The volume of gas that can be sorbed on a coal depends on pressure and temperature. As a laboratory coal sample is repressured with methane, initial pressure increases result in increased sorbed gas. Further pressure increases yield, decreasing incremental sorbed gas volumes until at sufficiently high pressures, no more gas can be sorbed, as all available coal surface area is carpeted with sorbed gas molecules. At any given pressure, the amount of sorbed gas varies inversely with temperature. Consequently, cooler coals hold more gas, and warmer coals hold less. For purposes of coal gas, the appropriate temperature is reservoir temperature, and the pressure–
gas content relationship is called a sorption isotherm.
A sorption isotherm, or simply an isotherm, for a given coal is measured in a laboratory by readsorbing a gas onto the coal sample or charging a coal sample with gas and measuring the gas content as pressure is reduced.
Coal sample preservation and preparation techniques are critically important in order to obtain accurate laboratory test results for all coal reservoir properties, including sorption isotherms.1 Detailed laboratory procedures for measurement of a sorption isotherm were presented by Mavor et al., Arri et al., and Greaves et al.2 Sorption isotherms are typically measured with pure component gases rather than gas mixtures. Gas content of coal holding a mixture of gases can be calculated from pure component isotherms and the extended Langmuir equation. As discussed in chapter 10, both free and sorbed gas compositions vary during depletion, something not captured with a mixed gas isotherm.
For reservoir engineering purposes, density of the sorbed gas is usually assumed to be density of the liquid at the atmospheric pressure boiling point. Density of sorbed methane is assumed to be 0.421 g/cm3, while nitrogen is assumed to be 0.808 g/cm3.3 As carbon dioxide is a solid at its atmospheric pressure boiling point, the density of the saturated liquid at the triple point, 1.18 g/cm3, is commonly used.4
Experimental gas content and pressure data for methane gas sorbed on a moist sample of medium-volatile bituminous coal from the San Juan Basin are presented in table 5–1 and plotted in figure 5–1.5 Initial increases in pressure are accompanied by additional sorbed gas. However, with increasing pressure, fewer and fewer gas molecules can find sorption sites, and the gas content asymptotically approaches a limit of about 700 scf/ton. At infinite pressure, the coal would be completely saturated with a monolayer of sorbed gas. Coal ash, moisture, and rank all affect the amount of gas a coal can hold, and coal deposits are so heterogeneous that even adjacent samples often exhibit different in-situ isotherms. Understanding of sorption behavior of a specific coal is greatly aided by proximate analyses of the isotherm samples.
Equations from various sorption models have been employed to describe experimental coal gas sorption data.
Among the most popular are the Langmuir and Freudlich isotherm equations.6 Interestingly, to date, virtually all experimental sorption data obtained from coals of all ranks and all geologic ages charged with pure gases of interest to coal gas engineering can be described with Langmuir’s equation:
V = VL ——— p (5.1)
p + pL where
V = gas content, scf/ton or cm3/g,
VL = Langmuir volume constant, scf/ton or cm3/g, p = pressure, psia or MPaa, and
pL = Langmuir pressure constant, psia or MPaa.
Consequently, over the years, virtually all coal gas plays have described sorption behavior with the Langmuir equation. This fortuitous circumstance is perhaps due to the fact that Langmuir’s equation accurately describes microporous sorption behavior, when sorbent pore dimensions and gas molecule sizes are comparable.
As pressure increases without bound, equation (5.1) indicates gas content approaches VL, the Langmuir volume constant. In a physical sense, the Langmuir volume constant represents the maximum amount of gas that can be sorbed onto the given sample at infinite pressure. When pressure equals the Langmuir pressure constant, pL, gas content calculated from equation (5.1) is ½ VL. Thus, the Langmuir pressure constant represents the half-saturation pressure, that is, the pressure at which the coal holds one-half the maximum gas volume.
Table 5–1. Fruitland gas content and pressure data Pressure, psia
Gas Content
scf/ton cc/gm
95.4 146.5 4.57
203.0 242.1 7.56
401.1 364.3 11.37
604.4 447.1 13.95
802.6 505.5 15.78
1002.0 548.8 17.13
1201.4 589.7 18.41
1401.8 621.6 19.40
1598.3 654.3 20.42
1798.9 682.3 21.30
Source: Hall, F. E., et al. 1994.
Fig. 5–1. Methane sorption data—San Juan Basin, Fruitland coal7
Early studies in coalbed methane employed a slightly different form of Langmuir’s equation:
V = VL ——–— bp (5.2)
1 + bp where
b = the archaic Langmuir pressure constant; the reciprocal of the current Langmuir pressure constant, pL. While either form of Langmuir’s equation describes gas sorption on coal, the form employing pL usually provides more physical insight.
Determination of Langmuir constants from a given set of sorption data has traditionally been done by fitting the data to a rewritten version of equation (5.1):
p p pL
—— = —— + —— (5.3)
V VL VL
The Langmuir volume constant, VL, is the reciprocal of the slope. The pressure constant, pL, is determined by dividing the intercept by the slope. Widespread availability of curve fit routines in various software packages and spreadsheets now permits fitting laboratory data directly to Langmuir’s equation. While this is a convenient approach, it loses the visual quality check easily done with the linearized form of equation (5.3). Data of Hall et al., plotted in the linearized form of equation (5.3) in figure 5–2, yields a Langmuir volume constant, VL, of 865.2 scf/ton and a Langmuir pressure, pL, of 536.4 psia.8 Figure 5–3 repeats the sorption data of figure 5–1 and the fitted Langmuir isotherm.
The relative efficiency of gas storage in coals and sandstones can be illustrated by calculating the equivalent sandstone porosity required to hold the same volume of gas as is sorbed in a coal. Mathematically,
Free gas in pore space = sorbed gas in coal On a unit volume basis,
1 pi
ϕeqSgi —— = VLρB ————
Bgi pi + pL where
ϕeq = equivalent sandstone porosity, decimal, Sgi = initial gas saturation, decimal,
Bgi = the initial gas formation volume factor, ft3/scf, ρB = bulk coalbed density, g/cm3, and
pi = initial reservoir pressure, psia.
Solving for equivalent porosity,
pi Bg ϕeq = VLρB ———— ——pi + pL Sgi
Typical temperature and pressure for a north San Juan Basin coal are 110°F and 1,500 psia, respectively, making the gas formation volume factor 9.40(10)–3 ft3/scf. Assume a bulk density of 1.8 g/cm3 for the coal and an initial gas saturation of 100% in the sandstone.
ϕeq = 0.337
Thus, a sandstone at this temperature and pressure would require a porosity of almost 34% to contain as much gas as this sample of San Juan Basin coal.
Fig. 5–3. Methane sorption data and Langmuir isotherm—San Juan Basin, Fruitland coal10