RUBY CANYON ENGINEERING ∙ Grand Junction, Colorado 

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# Evaluating Possible VAM Emissions Estimation Errors Based
O n Different Sampling Intervals (Quarterly, Monthly, Weekly)

Introduction

Currently, most coal mines reporting ventilation air methane (VAM) emission rates to MSHA are reporting using quarterly samples

- the minimum required frequency for calculating GHG emissions to Subpart FF. The mines can use either their own or MSHA data samples to represent the average VAM rate for each quar ter, and subsequently the annual emissions for the year. However, mine

- specific daily and weekly data sets show that significant day

- to

- day and week

- to

week variability can exist. Based on available high

- frequency datasets (hourly or weekly) of VAM

emissio ns, RCE set out to examine the uncertainty associated with using weekly, monthly, and quarterly data sampling based on using a random day selection approach. Based on the analysis, RCE determined that there appears to be a significant reduction in the unc ertainty of the actual VAM rates when going from quarterly to monthly, and from monthly to weekly sampling.



# Mine A Data

For Mine A, RCE used daily emission rates from a moderately gassy mine (avg. ~2.5 mmcfd) over a one year period. The variation in the me thane content was significant. Figure 1 displays
the VAM flow rate.

Figure 1: Variation in methane rate at Mine ARUBY CANYON ENGINEERING ∙ June 10, 2015 

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Figure 2 illustrates that the variation of the VAM is mostly attributable to the variation in the methane concentration as opposed to the fa n volumetric rate, which tends to be nearly constant, as the methane content trends very close to the overall VAM emissions rate.

Figure 2: Variation in VAM Rate and methane concentration



# Mine B Data

For Mine B shown in Figure 3 , RCE had access to the we ekly VAM and methane concentration data from a very gassy mine (avg. ~10.1 mmcfd).RUBY CANYON ENGINEERING ∙ June 10, 2015 

### 3 Figure 3: VAM rate and for Mine B



# Mine C Data

For Mine C shown in Figure 4, RCE had access to weekly VAM and methane concentration data from moderately gassy mine (avg. ~ 3

. 6 mmcfd).

Figure 4: VAM rate for Mine CRUBY CANYON ENGINEERING ∙ June 10, 2015 

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# Sampling Analysis

Because any real measurement taken to determine the VAM emissions rate occurs on a single day (regardless of being a weekly, monthly or quarterly sampling interval), RCE used a random number g enerator to select a day of the week, month or quarter and the corresponding flow or methane concentration value in the high frequency data sets. The datasets used for Mine A were daily and weekly for Mines B and C. As a result, for Mine A, RCE randomly selected a day of the week to represent weekly sampling, a day in the month for monthly sampling and a day in a quarter for quarterly sampling. For mines B and C, RCE randomly selected a week of the month for monthly sampling and a week of the quarter for quarterly sampling. Every iteration, using the random number generator, produces a different result because different time periods (days or weeks) are randomly selected within each sampling interval. RCE repeated this method with fifty iterations capturi ng the average VAM rate for each sampling interval over the entire one year data

set

For Example :

Table 1 shows the results of five iterations of the averaging process for Mine A where the average of the daily emissions of 2,520,970 cf/d represents the “ac tual” methane emissions, and the other sampling intervals represent estimates based on the day randomly selected for the sampling.

Table 1: Results of five iterations of the randomly selected days with in a sampling interval, cf/d

Iteration Daily Weekly Monthly Quarterly Delta Wkly Delta Mthly Delta Qtly

1 2,520,970 2,518,376 2,612,805 2,024,167

- 2,594 91,835

- 496,802

2 2,520,970 2,490,179 2,712,553 2,658,489

- 30,790 191,583 137,519

3 2,520,970 2,505,678 2,496,782 2,236,758

- 15,292

- 24,188

- 284,212

4 2,520,970 2,556,666 2,298,133 2,968,794 35,696

- 222,837 447,824

5 2,520,970 2,484,333 2,562,171 2,364,823

- 36,637 41,201

- 156,147



### For iteration 1, RCE randomly selected a day to represent the weekly, monthly and quarterly average VAM rate measurements within the year. The difference from actual was

- 2,594, 91,835
and

- 496,802 cubic feet per day for weekly, monthly and quarterly rando m selections respectively.



# Results

Figures 5 and 6 illustrate the variance in data sample measurement for all 50 iterations for Mine A. Figure 5 shows the actual values calculated while Figure 6 shows the difference from the actual value in terms of perce nt difference.

Note that the distribution around the actual value (2,520,970 cf/d) in Figure 5 corresponds to the

zero values line on the x

- axis in Figure 6. The results clearly show the deviations associated with the quarterly samples are greatest and the weekly samples the smallest.RUBY CANYON ENGINEERING ∙ June 10, 2015 

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Figure 5: Deviation from actual VAM rate based on sampling interval for Mine ARUBY CANYON ENGINEERING ∙ June 10, 2015 

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Figure 6: Deviation from actual expressed as the percent difference for Mine A.

RCE repeated a similar analysis for Mines B and C. For these mines, RCE considered the daily average of the VAM emissions based on weekly data to be the “actual” VAM rate or 10,115,000 cf/d for Mine B and 3,627,000 cf/d for Mine C. Unlike Mine A, RCE did not have hourly/daily measurements for Mines B and C. Figures 7 and 8 show the percent difference from actual VAM rate for both mines over a 12 month period.RUBY CANYON ENGINEERING ∙ June 10, 2015 

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Figure 7: Deviation from actual expressed as the percent difference for Mine B.

Figure 8 : De viation from actual expressed as the percent difference for Mine C.RUBY CANYON ENGINEERING ∙ June 10, 2015 

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RCE conducted a statistical analysis of each mine’s 50 iterations to determine the maximum possible error and the uncertainty at one standard deviation. Table 2 shows the lowest and highes t estimated divergence from the actual value for the three mines. The results show that the possible maximum errors (for both low and high ranges) decrease as the sampling frequency increases.

Table 2: Minimum and maximum errors possible based on 50 iterat ions

Mine Frequency Actual Value Min Value Max Value % Change Min % Change Max

Mine A Weekly 2,520,970 2,440,029 2,617,762

- 3.2% 3.8%

Monthly 2,520,970 2,269,133 2,790,904

- 10.0% 10.7% Quarterly 2,520,970 1,797,452 3,060,237

- 28.7% 21.4%

Mine B Monthly 10,114,965 8,775,116 11,007,874

- 13.2% 8.8%

Quarterly 10,114,965 6,751,170 13,667,846

- 33.3% 35.1%

Mine C Monthly 3,627,287 3,265,747 3,944,719

- 10.0% 8.8%

Quarterly 3,627,287 2,447,102 4,374,362

- 32.5% 20.6%



### Table 3 shows the average daily VAM emission rate for each mine using either the 4, 12, 52, or 365 data samples. Table 3 also show the standard deviations for each case. Again, the results show that the range of uncertainty decreases as the sampling frequ ency increases.

Table 3: Average and standard deviation of the 50 iterations

Mine Frequency Average (cf/d CH 4 ) Std Dev (cf/d CH 4 ) Std Dev/Avg

Mine A Daily (Actual) 2,520,970 0 0.0%

Weekly 2,525,366 40,503 1.6% Monthly 2,510,417 137,519 5.5% Quarterly 2,561,020 310,658 12.1%

Mine B Weekly (Actual) 10,114,965 0 0.0%

Monthly 10,098,118 521,609 5.2% Quarterly 9,646,562 1,450,069 15.0%

Mine C Weekly (Actual) 3,627,287 0 0.0%

Monthly 3,601,455 155,361 4.3% Quarterly 3,539,308 474,720 13.4%RUBY CANYON ENGINEERING ∙ June 10, 2015 

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# Conclusions

Using VAM emissions data recorded daily and weekly from three underground coal mines (one with daily sampling and two with weekly sampling)

, RCE analyzed the average daily VAM
emission s rate by randomly selecting the sampling d ay or w eek during a 12 month reporting period. Each case was run for a weekly, monthly, and quarterly sampling frequency over a 12 month reporting period.

For Mine A, the results showed that weekly sampling produced a small standard deviation of 1.6% compared to daily sampling. For all 3 mines, the results showed the standard deviations increased

to 4.3

- 5.2% when sampling frequency decreased from weekly to monthly sampling. Finally, the

results showed the standard deviations increased to 12.1

- 13.4% when sampling frequency decreased from monthly sampling to quarterly sampling. Due to the day

- to

- day variability in VAM emissions, ranges of maximum possible errors are also greater with decreased sampling frequency. Deviations from the actual; value for monthly sampli ng ranged from 8.8

- 10.7%, while deviations for quarterly sampling ranged from 20.6

- 35.1%.