Similarly, time required to desorb 95% of the gas is 0.253118
t95 = —–——— τ = 4.54τ 0.055743
Time required to release 95% of the gas from this sample is therefore t95 = 4.54(54.8 hr) = 248.8 hr = 10.4 days
Coal permeabilities in the Powder River Basin are on the order of several hundred millidarcies, making time required for this well to reach pseudosteady-state flow on the order of one to two weeks. As response times of matrix and cleat are roughly equal, well behavior is controlled by the interplay between gas release from the matrix and gas flow in the cleats.
Recent years have seen increasing interest in enhanced coalbed methane recovery (ECBM) via injection of nitrogen, CO2, and flue gas, and in CO2 sequestration. On a field or well scale, uptake of injected gases onto the coal matrix can be described by the mathematics developed above. For short injection times and in the near-wellbore region, additional mathematical sophistication is required. For example, Clarkson and Bustin studied the effect of pore structure and gas pressure on the sorption behavior of methane and CO2 on samples of Cretaceous coals from the Gates Formation in Western Canada.91
Table 2–11. Rock properties of selected coals
Basin Coal Rank Young’s modulus, Mpa Young’s modulus, psia Poisson’s ratio
naa na na 2,700 390,000 0.32
Warriorb Blue Creek 2,760 400,000 0.35
San Juanc Fruitland med. vol. 3,400 490,000 0.30
San Juand Fruitland med. vol. 5,600 810,000 0.35
WCSBe various sub. B/hi-vol. C 3,000 435,000 0.30
naf na na 1,000 145,000 0.20
nag na na 14,000 2,030,000 0.40
San Juanh Fruitland hi-vol. A 3,600 521,000 0.21
San Juani Fruitland med. vol. 4,500 650,000 0.32
Piceancej Cameo med. vol. 2,400 350,000 0.31
WCSBk na na 1.0 to 5,000 1.5 to 730,000 0.26–0.48
average = 4,296 622,100 0.31
na = not available
Sources: aGray, I. 1987. Reservoir engineering in coal seams. Part I. The physical process of gas storage and movement in coal seams. SPE Reservoir Engineering. V. 2 (no. 1).
p. 28. bLayne, A. W., and Byrer, C. W. 1988. Analysis of coalbed methane simulations in the Warrior Basin, Alabama. SPE Formation Evaluation. V. 3 (no. 3). p. 663. cJones, A. H., Ahmed, U., Bush, D. D., Holland, M. T., Kelkar, S. M., Rakop, K. C., Bowman, K. C., and Bell, G. J. 1984. Methane Production Characteristics for a Deeply Buried Coalbed Reservoir in the San Juan Basin. SPE/DOE/GRI 12876. Presented at the 1984 SPE/DOE/GRI Unconventional Gas Recovery Symposium, Pittsburgh, Pennsylvania, May 13–15. dIbid. eBustin, R. M., Cui, X., and Chikatamarla, L. 2008. fLevine, J. R., 1996. Model study of the influence of matrix shrinkage on absolute permeability of coal bed reservoirs. In Coalbed Methane and Coal Geology. Gayer and Harris, eds. Geological Society Special Publication No. 109. London: Geological Society. p. 197. gIbid. hMavor, M. J., Close, J. C., and Pratt, T. J. 1991. Summary of the Completion Optimization and Assessment Laboratory (COAL) Site. Report GRI-91/0377. Chicago: Gas Research Institute. iBell, G. J., Seccombe, J. C., Rakop, K. C., and Jones, A. H. 1985. Laboratory Characterization of Deeply Buried Coal Seams in the Western U.S. Paper SPE 14445. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 12–25. jIbid. kGentzis, T., Deisman, N., and Chalaturnyk, R. J. 2007. Geomechanical properties and permeability of coals from the Foothills and Mountain regions of western Canada. International Journal of Coal Geology. V. 69 (no. 3). p. 153.
Unconfined compressive strength (UCS) is a measure of intact rock strength and is defined as the maximum load at failure divided by the sample cross-sectional area. Dependence of coal UCS on rank was discussed by Palmer, but sample origin was not given.95 Unconfined compressive strength of subbituminous and high-volatile bituminous coals ranged from 5,000 to 8,500 psia, declined to a minimum of 1,000 psia in medium and low- volatile bituminous coals, and then rose to 5,500 psia for anthracitic coals. Gentzis et al. reported UCS values for western Canadian coals varied from 1,250 to 11,700 psia.96 Mavor and Gunter reported a UCS for the Fruitland coal of the San Juan Basin of 11,880 psia.97 The unconfined compressive strengths of coals are generally less than those of conventional sandstones and limestones, which range from 3,000 to 36,000 psia, and shales, 700 to 14,500 psia.
Cleat or void volume compressibility of a coal, analogous to pore volume compressibility of conventional reservoirs, is a measure of coal fracture volume loss due to applied loads. This property, also termed formation compressibility, primarily affects reservoir behavior in undersaturated coals above desorption pressure. As a coal seam depletes, decreases in reservoir pressure are matched by increases in rock stresses to support the lithostatic load. Voids in the coal, comprised of both coal cleats and pores of various sizes, deform over the course of depletion in response to these stress changes. Coal cleat compressibility, like pore volume compressibility of conventional reservoir rocks, is expressed mathematically as
1 dVp
cf = —– —— (2.27)
Vp dp where
cf = formation compressibility, psia–1 or MPa–1, and Vp = cleat volume, ft3 or cm3.
To be clear of thermal expansion effects, compressibility of coal and conventional reservoir rocks should be measured at isothermal conditions, ideally at reservoir temperature but practically at ambient temperature. On a unit volume basis, equation (2.27) can be written as
1 dϕ
cf = —– —— (2.28)
ϕ dp where
ϕ = porosity, fraction.
In practice, coal void volume compressibility is very difficult to measure, and values within a factor of two are regarded as excellent agreement. Controls on coal compressibility are poorly understood, making prediction of this parameter difficult. Coal rank and geologic age appear to minimally affect compressibility, if at all, while the role of other variables such as ash and mineral matter, maceral distribution, and coal lithotypes has not been reported. Compressibility values reported by various workers, collected in table 2–12, vary by almost an order of magnitude, ranging from a maximum of 2.50(10)–3 psia–1 down to a minimum of 3.00(10)–4 psia–1 (0.363 MPa–1 to 0.044 MPa–1). Median and average coal void volume compressibilities are 1.34 (10)–3 psia–1 and 1.43(10)–3 psia–1 (0.194 MPa–1 and 0.207 MPa–1), respectively.
Table 2–12. Cleat compressibility of selected coals
Basin Seam Age Rank Cleat compressibility, psia-1
Appalachiana Pittsburgh Pennsylvanian na 0.00187
San Juanb Menefee na na 0.00134
Piceancec Cameo Cretaceous na 0.00129
Warriord na Pennsylvanian na 0.00187
Warriore Marylee/Blue Creek Pennsylvanian na 0.000579
San Juanf na Cretaceous na 0.000924
San Juang Fruitland Cretaceous na 0.000961
San Juanh Fruitland Cretaceous na 0.001944
Warriori Marylee/Blue Creek Pennsylvanian hi-vol. A 0.0025
San Juanj Fruitland Cretaceous na 0.001015
Sydneyk Bulli Permian na 0.0003
Bowenl Gemini Permian hi-vol. A–med. vol. 0.00164
Sydneym na Permian hi-vol. A–lo-vol. 0.002352
na = not available
Sources: aMcKee, C. R., Bumb, A. C., and Koenig, R. A. 1988. Stress-dependent permeability and porosity of coal and other geologic formations. SPE Formation Evaluation. V.
3 (no. 1). p. 81. bIbid. cIbid. dMcKee, C. R., Bumb, A. C., and Koenig, R. A. 1987. Stress-dependent permeability and porosity of coal. Paper 8742 in Proceedings of the 1987 International Coalbed Methane Symposium. Tuscaloosa: University of Alabama. eSeidle, J. P., Jeansonne, M. W., and Erickson, D. J. 1992. Application of Matchstick Geometry to Stress Dependent Permeability in Coals. Paper SPE 24361. Presented at the SPE Rocky Mountain Regional Meeting, Casper, Wyoming, May 18–21. fMcKee, C. R., Bumb, A. C., and Koenig, R. A. 1987. gSeidle, J. P., Jeansonne, M. W., and Erickson, D. J. 1992. hShi, J. Q., and Durucan, S. 2003. Changes in permeability of coalbeds during primary recovery.
Part 2. Model validation and field application. Paper 0342 in Proceedings of the 2003 International Coalbed Methane Symposium. Tuscaloosa: University of Alabama; and Mavor, M. J., and Vaughn, J. E. 1997. Increasing absolute permeability in the San Juan Basin Fruitland Formation. Paper 9738 in Proceedings of the 1997 International Coalbed Methane Symposium. Tuscaloosa: University of Alabama. iZuber, M. D., Sawyer, W. K., Schraufnagel, R. A., and Kuuskraa, V. A. 1987. The Use of Simulation and History Matching to Determine Critical Coalbed Methane Reservoir Properties. Paper SPE/DOE 16420. Presented at the SPE/DOE Low Permeability Reservoirs Symposium, Denver, Colorado, May 18–19. jGash, B. W., Volz, R. F., Potter, G., and Corgan, J. M. 1993. The effects of cleat orientation and confining pressure on cleat porosity, permeability and relative permeability in coal. Paper 9321 in Proceedings of the 1993 International Coalbed Methane Symposium. Tuscaloosa: University of Alabama. kSpencer, S. J., Somers, M. L., Pinczewski, W. V., and Doig, I. D. 1987. Numerical Simulation of Gas Drainage from Coal Seams. Paper SPE 16857. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, September 27–30. lGray, I. 1987. Reservoir engineering in coal seams. Part 1. The physical process of gas storage and movement in coal seams. SPE Reservoir Engineering. V.
2 (no. 1). p. 28. mBustin, R. M. 1997.
For comparison, pore volume compressibilities of conventional reservoir rocks range from 10–6 to 10–4 psia–1, making coal cleat compressibility 10 to 1,000 times larger than that of conventional reservoirs.98 At typical coal seam temperatures and pressures, water compressibility is approximately 3(10)–6 psia–1, and gas compressibility, roughly the inverse of pressure, ranges from 4(10)–2 to 4(10)–4 psia–1. Median coal void volume compressibility is therefore about 500 times larger than that of water and roughly equal to that of methane at 800 psia. Sorption compressibility, discussed in chapters 7 and 9, depends on gas properties and sorption characteristics and ranges from 3(10)–4 to 3(10)–1 psia–1, at least an order of magnitude larger than the median coal cleat compressibility.
Compressibility of a coal deposit that contains both free gas and water is similar to that of a conventional reservoir plus sorption compressibility. Mathematically,
ct = cf + Swcw + Sgcg + cs (2.29) where
ct = total compressibility, psia–1, cf = cleat compressibility, psia–1, Sw = water saturation,
cg = gas compressibility, psia–1, Sg = gas saturation, and
cs = sorption compressibility, psia–1.
Coal cleat compressibility is important if no free gas is present, such as an undersaturated coal above the desorption pressure. Total compressibility of the system is now
ct = cf + cw ≈ cf