Diffusion of methane through coal

Diffusion of methane through coal Edward D. Thimons and Fred N. Kissell Pittsburgh Mining and Safety Research Center, US Bureau of Mines, 4800 Forbes Avenue, Pittsburgh, Pennsylvania 15213, USA (Received 10 September 19721

Both methane and helium flow through solid coal by Knudsen diffusion, even at relatively Knudsen permeabilities were determined for samples of Pittsburgh, high pressures. Pocahontas No.3, and Oklahoma Hartshorne coals. The average permeability for dry methane was I.3 X 10e6 cm2/s for Pittsburgh coal, 20 X 10e6 for Pocahontas No.3 coai, and 134 X 10-6 for Oklahoma Hartshorne coal. A molecular-sieve effect exists for methane in all three coals examined and it is very strong in Pittsburgh coal. If the methane is saturated with water vapour the permeability decreases by a factor of 3 to 25, depending on the coal. The Knudsen permeability of solid coal discs seems to bear no relation to coalbed permeability. Lag-time measurements indicate systems of both larger and finer pores and the presence of blind pores. This effect is again more pronounced in the Pittsburgh coal.

The diffusion of methane through coal has been a subject

of research for many years, particularly because of the many lives lost in coal-mine gas explosions. Unfortunately, estimation of a permeabi~ty coefficient related to the diffusion process which has meaning from an engineering standpoint is difficult. The reason for this is that structurally coal is an extremely heterogeneous material. The pore size varies from a few Grgstroms to frequently over a micrometre in size. Even a small lump of coal may contain an extensive network of microcracks. This means that coal has a broader range of passageway sizes than is normally found in porous materials. As a result, laboratory data may reproduce poorly, and the measured permeability depends on the sample size which determines the distribution of the pores and cracks. The situation is analogous if one considers an entire coalbed, where methane flows predominantly through cracks in the coalbed. Not only are these cracks of all sizes, but the flow is dendritic in nature. This means that the gas starts out in a small pore, migrates through successively larger pores to cracks, and then moves to the larger cracks that lead to working areas of the mine. This is no doubt one reason why laboratory diffusion work always stops short of engineering application, but another reason is that in situ measurements of coalbed gas migration characteristics generally have been unavailable. The Bureau of Mines has been engaged in a program to obtain gas-migration properties of underground coal seams. Some vaiues for the in situ permeability of the Pittsburgh, Pocahontas No.3, and Oklahoma Hartshorne coalbeds have been published recently by KisselI’, and it is possible that the laboratory-determined Knudsen permeability coefficient may have some bearing on the in sifu permeabihty. ~thou~ many coefficients are available in the literature, they were unsuitable for our purposes. In particular, we wanted the permeability of these three coals. Also, we wished to determine the effect of water on Knudsen diffusion and to learn something about the pore structure of these coals.

274

FUEL, 1973, Vol 52, October

SOME PREVIOUS WORK ON THE STRUCTURE OF COAL AND DIFFUSION THROUGH COAL As already noted, the size distribution of pores in coal is very broad. Mercury penetration measurements on coal powders have shown that pore sizes range’ from 50 to over 1000 A. Pores that are accessible to mercury have been called coal macropores. Experimental work also has shown that coal also contains a system of finer pores (micropores) less than 10 A in diameter which are not accessible to mercury. It has been estimated that these micropores account for about 95% of the internal coal surface, which ranges from 100 to 200 m2/g 3. Since virtually all of the methane in coal is physically adsorbed under pressure on this internal surface, most of the methane will be in the micropores. A transitional pore range between the micropores and the macropores has been defined by Can, Nandi and Walker’. Attempts have been made to measure a micropore diffusion coefficient by experimenting with fine coal powders4-.6. Presumably, if coal is ground finely enough, the cracks and macropores are eliminated and methane wilt flow from the micropores directly to the o{ltside. This means that the micropore coefficient can be directly calculated. Unfortunately, it is impossible to tell at what stage of fineness the macropores and cracks have been removed. Anderson7 reported diffusion coefficients of different-sized particles of Pittsburgh and Pocahontas No.3 coal. He still found a shift in the coefficient with size even at the finest mesh sizes, indicating that even at these not all the macropores had been eliminated. Still another difficulty is encountered with powders. The equation used to calculate the diffusion coefficient contains terms for the particle surface area and volume, and it has not been agreed how these quantities should be obtained. Some investigators’ have used the BET surface area obtained from a BET experiment on the same powder. Others have simply treated the coal particles as spheres whose diameters correspond to the mesh size studied.

E. 0. Thimons and F. N. Kissell: Diffusion of methane through coal

Depending on the approach, the resulting coefficient can vary by a factor of 1000 or more. These differences represent attempts to characterize the true effective length of diffusion path in the micropores, and on this basis the use of mesh size is incorrect. If larger coal particles are investigated, these difficulties are compounded. Here, one might imagine the structure and distribution of macropores and cracks to be even more critical than for fine powders. Airey’ has found that, if a particle is large enough (about 0.6 cm for the coal he measured), increasing the size still further affects the coefficient very little. He concluded that coal has a characteristic crack spacing and that increasing particle size beyond this spacing has little effect on gas emission. Thus cracks become the controlling factor with larger lumps. Similar conclusions have been reached by Bertand et ~1”. In other diffusion studies, instead of powders, gas was passed through discs of coal and the steady-state flow rate was measured. Pore-size heterogeneity remains a problem, but at least this technique has the advantage that the surface area is unambiguous. Different investigators8~““2 using two different coals have obtained coefficients ranging from lop5 to lO-‘O cm2/s. The sample-size problems encountered with powders and lumps are also encountered with discs. The larger the disc is, the more likely it is to contain a crack. Nevertheless, we selected flow through discs as the more useful method from an engineering standpoint, particularly because of the unambiguous surface area. It was hoped that the chance of getting a fractured sample could be minimized by making the disc as small as possible.

APPARATUS

AND TESTING PROCEDURE

Lumps of coal taken from the mine were cored without any further treatment, and the cores were sliced into discs averaging 3.6 mm in thickness and 5.8 mm in diameter. The discs were polished and examined under an optical microscope*. Those with evident fractures were discarded. Samples without visible fractures were mounted in a stainless-steel disc which had a hole in the centre just large enough to accommodate the sample. A thermo-epoxy adhesive was found to provide the best bond. F&ure 1 is a schematic diagram of the apparatus used to measure the permeability of the samples. Five identical units were constructed because testing a single sample could take several months. The testing sequence was as follows. The steel disc containing the sample was mounted in the system and the entire system was evacuated at room temperature for one week. After a week, valves Nos.1 and 2 were closed. The part of the system to the left of the sample remained evacuated. while dry methane at a pressure of 5 15 mmHg+ was introduced on the right side to create a pressure differential across the sample. The gasflow rate across the sample was obtained by measuring the pressure build-up on the left side, as indicated by a thermocouple vacuum gauge. The pressure on the left side was kept below 0.05 mmHg by periodically opening valve No.1 and re-evacuating. The pressure on the left side of the system was thus so low that this side was assumed to be a * After testing, several of the samples were examined with a scanning electron microscope which has much greater resolution than an optical microscope. No cracks were evident on any of them t 1 mmHg = 133 N/m’

Methane or helium tank O-l mmHg

figure

1

Schematic

diagram of testing apparatus

vacuum with respect to the right side of the system when the pressure differential across the sample was calculated. The flow of gas across the sample was recorded until it became steady. After this, the gas pressure was boosted by increments of 515 mmHg and measurements were taken until a new level of steady flow was reached. This was repeated until the pressure differential was 2060 mmHg. The same samples were then tested using helium, first at 5 15 mmHg and then at 1545 mmHg. Frequently, this entire sequence was repeated, beginning with the evacuation, to test sample reproducibility, which was within 10%. All measurements were conducted at room temperature. In experiments using methane saturated with water vapour, the sample was first subjected to a 775 mmHg differential of dry methane*. After steady flow was reached, the dry methane was evacuated and the saturated methane at 775 mmHg was substituted quickly. Readings were taken until a new steady flow was reached. The flow rate G was obtained by using the relationi (1) . ,

dt

where G (erg/s)? is the steady flow rate, dP$dt (dyn/cm* s) is the slope of the rectilinear portion of the P2 versus t pressure build-up curve (Figure 4), and V (cm3) is the volume of the left side of the system into which gas flows.

FLOW OF GAS THROUGH

COAL

Previous studies have established that the flow of gas through the pore structure of coal takes place by Knudsen diffusions. This would be expected, for it is known that Knudsen diffusion takes place in capillaries if the capillary diameter is less than the mean free path of the gas molecule. The mean free path of the methane molecule at room temperature and atmospheric pressure is about 500 A$. Mercury intrusion measurements have shown that most of the macropores are smaller than this. * As metal systems (and coal) retain moisture and require heat in addition to evacuation to remove water vapour effectively, the term ‘dry’ is relative “r To convert flow from erg/s to mmol/s multiply the value by lOOO/RT whereR = 8.314 erg/m01 *

1 A=

O-1 nm

FUEL,

1973, Vol 52, October

275

Diffusion of methane through coal: E. D. Thimons and F. N. IYissell

If the flow of gas is by Knudsen the relation3

diffusion,

microscope, this would show up in a plot of steady-state flow rate versus pressure differential. Figure 2 shows flow through an untracked sample where the transport of methane is by Knudsen flow and equation (2) is obeyed. Figure 3 shows flow through a cracked sample (then rejected) which more closely obeys equation (3). In essence, this provides an operational definition of a crack. By this definition a crack is an opening large enough to permit laminar flow to take place. A pore, on the other hand, is an opening so small that methane transport is by Knudsen flow alone. This distinction is somewhat arbitrary, for it might be imagined that there could be many samples with openings intermediate in size between ‘pores’ and ‘cracks’. In this intermediate region, flow will neither be pure Knudsen nor pure laminar. Such flow has been termed ‘slip flow’, and a plot of flow versus pressure differential for openings in this region will be intermediate between the curves of Figures 2 and 3. Surprisingly, none of the samples tested fell into this category. Either they followed equation (3), clearly exhibiting laminar flow as shown in Figure 3, or they followed equation (2), with Kk constant, at least to within the limits of experimental error.

it will obey

(2) where G (erg/s) is the steady flow rate, Kk (cm2/s) is the Knudsen permeability, P (dyn/cm2) is the pressure differential across the sample, L (cm) is the sample thickness, and A (cm2) is the sample cross-sectional area. Sevenster’ shows that for a given sample the permeability Kk will be inversely proportional to the square root of the gas molecular weight. This means that for a given sample the helium permeability should be twice the methane permeability. Knudsen flow takes place only in the gas phase of the porous medium. Under some circumstances there can be an additio~l contribution to the Knudsen flow from a moving layer of adsorbed gas molecules, called surface flow. Because methane is adsorbed and helium is not, the methane flow will be augmented by this and the helium flow will no longer be twice as high. Sevenster8 has observed a surface flow of methane in coal. The contribution from this moving layer of methane molecules was so great that the total methane flow was greater than the helium flow. Surface flbw is further discussed by Barrer and Grove14, Satterfield and Sherwood”, Roybal ef aE16,and Haul”. If a sample is cracked, the width of the crack will be much larger than the mean free path of the methane mdeeule, that is, much larger than 500 A. If this is the case, Iaminar, or PoiseuiIle flow through the crack will swamp the Knudsen flow and equation (2) will no longer hold. If the flow is laminar, the relation l4 G K,APP -=.A L

50,

LO-

I

I

r-i

I

Sample N”8 Pocahontas coal

z Y =300, ;; L203 5! L

(3)

is obeyed. Here K, (cm3 s/g) is the Poiseuille permeability constant, P (dyn/&2) is the mean pressure in the sample, and the other symbols are the same as before. If a sample has a fracture that escaped detection under the optical

Table 1

I

Pressure

Figure 2

1030 differential

1515 (mm Hg 1

Flow v. pressure for an unfracture~

2060

coal sample at

30%

Experimental Knudsen permeabilities, 1O6 Kk (cm*/s) mmHg He

CH4

Sample

Coal bed

515

1030

1545

2660

Average

515

1545

Average

3 11 14 15 8 9 10 18 21 23 26 27

Pitts~rgh Pittsburgh Pittsburgh Pittsburgh Pocahontas Pocahontas Pocahontas Pocahontas Hartshorne Hartshorne Hartshorne Hartshorne

0.87 1.8 1.9 24 25 16 15 14 15 92 16

0.48 981 1.7 1.8 23 26 14 14 15 17 8.6 18

951 995 1.9 1.8 25 28 14 13 12 17 8-5 15

996 2.1 1.7 21 27 17 13 58 14 97 13

050 0.90 1.9 1-8 23 26 15 14 25 16 9 16

38 96 140 150 67 59 41 55 62 67 41 82

40 92 140 140 66 62 37 51 57 47 36 64

39 94 140 145 66 60 39 53 60 57 38 73

276

FUEL, 1973, Vol 52, October

E. D. Thimons and F. N. KisseN: Diffusion of methane through coal 600~

, Sample

3

differential

Flow v. pressure for a fractured

RESULTS-DRY

I

I

coal

Pressure

figure

I

EFFECT OF WATER ON METHANE

DIFFUSION

NoI

Pittsburgh

500

I

I

(mmtig)

coal sample at 30%

METHANE

All the coal samples were tested using methane at pressure differentials of 515, 1030, 1545 and 2060 mmHg, helium at pressure differentials of 515 and 1545 mmHg. Table 1 is a summary of the permeability for every sample calculated by using equation (2). It will be seen that there is no distinct trend in the permeability coefficient with pressure differential, indicating that the gas flow is by Knudsen diffusion. The helium permeabilities of the Pittsburgh coal samples are about 100 times as high as the methane permeabilities, whereas the helium permeabilities for the Pocahontas and Hartshorne samples are only 3-4 times as high. Since the theoretical ratio for gas-phase Knudsen diffusion is 2, it appears that in part activated diffusion’, 18% r9 is taking place and all three coals are exhibiting a molecular sieve effect. Van Krevelen” has postulated a molecular sieve effect in coal due to its graphitic structure. This means coal has a system of large cavities separated by smaller passages of molecular dimensions. The smaller helium atom passes through this structure more easily than the larger methane molecule. The sieve effect appears to be very great in Pittsburgh coal, which also has the smallest permeability. Adsorption may also retard methane flow via pores which become effectively smaller. There is no evidence for the surface flow of adsorbable gas (methane) as reported by Sevenster. Such a surface flow would reduce the helium to methane permeability ratio below 2, which was never observed. Two major differences distinguish the coal Sevenster used from the ones in this report. First, the measured permeability was much lower (typically 10-l l cmz/s), and second, the amount of gas adsorbed is much higher. He reports that 7.25 cm3 of methane is adsorbed by 1 g of coal at 40 cm of mercury pressure, whereas the coals in this report adsorb less than a fourth of this under similar conditions. This difference in the amount adsorbed is most likely the reason why surface flow was not observed. Karn et al” have measured a coefficient of lo-lo cm2/s for some ‘attritus coal’ from the Pittsburgh coalbed. No surface flow was reported; the ratio of helium to methane permeabilities was 800 to 1, indicating a sieve effect even more pronounced than the one we observed.

It is well known from routine coal analysis that in situ coal contains several percent of water. Moreover, recent fieldwork suggests that water in coal plays an important part in governing the flow of gas underground’. As the methane in coal is probably saturated with water vapour, it seemed appropriate to assess the effect of water vapour on the Knudsen permeability”. As noted previously, each sample was tested with dry methane at 775 mmHg which was then replaced with methane saturated with water vapour. The resulting permeabilities are given in Table 2. It will be seen that water vapour reduces the permeability by a factor of 3 to 25. It appears that water accumulates progressively in the coal pore structure by multilayer sorption and capillary condensation a , thus decreasing the effective pore radii and reducing the gas-flow rate. We expected that the effect would be greater in Pittsburgh coal, which appears to have a smaller average pore diameter, but this does not seem to be the case. There is little doubt that a decrease by a factor of 3 to 25 in the diffusion coefficient has some effect on the pattern of methane flow in the underground coalbeds.

Table2 Comparison of permeabilities for dry methane and methane saturated with water (775 mmHg differential)

Sample

Coalbed

I@Kkfor CH4 (cm2/s)

11 14 I5 8 9 IO I8 21 23 26 27

Pittsburgh Pittsburgh Pittsburgh Pocahontas Pocahontas Pocahontas Pocahontas Hartshorne Hartshorne Hartshorne Hartshorne

0.79 I.7 I.8 23 25 15 I4 I3 I6 9.1 I6

106 Kk for CH4-Hz0 (cm2/s) 0.09 020 0.27 1.8 I.1 2.9 0.90 4.9 5.5 2.6 5.9

LAG TIMES WITH HELIUM Barrer and Grovel4 have shown that a theoretical may be calculated if the flow of a nonsorbed cylindrical capillary is given by the equation dc _=Ddt

‘lag time’ gas in a

d2c dx2

where c = concentration, t = time, x = distance, and D = the volume diffusion coefficient. The lag time L is given by

where 1 is the capillary length and D is given by equation (4). Experimentally, L may be obtained by extrapolating

FUEL, 1973, Vol 52, October

277

Diffusion of methane through coal: E. D. Thimons and F. N. Kissell

Temperature

(9)

3O’C

For helium in a carbolac carbon, Barrer and Gabor obtained D = 0.49 Ds. Thus a/b = 0.5 1 LH~, indicating the presence of some blind pores. The time-lag method presented a good way to obtain more information about the pore structure of coal, and so time lags were obtained for all the samples. The helium time lags are shown in Table 3. Also shown here are the transient diffusion coefficient D calculated from equation (5) the steady state coefficient Ds calculated from equation (6), and the quantity (a/b)& calculated from equation (9). It may be seen that the transient diffusion coefficient is much smaller than the steady-state coefficient, by factors of 5-40, and that a/b is much larger than the value 0.51 L obtained by Barrer and Gabor. This provides evidence for an extensive network of blind pores and also systems of larger and finer pores - not surprising in view of what was discussed about the micropore-macropore structure of coal.

0 Time

Figure 4

Graph to determine

(days)

permeability

and lag time

the rectilinear portion of the P2 versus t pressure build-up curve to cut the time axis. The intercept is L (see Figure 4. The diffusion coefficient calculated from the lag time is in fact a transient-state diffusion coefficient. On the other hand a steady-state diffusion coefficient D may be obtained from the Knudsen permeability by using the standard formula 13T21 Ds=-

If methane is used instead of helium, the lag-time equations are slightly more complicated. This is because methane is adsorbed on the coal whereas helium is not. The lag-time equation becomesr4> a4

(10)

KF and also

E

where E is the porosity’ of the material. For many porous materials, the steady-state and transient diffusion coefficients are equal. However, when the medium contains blind pores and crevices, and when it contains systems of both larger and finer pores, the coefficients will be different. The reason for this is that the large pores will for the most part determine the steady-state flux through the medium. On the other hand the fine pores and blind pores will delay the establishment of the steady state of floods. This is because in the transient state, before the steady state is established, every pore must receive its quota of molecules, either adsorbed or in the pore space23. The result of this is that the lag time is much increased and that the transient diffusion coefficient is smaller. Equation (5) was obtained by assuming a constant diffusion coefficient, that is, that the transient and steady-state coefficients are equal. Barrer and Gabor% have shown that if the diffusion coefficient varies exponentially with time towards a limit according to D = Ds( 1 - see bt)

(7)

then the time 1agL is given by z,=_a+ b

12 __ 6Ds

and also that for a nonsorbed

278

LAG TIMES WITH METHANE

(8)

L = f + 12(1 + 2W) b It follows that

(3,,,,-L

(I -z)

FUEL, 1973, Vol 52, October

asbefore.

(12)

The above assumes that the surface flow is zero and that the transient diffusion coefficient varies according to equation (7). D’ and Di represent the transient and steadystate diffusion coefficients in the presence of adsorption, H is the Henry’s law constant for adsorption of methane on coal, and r is the average pore radius. H is given by l3

(13)

where I/ is the volume (STP) of gas adsorbed pressures, per atm, multiplied by T/273, and A is surface area of the coal, both per unit volume of for a porous system of cylindrical capillaries, I follows that 2H v _=_

gas such as helium

(11)

6D$

r

E

at very low the internal coal. Now, = 2e/A. It

(14)

E. D. Thimons and F. N. Kissell: Diffusion Table 3

Lag-time measurements with helium

Sample No.

Coal

L He

3 11 14 15

Pittsburgh Pittsburgh Pittsburgh Pittsburgh

8 9 10 18

Pocahontas Pocahontas Pocahontas Pocahontas

21 23 26 27

Hartshorne Hartshorne Hartshorne Hartshorne

No.3 No.3 No.3 No.3

105D (cm2/s)

Iti K;” (cm2/s)

l@Ds km2/s)

(D/Ds)

(a/b) He

360 225 175 190

6.0 9.6 12.3 11.3

39 94 140 140

1.3 3.1 4.7 4.7

0.046 0.031 0.026 0.024

0.95 0.97 0.97 0.97

L L L L

220 270 280 390

9.8 8.0 7.7 5.5

66 60 39 53

O-66 O-60 0.39 O-53

0.148 0.133 0.197 0.104

0.85 0.87 0.80 O-89

L L L L

270 340 310

8.0 6.4 7.0 68

60 57 38 73

0.60 O-57 0.38 0.73

0.133 0.112 0.184 0.093

0.87 0.89 O-82 0.90

L L L L

(s)

320

Thesample length 1was @36 cm. ed to be 0.10 7

Tab/e 4

of methane through coal

The porosity

of Pittsburgh

coal was assumed to be c = 0.03; for Pocahontas

and Hartshorne

coals E was assum-

Lag-time measurements with methane

Sample No.

Coal

l@D’ TOP3 LCH4(s) (Cm%)

3 11 14 15

Pittsburgh Pittsburgh Pittsburgh Pittsburgh

1210 500 640 730

8 9 10 18

Pocahontas Pocahontas Pocahontas Pocahontas

21 23 26 27

Hartshorne Hartshorne Hartshorne Hartshorne

No.3 No.3 No.3 No.3

Sample length and porosities

0.73 1.77 I.38 1.21

1O6 KiH4 (cm2/s) D50 D90 1.9 1.8

IO5 0; (cm2/s) I.7 3.0 6.3 6.0

D’lD;

(a/b)cH,

0.044 o-059 0.022 0.020

0.96 0.94 0.98 0.98

L L L L L L L L

4.68 5.04 7.02 13.9

97 90 65 33

23 26 15 14

23 26 15 14

0.42 0.35 0.43 0.24

0.58 0.65 0.57 0.76

5.94 4.90 5.58 5.22

90 .9 110 96 .8 103

25 16 9 16

25 16 9 16

0.36 0.69 1.07 0.64

0.64 L 0.31 L 0.0 0.36 L

as before

For Pittsburgh coal V/e (dimensionless) Pocahontas coal V/e is 20, and for Hartshorne 25. Also, as before

is 40, for coal V/e is

(15) Table 4 shows the experimental methane lag times for each sample, the transient diffusion coefficient calculated using equation (lo), the steady-state diffusion coefficient calculated using equation (15) and (a/b)cH, calculated using equation (12). In general, the results are similar to those obtained with helium; Pittsburgh coal appears to have more blind pores than the other coals. These lag-time calculations have shown that the steady-state diffusion coefficient can be as much as 50 times as great as the transient coefficient. This is an

interesting result, for transient measurements on powders have generally given a smaller diffusion coefficient than This has generally steady-state measurements on discs’. been accounted for by assuming that the discs contained small cracks; however, it can be seen that some of this difference may be attributed to a real shift in the diffusion coefficient which takes place because of the basic nature of the coal pore structure.

MERCURY

INTRUSION

MEASUREMENTS

Since the lag-time measurements indicated systems of larger and finer pores, as well as the presence of blind pores, we thought it worthwhile to obtain some pore-size distribution curves from mercury-intrusion measurements. We

FUEL,

1973, Vol 52, October

279

Diffusion of methane through coal: E. D. Thimons and F. N. Kissell 6-

I

0

Figure 5

20

I

‘1’1”‘)

Lo 60

Pore distribution

100 200 Pore diameter,

of a coal from

I

I’I”‘l

LOO600 1000 2r (il

’

2000

in CP and p is the average pressure in atm. The viscosity of methane is O-012 cP, and the average pressures in the Pittsburgh, Pocahontas, and Hartshorne coalbeds are about 10 atm, 20 atm, and 6 atm, respectively. From equation (‘6), Qittsburgh coalbed = 8.3, Kpahontas coalbed = 1.7, and @artshome coalbed = 0.50 cm2/s_

4000

mercury-penetration

data

also thought these might indicate why a molecular sieve effect was obtained to a greater or lesser degree in all three coals. Mercury intrusion measurements to 2.57 X lo6 mmHg were performed on lumps and powders of all three coals. In every case, a pore-size distribution curve similar to Figure 5 was obtained. They all had a maximum around 4&60 A, a minimum around 70 A, and then a second maximum around 1OO- 120 A. The only distinct difference between Pittsburgh coal and the others was that the first maximum was higher and the second maximum was lower than the others. F&re 5 is distinctly different from a mercury injection pore-size distribution curve obtained by Zwietering and van Krevelen”. They obtained a curve with a single maximum around a pore diameter of 1000 A. However, Can, Nandi and Walker’ have obtained a curve with two maxima that was very similar to Figure 5.

KNUDSEN AND COALBED PERMEABI LITIES One of the objectives of this study was to see if the Knudsen permeability of coal discs correlated with the in sifu permeability of the coalbeds from which the discs were taken. Kissell’ has calculated in sifzl permeabilities for the Pittsburgh, Pocahontas No.3, and Hartshorne coalbeds. Roughly, the permeability of the Pittsburgh coalbed was found to be about 10 millidarcys, and that of the Pocahontas and Hartshorne coalbeds about 1 millidarcy. The permeability in darcys may be converted to a permeability in cm2/s by using the formula”

(16) where BO is the permeability

280

in darcys, q is the gas viscosity

FUEL, 1973, Vol 52, October

These may be compared with the values of KzH4 given in Table 1. Two things are evident: first, coalbed permeability is substantially larger than the permeability of small discs of coal; second, the permeability of the Pittsburgh coalbed is much larger than that of the other two, whereas the situation with discs of coal is exactly the opposite. Unfortunately, data are available for only three coalbeds, but it appears certain that no correlation exists. This is not surprising, since it is known that the flow of methane in a coalbed takes place primarily in cracks, whereas the flow in discs is primarily through the pore structure.

REFERENCES 1 2

7 8 9 10 11 12 13 14 15

16 17

18 19 20 21 22 23 24 25

KisselI, F. N. Rep. Invest. USBur. Mines 1972, No.7667 Gan, H., Nandi, S. P. and Walker, P. L. Jr Fuel, Land. 1972, 51, 272 Marsh, H. Fuel, Lond. 1965, 44, 253 Bolt, B. A. and Innes, J. A. Fuel, Lond. 1959, 38, 333 Nandi, S. P. and Walker, P. L. Jr Fuel, Lond. 1970, 49, 309 Nelson, E. T. and Walker, P. L., Jr J. appl. Chem. 196 1, 11, 358 Anderson, R. B., Bayer, J. and Hofer, L. J. E. Rep. Invest. US Bur. Mines 1966, No.6750 Sevenster, P. G. Fuel, Land. 1959, 38, 403 Airey, E. M. Int. .I. Rock Mech. Min. Sci. 1968, 5, 475 Bertand, C., Bruyet, B. and Gunther, J. Int. .I. Rock Mech. Min. Sci. 1970, 7, 43 Kam, F. N. Rep. Invest. US Bur. Mines 1970, No.7441 Van Krevelen, D. W. ‘Coal’, Elsevier, New York, 1961, PP 141 - 144 Barrer, R. M. and Barrie, J. A.Proc. R. Sot. 1952, A213, 250 Barrer, R. M. and Grove, D. M. Trans Faradav Sot. 1951. 47. 826-844 Satterfield, C. N. and Sherwood, T. K. ‘The Role of Diffusion in Catalysis’, 1st edn, Addison-Wesley, Reading, Mass., 1963, P 19 Roybal, L. A. and Sandler, S. I. 70th National AIChE Meeting, Atlantic City, N.J., 1971, paper 26E Haul, R. A. W. ‘Diffusion in Grenzflachen’ (Surface Diffusion), Bonn, 1956; reviewed in Angew. Chem. Int. Ed. Engl. 1956,68,444 Hanbaba, P., Jiintgen, H. and Peters, W. Chem.-Ing.-Tech. 1968, 40, 1039 Zweitering, P., Overeem, J. and van Krevelen, D. W. Fuel, Lond. 1956, 35,66 Grunekle, P. and Peters, W. 7th Int. Conf. on Coal Science, Prague, 1968 Carman, P. C. ‘Flow of Gases through Porous Media’, Academic Press, New York, 1956, pp 108, 125 Barrer, R. M. and Gabor, T.f’roc. R. Sot. 1959, A251, 353 Barrer, R. M. and Strachan, E. Proc. R. Sot. 1955, A231, 52 Barrer, R. M. and Gabor, T. F’r0c.R. Sot. 1960, A256, 285 Zwietering, P. and van Krevelen, D. W. Fuel, Lond. 1954, 33, 331