Coal Gas Composition and Gas Properties

3

Fig. 2–6. Example 2.3 in-situ gas content vs. density correlation

Coal gas composition depends primarily on coal rank and gas origin. Coal gas is predominantly methane, with the fraction of ethane and heavier hydrocarbons (C2+) steadily decreasing as rank increases. Wetter gases are more often found in subbituminous and high-volatile C bituminous coals, and leaner gases in higher rank coals. Thermogenic gases can have higher hydrocarbons (ethane, propane, butane, etc.) present, whereas biogenic gases are almost pure methane. Compared to conventional hydrocarbon plays, coals are cool, low- pressure reservoirs holding gas mixtures composed almost entirely of methane. Condensation of hydrocarbon liquids occurs rarely, if at all, in coal deposits. For reservoir engineering purposes, coals can be conceptualized as dry gas reservoirs. Consistent with this dry gas reservoir concept, coal gas mixtures remain above dewpoint pressure in the wellbore and surface equipment. More important for coal gas operations are corrosion, due to the presence of moisture and the steadily rising CO₂ fraction in the produced gas stream, and liquid loading in flowing coal wells due to produced and/or condensed water.

Gas properties of coal gas can be calculated similarly to conventional dry gas reservoirs as detailed in Lee and Wattenbarger or McCain.⁷⁷ Coal gas is assumed to be described by the real gas law, which can be written as

pV = ZnRT where

p = pressure, psia or MPa, V = volume, ft³ or m³,

Z = gas deviation factor or compressibility factor, n = number of moles,

T = temperature, °R or K, and

R = Universal gas constant, 10.732 psia-ft³/lb-mol-°R or 8.297(10)^–3 MPa-m³/kg-mol-K.

Calculation of the Z factor begins with gas composition or gas gravity. Gas gravity is employed to calculate pseudocritical and reduced temperature and pressure, followed by calculation of the Z factor. If gas composition is known, gas gravity is calculated from

where

γ_g = gas gravity,

y_j = mole fraction of component j,

M_j = molecular weight of component j, and M_a = molecular weight of air, 28.96.

Molecular weights of common coal gases are collected in table 2–8.

Critical temperature and critical pressure (the critical point) of a pure substance are the temperature and pressure at which the properties of the liquid and vapor phases are identical. Reduced temperature and reduced pressure are defined as temperature and pressure divided by their respective critical values.

T_r = —–TT_c

p_r = —–p p_c

where

T_r = reduced temperature, T_c = critical temperature, °R or K,

p_r = reduced pressure, and

p_c = critical pressure, psia or MPa.

Critical temperature and pressure for typical coal gas components are given in table 2–8.

Table 2–8. Physical properties of common coal gas comstituents

Gas Molecular weight Critical temperature, x°R Critical pressure, psia Critical temperature, K Critical pressure, MPa

methane 16.04 343.00 666.4 190.56 4.595

ethane 30.07 549.59 706.5 305.33 4.871

propane 44.09 665.73 616.0 369.85 4.247

i-butane 58.12 734.13 527.9 407.85 3.640

n-butane 58.12 765.29 550.6 425.16 3.796

i-pentane 72.15 828.77 490.4 460.43 3.381

n-pentane 72.15 845.47 488.6 469.71 3.369

water 18.02 1164.85 3200.1 647.14 22.064

nitrogen 28.02 239.26 507.5 132.92 3.499

CO₂ 44.01 547.58 1071.0 304.21 7.384

H₂S 18.02 672.35 1306.0 373.53 9.005

Source: Lee, J., and Wattenbarger, R. A. 1996.

Similarly for mixtures, pseudocritical temperature and pressure can be defined for calculating Z factors, although these computed pseudocritical values are not true critical values in that properties of the liquid and vapor phases do not become equal at this point. Pseudocritical temperature and pressure are given by

T_pr = —–T T_pc p_pr = —–p

p_pc where

T_pr = pseudoreduced temperature, T_pc = pseudocritical temperature, °R or K, p_pr = pseudoreduced pressure, and p_pc = pseudocritical pressure, psia or MPa.

Pseudocritical temperature and pressure for a mixture of hydrocarbon gases can be calculated from gas gravity with Sutton’s correlation⁷⁸

T_pc = 169.2 + 349.5γ_h – 74.0γ_h² (2.10)

p_pc = 756.8 – 131.0γ_h – 3.6γ_h² (2.11)

where

γ_h = hydrocarbon gas gravity.

Possible contaminants in coal gas include CO₂, H₂S, water vapor, and nitrogen. Whether of thermogenic and/

or biogenic origin, CO₂ is often present in coal gas and must be accounted for in fluid property calculations.

Although sulfur is present in peats and coals of all ranks, H₂S has not been reported in coal gas produced from undisturbed seams, far from coal mines. Anecdotal evidence indicates sour gas is sometimes encountered in coalmine methane when formation waters are pumped out of the mine and then recirculated for mine use, such as dust suppression. The presence of CO₂ and H₂S in coal gas can be accounted for by correcting the pseudocritical properties using the correlation of Wichert and Aziz.⁷⁹ Mole fractions of these two gases are used to adjust the pseudocritical properties according to the following equations.

A = y_H2S + y_CO2 (2.12)

ξ = 120(A^0.9 – A^1.6) + 15(y_H^0.₂⁵_S – y_H⁴_2S) (2.13)

T_pc΄ = T_pc – ξ (2.14)

T_pc΄

p_pc΄ = p_pc —————————— (2.15)

T_pc + y_H2S (1 – y_H2S)ξ where

A and ξ = constants in Wichert and Aziz correlation, T_pc΄ = adjusted pseudocritical temperature, °R, and p_pc΄ = adjusted pseudocritical pressure, psia.

If the coal gas mixture contains no CO₂ or H₂S, then T_pc΄ = T_pc and p_pc΄ = p_pc. As discussed by McCain, this correlation was developed for pressures between 154 psia and 7,026 psia, temperatures between 40°F and 300°F, CO₂ ranging from 0 to 54.56 mol%, and H₂S from 0 to 73.85 mol%.⁸⁰ Average absolute error in the calculated Z factor was 0.97%, with a maximum error of 6.59%. Thus it is accurate for most coal seam conditions and is often applied to low-pressure coal gases.

Corrections to adjusted pseudocritical pressure and temperature to account for the presence of nitrogen and water vapor are given by Lee and Wattenbarger as⁸¹

T_pc,cor = –246.1y_N2 + 400.0y_H2O (2.16)

p_pc,cor = –162.0y_N2 + 1270.0y_H2O (2.17)

T_pc΄ – 227.2y_N2 – 1165y_H2O

T_pc΄΄ = ————————————— + T_pc,cor (2.18)

1 – y_N2 – y_H2O p_pc΄ – 493.1y_N2 – 3200y_H2O

p_pc΄΄ = ————————————— + p_pc,cor (2.19)

1 – y_N2 – y_H2O where

T_pc,cor = pseudocritical temperature correction, °R, p_pc,cor = pseudocritical pressure correction, °R,

T_pc΄΄ = corrected pseudocritical temperature, °R, and

The Z factor can be calculated from pseudocritical properties using the correlation of Dranchuk and Abou-Kassem.⁸² Pseudoreduced properties of the gas mixture are defined as

T_pr΄΄ = —–— T (2.20)

T_pc΄΄

p_pr = —–— p (2.21)

p_pc΄΄

The Z factor is given by

Z = 1 + c₁ρ_pr + c₂ρ²_pr – c₃ρ⁵_pr + c₄ (2.22) where

A₂ A₃ A₄ A₅ c₁ = A₁ + —— + —— + —— + ——T_pr T_pr³ T_pr⁴ T_pr⁵

A₇ A₈ c₂ = A₆ + —— + ——

T_pr T_pr² A₇ A₈ c₃ = A₉

(

^{—— + —— Tpr Tpr2}

)

ρ_pr²

c₃ = A₁₀ (1 + A₁₁ρ_pr²)

(

^{—— Tpr3}

)

^{exp(–A11ρpr2)}

and the pseudoreduced density is given by

0.27p_pr

ρ_pr =

(

^{———– ZTpr}

)

The constants A₁ through A₁₁ are

A₁ = 0.3265 A₇ = –0.7361

A₂ = –1.0700 A₈ = 0.1844

A₃ = –0.5339 A₉ = 0.1056

A₄ = 0.01569 A₁₀ = 0.6134

A₅ = –0.05165 A₁₁ = 0.7210

A₆ = 0.5475

With the Z factor appearing on both sides of the equation, it is customarily solved iteratively. An expression for the derivative of Z with respect to pressure at constant temperature is given by Lee and Wattenbarger.⁸³ They also note this correlation is within engineering accuracy for

0.2 <= p_pr < 30, 1.0 < T_pr <= 3.0 and

p_pr < 1.0, 0.7 < T_pr < 1.0.

For pure methane, the corresponding pressures and temperatures are

0.92 MPa <= p < 138 MPa (133 psia <= p < 19,992 psia)

191 K < T <= 572 K (343°R < T <= 1,029°R) and

p < 4.59 MPa (666 psia)

133 K < T < 191 K (240°R < T < 343°R) They report the correlation is poor for

T_pr = 1.0 and p_pr > 1.0

but did not quantify the error. For pure methane, the corresponding pressures and temperatures are 4.59 MPa < p (133 psia < p)

191 K = T (343°R = T )

Thus, the correlation of Dranchuk and Abou-Kassem is adequate for calculating coal gas Z factors at reservoir conditions, and the loss of accuracy at very low wellhead pressures is usually not significant for reservoir engineering purposes.

Example 2.4. Average coal gas Z factors

The average coal gas composition reported by Scott of 93% methane, 3% each of CO₂ and wet gases, and 1%

nitrogen is assumed, along with properties of the wet gas fraction approximated by those of ethane.⁸⁴ Thus, the first step is calculation of normalized hydrocarbon fractions of methane, 0.9681, and C2+, 0.0319. Combining these fractions with the molecular weights shown in table 2–8 yields a hydrocarbon gas gravity of 0.569.

Pseudocritical temperature and pressure calculated from Sutton’s correlations, equations (2.10) and (2.11), are 344.1°R and 681.1 psia. Correcting for the presence of CO₂, the Wichert and Aziz correlation, equations (2.12) through (2.15), gives a ξ factor of 4.673 and adjusted pseudocritical pressure and temperature of 677.7 psia and 339.4°R. The Lee and Wattenbarger correction for nitrogen, equations (2.16) through (2.19), yields corrected pseudocritical pressure and temperature of 677.9 psia and 338.1°R.

Assuming coal seam temperatures of 65°F (18°C) and 150°F (66°C) gives pseudoreduced temperatures of 1.553 and 1.804, respectively. For pressures between 20 and 2,000 psia, the corresponding pseudoreduced pressures range from 0.0295 to 2.905. Equations (2.20)–(2.22) were used to calculate the coal gas Z factors shown in table 2–9 and plotted in figure 2–7. Inspection of these results indicates for the assumed composition and temperatures the Z factors steadily decrease with pressure. The low-temperature coal gas Z factor drops from a value near 1.0 to roughly 0.8 at 2,000 psia, a decline of about 20%, while the high-temperature coal Z factor begins at nearly the same value but drops to about 0.9 at 2,000 psia, a reduction of only 10%.

Table 2–9. Average coal gas Z factors

Pressure, psia Temp. 65°F Temp. 150°F

20 0.9974 0.9984

40 0.9948 0.9968

60 0.9922 0.9953

80 0.9896 0.9937

100 0.9870 0.9922

150 0.9805 0.9883

200 0.9741 0.9845

250 0.9677 0.9808

300 0.9613 0.9770

350 0.9550 0.9734

400 0.9487 0.9698

450 0.9424 0.9663

500 0.9362 0.9628

550 0.9301 0.9594

600 0.9240 0.9560

650 0.9180 0.9528

700 0.9121 0.9496

750 0.9062 0.9464

800 0.9005 0.9434

850 0.8948 0.9404

900 0.8892 0.9375

950 0.8838 0.9346

1,000 0.8784 0.9319

1,050 0.8732 0.9292

1,100 0.8681 0.9266

1,150 0.8631 0.9241

1,200 0.8583 0.9217

1,250 0.8536 0.9194

1,300 0.8490 0.9172

1,350 0.8447 0.9151

1,400 0.8405 0.9131

1,450 0.8365 0.9112

1,500 0.8327 0.9093

1,550 0.8290 0.9076

1,600 0.8256 0.9060

1,650 0.8223 0.9045

1,700 0.8193 0.9031

1,750 0.8165 0.9018

1,800 0.8139 0.9006

1,850 0.8114 0.8995

1,900 0.8093 0.8985

1,950 0.8073 0.8976

2,000 0.8055 0.8969

Fig. 2–7. Average coal gas Z factors vs. pressure