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

Stanley K. Hathaway, Secretary 

Jack W. Carlson, Assistant Secretary-Energy and Minerals 

BUREAU OF MINES 

Thomas V. Falkie, Director 
Ki <-;(!I I, Iq'r~d N 

Two-phase flow in coalbeds, by Fred N. Kissell and John 

C. Edwards. [Washington] U.S. Bureau of Mines [1975] 

16 p. illus. (U.S. Ilurcau of Mines. Report of investigations 

8066) 

Includes bibliography. 

1. Mcthanc. 2. Two-phase flow-Simulation methods. I. Edwards, 

John (I., jt. auth. 11. 1J.S. Ilureau of Mincs. 111. Title. (Series) 

TN23.U7 no. 8066 622.06173 

1J.S. 1)cpt. of thc Int. 1.ihrJ.r~. 
C ONTE NTS 

Page 

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

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

Background ............................................................... 2 

Computer simulation of two-phase flow .................................... 5 

Analysis of production history ........................................... 12 

Conclusions .............................................................. 14 

References ............................................................... 15 

ILLUSTRATI ONS 

Gas pressure curves from two regions in a deep mine in the 

Pocahontas No . 3 coalbed .......................................... 2 

Area of investigation in Zabetakis study ............................ 3 

In situ pressure versus time for the large-diameter borehole ........ 4 

Gas and water flow rates for the large-diameter borehole ............ 4 

Gas and water emission curves for a vertical borehole . .............. 5 

Gas and water relative-permeability curves used in computer model ... 9 

Capillary-pressure curve used in computer mode 1 ..................... 9 

Methane flow curves for three hypothetical cases with different 

initial water saturations ........................................ 10 

Gas relative-permeability curves and initial water saturation for 

cases 1-5 ....................................................... 11 

Methane flow curves for three hypothetical cases with gas relativepermeability curves of different slop? ............................ 11 

Water flow and gas-water ratio calculated by the Bureau of Mines 

model for case 2 .................................................. 12 

Gas-water ratio from Fields large-diameter multipurpose borehole .... 13 
TWO-PHASE FLOW IN COALBEDS 

by 

Fred N. Kissell and John C. Edwards2 

ABSTRACT 

Experimental work by the Bureau of Mines indicates that when a coalbed is 

degassed by boreholes, the flow of methane may actually increase with time. 

This phenomenon appears to be the result of a relative-permeability effect; 

that is, the coalbed permeability to the gas increases sharply with decreasing 

water saturation. This report reviews the background of experimental evidence 

indicating a relative-permeability effect, and presents the results of a 

computer simulation of two-phase flow in coal. 

INTRODUCTION 

A major characteristic of coalbed permeability is that the measured 

permeability to methane appears to increase with time. This was first 

reported by Kissell (6) ,3 who found that regions of a coalbed adjacent to 

older areas of a mine were considerably more permeable than regions adjoining 

freshly mined areas. Several factors could account for this. One is 

"destressing," the relaxation resulting from the strata movements that 

accompany mining (13). Another is the coal shrinkage resulting from the loss 

of methane (8). However, the most probable explanation is a relativepermeability effect in which the flow of methane is controlled in part by the 

degree of coalbed water saturation; the permeability to methane increases as 

the water in the coalbed decreases and makes more pore space available to the 

gas phase. This assumption was based on observation of the variations in gas 

and water flow from boreholes drilled horizontally into the coal. 

This Bureau of Mines report presents the background of experimental 

evidence for a permeability change caused by loss of water, and discusses the 

results of a computer simulation of two-phase flow in coalbeds. Although the 

relative-permeability concept is somewhat novel to flow through coalbeds, it 

has been employed extensively by the petroleum industry. 

lPhysical research scientist. 

Physicist. 

3~nderlined numbers in parentheses refer to items in the list of references 

at the end of this report. 
BACKGROUND 

Kissell used coalbed gas-pressure curves to estimate gas permeability. 

Figure 1 shms two curves obtained from a very deep mine in the Pocahontas 

No. 3 coalbed (5). These pressures were determined by drilling horizontal 

holes into the working face or rib of a development section. The holes were 

immediately sealed with inflatable packers so that no gas drained from the 

coal. The gas pressure in the open spaces between the packers soon reached 

equilibrium, which was assumed to represent the true gas pressure in the 

coalbed before drilling. For the calculation, the coalbed was assumed to be 

a homogeneous slab, to which a simple one-dimensional , unsteady-state f orm 

of the Darcy equation was applied. The upper curve in figure 1 was obtained 

from a hole drilled into a rib that had been mined 15 days before; thus, the 

rib had been exposed for 15 days prior to drilling and packing. The calculated permeability for this region of the coalbed was 0.57 md. The lower 

curve was obtained from a hole drilled into a rib that had been exposed for 

180 days prior to drilling and packing; the calculated permeability for this 

region was 280 md. 

D 

- 

- 

- 

- 

- 

180 days after 

- 

0 

U 

DISTANCE, ft 

FIGURE 1. - Gas pressure curves from two regions in a deep mine in the Pocahontas No. 3 

coalbed (5). 
In the same mine, a drainage hole drilled into the working face emitted 

7,260 ft3 /day of methane and 72 gal/day of water for several days after 

drilling. However, on the sixth day, the gas flow rose to 7,960 ft3/day and 

the water flow fell to 48 gal/day. This suggested that the permeability 

increase was a relative-permeability effect. 

Subsequently, Zabetakis (l5) made a survey of rib emissions in a gassy 

mine in the Pittsburgh coalbed. For this purpose, a standard ventilation 

survey was made at a working face in a development section. The return airway 

was then followed for several thousand feet, and the methane concentration 

was measured at 100-foot intervals. The rib survey was adjacent to solid 

coal. The coalbed also contained several gas and oil wells (fig. 2). 

Zabetakis found that although the wells were contributing more than half of 

the methane, after the data on the effects of the wells were corrected out, 

the rib emission was surprisingly constant. This meant that 100 feet of rib 

FIGUKE 2. - Area of investigation in Zabetakis study (15). - 
close to the working face and freshly exposed by mining was emitting methane 

at the same rate as a comparable 100-foot length several thousand feet from 

the face and exposed for many months. If the rib permeability to methane were 

constant, this could not have occurred since older ribs would yield considerably less methane than freshly exposed ribs. Zabetakis concluded that the 

methane permeability of the older rib was higher because of a decrease in the 

water content of the coal. 

2201 1 In still another projpressure 

180. 

160 

;140- 

w 

2 120- 

cn W Q:

a 100- 3 

C 

v, 

g 80 

60 

I ect , Fields (3-4) described 

a virgin area of the Pittsburgh coalbed degasified 

through a large-diame ter 

borehole drilled into the 

coal from the surface. At 

coalbed leve 1, the borehole 

was enlarged to a small room. - From this room, eight 3-inchdiameter holes were drilled 

i out horizontally about 600 

feet into the coalbed in a 

766 - radial fashion similar to days - - I 

-+ spokes on a wheel. One of 

- 

- 

- 

p 203 maximum in situ 

-A 2 holes connected 

L 3 holes connected 

i, 4 holes connected 

. . 

FlGUR E 3. - In situ pressure versus time for the large40 

20 

diameter borehole (4). - 

Compressor installed, 

and gas piped to 

0 100 200 306 400 500 600 700 800 

TIME. dovs methane- and water-flow 

t 11: Com;;r - the eight holes was packed 

gas company p~pellne 

f600!/ 2 'Gas flow IS regulated 

3- Gas flow at compressor 

5 400 LL 

766 days- - 

3 

SO that the pressure deep in 

the coal could be measured; 

the other seven were open to 

6 holes connected a negat~ve pressure of 

15 inches water gage is 

maintained at compressor - AI I 7 holes connected - 

PSI9 ' 9.0 psig 

Water flow 4 Y I I J 0 

0 100 200 300 400 500 600 700 800 

I drain gas. Pressure and 

TIME. days 

FlGUFiE 4. - Gas and water flow rates for the largediameter borehole (4). 

I I 

curves are shown in figures 3-4. 

1 

In the first 40 days, 

the pressure at the end of 

the packed hole fell from 

203 psig to 11 psig, a 

factor of 18. However, the 

methane flow from the other 

seven holes fell from 

1,121,000 ft3/day to 444,000 

ft3 /day, a factor of only 

2.5. After 40 days, the 

pressure stabilized in the 

range of 10 to 13 psig, but 

the flow began to rise. At 

400 days, it was slightly in 

excess of 700,000 ft3 /day. 

After this, it declined 

until at 500 days an exhausting compressor was connected 

by the gas company, which 

regulated the gas flow. 
at a rate that varied in a 

manner similar to that of 

the pressure. Initially it 

was 43 gal/min for all seven 

holes; after 40 days it was 

less than 7 gal/min, "and 

subsequently it stabilized 

at about 3.5 gal/min. 

6,000 

Another experimenta 1 

method for degasifying a 

coalbed in advance of mining 

is to drill a number of 

small-,diameter vertical boreholes into the coalbed. 

Duel (2) reported results 

obtained with 53 such holes, 

I I I I'IIIIIIIII In addition to the gas, 

I Tzo water flowed from the holes 

TIME, months most of them drilled into 

Appalachian coals. Since 

FIGURE 5. - Gas and water emission curves for a vertical the holes were cased and 

borehole drilled into a coalbed (2). cemented above the coal, all 

gas and water produced by 

the holes came from the coalbed. A typical flow curve 

for one of these holes (fig. 5) shows that the gas flow rises only as the 

coal is dewatered; over a period of about 1-1/2 years, a very substantial 

amount of water is removed from the coal. Thus a relative-permeability effect 

is again indicated. 

The rising methane flow rates reported by Fields and Deul seem 

,to rule out any effects due to strata movements and subsequent destressing. No mine was nearby. Only small-diameter holes were drilled into the 

coalbed and, although there was some destressing near each hole, it is unlikely 

this dould produce the long-term changes in figures 3-5. The rising methaneemission rate common during the mining of coal (2, Z) occurs because the mining 

machine exposes fresh coal as it digs forward; this is an entirely different 

phenomenon than that involved with rising flows from boreholes. 

COMPUTER SIMULATION OF TWO-PHASE FLOW 

Under a Bureau of Mines contract, Intercomp Resource Development and 

Engineering developed a theoretical computer model for methane flow in coalbeds (10). Its capabilities include the following: 

1. Two-dimensional, low-Reynolds-number, laminar (Darcy) flow; 

2. PVT properties as functions of pressure-viscosity, density, and 

compressibility factors ; 
3. Single-phase gas flow and two-phase flow of methane and water; 

4. Variable reservoir properties such as porosity, permeability, 

thickness, and elevations; and 

5. A mwing boundary to simulate the advancing working face of the 

mine. 

In previous applications of the model (ll), only the single-phase part 

of the program was used to any degree. The two-phase part of the computer 

code required a larger amount of input data, including the relative permeabilities of water and gas, capillary pressures, and initial water saturation. 

Because none of these data were available, and because the single-phase part 

of the computer code already had many variables, it was felt that pursuing 

the two-phase work would not be meaningful. 

More recently, however, data on relative permeability and capillary 

pressure have been obtained for coal (L, l2, l4) , and the unique rise in gas 

flow has been noted by Fields and by Deul. This suggested the the effort 

spent in simulating two-phase flow would be worthwhile. 

Three major characteristics were noted in the experimental field studies: 

1. Gas coalbed pressures in the vicinity of the mine fall more quickly 

than those expected for constant gas permeability (k), 

2. Rib gas emissions remain higher than those expected for constant gas 

permeability (15) , and 

3. Borehole gas flow rates increase and then pass through a maximum, 

sometimes after an initial decrease (2-3). 

The first and second characteristics require some estimate of what was 

expected, which is of ten difficult. Because the last characteristic represents 

an unequivocal test of a two-phase effect, an attempt was made to simulate 

increasing gas flow, which then passes through a maximum. 

The flow is initiated and maintained by the pressure difference between 

the gas in the entry (atmospheric) and the gas in the coal seam. The gas 

(water) fl& rate is proportional to the product of gas (water) relative 

permeability and the pressure gradient. This is formally expressed by 

Darcy 's law: 

where K = absolute permeability, 

Kr w = water relative permeability, 
J&. , = gas relative permeability, 

ug (w > = gas (water) viscosity, 

pg (1 = gas (water) density, 

V = gas (water) velocity at average flwing pressure, and the flow 

potentials are defined by 

where P, (w) = gas (water) pressure, 

G = acceleration due to gravity, 

and z = height of gas-water contact. 

It is seen from equations 1 and 2 that the relative permeabilities 

&, and Yw will influence the flow rates. They are functions of the water 

saturation, which changes with time. This makes them likely causes of a 

nonmonotonic decrease in flow rates. Because only relative-permeability 

effects on the gas flow rate were to be investigated, the model was restricted 

to a homogeneous coalbed with flow in one dimension. Otherwise, the same 

procedures used by Price (11) were used. 

Five cases were studied. The first three were identical in all respects 

except for the initial water saturation. The relative-permeability and 

capillary-pressure data used was reported by Taber (l4) for Pittsburgh coal 

at a simulated overburden pressure of 600 psi. Figure 6 gives the drainage 

curves for the relative permeability of gas and water. The capillary-pressure 

curve was represented by three linear segments (fig. 7). Other physical 

properties selected to define the coalbed system were as follows: 
Water viscosity ....................................................... 0.8 cp 

Gas viscosity ...................................................... 0.0125 cp 

Water density. ................................................... 62.4 lb/ft3 

Gas density ....................................................... 50 lb/~ft~ 

Water compressibility ................................... 3~10~~ vol/vol/psia 

Rock compressibility ..................................... 7X1OW6 vol/vol/psia 

Residual gas saturation. ............................................... 0.225 

Irreducible water saturation ............................................ 0.55 

Gas relative permeability at connate 

water saturation. ...................................................... 0.68 

Water relative permeability at 

residual gas saturation. ................................................ 0.1 

Average temperature in mine entry ..................................... 540" R 

Average pressure in mine entry ................................... 14.7 psia 

Initial gas pressure ................................................ 400 psia 

Absolute permeability ............................................... 2.5 md 

Porosity. ..... 

Width of coal section. ................................................ 400 ft 

Height section. ................................................. 

Depth of coal section. .............................................. Infinite 

Grid spacing .......................................................... 440 ft 

Time step for computation ............ 0.025 day for the period 0 to 0.1 day 

0.1 day for the period 0.1 to 5 days 

0.25 day for the period 5 to 15 days 

1.0 day for the period 15 to 30 days 

days for the period 30 to 200 days 

4.0 days for the period 200 to 360 days 
WATER SATURATION, S, 

WATER SATURATION, S, 

FIGURE 6. - Gas and water relative-perre- FIGURE 7. - Capi llary-pressure curve used 

ability curves used in corn- in computer model (u. 

puter model (UJ. 
In the Bureau of Mines computer model, the initial water saturation is 

determined by specifying the height of the gas-water contact. This, in turn, 

specifies the initial relative-permeability values in figure 6 and the initial 

gas and water flow rates. 

Figure 8 gives three methane flow curves4 computed with the Bureau of 

Mines model for a coal mine face 400 feet wide by 8 feet high in a coalbed 

initially pressurized to 400 psi. Only the initial water saturation varies 

(fig. 8). In case 1, the gas flow rate is appreciable at first , then it 

decreases monotonically with time. The initial water saturation was 0.7660, 

and the initial relative permeability to methane was about 0.072. 

In case 2, the initial water saturation is slightly higher at 0.7748; 

thus, the initial gas relative permeability is reduced from 0.072 to 0.0016. 

This in turn substantially reduces the initial gas flaw rate. However, 

instead of decreasing, the gas flaw rate increases. This happens because the 

increase in gas relative permeability caused by a loss of water from the coal 

is more than sufficient to counteract the decrease in flow caused by a 

pressure loss (equations 1 to 4). The gas flow ratesteadilyrises to a maximum 

at 86 days and then falls. 

TIME, days 

FIGURE 8. - Methane flow curves for three hypothetical cases with different initial water 

saturations. 

 he curves in figures 8 and 10 have been smoothed. Each curve also had 

several minor peaks and valleys that deviated about 10 or 15 percent from 

the smoothed curve shown. 
- 

- 

nit~al water saturation =0.7748 

v 

relative-permeability curve 

was critical. 

Figure 9 gives the gas 

relative-permeability curve 

used in all five cases. In 

case 4, the slope of the gas 

relative-permeability curve 

is increased; in case 5. it 

is decreased. In both 

instances, the initial water 

saturation is 0.7748, 

similar to case 2. For comparison, the initial water 

saturations for cases 1-3 

are also shown. 

Figure 10 gives the 

methane flow curves computed 

1 I I I I I , from the Bureau of Mines 0 50 100 150 200 250 300 

TIME, days 350 model. Cases 2, 4, and 5 

FIGURE 10. - hiethane flow curves for three hypothetical are shown, since they all 

have the same initial water 

cases with gas relat ive-permeabil ity curves saturation. When the slope of different slope. 
of the relative-permeability curve is increased, the methane flow maximum is 

higher and occurs earlier . 

It is clear that changes in relative permeability and initial water 

saturation can explain the increase in the methane flow rate. The relativepermeability effect takes place over an extremely small range of water saturations, at least for the homogeneous system postulated for the computer model. 

Systems that have initial water saturations in this critical range or higher 

will exhibit a maximum in the methane flow rate. 

ANALYSIS OF PRODUCTION HISTORY 

Wells drilled into gas sands for natural gas have emission rates that 

decline with time, and peaks are not observed. However, where the natural 

gas is produced from a "gas drive" oil reservoir by the method of pressure 

3.5 1 1 I I 3.5 I 

- 3.0 

Gas/water ratio 

-2.5 , 

13 

\ 

"9, 

.c 

m 

0 - 2.0 - 

6 - 

Ia 

E 

- 1.5 E 

U 

Ia 

3 

\ 

- 1.0 $ 

- 0.5 

I I 1 I 0 

0 100 200 300 400 

TIME, days 

FIGUKE 11. - Water flow and gas-water ratio calculated by the Bureau of Mines model for case 2. 
depletion, a rising methane emission due to two-phase effects may be observed. 

Muskat (2, p. 462) gives some production histories of early gas-drive oil 

reservoirs that were produced "wide open," and were unaffected by withdrawal 

restrictions, a free-gas cap, gas injection, or water-drive action. These 

show a rise in the gas-oil ratio as the pressure in the reservoir depletes. 

Since the oil production from a single well falls monotonically in such a 

case, a peak in the gas-oil ratio may correspond to a peak in the gas flow. 

In coalbeds, the liquid phase being produced is water and not oil. Also, 

the methane gas is adsorbed in the coal and not dissolved in the liquid phase. 

However, it may be that these differences are not very critical and that much 

the same sort of two-phase effects are taking place. 

Figure 11 gives the water flow and the gas-water ratio calculated by the 

Bureau of Mines model for case 2. The gas-water ratio peaks at 100 days. 

Figure 12 gives the gas-water ratio taken from ~ields' published gas and 

water flows for the large-diameter borehole (A). No peak similar to that in 

figure 11 or the gas flow curve in figure 4 was observed; at most there is a 

flattening of the gas-water ratio curve in the region of 400-500 days. At 

least for analytical purposes, the exhausting compressor was installed at 

an unfortunate time. 

0 100 200 300 400 500 600 700 800 

TIME, days 

FIGURE 12. - Gas-water ratio from Fields large-diameter multipurpose borehole (4). 
C ONCLUS I ONS 

The Bureau of Mines model for two-phase flow of methane and water in 

coalbeds can be used to simulate a maximum in the methane-emission rate from 

a face that is not bcing mined. Experimental data obtained by Fields and by 

Deul show that such a maximum exists in flow from boreholes. A rough 

similarity exists between results obtained at the large-diameter borehole 

and those obtained at early gas-drive oil wells produced wide open. 
REFERENCES 

Dabbous, M. K., A. A. Reznik, J. J. Taber, and P. F. Fulton. The 

Permeability of Coal to Gas and Water. SPEJ., v. 6, 1974, 

pp. 563-572. 

Deul , M. , and C . H. Elder . Degasificatim Through Vertical Boreholes in 

Methane Control in Eastern U.S. Coal Mines. BuMines IC 8621, 1973, 

96 PP 

Fields, H. H. , S. Krickovic, A. Sainato, and M. G. Zabetakis. Degasification of Virgin Pittsburgh Coalbed Through a Large Borehole. BuMines 

RI 7800, 1973, 27 pp. 

Fields, H. H. , J. H. Perry, and M. Deul. Commercial-Quality Gas From a 

Multipurpose Borehole Located in the Pittsburgh Coalbed. BuMines 

RI 8025, 1975, 14 pp. 

Kissell, Fred N. Methane Migration Characteristics of the Pocahontas 

No. 3 Coalbed. BuMines RI 7649, 1972, 13 pp. 

. The Methane Migration and Storage Characteristics of the Pittsburgh, Pocahontas No. 3, and Oklahoma Hartshorne Coalbeds. BuMines 

RI 7667, 1972, 22 pp. , 

Kissell, Fred N., J. L. Banfield, Jr., R. W. Dalzell, and M. G. Zabetakis. 

Peak Me thane Concentrations During Coal Mining--An Analysis. BuMines 

RI 7885, 1974, 17 pp. 

Moffat, D. H., and R. W. Weale. Sorption by Coal of Methane at High 

Pressure. Fuel, v. 34, 1955, p. 449. 

Muskat, M. Physical Principles of Oil Production. McGraw-Hill Co., 

1949, 922 pp. 

Price, H. S., and A. A. Abdalla. A Mathematical Model Simulating Flow of 

Methane and Water in Coal. BuMines OFR 10-72, 1972, 39 pp. ; available 

from National Technical Information Service, Springfield, Va. , PB 209 273. Cards are available from F. N. Kissell, Bureau of Mines, 

4800 Forbes Ave. , Pittsburgh, Pa. 15213. 

Price, H. S., R. C. McCulloch, J. C. Edwards, and F. N. Kissell. A 

Computer Model Study of Methane Migration in Coalbeds. Can. Min. and 

Met. Bull. , September 1973, 10 pp. 

Reznik, A. A., M. K. Dabbous, P. F. Fulton, and J. J. Taber. Air-Water 

Relative Permeability Studies of Pittsburgh and Pocahontas Coals. 

SPEJ.,v. 6, 1974, pp. 556-562. 

Stewart, I. McC. Diffusional Analysis of Seam Gas Emission in Coal 

Mines. Can. Min. and Met. Bull., April 1971, pp. 62-70. 
14. Taber, J. Jo, P. F. Fulton, M. K. Dabbous, and A. A. Reznik. Development 

of Techniques and the Measurement of Relative Permeability and 

Capillary Pressure Re lationships in Coal. BuMines OFR 22-74, 1974, 

80 pp. ; available from National Technical Information Service, 

Springfield , Va. , PB 232 244. 

15. Zabetakis, M. G. , T. D. Moore, Jr. , A. E. Nagel, and J. E. Carpetta. 

Methane Emission in Coal Mines: Effect of Oil and Gas Wells. BuMines 

RI 7658, 1972, 9 pp. 

fi U.S. GOVERNMENT PRINTING OFFICE: 1975-603-752/10 IN T.-BU.0 F MIN ES,PGH.,PA. 20475