Bureau of Mines Report of 1nvestigations/l974 

Peak Methane Concentrations 

During Coal Mining 

An. Analysis 

UNITED STATES DEPARTMENT OF THE INTERIOR 
Report of Investigations 7885 

Peak Methane Concentrations 

During Coal Mining 

An Analysis 

By Fred N. Kissell, J. L. Banfield, Jr., R. W. Dalzell, 

and M. G. Zabetakis 

Pittsburgh Mining and Safety Research Center, Pittsburgh, Pa. 

UNITED STATES DEPARTMENT OF THE INTERIOR 

Rogers C. B. Morton, Secretary 

BUREAU OF MINES 

Thomas V. Falkie, Director 
CONTENTS 

Page 

Abstract ................................................................. 1 

Introduction ............................................................. 1 

Acknowledgments ....................................................... 2 

Experimental work ........................................................ 2 

Results and discussion ................................................. 4 

All methane peaks ................................................. 4 

Extreme values ..................................................... 12 

Conclusions .............................................................. 15 

References ............................................................... 17 

ILLUSTRATIONS 

Recorder chart from methane monitor located near working face ........ 2 

Scrubber exhaust toward rear of machine .............................. 5 

Scrubber exhaust toward side of machine .............................. 5 

Peak methane concentrations from table 1 plotted on normal 

probability paper. mine C. Pittsburgh coalbed ...................... 6 

Peak methane concentrations plotted on log-normal probability paper. 

mine A. Illinois No . 6 coalbed ..................................... 6 

Highest peak methane concentrations at right bit and l e f t b i t 

plotted on type I extreme-value probability paper .................. 13 

Highest peak methane concentrations at scrubber plotted on type I 

extreme-value probability paper .................................... 14 

TABLES 

1 . Peak methane concentrations from mine C. Pittsburgh coalbed .......... 4 

2 . Summary of results from mines A. By and C ............................ 8 

3 . Ratio S.median, type of distribution, and ratio scrubber 

median:return median ............................................... 10 
PEAK METHANE CONCENTRATIONS DURING COAL MINING 

An Analysis 

Fred N. Kissell,' J. L. Banfield, Jr.,2 R. W. Dal~ell,~ 

and M. G. Zabetakis4 

AB S TRAC T 

Methane concentration peaks were measured by the Bureau of Mines at coal 

mine working faces during entry development. The statistical distribution of 

peaks was found to be normal or log normal depending on how well the methane 

was being mixed into the ventilation airstream. A normal distribution 

indicated good mixing, whereas a log-normal distribution indicated that mixing 

was poor. In addition, the "highest" peaks over selected intervals were found 

to fit a type I extreme-value distribution, a result similar to that obtained 

while mining longwall faces. 

INTRODUCTION 

Since its establishment in 1910, the Bureau of Mines has been actively 

concerned with decreasing the hazards associated with the presence of methane 

in coal mines. In practice, a methane ignition is most likely to occur near 

the working face, where a continuous miner releases methane into the mine 

atmosphere as it breaks coal. If the cutter picks strike a hard surface such 

as sandstone, an ignition by frictional spark may result. 

The maximum allowable methane concentration in the working place as 

measured not less than 12 inches from the roof, face, or rib must be less than 

1 volume-percent (12)~ whereas the lower explosive limit is 5 percent. 

Although this difference theoretically provides a safety factor, in practice 

face ignitions are not uncommon in U.S. coal mines. The vast majority of such 

ignitions do no harm to the men working nearby; however, in some cases 

injuries and death result. When an ignition occurs at the face the possibility of a major disaster is always present, particularly if the burning methane 

ignites coal dust. 

lPhysical research scientist. 

2 Mining engineer. 

3 Chief, Ventilation Group. 

4 Supervisory research chemist. 

5 Underlined numbers in parentheses refer to items in the list of references at 

the end of this report. 
TIME, hr 

FIGURE 1. - Recorder chart from methane monitor located near working face. 

Methane emission at the immediate working face varies substantially, 

generally increasing as the mining machine cuts into the solid coal and then 

dropping to some background value as the machine backs away in preparation for 

another cut. A typical recorder chart from a methane monitor located near the 

working face is shown in figure 1. Each peak corresponds to one complete 

shear, which in this case involves sumping in about 2 feet, raking the cutter 

head down, and loading the coal. The peak methane concentrations are several 

times higher than the average. In practice, if the working face is not 

adequately ventilated, these peaks may exceed the lower explosive limit even 

when the average concentration is satisfactory (10). - 

High peak concentrations of methane also occur during longwall mining. 

Lavtsevich (5) has found that the statistical distribution of "highest" concentrations at a longwall face is given by the first or second type -limiting 

distribution (extreme value) laws: 

G1 (x) = exp [-e -a(*-u>, , 

and 32 (x) = @, (In X) , 

where @ (x) is the probability that a given maximum value of a random variate 

(C& concentration) is less than x, and cu and u are parameters related to the 

slope and intercept of extreme probability plots. 

The purpose of this investigation was to examine the distribution of 

methane concentration peaks obtained during entry development in room-andpillar mining. Given the proper distribution of peaks within the legal limit, 

it might be possible to predict with the extreme-value laws the probability 

of surpassing this limit, and perhaps the explosive limit, within a given time 

interval. 
ACKNOWLEDGMENTS 

The authors gratefully acknowledge the assistance given by Bureau of 

Mines engineers of the Technical Support Center, Pittsburgh, Pa., who have 

participated in the collection and evaluation of data: J. D. Hadden, 

R. A. Haney, S. M. Hoover, H. Schade, A. Reisz, and E. J. Miller. 

ExFJERIMENT-4L WORK 

Face emission data were collected by the Bureau of Mines Technical 

Support Center as part of a study of the effect of integral machine-mounted 

dust scrubbers on methane distribution in the working place. Face area methane concentrations were monitored in two mines called A and B in the Illinois 

No. 6 coalbed and one in the Pittsburgh coalbed called mine C. Two-step and 

fullface continuous miners were used; both inside and outside entries were 

mined. Face ventilation was supplied by auxiliary tubing (blowing or exhaust) 

or line brattice (blowing). Intake air quantities at the inby end of the 

tubing or brattice ranged from 3,300 to 8,500 cfm; the distance between the 

face and the tubing (or brattice) end ranged from 5 to 25 feet. In every case, 

the mining machine was equipped with a dust scrubber. The scrubber air inlet 

was between and below the cutter booms, directly above the shovel, and was 

7-1/2 feet outby the face. The exhaust was approximately 12 feet outby and 

varied as illustrated in figures 2-3. All entries were in development 

sections. With the two-step miner, only methane emission data obtained with 

box cuts were used because this yielded results that were comparable with 

those obtained with a fullface miner where every major cut is a box cut. Data 

taken during the mining of crosscuts were not used. 

Methane monitors were located on the body of the machine, in the intake, 

and in the return (figs. 2-3). At least three locations were monitored. The 

intake (A), the scrubber exhaust (D), and the return (F). In most instances 

monitors-were also located on the corner of the machine directly behind the 

right bit (B), - and the left bit (C), - and at the diffuser fan (E). 

Monitoring was conducted over intervals ranging from several days to 

2 weeks. A mining engineer was always present to record the progress of 

mining, to mark recorder charts, and to determine the ventilation air quantity 

and tubing-to-face distance. Otherwise, mining proceeded normally. 

During each series of measurements, methane peak heights were recorded on 

charts similar to that in table 1. In general, peaks occurred almost simultaneously at all locations outby the face. A separate line appears in table 1 

for each sump cut. Thus (table I), three cuts were made in the various 

entries of the working section with a face-to-tube distance of 8 feet, two 

cuts with a face-to-tube distance of 9 feet, etc. Typically, each set of data 

had about 80 sump cuts. 
TABLE 1. - Peak methane concentrations from mine C, Pittsburgh coalbed 

RESULTS AND DISCUSSION 

All Methane Peaks 

Air 

quantity 

in tubing, 

cfm 

7,600 

7,600 

7,100 

7,600 

7,200 

7,600 

7,600 

7,200 

7,200 

7,100 

7,600 

7,200 

7,100 

7,200 

7,100 

7,100 

7,600 

7,200 

7,200 

Peak concentration data of the sort listed in table 1 were ranked" and 

then plotted on probability paper (4). Data points from each mining location 

were plotted separately with no initial attempt to determine or separate the 

effect of brattice or tube-to-face distance or the particular entry mined. 

Distance 

of tube 

from face, 

ft 

8 

9 

10 

11 

12 

14 

SRanking was done as follows: (1) Rank the peak heights x from the smallest 

100 to the largest. Thus, xl(x,s%-% . (2) Plot the x's versus (i-1/2) on 

the probability paper. (i = 1, 2, 3, n). Thus the lowest peak is 

Return 

- F 

0.32 

.32 

.36 

.39 

-38 

.36 

-30 

.40 

-35 

.40 

.40 

.34 

.36 

.29 

.38 

.34 

.36 

.43 

.42 

Intake 

- A 

0.08 

.04 

.07 

.04 

.07 

.08 

.08 

.07 

.07 

.07 

.04 

.04 

.07 

.04 

.07 

.07 

.04 

.07 

.07 

Scrubber 

- D 

0.27 

.25 

-46 

.41 

plotted at (1/2) 100; the second at (3/2) - loo; and so on (4). As an 

n n 

Di ffuser 

fan 

- E 

0.24 

.24 

.18 

.15 

example, suppose there are 50 peaks. Then n = 50 and the lowest peak is 

plotted at 1 percent, the next highest at 3 percent and so on until the 

highest peak is plotted at 99 percent. 

Right 

bit 

- B 

0.29 

.31 

.29 

.35 

.31 

.31 

.28 

.29 

.26 

.28 

.35 

.23 

.31 

.25 

.28 

.29 

.28 

.32 

.35 

Left 

bit 

- C 

0.64 

.43 

.53 

.58 

.43 

.54 

.43 

.53 

.43 

.70 

.64 

.51 

.45 

.33 

.53 

.50 

.59 

.56 

.60 

.17 

.50 1 

-36 1 .09 

.30 

.46 

.38 

.53 

.39 

.27 

.43 

.23 

.43 

.46 

-39 

.46 

.50 

.17 

.15 

.15 

.28 

.28 

.12 

.19 

.10 

.19 

.24 

-13 

.22 

.20 
FIGURE 2. - Scrubber exhaust toward reor of machine. FIGURE 3. - Scrubber exhaust toward side of 
9 9 -1- 7-7- ----[

98 -- 

95 - 

, 90 -- 

Y 

280- 

LL 

0 70 -- (F) 

t6 60e 

k? 50 Scrubber 

UJ 

a 40 - (D 1 

W 

2 30 - 

5 20 - 

3 

2 

2 lo - 

Scrubber quantity = 0 cfrn 

5 - 

2 - 

FIGURE 4. - Peak methane concentrations from table 1 FIGURE 5. - Peak methane concentra

plotted on nornlal probability paper, mine normal probability pap

C, Pittsburgh coalbed. No. 6 coolbed. 
Thus, figure 4 shows the peak methane concentrations from table 1 at the 

scrubber (location D) and at the return (location F) for all entries and for 

tube-to-face distances of 8 to 14 feet plotted on normal probability paper. 

The trend line through the plotted points indicates that in this case, the 

peak heights at the scrubber and return locations are normally distributed. 

Examination of the available data showed that the peaks for any one set 

were either normally (fig. 4) or log normally (fig. 5) distributed. A total of 

43 sets of emission peaks similar to those shown in table 1 were ranked and 

plotted on normal or log-normal probability paper to find which distribution 

fit best. Table 2 summarizes the pertinent results obtained. Column 5 gives 

a measure of the scatter (84.13 percent value minus the median), which is 

actually the standard deviation (S) for a normal distribution; column 6 gives 

the ratio S:median, which is the coefficient of variation for a normal 

distribution. 

Upon examining table 2, several conclusions can be drawn: 

1. For a given test, not all the locations gave similar distributions. 

For instance, in the test listed as mine A--scrubber 4,400 cfm--entries less 

than 40 feet in depth, the scrubber and right bit peaks were normally 

distributed, but the left bit and return peak concentrations were log normally 

distributed. Different locations will give different concentrations and different distributions. 

2. If the ratio S:median was less than 0.3, the peak heights in most 

cases followed a normal distribution. If the ratio was greater than 0.3, the 

peak heights in most cases followed a log-normal distribution. 

3. If the peaks were normally distributed the ratio scrubber 

median:return median tended to be below 2; whereas a log-normal distribution 

was generally accompanied by a ratio of scrubber/return medians greater than 2. 

Table 3 lists the ratio S:median in increasing order, with an indication 

of the type of distribution (normal or log normal) and values for the ratio 

scrubber median: return median. 

Environmental air pollution samples are known to be log normally distributed (6), but why coal mine emission peaks should be normally distributed 

in some instances and log normally in others has not been explained. However, 

in coal mines the type of distribution could be determined by the degree of 

mixing of methane with the ventilation air. A normal distribution would 

indicate rapid and complete mixing, whereas a log-normal distribution would 

indicate that mixing (at that location) is incomplete. 
TABLE 2. - Summary of results from mines A, B, and C 

Scrubber 

qunntit-v, 

c fnl 

Sample location 

MlNE 

0.06 

.23 

.34 

.28 

.090 

,275 

. 250 

.305 

,086 

.213 

.295 

.270 

.I10 

.335 

.3 24 

,360 

Median 

peak,' 

pct ~11, 

I 

0 

4,400 

0 

4,400 

--- 

84.13 pct 

value, 

pct CII, 

S," 

pct Cl14 

2 

4,600 

AZOVEEIBER 

Return.. .......... Scr~il~t~er. ......... LefL bit.. ........ Rigllt hit., ....... 

Return.. .......... Scrubber. ......... 

.......... Lei t bit 

Rigllt bit.. ....... 

Keturn ............ 

.......... Scrubber 

1,eJ-t bit. ......... Iliglll: biL. ........ 

Keturn. ........... ......... Scrubl~er. 

......... 1,ef t bit. 

....... Iiigl~t- bit.. - 

197 

S 

median3 

0.033 

.17 

. 26 

.19 

.05 2 

.216 

.I80 

.210 

.060 

.165 

. 220 

.165 

.084 

. 26 

. 245 

,255 

0.027 

,060 

.080 

.090 

.038 

,059 

.070 

.095 

. 0 28 

.050 

. 0 75 

. 105 

.026 

,075 

.079 

. 105 

Jag normal.. 

Normal.. .... 

..... ..... do 

Scrubber median 

return median 

MINE B, AUGUST 1972" 

1.25 

Return, left side. 

Keturn, 

right side. 

,........ Scrubber. 

Entries <

Do. 

Do. 

110 . 

Entries <

Do. 

Do. 

DO. 

Entries >

Do. 

Do. 

Do. 

Entries >

Do. 

Do. 

Do. 

0.818 Log normal.. 

.353 ..... do ..... .308 ..... do ..... 5.15 

.474 ..... do. .... 

Log normal.. 

Normal... ... .388 Log normal. . .452 Normal.. .... 

1.02 

1.09 

...... Normal 

.... ... .do.. 

..... ..... do 

...... Nonnal 

.... ... .do.. 

..,.. ... do.. 

Distribution 

.47 

.30 

.34 

.6 36 

.31 

.39 

.32 

.412 

MINE B, JULY 19726 

Return se

innnedia

behind m

Data from 

Keturn se

immedia

behind m

Data from 

6,400 Return, left side. 

Itelurn, 

rjgl~l: side. 

Scrubber .......... 

6,400 ReLurn, left side. 

Return, 

right side. 

Scrubber .......... !

Comm

0.320 

.35 

.40 

0.050 

.03 7 

.050 

,032 

.038 

.039 

2.75 

3.10 

0.023 

.022 

.030 

0.343 

,327 

.43 

0.222 

.170 

.222 

. 105 

.123 

,124 

0.225 

.218 

.2 25 

.304 

.31.0 

.314 

Log normal. . ..... do. .... ..... do ..... ..... do. .... 

Log normal. . Normal.. .... Not clear. .. ..... Normal. 

0.072 

.072 

,075 

0.275 

.255 

,275 

.336 

.348 

.353 
MINE B , JULY 197 Z6 - -CONTINUED 

6 ,/IOU Return, behind 

miner. 

1Zetur11, nearest 

crosscut. 

Scrubber, ......... 

0.361 

.275 

.465 

0.336 

.255 

.435 

0 

3,300 

5,200 

'S equals the 811.13 percent value minus the median peak value. This is the standard deviation if the distrib

normal. 

3,, S Ihe quantiLy ----- is the coefficient of variation if the distribution is normal. 

median 

"~ovember 1972; blowing line brattice on right side; brattice-to-face distance, 7 to 25 ft (average 17.1 ft)

quantity, 4,000 to 6,700 cfm; two-step ripper. 6 

August 1972; blowing tubing; tube-to-face distance, 14 to 22 fl: (average 19.2 ft) ; air quantity, 4,400 to 6

fulllace miner; 8 right off west mains. 6 July 1972; blowing Lubing; tube-to-face distance, 10 to 25 ft (average 18.7 ft); air quantity, 3,300 to 4,3

fulllace miner; 8 right off west mains. 7 December 1972; exliaust tubing on right side; tube-to-face distance, 5 to 14 ft (average 10.7 ft); air quan

6,200 to 8,500 cfm; dilfuser fan, 2,000 cim; fullface miner; 5 north off west mains. 

'~e~tember 1972; exhaust tubing on right side; tube-to-face distance, 12.5 ft only; air quantity, 7,000 to 8

diffuser fan, 2,000 cf~r~; fullface miner; 5 north off west mains. 

0.025 

. 0 20 

,030 

Return ............ Scrubber .......... Left bit.. ........ Rigllt bit. ........ 

Keturn. ........... Scrubber .......... ........ Left bit.. 

liigllt bit.. ....... 

Return ............ Scrubber. ......... 

......... Left bit. 

Right bit ......... 

0.400 

.484 

.610 

.330 

.385 

.510 

.563 

,360 

.475 

.655 

.615 

.430 

0.362 

.390 

.520 

.296 

.3 20 

.330 

.455 

. 290 

.365 

.5 25 

.475 

.310 

0.038 

.094 

.090 

.034 

.065 

.I80 

.I08 

.070 

.I10 

.I30 

.I40 

.I20 

0.074 

.073 

,069 

Normal.. .... ..... .... ) do. ..... do. .... ..... do. .... 

Normal ...... Log normal. . 

... Not clear 

Normal. ..... Normal ...... ..... .... do. 

..... do ..... ..... do, .... 

0.270 

,595 

MINE C, DECEWER 19727 

5,200 

I Log normal.. 

..... do,. ... lThe median peak is the 30 percent value. 

0.104 

. 241 

.I73 

.I14 

.203 

.545 

.237 

.241 

.3C1 

.248 

. 254 

.3F7 

Return ............ .......... Scrubber 

MINE C, SEPTEM13ER 19728 

11.71 

1.03 

1.43 

0.325 

,665 

.... Normal.. 

1 Log normal.. 

Normal ...... 

0.055 

,070 

Data from 

0.2Q 

,118 1 220 
TABLE 3. - Ratio S:median, type of distribution, and 

ratio scrubber median:return median1 

Not 

clear 

 median 

0.069 

.072 

.072 

. 0 74 

-075 

.078 

.lo4 

.lo5 

14 

.I18 

.I23 

.I24 

.I70 

.I73 

.200 

.203 

.222 

.222 

.237 

.241 

.241 

Log normal 

scrubber median 'values in parentheses are 

return median 

Normal 

(1.71) 

(1.25) 

(1.25) 

(1.71) 

(1.06) 

(1.09) 

(1.06) 

(1.09) 

(1.09) 

(1.02) 

(1.06) 

(1.03) 

(1.02) 

(1.02) 

(1.03) 

(1.06) 

For instance, if mixing in the face area were complete, that is, if all 

the ventilation air swept the face and the methane was immediately mixed into 

that air, the methane concentration at every point in time would be identical 

at every location. The ratio scrubber median:return median would always be 

1.0. The fact that higher values of this ratio are generally accompanied by a 

log-normal distribution suggests incomplete mixing. 

Further support of this explanation comes from examining the face ventilation system in each of the three mines studied. In mine B, blowing tubing 

was used for face ventilation. The airflow was 3,300 to 6,200 cfm, and the 

exit velocity from the tubing was between 25 and 47 ft/sec. A blowing tubing 

with a high exit velocity is generally regarded as the best way to insure that 

the airstream reaches the face (L, 8-9). Mixing was good, and the peak distributions were generally normal. 

Not 

clear 

(1.03) 

Face mixing at mine C was almost as good as at mine B. At mine C 

exhaust tubing was used. The airflow was about 7,500 cfm, and mixing was 

enhanced by means of a machine-mounted 2,000-cfm diffuser fan (1, 8, 11). 

Exhaust ventilation alone is not as effective as blowing ventilation with comparable air quantities and velocities; however, the diffuser fan considerably 

Log normal 

(1.25) 

(1.71) 

(2.20) 

(2.20) 

 median 

0.248 

.273 

.290 

.294 

.300 

.301 

.?08 

.310 

.320 

.340 

.353 

.387 

.388 

-412 

.452 

.470 

.474 

.545 

.6 36 

.731 

.818 

Normal 

(1.43) 

(4.15) 

(3.10) 

(1.43) 

(1.43) 

(1.43) 

(3.10) 

(4.15) 
improved mixing in the immediate face area. In most instances the peak distribution was normal (table 2). 

At mine A, a blowing line brattice was used. The airflow varied between 

4,000 and 6,700 cfm, but as the area behind the line brattice averaged about 

20 ft2, the exit velocity was only between 3.3 and 5.6 ftlsec. Luxner (I) 

found that a blowing line brattice with an exit velocity of 12.8 ft/sec 

provided an adequate sweep of the face in an empty heading; however, with a 

lower exit velocity of 6.4 ft/sec, the primary airstream in most instances did 

7 not reach the face. It seems likely that the 3.3 to 5.6 ftlsec velocity 

observed at mine A provided poor face mixing especially since the heading was 

crowded with machinery. Thus it follows that in all of the tests with the 

scrubber - off the peak distribution should be, and was, log normal. This was 

in spite of the fact that mine A had the lowest average return methane concentration of all three mines. With the scrubber on, mixing was improved 

somewhat; peak distributions became normal in about half the cases (table 2). 

These results from the three mines indicated that the kind of face ventilation used determined the distribution of methane peaks, and also possibly 

that the scrubber had some effect. Another important variable in face ventilation is known to be the line brattice position; that is, the line bratticeto-face distance (I). Accordingly, it seemed worthwhile to see whether the 

peak distribution was different at shorter brattice distances than it was at 

longer brattice distances. 

Since mine A had the poorest methane-air mixing, these data were 

re-examined first. In the initial ranking, all line brattice positions were 

lumped together; however, the methane peaks were now separated into two 

categories--those obtained when the line brattice distances was 115 feet and 

those obtained at >15 feet--and each category was ranked separately. 

In practice, when the line brattice is moved close to the face, ventilation improves and the average methane content of the air close to the face 

sharply drops (7). It is likely that mixing is also improved, and therefore 

it is possible that peaks ranked in the 515-foot category were more likely to 

stay as normal distributions. This was found to be the case. For instance, 

the first four distributions in table 2 are log normal (mine A, scrubber 

quantity 0 ch, entries <40 feet). When the peaks were separated into the two 

categories and reranked, the 515-foot peaks more closely fit a normal distribution, whereas the >15-foot peaks retained a log-normal distribution.' The 

7Lux~er interpreted his results in terms of "tight rib distance" instead of 

velocity. This is the distance between the line brattice and the nearest 

rib. For a given airflow quantity, a decrease in tight rib distance means 

a velocity increase. Luxner had concluded that at 10,000 cfm, a tight rib 

distance of 2 feet provided better ventilation than a distance of 4 feet. 

The entry was 6.5 feet high, and so the rib distances of 2 feet and 4 feet 

have been interpreted as corresponding to velocities of 12.8 ft/sec and 

6.4 ftlsec, respectively. e The 15-foot value was selected because this provided enough peaks, both above 

and below, for an accurate ranking. 
same effect was observed with the other mine A log-normal distributions. The 

closer the line brattice, the better the mixing, and so the greater the chance 

of a normal distribution. 

This effect was not so pronounced in the case of mines B and C especially 

since mixing at all observed tubing distances was generally good and few lognormal distributions were obtained. In the case of mine By not enough peaks 

were measured at distances less than 15 feet to make an accurate ranking, and 

so 19 feet was used instead. When the two log-normal distributions were 

reranked for S19 feet, they more closely fit a normal distribution, similar to 

mine A. For mine C, December 1972, reranking for shorter tubing distances had 

no effect on the one log-normal distribution. For mine C, September 1972, 

reranking was not possible because all peaks were obtained at the same tubing 

distance of 12.5 feet. 

Extreme Values 

In the previous section, the distribution of - all peaks within a given 

data set were examined and found to be normal or log normal. On the other 

hand, if one considers only the highest peak (extreme value) in a given 

interval, then a distribution of highest peaks may be obtained for a number of 

such intervals. As an example, if measurements are made over 50 half-hour 

intervals, the distribution of the 50 peaks may be plotted if the highest peak 

in each half-hour is taken. 

This distribution of "highest" peaks is known as an "extreme value" distribution; the statistical theory of extreme values has been studied most 

extensively by E. J. Gumbel (2). Extreme-value theory has been applied successfully to a wide variety 07 natural phenomena (3). As noted previously, 

Lavtsevich (5) - has found that the distribution of the extreme values (highest 

methane concentrations) at a longwall face was given by the extrene-value laws. 

To evaluate a given series of extreme values (highest peaks), these data 

are first ranked and the values plotted in a fashion somewhat similar to that 

used in studying peak values. However, extreme-value probability paper was 

now used rather than the normal or log-normal paper. If the plotted points 

followed a straight line, the data fitted an extreme-value distribution. 

The quantity of data required for an extreme-value probability plot is 

quite large; the most that Lavtsevich presents are 16 highest (or extreme 

value) points. Of the three mines in table 2, only mine A, which was 

monitored for 2 weeks, yielded enough emission data for an extreme value plot. 

Before an extreme-value plot can be made, an interval has to be selected 

from which each highest peak is taken. Lavtsevich used 1/2 hour for one set 

of data, and one shift for another set of data. It was found convenient to 

select the mining of one entry between crosscuts as the interval. Methane 

concentration data of the type shown in figure 1 were grouped on an entry-byentry basis. When a series of cuts were made in a given entry, the highest 

box-cut emission peak was determined. Then the highest peak was determined in 

the next entry between crosscuts, as so on. In the course of 2 weeks of 

methane monitoring in a working section, 56 such peaks were obtained. Extremevalue plots for the left bit and right bit locations are show. in figure 6, 

and extreme value plots for the scrubber location are shown in figure 7. The 

existence of straight lines through the plotted points indicates that these 

data fit the first (type I) limiting distribution law: 

This is the expected distribution for the highest values if the initial distribution is normal or log normal. 

According to Lavtsevich, for large fluctuations of the concentration 

(standard deviation - >0.30), the highest values will follow the second limiting 

law of distribution: 

P2 (x) = Gl (ln x) . 

Since the largest standard deviation observed in any test was 0.18 (mine C, 

December 1972, 3,300 cfm, 

99.98. scrubber), it is likely that 1 41000 the highest peaks from mines 

99.95 - B and C would also fit an 

99.93 - extreme-value distribution 

99.9 - of the first type rather 

99.8 - than the second. - 400 

99.7 - 

i: 99.5 - --I 200 Although the highest 

,w 99.3 - peak concentration shown in 

99.0 - figure 6 is 0.71 percent 

o methane, extrapolation of 

5 98.0 - the plotted points can yield y 97.0 - the probability of higher Lr 

W 95.0 - concentrations. For 

93.0 - z w rr instance, extrapolation of 90.0 - the "left bit" values to 

k 

A 83.0 - 1.0 percent methane gives 

3 0.99967 for the probability 2 70.0 - 

2 of values less than 1.0 per- 0 50.0 - cent. This means that the 

30.0 - probability of achieving 1.0 percent or more in any 

10.0 - given entry in mine A is 5.0 - 

1.0 - 1.0 -0.99967 = 0.00033. 

.OOOI The extrapolation in 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 08 0.9 1.0 figures 6-7 also gives an 

CH4, PCt indication of the "return 

FIGURE 7. - Highest methone concentrations at period. I' This is the recipscrubber plotted on type I extreme-volve rocal of the 1.0 percent or 

probability paper. greater methane probability, which also means it is the 
average number of observations necessary for the methane concentration to 

assume a value of more than 1 percent on one occasion. For the "left bit" 

values, the return period is about 3,000, meaning that in mine A a concentration of 1 percent or more is reached at the left bit only once in mining 

3,000 entries between crosscuts. The return period for the right bit extreme 

values is 4,000 for 1.0 percent or more methane and, as expected, the return 

period is even greater for the scrubber. 

A similar extrapolation could be made to higher percentages of methane 

and the return period determined. However, for the mine A data the return 

period would be extremely high, and the probability of reaching 5 percent 

methane, for instance, would be minuscule. 

Not enough data are available to obtain return periods or probabilities 

for mines B and C; however, it is likely that these have a much greater probability of reaching 1 percent or more methane. Table 2 shows the median 

return concentrations in mine A were always below 0.1 percent, whereas those 

of mines B and C were generally above 0.3 percent. 

These probabi1i.t~ predictions assumed that mining conditions do not 

change appreciably from those that existed when the data were gathered; 

however, as it is quite possible that the conditions imposed by this restriction are difficult to meet, the practical value of such predictions for the 

long range is limited. For instance, when it is assumed that "conditions do 

not change appreciably," it is assumed the following all remain the same: 

(1) The amount of methane in the coal; (2) the characteristics of the 

coalbed that affect gas flow to the face; (3) the rate of advance of the 

mining machine; (4) the ventilation air quantity; (5) the manner in which 

the tubing or brattice is advanced. 

It is known that over the long range many of these factors will change. 

For instance, mining in a virgin area of the coalbed will produce more methane 

than mining in an area that has been degassed. The rate of advance of the 

mining machine will be influenced by the available haulage. The ventilation 

air quantity may fall considerably below the range of quantities used while 

data was taken. Because of these factors, it seems unlikely that probability 

prediction would have long-range application or that data obtained in one part 

of a mine would apply to other parts of the mine. However, probability predictions may find some utility for short-range forecasting in a given working 

section. Additional research is needed. 

I CONCLCSIONS 

Peak methane emissions measured at the working face during development 

room-and-pillar mining are normally or log normally distributed. The difference is attributed to the extent to which methane and air are adequately 

mixed in the immediate face area. A normal distribution indicates complete 

mixing, whereas log-normal distribution indicates incomplete mixing. 
In mine A, the highest peaks fit a type I extreme-value distribution. 

Extrapolation of the plotted points on type I extreme-value probability paper 

shows a return period of 3,000 or more for 1.0 percent or greater methane 

concentrations. This means that 1.0 percent or greater methane concentrations 

are achieved, on the average, only once in mining 3,000 entries provided 

mining conditions do not change appreciably. Mines B and C have a greater 

probability of reaching 1.0 percent or more methane. 

Probability plotting may be a powerful technique for predicting dangerous 

methane concentrations. Additional research is needed to establish its 

applicability for use underground. 
REFERENCES 

Coal Age. The ABC's of Ventilation for Continuous Miners. Coal Age 

Spec. Rept., February 1969, pp. 96-101. 

Gumbel, E. J. Statistics of Extremes. Columbia University Press, New 

York, 1958, 375 pp. 

. The Theory of Extremes. Discovery, May 1964, pp. 28-31. 

Hahn, G. J., and S. S. Shapiro. Statistical Models in Engineering. John 

Wiley & Sons, Inc., New York, 1967, 355 pp. 

Lavtsevich, V. P. Predicting Dangerous Methane Concentrations. Soviet 

Min. Sci., 1970, No. 4, pp. 396-399. 

Leidel, N. A., and K. A. Busch. Statistical Methods for the Determination of Noncompliance With Occupational Health Standards. Public 

Health Service TR-76, 1973, 45 pp. 

Luxner, J. V. Face Ventilation in Underground Bituminous Coal Mines. 

Airflow and Methane Distribution Patterns in Immediate Face Area-Line 

Brattice. BuMines RI 7223, 1969, 16 pp. 

Schlick, D. P., and R. W. Dalzell. Ventilation of Continuous-Miner 

Places in Coal Mines. BuMines IC 8161, 1963, 18 pp. 

Shuttleworth, S. Ventilation at the Face of a Heading, Studies in the 

Laboratory and Underground. Int. J. Rock Mech. Mining Sci., v. 1, 

1963, pp. 79-92. 

Stahl, R. W., and F. F. Kapsch. Survey of Face Ventilation Practices in 

Coal Mines. BuMines RI 5560, 1960, 13 pp. 

Todhunter, J. S. Face Ventilation and Dust Control. Min. Cong. J., 

January 1962, pp. 38-48. 

U.S. Code of Federal Regulations. Title 30--Mineral Resources; Chapter I--Bureau of Mines, Department of the Interior; Subchapter 0--Coal 

Mine Health and Safety; Part 75--Mandatory Safety Standards, Underground Coal Mines; Subpart D--Ventilation. Federal Register, v. 35, 

No. 226, Nov. 20, 1970, pp. 17898-17906. 

t U.S. GPO: 1974-705-601/609