The number of desorption samples that should be taken from a given well depends on several factors.
Characterizing a single seam in an infill well requires fewer samples than does characterizing multiple coals intercepted by a wildcat exploration corehole. Many operators restrict the number of samples in an effort to minimize costs without realizing that the cost of desorbing of a few additional samples is relatively small compared to overall well costs. In addition, the cost of bad decisions based on inadequate data can be enormous compared to the cost of additional desorption samples. In practice, the minimum number of samples is often two per seam for dominant coals and one per seam for minor coals. At the other extreme, some operators elect to canister all recovered coal.
Not only is the number of samples recovered important, but the type of samples is also important. Desorbing only low-density, high-quality coal intervals will provide no information on the gas resource held in denser rocks and will preclude correlation of gas content with bulk density. In spite of the importance of this topic, only a few workers have considered it theoretically.
Diamond and Schatzel recommend canistering the entire recovered coal section, splitting the core at natural breaks, such as shale partings, into several discrete samples.41 Note that exclusion of shales and bone coals precludes determination of gas held in them, and reserve estimates must be reduced accordingly. The Gas Research Institute recommends sampling one-third of the “vertical reservoir profile” but does not address the number of samples required to do so.42 Mavor et al. employed statistical arguments to determine the number of samples required to estimate gas content to within 10% at a 95% confidence level.43 An example calculation using a San Juan well determined that 9 ft of the 57 ft of net coal, approximately 16%, were required. Note that this example required a bulk density distribution obtained from offset wells. Thus, from a theoretical basis, the recommended sample interval ranges from one-sixth of the coal seam to the entire coal seam.
Review of four sets of published gas contents will demonstrate that at least 80% of the samples from a single seam should be desorbed to determine gas content with over 90% confidence. However, sampling only one-third of the coals in a borehole will give an approximate idea of gas content distribution across the seams.
Seven whole core desorption samples from the Southern Ute 5–7 well discussed by Mavor et al. are reproduced here as table 4–5.44
Table 4–5. Southern Ute 5–7 measured gas contents
Zone Top depth, ft Bottom depth, ft Gross thickness, ft Average density, g/cm3 Average ash, % Average in-situ gas content, scf/ton
1 1,312.50 1,314.50 2.3 1.740 0.5772 209.3
2 1,321.25 1,339.00 18.0 1.489 0.2991 353.5
3 1,340.75 1,347.75 7.3 1.619 0.4428 279.0
4 1,349.00 1,362.25 13.5 1.466 0.2729 367.1
5 1,449.25 1,449.50 0.5 2.081 0.9555 13.1
6 1,451.00 1,472.75 22.0 1.440 0.2442 382.0
7 1,484.50 1,486.75 2.5 1.502 0.3136 346.0
66.1 0.4436 278.6
stdev = 131.64
stdev/avg = 0.473
Source: Mavor, M. J., et al. 1996.
Note: Thickness-weighted average gas content = 349.8 scf/ton.
These gas contents are sound, with minimal experimental error. For the sake of argument, they are assumed to be completely accurate, giving an average gas content of 278.6 scf/ton. Gas content determined from a single sample, then two samples, then three samples, etc. will be discussed. If a single sample were selected for desorption, only one would be within 20% of the correct number. That is, only one sample, sample 3, with a gas content of 279.0 scf/ton, would be within 20% of the correct value of 278.6 scf/ton. Desorption of a single sample in seven, or 14.3% of all samples, gives a gas content within 20% of the true gas content. Desorption of any of the other six samples will yield a gas content varying from the correct gas content by more than 20%. Repeating the exercise with a tolerance of 10% gives the same result of one sample in seven, sample 3, being sufficiently close to the true value. Because the gas content of sample 3 is so close to the correct gas content, the same conclusion of gas content from only one sample in seven results from tolerances of 1% and 5% around the correct gas content.
Turning the other way, if true gas content is desired to be known only to within 25%, then three samples, samples 1, 3, and 7, or 43% of the samples are sufficiently close to the true gas content. These three samples represent 43% of the total population of seven samples, so randomly selecting a single sample for desorption will give a gas content within 25% of the correct gas content in only 43% of the cases.
Repeating this exercise with two samples of the seven, there are 21 different pairs of samples. The number of sample sets is the combination of n total samples taken r at a time. For seven total samples taken two at a time, the number of possible combinations is
7! 7(6)5!
————— = ———— = 21 2!(7 – 2)! 2(5!)
Averaging the gas contents of the pairs, 43% of them will provide a gas content within 25% of the true value, while only 5% of them will yield a gas content within 1% of true gas content. These results, along with those from gas content uncertainty tolerances of 5%, 10%, and 20% uncertainty, are collected in table 4–6.
Table 4–6. Gas content uncertainty vs. number of samples—example #1
Uncertainty in gas content One sample Two samples Three samples Four samples Five samples Six samples
1% 14.3% 4.8% 5.7% 5.7% 9.5% 14.3%
5% 14.3% 14.3% 11.4% 11.4% 28.6% 57.1%
10% 14.3% 19.0% 17.1% 40.0% 42.9% 85.7%
20% 14.3% 42.9% 57.1% 74.3% 95.2% 100.0%
25% 42.9% 42.9% 74.3% 97.1% 100.0% 100.0%
Note: Five samples are required to be 95% certain that gas content is known to within 20%.
If three samples of the seven are desorbed, a total of 35 triplets are possible. Only 6% of these triplets will yield an average gas content within 1% of the true number, yet almost three-quarters of them, 74.3%, will give an average gas content within 25% of the correct value. Repeating this exercise for four samples (also 35 possible combinations), five samples (21 possible combinations), and six samples (7 possible combinations) fills out table 4–6.
Table 4–6 quantifies the intuitive conclusions that increasing the number of desorption samples taken from a given seam provides a more accurate estimate of coalbed gas content. Many reservoir parameters such as thickness and drainage area are not known to within better than 20%, thus the 20% row of table 4–6 can be considered. Desorbing a single sample will provide the true gas content within 20% in only one out of seven samples. Gas contents from six of the seven samples will differ from true gas content by more than 20%.
Desorbing a pair of samples gives true gas content within 20% in just under one-half, 42.9%, of all possible pairs. Just over one-half of all possible triplets, 57.1%, give an average gas content within 20% of the true value.
Almost three-quarters of all possible sets of four samples, 74.3%, give average gas contents within 20%. Over 95% of the various combinations of five and six samples provide an average gas content within 20% of the true value. Consequently, to be 95% certain that true gas content is known to within 20%, at least five samples must be desorbed. In other words, five out of seven samples, or 71%, of the samples must be desorbed.
Further complicating determination of “true” gas content, Mavor et al. reported a thickness-weighted gas content of 349.8 scf/ton.45 Note that determination of this gas content required use of wireline logs, which would not be available when the core barrel was opened up and the decision of how many samples to desorb must be made.
As a second example, consider the sidewall core (SWC) gas contents provided by Waechter and reported in table 4–7.46
Assuming the average gas content from the five samples, 213.4 scf/ton, is the true gas content and repeating the above exercise of gas content determination with one, two, three, or four samples yields table 4–8. From the table, it is seen that to be 95% certain the gas content is known to within 20% requires three or four samples.
Table 4–7. HWA sidewall core measured gas contents Zone Depth, ft In-situ gas content, scf/ton
1 1,252.60 239.8
2 1,253.00 208.7
3 1,254.00 237.7
4 1,258.00 78.7
5 1,258.40 301.9
average = 213.4
stdev = 82.6
stdev/avg = 0.387
Source: Waechter, N. B. 2003.
Table 4–8. Gas content uncertainty vs. number of samples—example #2
Uncertainty in gas content One sample Two samples Three samples Four samples
1% 0.0% 0.0% 0.0% 20.0%
5% 20.0% 10.0% 20.0% 60.0%
10% 20.0% 20.0% 40.0% 60.0%
20% 60.0% 50.0% 90.0% 100.0%
25% 60.0% 50.0% 100.0% 100.0%
Note: Three samples are required to be 90% certain that gas content is known to within 20%.
The third set of gas contents was reported by Kelso et al. from coals of the Great Divide Basin, part of the Greater Green River Basin.47 Cores and cuttings were desorbed from three wells that penetrated several coals over a 3,000 ft interval. Gas contents from two cores from the UPRC-9 well were selected for investigating the number of samples required to characterize these coals. Gas contents of five samples from 2,183.5 ft to 2,187.5 ft, labeled core 1 here and collected in table 4–9, were deeply undersaturated, with an average gas content of 6.68 scf/ton.
Table 4–9. UPRC-9—core 1 measured gas contents Zone Top depth, ft In-situ gas content, scf/ton
1 2,183.5 1.79
2 2,184.5 4.32
3 2,186.5 17.57
4 2,186.5 6.50
5 2,187.5 3.22
average = 6.68
stdev = 6.33
stdev/avg = 0.947
Source: Kelso, B. S., et al. 1991.
Repeating the exercise of calculating average gas contents from various numbers of samples gives table 4–10.
Reported gas contents varied widely, leading to the confusing result that one-fifth of the single samples would be within 20% of true gas content but only one-tenth of the pairs would. Moreover, to determine gas content within 20% at greater than an 80% confidence level would require desorbing all five samples.
Table 4–10. Gas content uncertainty vs. number of samples—example #3
Uncertainty in gas content One sample Two samples Three samples Four samples
1% 0.0% 0.0% 0.0% 20.0%
5% 20.0% 0.0% 0.0% 20.0%
10% 20.0% 0.0% 0.0% 40.0%
20% 20.0% 10.0% 20.0% 80.0%
25% 20.0% 10.0% 20.0% 80.0%
Note: Four samples are required to be 80% certain that gas content is known to within 20%.
The fourth example comes from gas contents from a second core in this same well. Gas contents of four samples taken from a deeper seam, between 2,515.8 ft and 2,518.5 ft, are in table 4–11.
Table 4–11. UPRC-9—core 2 measured gas contents Zone Top depth, ft In-situ gas content, scf/ton
1 2,515.8 12.57
2 2,516.5 9.48
3 2,517.5 5.82
4 2,518.5 11.97
average = 9.96
stdev = 3.07
stdev/avg = 0.308
Source: Kelso, B. S., et al. 1991.
This coal is also deeply undersaturated, with an average gas content of 9.96 scf/ton. The number of samples required to determine gas contents with selected degrees of confidence and selected tolerances are displayed in table 4–12.
Table 4–12. Gas content uncertainty vs. number of samples—example #4
Uncertainty in gas content One sample Two samples Three samples
1% 0.0% 0.0% 0.0%
5% 25.0% 0.0% 25.0%
10% 25.0% 33.3% 75.0%
20% 25.0% 66.7% 100.0%
25% 50.0% 100.0% 100.0%
Note: Three samples are required to be virtually certain that gas content is known to within 20%.
Note that to determine gas content to within 20% with 95% confidence would require desorbing at least three of the four possible samples. Undersaturation is only known after samples have been desorbed, isotherms measured, and reservoir pressure determined. Selection of desorption samples, cores or cuttings, is almost always completed before any indication of undersaturation. In practice, if undersaturation is suspected, the operator frequently elects to desorb additional, perhaps all, samples from the seam.
These four examples of single-seam desorption tests considered whole core samples and sidewall cores from saturated and undersaturated coals. From the four examples, it can be concluded that it is generally necessary to desorb at least 80% of the samples from the seam to determine gas content to within 20% with 90% or greater confidence.
The question of how many seams should be tested in a given prospect can be addressed with data from three wells drilled in the Rock Springs Formation of the Great Divide Basin.48 Data from two cores taken from one of the wells, the UPRC-9, were discussed above. Data for all 74 samples are presented in table 4–13, where cuttings data have been corrected to whole core equivalent by multiplying by 4/3. Average in-situ gas content was 178.2 scf/ton.
Table 4–13. Great Divide Basin measured gas contents
Well 1 UPRC-9 Well 2 UPRC-1 Well 3 UPRC-33
Core depth, ft Gas content,
scf/ton Cuttings depth, ft Gas content,
scf/ton WCE gas content,
scf/ton Cuttings depth, ft Gas content,
scf/ton WCE gas content, scf/ton
1,769.5 26.25 3,036.5 34.16 45.55 519.5 809.10 1,078.80
1,782.5 5.66 3,126.0 34.23 45.64 1,459.5 1.00 1.33
1,797.5 22.86 3,162.5 35.07 46.76 1,769.5 1.00 1.33
1,804.5 52.04 3,162.5 29.90 39.87 2,819.0 87.50 116.67
1,819.4 15.87 3,345.0 117.75 157.00 2,838.0 79.50 106.00
1,825.5 43.42 3,345.0 127.90 170.53 3,061.5 233.80 311.73
1,827.5 22.32 3,399.0 155.94 207.92 3,119.5 183.70 244.93
2,183.5 1.79 3,479.0 80.68 107.57 3,210.0 58.20 77.60
2,184.5 4.32 3,539.0 161.10 214.80 3,393.0 205.20 273.60
2,186.5 17.57 3,629.0 225.18 300.24 3,475.0 591.20 788.27
2,186.5 6.50 3,667.0 371.68 495.57 3,566.0 475.90 634.53
2,187.5 3.22 3,707.0 396.42 528.56 3,674.0 373.40 497.87
2,292.0 1.79 3,786.0 434.98 579.97 3,790.0 386.30 515.07
2,295.5 1.86 3,835.0 336.60 448.80 3,891.0 290.30 387.07
2,313.9 4.05 3,917.0 269.90 359.87 4,206.0 369.20 492.27
2,316.8 5.84 3,961.0 203.01 270.68
2,321.2 5.92 4,037.0 363.64 484.85
2,324.8 4.51 4,065.0 262.23 349.64
2,325.5 2.89 4,119.0 226.21 301.61
2,329.7 6.79 4,146.0 281.76 375.68
2,330.5 1.11 4,173.0 270.76 361.01
2,332.5 4.78 4,219.0 226.63 302.17
2,336.9 5.92 4,256.0 268.56 358.08
2,365.4 6.63 4,296.5 337.32 449.76
2,367.6 7.96 4,372.0 74.59 99.45
2,479.0 2.12 4,397.5 150.70 200.93
2,515.8 12.57
2,516.5 9.48
2,517.5 5.82
2,518.5 11.97
2,535.5 9.17
2,587.7 4.94
2,589.8 21.18
Note: WCE = whole core equivalent = cuttings × 4/3.
Avg. WCE gas content = 178.2 scf/ton.
If only every fourth sample was desorbed, average gas content is 200.3 scf/ton, 12% higher than the full average, and a plot of gas content versus depth, figure 4–8, shows erratic gas content behavior.
The gas content of the shallowest sample, at a depth of 520 ft, appears spuriously high, while the remaining data fall into two intervals. In the first interval, from 1,700 to 2,600 ft, the coals appear to be deeply undersaturated.
Below 2,600 ft, gas content increases with depth, as expected, but questions of undersaturation cannot be resolved without isotherms. The deepest sample, from 4,400 ft, appears erroneously low. Based on gas content alone, production tests should be confined to coals below depths of 3,400 ft.
Assuming every third sample was desorbed, average content rises to 202.1 scf/ton (13% high), and a plot of in-situ gas content versus depth, figure 4–9, shows the same behavior as before, although the data exhibit more scatter.
Fig. 4–9. Great Divide Basin—gas content vs. depth (1/3 of samples desorbed)
With gas content as the sole criterion, production tests should be confined to those coals deeper than 3,200 ft.
Using every other sample results in an average gas content of 190.4 scf/ton (7% high), and the character of the gas content versus depth plot, figure 4–10, suggests three intervals, not two.
Fig. 4–10. Great Divide Basin—gas content vs. depth (1/2 of samples desorbed)
The first interval, from depths of 1,700 to 2,600 ft, remains unchanged. Between 2,600 feet and 3,600 ft, gas contents increase with depth, as before. Below 3,600 ft, gas contents could be interpreted either as roughly constant at 450 scf/ton or declining with depth. Production tests should be confined to zones below 3,100 ft.
A plot of all data, figure 4–11, is best interpreted as three separate intervals with gas content steadily falling with depth below 3,600 ft. Production tests should be confined to coals in the interval between 3,100 ft and 4,300 ft deep.
Although this example is somewhat transparent, it demonstrates that reasonable average gas contents could be obtained by desorbing as few as 25% of the samples, in good agreement with the GRI recommendation of sampling one-third of the “vertical reservoir profile.”49 However, behavior of gas content with depth—deep undersaturation in shallow seams, then gas content increasing with depth, followed by gas content decreasing with depth—was suggested when every other sample was desorbed but only fully evident when all samples were desorbed. As expected, identification of zones for possible production tests was clearer when all data were employed.
0 200 400 600 800 1000 1200
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
insitu gas content, scf/ton
depth, feet UPRC-9 UPRC-1 UPRC-33
Fig. 4–11. Great Divide Basin—gas content vs. depth (all samples desorbed)