the moment i Mine water inflow i ­1 Precipitation at the moment i ­1 Precipitation at the moment i ­24 Precipitation at the moment i ­56 Precipitation at the moment i ­84 Air temperature at the moment i F = 353.4; Sig. = 0.00; r = 0.93; Sig. = 0.00; Adjusted R² = 0.86 There is explained 83% of the variance in the dependent variable (R² = 0.86) by the regression model. The coefficient of correlation is as high as r = 0.93; Sig. = 0.00. The model is statistically significant (F = 353.4; Sig. = 0.00). The mine water inflow at the moment i­1 ( = 0.908; Sig. = 0.000), the precipitation at the moment i­1 ( = 0.018; Sig. = 0.048) and the air temperature at the moment i ( = 0.047; Sig. = 0.000) impact the mine water inflow at the moment i (Table 3). Figure 6 shows recorded groundwater inflow rates to the Stavalj Coal Mine and those computed applying Equation 6, for the entire study period. In this way a strong correlation between computed and recorded groundwater flow rates was established. It can be used to predict in the short term (for the next day) the expected mine water inflow rate to the mining operations in the event of heavy rainfall. Fig. 6. Real and computed groundwater inflow rates to the Stavalj Coal Mine applying multiple linear correlation (Equation 6) Multiple linear regression was also used to predict mean weekly inflow rates, as follows: Qin flow, j a b1 Qin flow, j b2 Pj b3 T j (7) where: Qin flow Pj ­1 Tj ­1 a, b1, b2, b3 -- -- -- -- mean weekly inflow rate to the Stavalj Coal Mine, j-th week; weekly (7-day) precipitation total for week j­1; mean weekly air temperature for week j­1; dimensionless parameters defined by the least square method. After the dimensionless parameters were computed, Equation (7) became: Qin flow, j 27.798 0.5828 Qin flow, j 0.0041 Pj 0.1171 T j (8) Analysis of the impact of the predictor (Equation 8) on the variable (mean weekly mine water inflow), are shown in Table 4. There is explained 54% of the variance in the dependent variable (R² = 0.54) by the regression model. The coefficient of correlation is r = 0.73; Sig. = 0.00. The model is statistically significant (F = 179.1; Sig. = 0.00). The mean weekly mine water inflow related to the previous week j­1 ( = 0.590; Sig. = 0.000) and mean weekly temperatures of the previous week ( = 0.219; Sig. = 0.000) affect the mean weekly mine water inflow (Table 4). Statistical significance for both variables is at the 0.01 level. Likewise, total precipitation for the previous week affects the mean weekly mine water inflow ( = 0.180; Sig. = 0.049) (Table 4). This significance is at the very threshold limit value of statistical significance (0.05), but it also exceeds it, thus the impact has been confirmed. TABLE 4 Analysis of the impact of the predictor (Equation 8) on the variable (mean weekly mine water inflow) Dependent variable Independent variables Standardized Coefficients Sig. Mean weekly (7 days) mine water inflow Mean weekly, but related to the previous week (j ­1), mine water inflow Total precipitation for the previous week (j ­1) Mean weekly temperatures of the previous week (j ­1) F = 179.1; Sig. = 0.00; r = 0.73; Sig. = 0.00; Adjusted R² = 0.54 Figure 7 shows recorded mean weekly groundwater inflow rates to the Stavalj Coal Mine and those calculated from Equation (8), for the entire study period. Equation (8) can be used to predict mean weekly inflow rates to the Stavalj Coal Mine, or to predict in the short term (7 days) the expected average mine water inflow to the mining operations in the event of heavy rainfall. Fig. 7. Real and computed mean weekly groundwater inflow rates to the Stavalj Coal Mine applying multiple linear correlation (Equations 8) 5. Discussion The application of proposed multiple regression models required for the simulation of daily rates of mine water inflow (Equations 4 and 6) as well as the statistical analysis of the impact of the predictor on the analysed variable (Tables 2 and 3) have indicated that precipitation, temperatures and mine water inflows recorded for previous days justify statistically the formation of the proposed regression equation. However , it is statistically proved that previous precipitation recorded for 24, 56, and 84 days is not statistically justified to be used in the contemplated regression equations (Tables 2 and 3). In this case, for the above reasaons, the following regression dependence was used for simulation requirements of mine water inflow daily rates of the Stavalj Mine: Qin flow,i a b1 Qin flow,i b3 Ti (9) where: Qin flow P T a, b1, b2, b3 -- -- -- -- mean daily water inflow to the Stavalj Coal Mine on days i and i­1; daily precipitation totals on days i­1; mean daily air temperature on the i-th day; dimensionless parameters defined by the least square method. After the dimensionless parameters were computed, Equations (9) became: Qin flow,i 6.20522 0.90681 Qin flow,i 0.00736 Pi 0.02617 Ti (10) Analysis of the impact of the predictor (Equation 10) on the variable (mean daily mine water inflow), are shown in Table 5. TABLE 5 Analysis of the impact of the predictor (Equation 10) on the variable (mean daily mine water inflow) Dependent variable Independent variables Standardized Coefficients Sig. Mine water in flow at the moment i Mine water inflow at the moment i­1 Precipitation at the moment i­1 Air temperature at the moment i­1 F = 10615.4; Sig. = 0.00; r = 0.93; Sig. = 0.00; Adjusted R² = 0.86 The regression model explains 86% of the variance in the dependent variable (R² = 0.86). The coefficient of correlation is as high as r = 0.93; Sig. = 0.00. The model is statistically significant (F = 10615.4; Sig. = 0.00). The mine water inflow at the moment i­1 ( = 0.909; Sig. = 0.000), the precipitation at the moment i­1 ( = 0.018; Sig. = 0.048) and the air temperature at the moment i ( = 0.047; Sig. = 0.000) affect the mine water inflow at the moment i (Table 5). To determine mean daily inflow rates that can be expected in the next two, three, four,... seven days, correlations were established like in Equation (9), where the series of independent variables (precipitation, temperature and water inflow) reflected the time step for which the prediction was made (i­1, i­3, ... i­7). For example, a time step of two days was used for the independent variables to predict mean daily inflow rates, that is: Qin flow,i a b1 Qin flow,i b3 Ti (11) The same principle was applied to establish the correlations needed to predict mean daily inflow rates to the mining operations in the next 3, 4, 5, 6, and 7 days. The dimensionless parameters were determined applying the above-described procedure. The coefficients of correlation between recorded and computed daily inflow rates are shown in Table 6. TABLE 6 Coefficients of correlation between computed and recorded daily inflow rates to the mining operations for different prognostic time intervals as well as anaysis of predictor impact on variable (mean daily mine water inflow) Time interval 1 day Adjusted R² 0.86 F 10615.4** Coefficient of 0.932** correlation (r) Qi­n () 0.909** Ti­n () 0.047** Pi­n () 0.019* 2 days 0.75 4851.9** 0.867** 0.819** 0.091** 0.025** 3 days 0.64 2943.7** 0.805** 0.728** 0.139** 0.017* 4 days 0.56 2085.3** 0.753** 0.645** 0.185** 0.014 5 days 0.49 1590.4** 0.707** 0.573** 0.220** 0.012 6 days 0.44 1262.2** 0.665** 0.505** 0.251** 0.011 7 days 0.39 1046.7** 0.629** 0.450** 0.273** / * Statistical significance at the level of 0.05 ** Statistical significance at the level of 0.01 The multiple linear correlation method applied to simulate and generate short-range (one to seven day) predictions of mine water inflow rates to the Stavalj Coal Mine yielded good results. Analyses presented in Table 6 indicate that mine water inflows, precipitation and temperatures registered in time intervals of one, two or three days can be used for the prognosis of the mine water inflow up to 3 days in advance. After the third day precipitation loses statistical significance thus for the requirements of the simulation of mine water inflow for time intervals (4, 5, 6, and 7 days) only mine water inflows and temperatures can be used. The coefficients of correlation were from 0.63 to 0.93 (Equation 9 and 10 and Table 6). A common feature of the simulations and derived prognostic equations was that the computed values were generally higher than recorded values in the winter months, and vice-versa in the summer months (Figure 8). The apparent differences were a result of snowfall and the temperature regime in the Stavalj Coal Mine area (alt. 1040 m), where the long-term mean air temperature was 6.4oC (1960-2011), and the mean monthly temperatures in December, January and February were almost always sub-zero. For this period, the model considered snowfall at the time of occurrence, and not from the time snowmelt and infiltration into the underground began. For the duration of snow cover on frigid days, the computed inflow rates were higher than recorded rates, by up to 18% (Figure 8, black circles). When there was infiltration due to snowmelt, the computed inflow rates were up to 15% lower (Figure 8, red circle), compared to measured rates. These differences are numerically represented in Table 7. 80 groundwater inflow in the mine Q (l/s) 50 May-05 Jun-05 Aug-05 Sep-05 Mar-05 Apr-05 Oct-05 Jul-05 Nov-05 Dec-05 Feb-05 Jan-05 Qinflow,measured Qinflow,calculated Fig. 8. Real and computed groundwater inflow rates to the Stavalj Coal Mine applying multiple linear correlation (Equation 10), year 2005 Due to a lack of data, the model did not take into account the temporal redistribution of precipitation occurring in the form of snow and remaining on the ground surface as snow cover. TABLE 7 Mean monthly and absolute maximum and minimum monthly departures from computed inflow rates, relative to recorded rates (%), derived for the year 2005 using Equation (10) Month Jan Av ­0.2 Max 6.8 Min ­7.3 Feb 0.2 4.9 ­12.9 Mar ­0.8 15.5 ­18.0 Apr 0.0 7.8 ­9.0 May 0.1 4.0 ­4.2 June 0.2 3.0 ­2.7 July 0.0 5.1 ­1.6 Aug ­0.1 5.3 ­4.2 Sep ­0.3 3.9 ­5.7 Oct 0.5 4.2 ­1.4 Nov ­0.9 3.1 ­12.6 Dec ­0.4 8.2 ­4.1 Distinct differences between seasonal inflow rates to the mine (Fig. 9) corroborated the above findings. These differences were more pronounced in the coldest years, like 2003, 2005 and 2008 (Fig. 9). In 2011, which was the warmest year with very little snow, the differences between seasonal inflow rates were virtually negligible as the groundwater inflow to the Stavalj Coal Mine was rather uniform throughout the year (Fig. 9). Fig. 9. Mean seasonal mine water inflow rates to the Stavalj Coal Mine 6. Conclusion Regression models are commonly used to simulate or predict dependent variables. Multiple linear regression was applied in the present research to simulate and produce short-range predictions of groundwater inflow rates to the Stavalj Coal Mine. To establish correlations, the independent variables used included daily precipitation totals, temperatures and daily groundwater inflows for time steps of i = 1, 2, 3..., or for the time periods for which the mine water inflow prediction was generated. For short-range predictions of one day (i = 1), applying the theory of multiple linear regression, the equation Qin flow,i 6.20522 0.90681 Qin flow,i 0.00736 Pi 0.02617 Ti produced very good results; the coefficient of correlation between recorded and computed inflow rates was 0.93. The same principle was applied to derive the dependencies needed to predict inflow rates to the mining operations in the next 2, 3, ... 7 days. As the prognostic time interval grew, the coefficient of correlation between computed and recorded values decreased, such that for the prognostic time interval of 7 days r = 0.63, which was still a strong enough correlation. However, although the correlation coefficients are satisfactory, the impact of precipitation loses statistical significance for short-range predictions exceeding three days ,thus, for these prognoses, there may be used only mine water inflows and mean daily temperatures with lengthening of time interval, for which short range predictions (4, 5, 6, and 7 days) are made. It should be noted in closing that had snow data been available, the coefficients of correlation would have been much higher (i.e. the derived dependencies would have simulated groundwater inflow rates to the mining operations much better). In fact, the applied models did not take into account the time interval during which water was stored in the snow cover on the ground surface, or the period of snowmelt following an air temperature increase. Acknowledgment We express our gratitude to the Stavalj Coal Mine for making available mine water inflow monitoring data. We also thank the National Hydrometeorological Service for providing access to meteorological data, as well as Project 47003 funded by the Ministry of Education and Science.

Journal

Archives of Mining Sciencesde Gruyter

Published: Dec 1, 2015

References