Seals are widely used in underground US coal mines to isolate mined-out workings, thereby reducing the ventilation load for the mine. With increased longwall panel sizes being realised by current mining equipment, large, mined-out areas of coal mines must be either ventilated or isolated from active workings by mine seals. Areas behind mine seals can be very expansive, potentially consisting of multiple longwall panel gobs or mined-out areas of super sections with pillared, high-extraction areas. In general, sealed mine sections are typically designed to become inert over time as coal bed gas is emitted from the coal and the oxygen component is diminished through oxidation or leakage. Consequently, mine seals are designed to isolate active workings from mined-out sections that are rich in gases emitted from the coal bed and depleted in oxygen.

Two mining disasters during 2006 had a profound effect on mining law in the US. The first of these events was the methane explosion at the Wolf Run Mining Company’s Sago Mine which resulted in 12 fatalities and one injury in January 2006 [1]. Later in 2006, the Darby No. 1 Mine experienced a methane explosion which killed five workers and injured another [2]. A common element in these two explosions was the close proximity of mine seals that isolated mined-out workings to the active work sites where the miners were killed or injured. Methane–air mixtures behind the seals were ignited either within the mined-out, isolated workings or at the seal line interface. As a consequence of both mine explosions, the seal lines were heavily damaged and were no longer functional as ventilation structures.

A National Institute for Occupation Safety and Health (NIOSH) investigation of mine seal design resulted in a publication by Zipf et al. [3]. This research presented data on the explosive force of methane–air mixtures and demonstrated the inadequacy of the pre-2007 design standard of 140 kPa (20 psi) to withstand the energy associated with a mine explosion. The authors recommended a new set of design parameters for underground mine seals. These research recommendations were largely adopted by US coal mining regulators and were included in new law that was covered in the revised regulation [4]. The regulations greatly increased the structural strength requirements of underground mine seals from the previous 140 kPa (20 psi) standard. The new design parameters allow mine operators to choose from more than one design strength standard and monitoring requirement, but did not address acceptable rates of leakage through the higher strength mine seals. Leakage rates were determined for the prior 140 kPa (20 psi) seal standard and the performances for a variety of seal designs had been reported for testing conducted at a limestone mine [5].

Although the strength of US mine seals has been greatly increased in the US since the Mine Improvement and New Emergency Response Act (MINER Act) of 2006, some questions regarding mine seal performance remain unanswered. Many US coal mine operators have chosen to install the 830 kPa (120 psi) design option (instead of the 340 kPa (50 psi) option) which requires only periodic monitoring of the gas composition behind the mine seal through a sample pipe. Under these circumstances, the gas composition behind seals is not well established and changes in gas composition behind the seals are poorly defined, due to the limited sampling frequency and the lack of reported data from these sites. No leakage rates around or through 340 or 830 kPa (50 or 120 psi) seals have been reported. Many factors have been forwarded as possible influences on seal leakage rates but few measurements have been available to evaluate their individual contribution. The contraction and expansion of gases in mine gobs due to changes in barometric pressure have been documented and may be the most established factor affecting mine seal leakage rates [6,7].

NIOSH configured a research study which was designed to utilise instrument-based data from field monitoring sites to investigate mine seal leakage rates in underground coal mines. Field monitoring included continuous measuring and recording equipment installed on a set of mine seals, in the adjacent airways and at the surface. A key objective of the study was to measure leakage rates through the mine seals. Barometric pressure was measured at the surface and underground near the monitoring site since it was expected to be a contributor to variation in seal leakage rates. One method of analysis chosen for seal leakage rates utilised the application of the Atkinson equation [8]). In this way, changing pressure at a seal could be related to leakage or flow and seal resistance. This relationship could be described as linear or exponential based on the field data.

A second method of analysis included was a time series analysis to relate leakage rates to changes in barometric pressure that may not be site specific. Two accepted methods of time series analysis are the rescaled range technique [9,10] and the ARIMA approach, commonly referred to as the Box–Jenkins method [11,12].

Field monitoring was conducted through a cooperative research agreement between Signal Peak Energy Bull Mountain No. 1 Mine operator and NIOSH. The monitored study site is shown in Figure 1, where the study panel is the one Right longwall panel measuring 380 by 4900 m (1250 by 16,000 ft). The mine operator had completed the first longwall panel and was mining the second when the study was performed. As with many western US coal mines, the mined coal seam has a relatively high spontaneous combustion potential. The mine began one Right longwall panel using a bleeder system but switched to bleederless system.

An unusual feature of this mine is the application of an Australian Safety in Mines Testing and Research Station (SIMTARS) atmospheric monitoring system. The mine operator is working the thick Mammoth seam of relatively low-rank coal in the four corners region of Montana that is either of high-volatile bituminous C or sub bituminous coal rank. Due to the low rank of the mined coal, no methane is emitted from the coal bed with mining. Gas emissions from the mined seam consist entirely of carbon dioxide, although the gas present in the ventilation system may not be a ‘seam gas’ but could be a product of adjacent strata rock reactions or oxidation.

The underground monitoring site is shown in Figure 2. Entries are numbered from right to left in the figure. Instrument arrays were installed in entries 1 and 7 to produce data from the upwind and downwind sides of the seal line. Monitoring instrumentation consisted of a 0–25% oxygen sensor, a 0–5% methane sensor, a 0–3% carbon dioxide sensor, a digital flow metre, a digital barometer and a differential pressure monitor. With the exception of the differential pressure sensor and the barometer, an instrument array was installed on either end of the seal line. The differential pressure metre was installed on the number seven seal sampling line. The air sweeping the seal line was classified as intake air. Barometric pressure was measured at Entry 1 and differential pressure was measured at Entry 7.

Raw data consisted of measurements of data which were recorded every five minutes from 2:00 pm on 1 February through 12:20 pm on 17 May. In all but the final stage of analysis, data for the months of February and March, and for the months of April and May, respectively, were treated as two separate data-sets since it was thought that there could be some difference in the findings due to the change of season. Analysis of the monitoring data was conducted using two methods. The first is the Atkinson equation. The equation related leakage or flow quantity to head pressure, resistance and flow turbulence [13]. The Atkinson equation form used in the study is shown by the equation given below: Hl=RQn where H_l = head loss, R = resistance, Q = air quantity, n = exponent for quantity where n = 1 indicates laminar flow.

In fluid mechanics, H_l is shown to be proportional to Q² [8].

A second method of analysis used is a time series analysis. A time series is made up of observations of a variable made over time. The time interval between observations must remain constant throughout the series. Time units may be as small as minutes or as large as years. The purpose of time series analysis is to recognise the process or model underlying the observed data; identification of the model then makes it possible to forecast future observations.

After working with both statistical approaches, the classical method of time series analysis – the Box–Jenkins method – was chosen for this study [11,12] over the rescaled range technique [15]. The method uses four possible components of a time series: trend, seasonal cycles within a year, larger cycles over a period of one or more years and random error. One or more of these components is assumed to be present in every series. If only random error is present, then the observation at any given time point is considered to be independent of observations at previous time points, and no model can be identified. If in addition to random error, one or more of the other components is present, then the observation at any given time point is considered to be related to or influenced by observations at previous time point(s). The correlations between observations at a given time point and observations at an earlier time point are known as an ‘autocorrelations’.

The abbreviation for a Box–Jenkins model, ARIMA, stands for auto regressive (AR), integrated (I), moving average (MA) model. The term ‘integrated’ refers to the trend component. Theory holds that an observation at a given time point can be influenced either by the true value of an observation at a preceding time point (autoregressive), by the random error component of an observation at a preceding time point (moving average) or by both factors.

Time series analysis was initially applied separately to the February–March and April–May data-sets. Due to the extremely large size of the full data-sets (more than 17,000 data points for February and March and more than 13,000 data points for April and May), reduced data-sets consisting of hourly measurements were used for analysis. It was felt that the use of the reduced data-sets would lessen the amount of noise and make patterns easier to identify. Hourly measurements were defined as the first measurement of every hour rather than as the average of the 12 measurements within every hour. Originally, the sets of data from February–March and April–May, respectively, were analysed separately. However, the sets were combined in the final analysis because of the similarity of results. A total of 14 hourly observations were missing because of power interruptions. Data for these time points were interpolated using statistical software produced by SAS [18].

The key parameters to be related by the time series analysis were barometric pressure and leakage rate to produce a model which would predict leakage rate based on barometric pressure data. During the analysis, it was shown that the output from the CO₂ concentration instrumentation used in the monitoring study produced a stepwise data trend at the leakage rates being measured (vertical groupings of data in Figures 5 and 6). The stepwise nature of the CO₂ concentration measurement instrumentation plot sufficiently modified the trend of CO₂ flow in the form of seal leakage data such that barometric pressure and leakage rate could not be meaningfully compared or modelled using time series techniques. The leakage of CO₂ was observed to trend well with differential pressure (Figure 6). Consequently, the two parameters used and compared for the time series analysis were barometric pressure and differential pressure.

As stated earlier in this paper, the influence of barometric pressure on the contraction and expansion of gases in mine gobs has been documented [16]. Therefore, time series analysis was used to meet two objectives: to describe the pattern of changes in barometric pressure over time, and to learn if changes in differential pressure at the mine seal were related to changes in barometric pressure.

A time series is a set of data collected on a single variable over a number of equally spaced time points. For example, data could be collected on temperature at a location every hour over a two-week period. The classical method of analysing a time series, the Box–Jenkins method, is used to uncover the model, i.e. pattern or process that explains the behaviour of the series. This method is based on the premise that the behaviour of a series can be explained by one or more of four components: (1)

Trend: general upward or downward movement over time.

The Box–Jenkins method proceeds by addressing the following questions in the order they are listed: (1)

Do changes over time reflect only random fluctuations or is there evidence that an underlying pattern of some type is present?

The examination of a plot of autocorrelations, known as a ‘correlogram’, is one of the key steps in the process. In the context of the current study, an autocorrelation quantifies the correlation between values of barometric pressure at different time points. A correlogram is a plot of autocorrelations at a succession of lags. The term ‘lag’ refers to the degree of separation in time. For example, the lag 1 autocorrelation is the correlation of observations at time points 2, 3, 4, 5, 6, 7, etc., with observations at time points 1, 2, 3, 4, 5, etc.

Cross-correlation analysis revealed that the strongest cross-correlations occurred at lag 0 and lag 1 (Figure 8). Each lag is equivalent to a 1–12 h time interval. A positive correlation is equal to a direct relationship between the two parameters; a negative correlation represents an inverse relationship between parameters. The correlation at lag 0 was negative (r = −0.542), whereas the correlation at lag 1 was positive (r = 0.686). The negative correlation at lag 0 implies that increases in Entry 1 barometric pressure tend to occur at the same time (an instantaneous response) as decreases in Entry 7 differential pressure, and vice versa. The strong positive lag 1 correlation implies that an increase in Entry 1 barometric pressure from time 1 to time 2 (for 12-h intervals) tends be followed by an increase in Entry 7 differential pressure from time 2 to time 3, and a decrease at Entry 1 tends to be followed by a decrease at Entry 7. Therefore, a change in Entry 1 barometric pressure can be helpful in predicting the direction of the next change in Entry 7 differential pressure.

The cross-correlation data agree with the observational and empirical data. With the mine seals outgassing essentially throughout the monitoring study, an increase in barometric pressure produced an immediate decrease in differential pressure at the seal line. This inverse relationship agrees with the lag 0 negative response in the cross-correlation analysis (Figure 8). After the initial response of the ventilation system to the barometric pressure change, the cross-correlation analysis shows that at lag 1, barometric pressure and differential pressure show a direct relationship and produce the highest r value of any 12-h lag period. This finding corresponds well to the empirical 8-h delay (Figure 4) and 10-h delay (April–May data-set) observed in the graphs of CO₂ flow and barometric pressure.