Bureau of Mints Report of Investigations/ 1972 

Methane Diffusion Parameters far Sized 

Coal Particles 

A Measuring Apparatus and Some PreWary Results 

UNITED STATES DEPARTMENT OF THE INTERIOR 
Report of ~nvestigations 7697 

Methane Diffusion Parameters for Sized 

Coal Particles 

A Measuring Apparatus and Some Preliminary Results 

By R. J. Bielicki, J. H. Perkins, and F. N. Kissell 

Pittsburgh Mining and Safety Research Center, Pittsburgh, Pa. 

UNITED STATES DEPARTMENT OF THE INTERIOR 

Rogers C. B. Morton, Secretary 

BUREAU OF MINES 

Elburt F. Osborn, Director 
CONTENTS 

Pane 

Abstract ................................................................. Introduction ............................................................. Sorption isotherm ........................................................ Desorption from fine-sized and powdered coal ........................ Apparatus ................................................................ Sample preparation ....................................................... bsults .................................................................. Effect of total pressure ............................................ Pittsburgh coal ................................................ Pocahontas coal ................................................ Effect of size ....................................................... Pocahontas No . 3 coal .......................................... Pittsburgh coal ................................................ Conclusions ............................................................... References ............................................................... 

1 . Equilibrium sorption isotherm for methane on dry Pittsburgh coal 

as derived by Ruppel ............................................... 2 . Desorption apparatus ................................................. 3 . Typical desorption curve for 180- to 200-mesh Pittsburgh coal ........ 4 . Three-stage desorption for 112- to 114-inch Pocahontas No . 3 coal .... 5 . Desorption curves for three sizes of Pocahontas No . 3 coal ........... 6 . A typical adsorption curve for Pocahontas No . 3 coal ................. 7 . Desorption curves for two sizes of Pittsburgh coal ................... TABLES 

1 . Five-step desorption on 180- to 200-mesh size Pittsburgh coal ........ 2 . Three-step desorption on 112- to 114-inch Pocahontas No . 3 coal ...... 
METHANE DIFFUSION PARAMETERS FOR SIZED COAL PARTICLES 

A Measuring Apparatus and Some Preliminary Results 

by 

R. J. Bielicki,' J. H. Perkins? and F. N. Kissel13 

ABSTRACT 

A sorption apparatus for measuring the equilibrium sorption isotherm and 

the rate of diffusion of methane from fine-sized coal was designed and constructed. Preliminary work that used Pittsburgh and Pocahontas No. 3 coal 

shows that the diffusion coefficient varies with pressure and that the fracture spacing in these two coals is substantially different. 

INTRODUCTION 

Methane gas is formed during the coalification process. Most of it has 

escaped during this process; however, many coalbeds, especially deeper ones, 

still retain considerable volumes of the gas. When the coalbed is mined and 

the methane escapes into the mine workings, those who labor there may be 

exposed to considerable danger. 

The methane in a coalbed often is under considerable pressure. Several 

hundred pounds per square inch (psi) is common, and pressures as high as 1,000 

psi have been measured. Mine workings are, however, at atmospheric pressure, 

and this difference in pressure causes methane to flow. 

The methane present in the coal exists in two states, the "free gas" 

state and the adsorbed state. The difference between these is that the free 

gas is compressed in the fractures and macropores of the coal, but the 

adsorbed gas adheres to the large internal surface that coal is known to have. 

At normal coalbed pressures, most of the gas is adsorbed. Daines (4)4 has 

found that the amount of gas in the adsorbed state at pressures of 300 psi is 

10 times as great as the amount of free gas. Bertard, Bruyet, and Gunther (2) 

have considered the entire volume of gas fixed by coal under stress as being 

adsorbed. It follows that most of the gas emitted into the mine was adsorbed 

on the coal originally. 

=Physical science technician. 

physicist. 

"physical research scientist. 

4Underlined numbers in parentheses refer to items in the list of references at 

the end of the report. 
To gain some knowledge about the nature of this emission process, a number of workers have studied the equilibrium sorption isotherm of methane on 

coal and also the rate of desorption of methane from fine-sized and powdered 

coal. 

SORPTION ISOTHERM 

The equilibrium sorption isotherm is the curve relating the quantity of 

methane adsorbed to the pressure of that quantity; a typical curve for adsorption of dry methane on Pittsburgh-bed coal is shown in figure 1.. Most of the 

recent sorption work on U.S. coals has been done by Ftuppel (6), who has determined isotherms for coals of various sizes (up to 114-inch) at pressures up to 

150 atmospheres. 

Desorvtion From Fbe-Sized and Powdered Coal 

To understand the sorption rate phenomenon, Hofer, Bayer, and Anderson 

(5) measured sorption rates on samples of fine-sized Pittsburgh and Pocahontas 

No. 3 seam coals at near-atmospheric pressure. Among their conclusions were: 

(1) The rate of sorption is a function of particle size; the rate increases 

eightfold as the particle size decreases from 6 to 8 mesh to 270 to 325 mesh. 

(2) The adsorption and desorption curves are identical. (3) The sorption process appears to be diffusion controlled. 

Airey u) did desorption studies using coal samples that ranged in size 

from 112-inch to 200 mesh. He equflibrated his samples at pressures of 50, 

150, and 300 psi and then let them desorb at atmospheric pressure. He concluded that the desorption phenomenon could be described by a mathematical 

model, based on Darcy's law, that incorporated a crack system. The empirical 

equation he determined was 

where V(t) is the amount desorbed in time t, A is the gas content of the coal, 

and t, is a time constant, with t, proportional to mesh size up to 1/4-inch. 

Airey's results emphasized the importance of studying the desorption of sizes 

of coal other than powdered. 

APPARATUS 

An apparatus for measuring equilibrium sorption isotherms and also 

desorption rates of fine-sized coal was designed and built. Desorption rates 

can be measured from samples up to 2 inches,in size and at pressures up to 

1,000 psi. 

The apparatus is unique because the pressure changes that occur in the 

bed pressure as the coal is mined can be simulated. . For example, if the coal 

sample has been equilibrated at 200 psi, the pressure in the sample cylinder 

can be reduced to 150 psi and held constant at that new pressure while the 

desorption resulting from that pressure change is measured. The apparatus 
PRESSURE, abs . atm 

FIGURE 1. - Equilibrium Sorption Isotherm fa Methane on Dry Pittsburgh Coal as Derived by 

Ruppl. The volume was co kulatd at standard temperature and pressure. 
SECTION 2 SECTION 1 

A Electronic control unit G Reservoir known volume 

B Transducer 0-1.000 psi0 H Air-operated valve 

C Transducer 0-20 psia I Solenoid 

D Valves J Sample cylinder 

E Collection cylinder K Capacitance manometer 

F . Micrameterinq valve 

FIGURE 2. - Desorption Apparatus. 

consists of three sections (fig. 2): (1) A reservoir cylinder of calibrated 

volume for measuring the amount of gas used in the experiment; (2) the sample 

cylinder used to hold the coal sample; and (3) a collecting cylinder where the 

desorbed gas is collected. Each of tbese sections can be isolated, and the 

gas can be retained in the desired cylinder. 

To determine the volume of the desorption apparatus, a cylinder of known 

volume was placed in series with the apparatus. The known-volume cylinder was 

pressurized with helium while the desorption apparatus was evacuated. The 

helium was released into the apparatus one section at a time, and the system 

was tested for leaks with a helium leak detector. The volume of each section 

was then computed using Boyle's law. 

The same procedure, using helium, was followed for determining the free 

space of the coal-sample cylinder. 

In calculating volumes using methane gas, the equation of state for methane was taken as 
where P = pressure in atmospheres, 

V = volume in liters, 

Z = the compressibility factor for methane, 

R = the gas constant, 

T = temperature in degrees Kelvin, 

and n=moles. 

Although more accurate equations of state are available, this equation gives 

results that are within experimental error. 

To determine the amount of methane adsorbed on the coal, the reservoir 

cylinder was pressurized with methane. When the temperature in the reservoir 

cylinder stabilized, the pressure was recorded to determine the number of 

moles of methane present. The gas then was allowed to flow into the sample 

cylinder. When the pressure stopped falling noticeably, the sample cylinder 

and reservoir were again isolated. The remaining number of moles of methane 

present in the reservoir was' subtracted from the initial quantity to determine 

the number of moles of methane that were introduced into the sample cylinder. 

The amount of methane adsorbed at any time could be determined by taking the 

difference between the number of moles in the free space at that time and the 

number of moles introduced to the sample. 

To determine the amount of methane desorbed, the following procedure was 

followed: 

1. The pressure in the sample cylinder was reduced by releasing the gas 

into the reservoir cylinder. 

2. To account for the gas desorbed during step 1, an expected pressure 

increase in the reservoir cylinder could be determined for a given decrease in 

pressure in the sample cylinder. The initially desorbing gas causes the pressure in the reservoir cylinder to be greater than the expected pressure, and 

the amount of initially desorbed gas then can be calculated by taking the difference between these values; that is, actual pressure in the reservoir cylinder minus expected pressure in the reservoir cylinder equals excess pressure 

resulting from initially desorbed gas. 

3. When the pressure in the sample cylinder reached the desired level, 

the valve leading to the reservoir cylinder was closed. 

4. To maintain a constant pressure in the sample cylinder, the excess 

gas that resulted from desorption was released into the collecting cylinder. 

5. Because the volume of the collecting cylinder was known, the amount 

of gas desorbed could be calculated from the pressure reading in this 

cylinder. 
6. The total amount of desorbed methane could be determined at any time 

by adding the amount of methane in the collecting cylinder to the amount of 

methane desorbed during the initial pressure drop. 

When desorption rates for low pressures (for example, atmospheric and 

lower) were measured, it was observed that pressure buildup in the collecting 

cylinder could retard the flow of gas from the sample cylinder. For this 

reason, when the pressure in the collecting cylinder was equal to one-half the 

pressure in the sample cylinder, the collecting cylinder was pumped out, which 

allowed the gas that resulted from desorption to flow freely into the collecting cylinder. 

As mentioned previously, the unique feature about this apparatus is that 

it can measure desorption rates from coal samples incrementally at elevated 

pressures while holding the gas pressure over the coal sample constant. This 

is accomplished by using a capacitance manometer to monitor the pressure in 

the sample cylinder. Essentially, the capacitance manometer is a sensitive 

differential pressure transducer capable of measuring pressure changes of less 

than 0.01 psi at a pressure of 300 psia. With a small pressure change, an 

air-operated valve controlled by the capacitance manometer is activated. This 

allows the excess desorbed gas to flow through a micrometering valve into a 

collecting cylinder. When the excess gas, equal in amount to the gas desorbed, 

has been released from the sample cylinder, the capacitance manometer senses 

the drop in pressure and closes the air-operating valve. The result is that 

it is possible to desorb a sample at a series of intermediate pressures that 

are held constant, rather than just reducing the pressure from some initial 

value to atmospheric. 

SAMPLE PREPARATION 

Coal for each sample to be tested was crushed to 1- by 112-inch size, 

screened, and then floated in carbon tetrachloride to remove foreign mineral 

matter. The cleaned samples were dried in a vacuum oven at 100" C for about 

24 hours. The dried coal was weighed and put into the sample cylinder. The 

coal was reheated to approximately 70" C, in the sampling cylinder under 

vacuum, to insure the removal of air and moisture that may have been adsorbed 

while loading into the cylinder. Thereheatingprocess was repeated until the 

pressure in the cylinder stabilized. 

RESULTS 

For these preliminary experiments the importance of two factors on the 

desorption rate had to be determined: The effect of total pressure and the 

effect of particle size. 

Effect of Total Pressure 

Airey (l) has desorbed coal from initial pressures of 50, 100, and 150 

psi to atmospheric pressure. However, a more sensitive method of assessing 

whether a pressure effect exists is to desorb to a series of intermediate 

pressures. This was done on two types of coal, 180- to 200-mesh Pittsburgh 

coal and 112- to 114-inch Pocahontas No. 3 coal. 
Pittsburgh Coal 

180-200 mesh Pittsburgh coal desorption 

0 I st step (26.0 atm- 18.6 atm) at 

room temperature 

The Pittsburgh coal was 

pressurized to 26.0 atmospheres, and after equilibrium was achieved, the pressure was reduced to 3.9 

atmospheres in five stages. 

1 The stages are shown in 

table 1, and a typical 

desorption curve for this 

sample is shown in 

figure 3.' 

TABLE 1. - Five-step desorption on 180- to 200-mesh size 

Pittsburgh coal 

20 

0 

Pocahontas Coal 

0.1 1.0 10 tion to take place, and the 

diffusion parameter D/aa . TIME. hr It shows that as the pressure decreases the desorpFIGURE 3.-TypicalDesorptionCurvefor180-to200-Mesh tion time increases. ~f 

Pittsburgh Coal. methane is escaping from 

this fine powder by a 

diffusion-controlled process, it follows that the diffusion parameter is 

decreasing as the pressure falls. 

- - 

I I I I I III I I I11111 

The Pocahontas coal was pressurized initially to 21.4 atmospheres and 

then desorbed in three stages. Table 2 gives these quantities and also the 

time for 25-percent desorption. This 25-percent figure is available because 

the rate of emission from the Pocahontas lumps was much slower than it was for 

Table 1 gives the initial and final pressures for 

each desorption step, the 

amount of gas desorbed in 

each step, the time required 

for 75 percent of the desorp- 

=All of the desorption curves for coal were obtained at room temperature. 

Time for 

75-pct 

desorption, 

min 

10 

14 

18 

21 

45 

CH, desorbed, cu? /g 

(1 c&/g = 32 ft3/ton) 

2.28 

1.69 

1.80 

1.31 

1.38 

D/aa, sec-' 

1.55 x 10-4 

1.11 x lo4 

.86 X 10'~ 

.74 x 

.34 x 10'~ 

F ina 1 

pressure, 

atm 

18.6 

13.9 

9.1 

6.3 

3.9 

Step 

1 

2 

3 

4 

5 

Starting 

pressure, 

atm 

26.0 

18.6 

13.9 

9.1 

6.3 
the Pittsburgh coal powder. Emission rate curves for all three steps are 

given in figure 4. 

TABLE 2. - Three-step desorption on 112- to 114-inch 

Pocahontas No. 3 coal 

In both tables the diffusion parameter D/a2 is obtained from a solution 

to the diffusion equation, valid for spherical particles: 

Here, Mt/& is the fraction desorbed at time t (seconds), D is the diffusion 

parameter ( and a is the sphere radius (centimeters). This seconds 

Step 

1 

2 

3 

solution may be written in terms of the dimensionless parameter Dt/a2, and 

Dt/a2 versus Mt/& is presented graphically in a publication by Crank (3). 

KEY 

>-to&in Fbcahontas coal desorption 

80 1 (Room temperature) 

o 1st steD (21.4 .atm to 6.67 otm) 

D/a2, sec" 

5.8 X 

3.5 x 

2.5 X 

Starting 

pressure, 

atm 

21.4 

6.67 

2.23 

CI& desorbed, c$ Ig 

(1 cm3Ig = 32 ft /ton) 

5.1 

3.8 

2.4 

P 

0 2d st& ( 6.67 atm to 2.23 atm) 

A 3d step ( 2.23 atrn to 0.88 atm) 

F ina 1 

pressure, 

atm 

6.67 

2.23 

.88 

Time for 

25-pct 

desorption, 

min 

144 

245 

288 

10 

TIME, hr 

FIGURE 4. - Three-Stage Desorption for ?4- to %-Inch Pocahontas No. 3 Coal. 
In both cases, the diffusion parameter shows the anticipated decrease as 

the pressure falls. It appears that the decrease in the diffusion parameter 

is less for the Pocahontas coal than for the Pittsburgh coal; however, the 

first desorption step for the Pocahontas coal is very large compared with that 

of the Pittsburgh coal, and the value of 5.8 X 10" must be regarded as an 

average over many smaller steps. 

Hofer, Bayer, and Anderson (5) have also obtained diffusion parameters 

for these same coals. For 270- to 325-mesh Pittsburgh coal they got a ~/a~ of 

1.16 X 10'~ sec'', and for 6- to 8-mesh Pocahontas coal, a ~/a' of 5.9 X lo-' 

sec'l . However, they did not note a pressure effect on the rate of sorption. 

Effect of Size 

Bertard and others (2) have claimed that when ?he dimensions of a piece 

of coal exceed the fissuring network, the desorption rate will be practically 

independent of size distribution. They also claim that the fissuring network 

generally does not exceed 1 millimeter. This was found to be true for the 

Pocahontas No. 3 coal, but for the Pittsburgh coal the fissuring network was 

112-inch or more. 

Pocahontas No. 3 Coal 

Desorption curves for Pocahontas No. 3 coal in three size ranges are 

shown in figure 5. It may be seen that there is very little difference in the 

desorption curves for 1116- to 1132-inch and 112- to 114-inch size coals and 

that 20 to 65 mesh (approximately 1132- to 11128-inch) desorbs slightly 

TIME. hr 

FIGURE 5. - Desorption Curves for Three Sizes of Pocahontas No. 3 Coal. 
faster. The spacing of the fissure network is 1116-inch or less, in agreement. 

with the results of Bertard and others. 

Precautions were taken to insure that the samples were fully equilibrated 

before they were desorbed. The apparatus is designed so that adsorption curve 

data may be calculated for each sample. This is used to insure that the 

sample is fully equilibrated. A typical adsorption curve is shown in figure 6. 

This particular sample, 1116- to 1132-inch, required 3 weeks to fully equilibrate, and it adsorbed 15.1 cubic centimeters per gram at 21.4 atmospheres 

pressure. If all the samples of this coal are fully equilibrated, they will 

adsorb the same amount of gas at a given pressure. The 112- to 114-inch and 

20- to 65-mesh samples also were pressurized to the same initial pressure, 

21.4 atmospheres, and each adsorbed about 15 cubic centimeters per gram of 

methane, which showed that they were properly equilibrated. 

Pittsburgh Coal 

Desorption curves for 1116- to 1132-inch and 112- to 114-inch Pittsburgh 

coal are shown in figure 7. As with the Pocahontas coal, both samples were 

allowed to equilibrate before desorbing, although this required several 

months. An attempt was made to test Pittsburgh coal in the size range 1- to 

112-inch, but in 9 months this sample had not reached adsorption equilibrium, 

and it was discarded. 

It is evident from figure 7 and also from the very slow adsorption on 

1- to 112-inch coal that even the 112- to 114-inch size was less than the 

fissure spacing. 

I / KEY 

ot6-to&-in Pocahontas adrorptbn 

Equillbrated, 21.4 atm at room 

TIME, hr 

FIGURE 6. - A Typical Adsorption Curve for Pocahontas No. 3 Coal. 
100 I I 1 11 111 I I 11 1111 1 1 111111 I I 111111 

KEY 

60 - - 

I 

40 - 

0.1 1 .o 10 100 1,000 

TIME. hr 

FIGURE 7. - Desorption Curves for Two Sizes of Pittsburgh Coal. 

CONCLUSIONS 

1. An apparatus for measuring adsorption and desorption rate curves for 

methane on fine-sized coal was designed and constructed. 

2. The unique feature of this apparatus is that the coal samples may be 

desorbed at intermediate pressures that are held constant. 

3. The diffusion parameter varies with pressure in both Pittsburgh and 

Pocahontas No. 3 coals, and decreases as the pressure decreases. 

4. The spacing of the fissure network in Pocahontas No. 3 coal is 1116- 

inch or less, whereas in the Pittsburgh coal it is 112-inch or more. 
REFERENCES 

1. Airey, E. H. Gas Emission From Broken Coal. An Experimental and Theoretical Investigation. Internat. J. Rock Mech. and Min. Sci., v. 5, 1968, 

pp. 475-494. 

2. Bertard, C., B. Bruyet, and J. Gunther. Determination of Desorbable Gas 

Concentration of Coal. Internat. J. of Rock Mech. and Min. Sci., v. 7, 

1970, pp. 43-65. 

3. Crank. J. The Mathematics of Diffusion. Oxford Press, London, 1956, 

p. 90. 

4. Daines, M. E. Apparatus for the Determination of Methane Sorption on Coal 

at High Pressures by a Weighing Method. Internat. J. Rock Mech. and 

Min. Sci., v. 5, 1968, pp. 315-323. 

5. Hofer, L. J. E., James Bayer, and Robert B. Anderson. Rates of Adsorption 

of Methane on Pocahontas and Pittsburgh Seam Coals. BuMines Rept. of 

Inv. 6750, 1966, 13 pp. 

6. Ruppel, T., C. Grein, R. E. Kelly, and D. Bienstock. Adsorption of Methane on Coal to 140 Atmospheres Pressure. Pres. at 157th Nat. Meeting, 

Div. of Colloid and Surface Chem., Am. Chem. Soc., Minneapolis, Minn., 

April 1969. Copies of this paper may be obtained from Thomas C. Ruppel, 

Pittsburgh Energy Research Center, U.S. Bureau of Mines, Pittsburgh, 

Pa. 15213. 

U.S. GOVERNMENT PRINTING OFFICE: 1972-709.073:539