1 Bureau of Mines Report of Investigations/ 1972 

Methane Migration Characteristics 

of the Pocahontas No. 3 Coalbed 

UNITED STATES DEPARTMENT OF THE INTERIOR 
UNITED STATES DEPARTMENT OF THE INTERIOR 

Rogers C. B. Morton, Secretary 

BUREAU OF MINES 

Elburt F. Osborn, Director 
This publication has been cataloged as follows : 

Kissell, Fred N 

Methane migration characteristics of the Pochantas No. 3 

coalbed. [Washington] U.S. Dept. of the Interior, Bureau of 

Mines 1319721 

19 p. illus. (U.S. Bureau of Mines. Report of investigations 

7649) 

Includes bibliography. 

1. Methane. I. Title. (Series) 

TN23.U7 no. 7649 622.06173 

U.S. Dept. of the Int. Library 
CONTENTS 

Page 

Abstract ........ .............................,............................ 1 

Introduction .................................,........................... 1 

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

Evidence for the crushed zone ........................................... 2 

The source of methane during idle periods ............................... 2 

Results from the laboratory-desorption rates from'lumps ............ 3 

Results from the mine .............................................. 4 

Estimation of coalbed permeability and sorption capacity ................ 5 

Methane flows from the working face when the mine is in operation ....... 8 

Comparison with other coalbeds .......................................... 11 

Conclusions ............................................................. 11 

References .............................................................. 13 

Appendix A...Notation ................................................... 14 

Appendix B...Calculation of permeability and sorption capacity .......... 15 

Ap.pendix C...Calculation of permeability ................................ 18 

Appendix D...Expected flow from horizontal bo.reholes .................... 19 

ILLUSTRATIONS 

1 . A pressure curve .................................................... 2 

2 . Desorption curves for coal .......................................... 4 

3 . Methane flow from face area ......................................... 5 

4 . Pressure versus distance taken 360 hr after mining ................. 6 

5 . Location of hori.zonta1 boreholes .................................... 7 

6 . Methane flow from the face area during cutting ...................... 9 

7 . Pressure curves before and after a hypothetical 19-ft advance ....... 10 
METHANE MIGRATION CHARACTERISTICS 

OF THE POCAHONTAS NO. 3 COALBED 

by 

Fred N. Kissell ' 

ABSTRACT 

Methane-flow and pressure data taken from a mine in the Pocahontas No. 3 

coalbed are compared with flow rates from lump coal obtained in laboratory 

experiments. From this, it is concluded that the main source of gas is the 

intact coalbed rather than a "crushed zone" near the working face. The 

permeability and sorption capacity of the intact coalbed are calculated and 

gas emission rates are theoretically accounted for. 

INTRODUCTION 

The Bureau of Mines has been concerned with the necessity of pinpointing 

the source of methane in coal mines, if preventive techniques are to be used 

to control methane emission. Various workers (lo, 13) , particularly in 

Europe, have hypothesized that much of the methane emitted at the longwall 

working face originates in a high-permeability relaxed or fracture zone, which 

extends into the coal being worked and also into adjacent strata. Fracturing 

in the coal being worked takes place because increased stress levels resulting 

from the removal of adjacent coal have exceeded the compressive strength of 

coal in the zone, partially crushing it and increasing its permeability. 

Fracturing in the adjacent strata takes place because of caving. Although a 

large quantity of methane may be stored in coal, frequently under high pressure, the permeability of an undisturbed coalbed may be quite low and the gas 

does not flow freely to the working areas. However, crushing the coal greatly 

increases its permeability so the gas in the crushed zone flows easily into 

the mine. 

On the other hand, Cervik (2) implies that a source of methane in 

U.S. mines is in the intact coal beyond the crushed zone. This seems to be 

a likely hypothesis because most U.S. coals are mined at shallower de,pths than 

European coals. Because U.S. mines are shallower, the ground pressure is less 

and the crushed zone may be less extensive. The ,permeability of the undisturbed coalbed may be considerably higher, given the enormous changes in 

lphysical research scientist. 

"underlined numbers in parentheses refer to items in the list of references 

preceding the appendixes. 
permeability shown in laboratory permeability-stress experiments with coal. 

Also, the roof is not immediately caved. 

That some basic difference in the source of methane may exist while 

mining, U. S. coalbeds and those in Europe have never been subjected to experimental test. It is the intent of this report to ascertain if a coalbed 

crushed zone really exists while mining by the advancing room-and-pillar 

method in the Pocahontas No. 3 coalbed, and whether the main source of 

methane is in this zone or in the unmined and intact coal adjacent to it. 

At the same time, an attempt will be made to explain theoretically the gas 

flow rates observed in a working mine in terms of what is known about the 

desorption and flow characteristics of Pocahontas No. 3 coal. 

ACKNOWLEDGMENTS 

Acknowledgment is due the Bureau of Mines people who have contributed 

data: Jack Perkins for the lump desorption results and John D. Kalasky and 

Joseph D. Hadden for the information from the Beatrice mine. 

EVIDENCE FOR THE CRUSHED ZONE 

The Bureau of Mines has been engaged in a program of drilling deep 

horizontal holes into coalbeds, packing them with inflatable packers, and 

measuring gas pressures. In contrast to results obtained by Gunther (4) , the packers generally have succeeded in sealing the hole effectively; also, 

the seam permeability always has been high enough to insure that the pressure 

measured was a true equilibrium pressure--that is, it gives a true indication 

of the actual gas pressure in the fractures. 

A curve of gas pressure versus depth in a horizontal hole in the 

Pocahontas No. 3 coalbed is shown in figure 1, along with the curve that might 

Constant - permeability - 

- 

Measured from Pocahontas 

No. 3 seam - 

- 

- 

be expected if the coalbed 

had a constant permeability. 

It is clear from inspection 

of these curves that a zone 

of sharply increased permeability is in approximately 

the first 10 ft. This is 

the crushed zone. 

THE SOURCE OF METHANE DURING 

IDLE PERIODS 

The role of the crushed 

zone in contributing to gas 

flow is most easily assessed 

10 20 30 40 50 60 70 80 by comparing laboratory flow 

DISTANCE INTO SEAM FROM FACE, ft rates from lump coal with 

those measured at a working 

face in a mine when the mine 

FIGURE 1. - A Pressure Curve. is idle. It is assumed that 
the coal in the crushed zone simply consists of a large quantity of desorbing 

lumps and, because of the high permeability of the zone, gas flow to the face 

area is unimpeded. If the flow rate per ton of coal observed in the laboratory is equal to or exceeds that from a working face during an idle period 

when operation of the mining machine does not contribute to the gas flow, 

then this would be strong evidence that the crushed zone is in fact the main 

source of gas. On the other hand, if the laboratory flow rate falls short 

of the gas flow from the working face, then an additional source of gas in the 

mine is indicated. 

Results From the Laboratory-Desorption Rates From Lumps 

Recent work on the desorption of methane from lump coal in the laboratory 

has been done by Airey (1). He found that the room temperature desorption of 

methane from lump coal follows the empirical formula 

where V(t) is the amount of methane desorbed in time t, and A and to are constants dependent on initial pressure and lump size, respectively. A theoretical estimation of flow rate based on unsteadly-state Darcy flow from a thin 

slab was not a good fit to this equation, and a more accurate fit could be 

obtained by assuming that a distribution of s,lab thicknesses existed within 

a given slab. Airey also found that the para.meter to varied directly with 

lump size for smaller lumps, but that for larger sizes the variation of to 

with size is considerably less. This was to be expected because it is known 

that coal has a basic structure of fine cracks and that larger lumps always 

contain numerous fractures. Because large lumps have smaller variation of 

to with size, the desorption curves of large lumps are much less affected by 

size. Figure 2 shows a desorption curve by Airey for k- to %-in size range 

coal and also a desorption curve for 6- to 12-in size range coal based on an 

extrapolation of his parameter to. It may be seen that for the 75- to 

325-hour period, the difference in the amount desorbed is about 25 ft3 per 

ton; however, the rates of emission in cubic feet per ton-hour for the two 

size ranges are very similar. 

The room temperature desorption rate of k- to %-in size Pocahontas No. 3 

coal has been measured by the Bureau of Mines (fig. 2). Despite the fact that 

the total amount of gas desorbed is greater than that for the coal used by 

Aire~,~ theemission rate, 0.3 ft3 per ton-hr, between 75 and 325 hours is 

similar . Preliminary results on larger Pocahontas coal indicate a similar 

3To some extent the amount desorbed is greater because Perkins used dry 

coal, which is known to have greater capacity for absorbing methane 

than moist coal. The effect of moisture on the lump emission rate is 

not known, but more than likely it would be reduced. 
0 6 in-12 in size coal (extrapolated) 

No. 3 seam (Perkins) 

Initial pressure = 20 atm 

Final pressure = I atm 

- 

- 

I I I 1 

emission rate. Because of 

this, it can be assumed that 

the lump emission rate may 

be compared directly with 

flow rates from a hypothetical crushed zone where the 

coal falls within a size 

range of to 12 in, provided the time period, 

initial pressures, and 

coal are all similar. 

Results From the Mine 

Some methane flow data 

were obtained recently in 

the Beatrice mine. This 

mine, operated in the 

Pocahontas No. 3 coalbed, 

is located near Keen Mountain, Va. Unit No. 7, 

section 3d North, where flow 

measurements were taken, is 

being worked by the advancing room-and-pillar method. 

The overburden here is 

approximately 2,000 ft u 

0 1 00 2 00 300 thick. Anemometers and 

Time t, hr 

400 500 recording methanometers 

set up in the intake and 

return airways were used 

to obtain the methane flow FIGURE 2. - Desorption Curves for Coal. from the face area. 

Mining stopped on June 26, 1970, for 2 weeks. Figure 3 shows the flow 

rate during this idle period as well as the flow before and after idleness 

when mining was in progress. The 75- to 325-hour period selected above 

corresponds to the interval from June 29 to July 10. During this time 

the methane flow from the face area averaged about 74 cfm and the total 

variation was about 213 percent. 

The face area in this section was 2,400 ft2, and a crushed zone 10 ft 

wide would contain 970 tons of coal. If the laboratory flow rate obtained 

by Perkins between 75 and 325 hr is applied to this 970 tons of coal, the 

theoretical flow rate is 5 cfm. This is much less than the 74 cfm observed 

in the mine during the corres.ponding June 29 to July 10 period. A wider 

crushed zone would produce more than 5 cfm, but this is difficult to 

visualize. Calculations,given in appendix C yield a crushed zone thickness 

of 8.6 ft. A zone 20 ft thick would still only account for 10 cfm. Thicker 

zones would not permit the steep gradients shown in figures 1 and 4 to exist. 

A source of gas other than the crushed zone is indicated. 
CALENDAR TIME, days 1 

FIGURE 3. - Methane Flow From Face Area. 

During mining, the roof and floor in th.e working face area were both 

intact; very little gas was issuing from adjacent strata. It follows that the 

primary source of gas during the idle period. must'be behind the crushed zone 

in the undis turbed coalbed. 

1 ESTIMATION OF COALBED PERMEABILITY AND SORPTION CAPACITY 

Assuming the primary source of methane in this idle mine is in the 

coalbed behind the crushed zone, the 74-cfm flow rate from figure 3 can be 

used to obtain the coalbed permeability and sorption capacity if a pressure 

curve such as figure 1 is known. In fact, the Bureau of Mines has obtained 

Ipressure curves from measurements in the same section. One taken 360 hr 
DISTANCE FROM FACE, ft 

FIGURE 4. - Pressure Versus Distance Taken 360 Hr After Mining. 

after mining is shown in figure 4. From figure 4 alone, the ratio 

permeability may be estimated if it is assumed that flow from the sorption capacity 2 

coalbed follows the Darcy equation for unsteady-state flow of gases (L-2, 8) 

The symbols are shown in appendix A. Details of the calculation are shown in 

K appendixes B and C and - = 0.57 millidarcy (md). S 

Next, the permeability K may be estimated inde.pendently using the slope 

of figure 4 at 0 psig and the observed emission of 74 ch. This calculation 

is shown in appendix C. The permeability K obtained is 0.32 md. 
Hole 

A 

B 

C 

D 

E 

X 

B 

The face was at this point 

during the idle period 

LEGEND 

Length. ft Gasflow. ft of hole 

0 - 100 200 

Scale, feet 

FIGURE 5. - Location of Horizlontal Boreholes. 

K Since both - and K are known, a sorption capacity S of 0.56 may be calcu- S lated. This is much higher than coal porosity, which mercury intrusion 

studies (14) have shown to be around 5 or 10 pct. However, coal has a great 

capacity for adsorbing gas. At 650 psi, 1 g of finely powdered Pocahontas 

coal can absorb at least 20 cm3 of gas. This corresponds to a sorption 

capacity of 0.59, and thus a measured value of 0.56 for solid coal is not 

unreasonable. 

It is possible to obtain a rough check on these values of K and S by 

calculating the expected emission from a horizontal borehole drilled into the 

working face. During the idle period mentioned previously, several holes 

were drilled horizontally into the coal to drain out methane (fig. 5). For a 

250-ft hole the measured gas flow rate ranged from 10,000 to 15,000 ft3 per 

day. The calculated flow using K=0.32 md and S =0.56 is shown in appendix D. 
3. Increased emission from the intact coalbed behind the crushed zone 

because mining has advanced the crushed zone and created a steeper pressure 

gradient. 

The 60 to 120 cfm over the increased background flow may be attributed to 

sources 1 and 2; that is, degradation at the face and advance of the highpermeability crushed zone. On the other hand, the background increase itself 

may be attributed to source 3. 

K 

41t is possible that is slightly less than the 0.57 md value given. One of 

the holes drilled into the face (fig. 5, hole X) at the beginning of the 

idle period was sealed with inflatable packers and the pressure measured 

was 649 psig. Twelve days later (still during the idle period) the pressure had fallen only 13 psi. Calculations similar to those given in 

K appendix B would indicate - = 0.4 md. This also would make the calculated S 

borehole flow rate somewhat lower, and thus in better agreement with the 

measured values. 
200 Breakthrough 2-1 (cut 2) began IO:55 a.m., June 26,34 tons 

' 

'\ 

140 

z I20 ---- - 

I? roo - I 1 I I i I I I I I 

=E 

W 

No. 2 entry (cut 3) began I:15p.m., July 27. 60 tons 

170 - 

No.2 entry (cut4) began 2:30 p.m., Aug.20, 30 tons 

-,---Machine idle or tramming out 

150 

130 

No. l entry (cut 4) began I: 45 p.m., June 26. 58 tons 

220 1 I 1 I I I I 1 I 1 I 1 

- 

- 

-10 0 10 20 30 40 50 60 70 80 90 100 

TI ME, min 

FIGURE 6. - Methane Flow From the Face Area During Cutting. 

Using these three sources as a basis, it: is possible to approximately 

account for the flow rates shown in figure 6 in terms of the various properties of the coalbed; that is, the pressure curve shown in figure 4, the 

desorption curve for Pocahontas No. 3 coal given in figure 2, and the 

calculated permeability and sorption capacity. 

110 9 -,,- - .- - -- -.-- ' [ - 

70 I I I I I I I I I I 6 
- - 

Pressure gradient curve 

, before advance - 

- - 

Pressure gradient after 

- hypothetical 19-ft advance - 

- - 

I I 

0 20 4 0 60 80 1 00 120 140 160 

DISTANCE FROM FACE, ft 

FIGURE 7. - Pressure Curves Before and After a Hypothetical 19-Ft Advance. 

Source 3 may be estimated as follows: the average cut shown in figure 6 

yielded about 50 tons of coal. This results from an advance of 19 ft in a 

4- by 16-ft heading.. Figure 7 is figure 4 redrawn to show the effect on the 

pressure curve of a hypothetical 1g6ft advance. The slope at the "pressure 

face" increases by a factor of 1.6. Given the same permeability, 0.32 md, 

the flow from the pressure face would be about 74 x 1.6 = 120 cfm. Thus the 

coalbed behind the crushed zone contributes 120 cfm. 

5The 1.6 is obtained by fitting the theoretical curve to the hypothetical 

pressure curve after a 19-ft advance. The procedure is the same as that 

K given in appendix B for the curve in figure 4, except that - = 0.57 is used S 

and t, is calculated. In this case, t, is not the time since mining, but 

simply becomes a parameter. Next, the slope at the pressure face is calculated using the equations detailed in appendix C. 
The contribution from sourcesland2(clegradation at the face and advance 

of the crushed zone) may be approximated as follows: The area between the 

curves in figure 7 was integrated graphically to obtain the amount of gas to 

be found in the coal. It is assumed that the advance was made in 1 hr, the 

sorption capacity of the coal was the value obtained previously, 0.56, and 

that complete desorption takes place. This gives an emission of 280 cfm. 

This volume is considerably higher than the 60 to 120 cfm emission rate 

actually measured in the mine. Most of the error probably is due to the 

assumption that complete desorption occurs in 1 hr (appendix B). Data given 

by Airey (1) and Perkins (fig. 2) would indicate that larger lumps are 25 pct 

desorbed i; 1 hr, and if this is correct, an average emission of 70 cfm would 

result. 

At present there is no way to separate the contributions of sources 1 and 

2, or to obtain a more accurate value for the percentage desorbed without 

additional experimental information. 

The results for a typical mining cycle may be summarized as follows: 

Measured emission Estimated emission 

Source (from mine), cfm (theoretical), cfm 

1. Degradation at face 

2. Advance of crushed I 60 to 120 70 (assuming 25-pct 

zone desorption). 

3. Emission from seam 90 to 150 120 

behind crushed zone 

It can be seen that the observed emission rates can be theoretically justified 

to an approximate degree. It appears that during mining the crushed zone 

plays a more important role, than during the idle period, but still is not 

the main source of gas. 

COMPARISON WITH OTIIER COALBEDS 

There is some evidence that the Pocahontas No. 3 coalbed may not be as 

permeable as other U.S. coalbeds. Horizontal boreholes in the Pittsburgh 

bed have given gas emission rates 10 times higher than the Pocahontas No. 3 

(g), even with a lower gas pressure. Another study (9) has shown that the 

increase in methane emission resulting from mining a face in the Pittsburgh 

bed is typically about 10 cfm. This is considerably lower than the measured 

60 to 120 cfm shown from sources 1 and 2. It is likely that the permeability 

of the Pittsburgh bed is considerably higher, perhaps by a factor of 50. 

Also the crushed zone is likely to be much less extensive. 

CONCLUSIONS 

The various sources of methane in the Pocahontas NO. 3 coalbed have been 

estimated for an advancing room-and-pillar--mining operation. Consideration of 

gas flows during 2 weeks when the mine was idle allow the calculation of the 

coalbed permeability and sorption capacity* Also, it can be concluded that 
the crushed zone is not the main source of gas, whether during mining or not. 

Even though the results are rather crude, the analysis nevertheless provides 

a framework for more detailed and more accurate approximations in the future. 

Even at the present state, the analysis indicates what sort of methane 

control scheme is likely to be successful in this coalbed. For instance, the 

low permeability obtained, 0.32 md, indicates that vertical wells may not 

provide a very efficient means of degasifying large areas. It indicates 

that drilling horizontal holes directly into the face will be much more 

effective than drilling into just the outside entries (5). Also, the 

analysis indicates that when the mining machine is operating in this coalbed, 

the major source of gas is within 50 ft of the machine. 

It appears that Cervik's suggestion that most of the methane in U.S. 

coalbeds comes from within the intact coalbed is partly correct for the 

Pocahontas No. 3 seam. His suggestion may be more correct for other beds 

such as the Pittsburgh coalbed. 
REFERENCE: S ' 

Airey, E. M. Gas Emission From Broken Coal. An Experimental and 

Theoretical Investigation. Internat. J. Rock Mech. Min. Sci., v. 5, 

1968, pp. 475-494. 

Carmen, P. C. Flow of Gases Through Porous Media. Academic Press, 

New York, 1956, 182 pp. 

Cervik, Joseph. An Investigation of the Behavior and Control of Methane 

Gas. Min. Cong. J., v. 53, July 1967, p. 52. 

Gunther, J. Etude de la Liason Gaz-Charbon (Investigation of the 

Relationship Between Coal and the Gas Contained in It). Rev. Ind. 

Min., v. 47, 1965, Safety in Mines Research Establishment (SMRE) 

Trans. No. 5134, pp. 693-708. 

Hadden, J. D., and Albert Sainato. Gas Migration Characteristics of 

Coalbeds. BuMines Tech. Prog. Rept, 12, May 1969, 10 pp. 

Hofer, L. J. E., James Bayer, and R. 13. Anderson. Rates of Adsorption 

of Methane on Pocahontas and Pittsburgh Coal Seams. BuMines Rept. 

of Inv. 6750, 1966, 13 pp. 

Karn, F. S., R. A. Friedel, B. M. Than~es, and A. G. Sharkey, Jr. Gas 

Transport Through Sections of Solid Coal. Fuel, v. 49, No. 3, 1970, 

p. 249. 

Katz, Donald L. (ed.). Handbook of Natural Gas Engineering. McGrawHill Book Co. Inc., New York, 1959, 802 pp. 

Krickovic, Stephen, Charles Findlay, and W. M. Merritts. Methane 

Emission Rate Studies in a Northern West Virginia Mine. BuMines 

Tech. Prog. Rept. 28, 1970, 11 pp. 

Lama-Mahajan, Ripu Daman. Outbursts of Gas and Coal. Coll. Eng., 

v. 45, 1968, p. 103. 

Merritts, W. M., W. N. Poundstone, and B. A. Light. Removing Methane 

(Degasification) From the Pittsburgh Coalbed in NorthernWest Virginia. 

BuMines Rept. of Inv. 5977, 1962, 35) pp. 

Sevenster, P. G. Diffusion of Gases Through Coal. Fuel, v. 38, 1959, 

p. 403. 

Shilo, L. Ya. (The Nature of the Movement of Methane in the Face Zone 

of a Seam.) Ugol' Ukrainy (Coal of Ukraine), v. 9, No. 6, June 1965, 

pp. 45-48. (BuMines Library Transl. No. 2980.) Avail. BuMines 

Library, Pittsburgh, Pa. 

van Krevelen, D. W. Coal. D. Van Nositrand Co., New York, 1961, 514 pp. 

Zwietering, P., J. Overeem, and D. W. van Krevelen. Chemical Structure 

and Properties of Coal XIII-Activated Diffusion of Gases in Coal. 

Fuel, v. 35, 1956, p. 66. 

'~itles enclosed in parentheses are translations from the language in which 

the item was originally published. 
APPENDIX A. --NOTATION 

P = pressure (atm). 

Q = methane emitted (cm3). 

t = time (sec). 

= pressure at which Q is measured (atrn). 

A = face area (cm2). 

1 = viscosity of methane (cp). 

x = distance into coal seam from working face (cm). 

K = permeability (darcy) . 

= face gradient (2) = average pressure (atm). 

P (x,t) = pressure in the coalbed at point x and time t (atrn). 

P.e.. = gas pressure in the undisturbed bed (atrn). 

Xo = pressure face. 

x~ = distance from pressure face to point x in seam = (x-xo) (cm). 

= time since mining (sec). 

P = gas density (5) = radius of borehole (ft). 

r = drainage radius of borehole (ft). 

h = length of borehole (ft) . 

S volume of gas adsorbed per atmosphere = sorption capacity total volume of coal 
APPENDIX B.--CALCULATION OF PERMEA.BILITY AND SORPTION CAPACITY 

It is assumed that methane flow in the coalbed follows the unsteady-state 

Darcy equation for gas flow, and it is assumed that the bed is a homogeneous 

semi-infinite slab; the end of the slab being the coal face. Before mining, 

the slab is at uniform pressure PIIeBm. At the time of mining, the end of the 

slab (face) is reduced to atmospheric pressure. 

It also is assumed that the desorption from the pore structure of the 

coal is fast compared with the time required for the gas to flow to the face. 

The equation is 

and an approximate solution is (8) - 

P2(x,t)-y2Beam = erfc 1 

P2a t u -P28 e am 

where erfc signifies complementary error function and erfc = 1 minus the 

probability integral. Values of the probablility integral may be obtained 

from standard tables. 

t, FK 

Also above, t, = dimensionless time = 

7x;se 

K is obtained by fitting the error function curve to figure 4 using the 

S 

following values : 

tm = 360 hr. 

- 

P = 340 psia. 

e am = 680 psia. 

n = 0.012 cp. 

From this, - - 0.57 md. S 

In figure 3, xo= 8.6 ft. The next step is the calculation of the 

gradient at the pressure face. If the error function curve is differentiated 

the result is: 
d9 - P2s e am exp (- 7) 6 TS 

4KPtm 

At the pressure face x, = 0, so 

P Zp$ = seam + 

a tm From this, - dP = 0.5 - . The Darcy equation is: dx cm 

QP, K dP =- P- At r] dx 

dP atm If - = 0.5-, A = face area = 2.23 x lo6 cm2 and = flow (at tm = 360) = dx cm t 

f t3 63 --;- = 3 X 10 4 cm3 then K = 0.32 md. mln sec' 

The Desorption Problem 

Coal is known to have a system of fine pores called micropores, which are 

approximately 10 A in diameter, and also a system of larger pores (or cracks) 

called macropores, which range in size from micropore dimensions up to micron 

size. Most of the methane in coal is adsorbed on the surface of the micropores. When coal is mined, the coalbed is progressively exposed, and the gas 

pressure in the bed falls. Methane then migrates from the micropores into the 

larger pores and cracks that lead to the working area of the mine. This may 

be viewed as a two-step process. First, methane diffuses from the micropores 

into the cracks, and second, the methane flows through the cracks (by laminar 

or Darcy flow) to the working area. 

If the diffusion step is assumed to be rapid, compared with the second 

step, then the gas adsorbed in the coal micropore structure will be in equilibrium with the gas pressure in the cracks, and the second step will be the 

rate-controlling step. However, if the micropore diffusion coefficient is 

very small the first step will be slower, and the pressure gradient curve and 

the face emission will be affected. Some evidence has been presented that the 

diffusion coefficient is quite small; that is, 

2 (D = 10-l~ to 10-l3 x) sec 

notably by P. G. Sevenster (g), P. Zwietering (E), and F. S. Karn (7). 

However, the coefficients given by Sevenster and Zwietering are based-on a 

BET surface area measurement of powders, not on an area calculated from the 
particle diameter. This leads to a low value for the diffusion coefficient. 

The disks used by Karn were tested only if they were sound; that is, the 

coefficient was low due to absence of micracracks. The point is that a 

typical piece of coal has microcracks even though these may not be immediately 

evident. 

If the diffusion coefficient for powders is based on a surface area calculated from the particle radius (which is much smaller than the BET area), 

the coefficient is about lo-* cm2 per second (6). Bureau of Mines measure2 - ments on disks have given 5 x lCT7 cm per second. The existence of a basic 

microcrack structure has been confirmed by Airey. Although even is not 

large, the presence of a microcrack structure makes the area through which 

the gas may diffuse quite large. Thus it is assumed the desorption and 

diffusion from the pore structure into the microcracks is fast enough to 

maintain equilibrium, and the second step is the rate-controlling step. The 

IDarcy equation is then written for this second step. It should be noted that 

the high value of 0.56 obtained for sorption capacity indicates that the 

assumption is reasonable in this case. 

1 It appears that the diffusion is not fast enough to completely desorb 

lumps in an hour if the pressure is changed abruptly. Data from Airey (1) 

'and Perkins indicate that lumps over 114-in size are approximately 25 pct 

besorbed in an hour, and so this 25 pct factor is used in estimating 

sources 1 and 2. 
APPENDIX C.--CALCULATION OF PERMEABILITY 

Because the high-permeability crushed zone is present, the gradient 

exactly at the working face will not give a correct value for coalbed permeability. Rather, a hypothetical "pressure face" is established. This is the 

point in the coal seam where, for the purpose of calculation, the pressure is 

assumed to be 1 atm. This point generally is about 10 ft back into the seam 

fromtheworking face. It shouldbenoted that the distance in appendix B is 

x --the distance to the pressure face, not the "working face." 

P 

The pressure face is obtained as follows: 

Two measured pressures from the mine are selected, for example, points 1 

and 2 in figure 4. 

The value for the pressure face x, is such that 

since 

then (td xfIpoint 1 = (tb ~g)~~~~t 2* It then can be shown 

where B 

(+) point 1 
APPENDIX D . - -EXPECTED now FROM HORIZONTAL BOREHOLES 

If the Darcy equation is solved for unsteady-state flow from a well or 

borehole, the result is (8) 

where Qt is a dimensionless total production number given by 

Here td = 2.634 x loo4 t 3 K 

r2 So If t = 10 ~IK, r = 7 ft, r, = 1.5 in, and 

K 

- = 0.574, then QT= 32,000 ft3 per day. S 

It should be noted that this equation applies for radial drainage only. 

If the coal seam is 4 ft thick, drainage is no longer radial when r exceeds 

2 ft. Thus these results are only very approximate. The actual flow for 

r = 7 ft would be less than the calculated flow. This has been observed, 

as the actual flow rate was some 10,000 to 15,000 ft3 per day.