Stochastic modelling of coalbed methane resources: A case study in Southeast Qinshui Basin, China

International Journal of Coal Geology 99 (2012) 16–26

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Stochastic modelling of coalbed methane resources: A case study in Southeast Qinshui Basin, China Fengde Zhou a, b,⁎, Guy Allinson a, d, Jianzhong Wang c, Qiang Sun c, Dehua Xiong c, Yildiray Cinar a, d a

School of Petroleum Engineering, University of New South Wales, Sydney, NSW 2052, Australia Key Laboratory of Tectonics and Petroleum Resources (China University of Geosciences), Ministry of Education, Wuhan 430074, China China United Coalbed Methane Corporation Ltd. Jincheng, Shanxi 048000, China d Cooperative Research Centre for Greenhouse Gas Technologies, Canberra 2600, Australia b c

a r t i c l e

i n f o

Article history: Received 21 November 2011 Received in revised form 16 May 2012 Accepted 18 May 2012 Available online 26 May 2012 Keywords: Coalbed methane resources Uncertainty analysis Karst collapsing column Reservoir modelling

a b s t r a c t This paper presents a stochastic analysis of coalbed methane (CBM) resources for a coal seam in southeast Qinshui Basin, China. Log and laboratory data are used to predict the coal thickness, coal ash content and coal gas content. Using reservoir modelling, the distributions of the karst collapse column (KCC), coal seam thickness, coal quality and coal gas content are generated. The convergent interpolation and sequential Gaussian simulation methods are used to model the surface and structure of the coal seam. The structural models are determined by the surface structure and coal seam thickness. Based on the structural models, the coal and KCC are converted to two facies and their distributions are obtained using object modelling. The coal density distributions are simulated based on each facies model using the sequential Gaussian simulation. Finally, different realisations are used to study CBM resources. The results show that the heterogeneities in coal seam thickness and coal quality lead to significant uncertainty in estimating CBM resources. A model with lower heterogeneity gives a greater CBM resource. The distributions of KCC, coal seam thickness, coal quality and gas content are the main sources for uncertainty in CBM resource estimation. The density variogram and top structure contribute less to the uncertainty in CBM resources. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Estimating CBM resources is crucial for planning and the design of producing a coal seam. The resource estimation is highly uncertain due to lack of data, especially at the beginning of the CBM production. Hence, the uncertainty involved in the CBM resource estimation must be assessed. Coal seam thickness, coal density, KCC — also known as “no-coal column” and coal gas content are mentioned to be four major parameters that introduce the uncertainty in resource estimation (Wang et al., 1997; Zuo et al., 2009). The uncertainty comes mainly from two sources, namely well log interpretation and predicted distribution of each parameter. A robust log interpretation model and using data from more wells can therefore minimise the uncertainty. In addition, an appropriate geological model with spatial distributions of the parameters can improve the reliability of resource estimation. Reservoir modelling can give different equal probability realisations for different reservoir properties. It differs from Monte Carlo simulation in that Monte Carlo cannot predict the distribution of CBM resources in

⁎ Corresponding author at: School of Petroleum Engineering, University of New South Wales, Sydney, NSW 2052, Australia. Tel.: + 61 2 9385 5194. E-mail address: [email protected] (F. Zhou). 0166-5162/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2012.05.004

3D. It just gives a probability distribution of resources based on the probability distributions of input variables. The probability distributions of input variables can be obtained from the measured data. Geostatistics can be used to determine the distributions of coal thickness (Jakeman, 1980; Mastalerz and Kenneth, 1994), coal quality (Beretta et al., 2010; Cairncross and Cadle, 1988; Hagelskamp et al., 1988; Heriawan and Koike, 2008a; Hindistan et al., 2010; Liu et al., 2005) and coal tonnage (Heriawan and Koike, 2008b). These distributions can be then used to assess the uncertainty in CBM resource estimation. Coal thickness can be determined from drilling and log data and coal quality can be interpreted from well logs. The distribution of coal thickness and quality can then be predicted using a geostatistical method such as sequential Gaussian simulation and ordinary kriging (Beretta et al., 2010). There are 22 provinces with karst collapsing in south China (He et al., 2009). Karst collapsing is named “KCC” in the coal industry (Wang et al., 1997). It is also an uncertain parameter in assessing the CBM resources. Zuo et al. (2009) suggest that 3D seismic is an efficient tool to identify the presence of KCC. The KCC includes modern KCC and Palaeo-KCC, the latter of which is mostly caused by groundwater or by climatic conditions. The mechanisms causing KCC include gravity, erosion, vacuum suction erosion, vibration and load. The width of a single KCC ranges from 47 m to 387 m, while its length ranges from 110 m to 1139 m (Zuo et al., 2009).

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

Coal ash and sodium content (Heriawan and Koike, 2008b), volatile content (Hagelskamp et al., 1988), and sulphur content (Bancroft and Hobbs, 1986; Beretta et al., 2010) need to be studied as part of the assessment of coal quality. The electrical, magnetic, nuclear and acoustic logs can be correlated with experimental data to calculate coal quality parameters and coal gas content (Fu et al., 2009). This paper presents an uncertainty analysis of CBM resources using the stochastic reservoir modelling for a CBM field in southeast Qinshui Basin in China. Because of the significant uncertainty involved in the prediction, multiple variables and methods are considered. The log and laboratory data are used to predict the coal thickness, coal ash content and coal gas content. Then the KCC and coal seam data are transferred into two discrete facies and are analysed using facies modelling. The uncertainty is studied by analysing the top structure of the coal seam and coal seam thickness. Finally, the uncertainties of CBM resources are analysed based on the stochastic reservoir modelling of these parameters as well as KCC, coal seam thickness and gas content.

2. Field description 2.1. Location The study area lies between the Qinshui county and Gaopin city in Shanxi province. It is 260 km south from Taiyuan city and 60 km northwest from Jincheng city. The topography of ground surface shown in Fig. 1 indicates a rugged-topography and a maximum of 300 m difference between the highest and lowest altitudes. The rugged-topography is considered to increase the cost of CBM production.

0

2km

Depth(m) 1300 1250 1200 1150 1100 1050 1000 950 900 850 800 750

90

0

W-7

17

2.2. Geological data From bottom to top, the stratigraphy structure can be divided into three systems (Ordovician, Carboniferous and Permian) and five groups (Fengfeng, Benxi, Taiyuan, Shanxi and Low Shihezhi). The main coal seams are #3 and #15, which belong to the Shanxi and Taiyuan groups, respectively (Fig. 2). The coal quality is of low rank in the Benxi group which was formed in the lagoon and gulf environments. In the Taiyuan group, the coal was formed in a continental– oceanic interaction environment. In the Shanxi group, the coal was formed in delta and fluvial environments, which accumulated mainly in the lake plain, blocked channel and delta plain (Liang et al., 2002). For the study area there was no sedimentological data available hence geology could not be related to coal properties such as coal thickness, coal density and ash content. 2.3. Laboratory data A summary of the desorption and coal quality data obtained from 71 coal samples from 6 wells (W-1 through W-6 shown in Fig. 1) is given in Table 1. The desorption data includes the total gas content, natural desorption gas content, losing gas content, residual gas content and desorption time. Coal quality tests include the moisture content (Mad, %), ash content (Ad, %), volatile content (Vdaf, %), true and apparent coal density (g/cm 3), and elementary analysis (carbon content (Cdaf), hydrogen content (Hdaf), oxygen content (Odaf) and nitrogen content (Ndaf)). All these coal samples were kept in an airtight canister for 10 min after having been cored out during drilling. The temperature in the adsorption test was similar to the underground coal seam temperature. This was achieved by immersing the entire setup in a water-filled thermostatic bath. The desorption tests follow the Chinese industrial standard QB/MCQ1001-1999.

0 50 km

Beijing

1050

W-6

0

95

10

00

Qinshui Basin 2

Gas content (m3/t)

W-5

W-4

0

120

Basin boundary

0

115

Study area CBM well with logs

50

10

00 11

W-3

0

CBM wells

95

1250

1000

KCC location W-2

W-1

W-6 Well locations for sampling 1000

Ground surface isoline

Fig. 1. Structural contour map showing the elevation of the ground surface and locations of KCC and CBM wells (the map of Qinshui Basin was modified from Wei et al., 2007).

18

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

shows the relationship between the coal ash content and RGC. The correlation is given by —
 2 RGC ¼ −0:1113⋅Ad þ 11:165 R ¼ 0:19 :

ð2Þ

Note that two influence points of high ash content can change the correlation significantly. The poor correlation (R 2 = 0.19) is attributed to the fact that the samples are taken from five different wells that are located in different parts of the area (Fig. 6). The heterogeneous nature of coal must also be a reason for this. Since both the coal quality and pressure affect the RGC, it is also related to the ash content and samples' depth. The relationship is given by —
 2 RGC ¼ 3:05−0:164⋅Ad þ 0:014⋅Depth R ¼ 0:42 :

Fig. 2. Stratigraphy of the study area at well W-1 and the two main coal seams #3 and #15.

ð3Þ

This shows that RGC has a positive relationship with the measured depth, but a negative correlation with the ash content. The results show that the RGC obtained from the ash content and depth has a better correlation with the experimental data (Fig. 7). This suggests that the depth should be included in a correlation between the ash content and RGC although this alone is not sufficient for an accurate estimation either. The minimum, maximum and mean RGCs by measurement are 3.20 m 3/t, 16.80 m 3/t and 9.64 m 3/t, respectively. The values calculated using Eq. (2) are 7.88 m 3/t, 11.78 m 3/t and 9.85 m 3/t, respectively. The values calculated using Eq. (3) are 6.56 m 3/t, 13.79 m 3/t and 9.77 m 3/t, respectively.

2.4. Well log data

3.2. Top structure

The logs of the coal seam have unique characters, which are presented by low DEN, low GR and low SP, and high resistivity, high AC and high neutron. First, clean coal, sandstone, shale, and limestone were determined in the log interpretation. The coal has a low density and a low GR response, while the limestone has a lower GR and a higher DEN. The sandstone has a lower GR response and a density similar to that of the limestone (Fig. 3). Well logs from 22 wells were used in the coal quality interpretation and reservoir modelling.

The top and bottom depths for 137 wells in coal seam #3 (CS-3) are determined from the well log data. Two methods, the convergent interpolation (CI) (Bernstein, 1976) and kriging, are compared for the CS-3's top structure modelling. Fig. 8 shows the semivariance of well tops of CS-3. Appendix A describes how semivariance is calculated. The figure indicates that north–south (N–S) is the major direction with a range of 3430 m, and east–west (E–W) is the minor direction with a range of 1612 m. The structure constructed by the CI method is a completely westdipping incline. The structure constructed by kriging considering the variogram shows the same trend, but the structure is elliptic in most areas (Fig. 9). Both methods are controlled by the well tops data of CS-3. The top structure has no strong effect on CBM resources compared to the coal thickness. Therefore, the top structure constructed by the CI method is selected for the further study reported in the sections that follow.

3. Results 3.1. Coal quality and gas content In order to use the density for log interpretation, it must be compared and corrected using the laboratory density. Fig. 3 shows that the coal density from logs can be used in coal property calculations directly because they are similar to the coal density measured in the laboratory. 3.1.1. Ash content The ash content has a strong correlation with the coal density. Fig. 4 shows the relationship between the coal density and ash content (dry basis). Most samples' densities are less than 1.6 g/cm 3 except for one with 2.2 g/cm 3. The ash content can be calculated from — Ad ¼ 88:36⋅ρ−114:21

ð1Þ

3.3. Distribution of coal thickness In order to analyse the spatial distribution of coal thickness, its variogram should be analysed with the KCC regions excluded. Two coal seam thickness distribution models were established using the CI and sequential-Gaussian simulation (SGSIM) methods based on the spatial variogram shown in Fig. 10. The thickness of CS-3 modelled by the CI method has a good horizontal continuity than that modelled by the SGSIM method (Fig. 11). Both models present different realisations for the coal seam thickness.

where Ad is the coal ash content in % and ρ is the coal bulk density in g/cm 3.

3.4. Reservoir structural model

3.1.2. Raw gas content The raw gas content (RGC) is proportional to the coal quality. The RGC has a better relationship to the ash content than other coal quality parameters such as coal volatile, carbon content and density. Fig. 5

Using the well tops, bottoms, the top structure and coal seam thickness of CS-3, the reservoir structure model is built (Fig. 12). In the study area, there are only 3 individual faults in the northwest direction that have a negligible effect on CBM resource estimates.

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

19

Table 1 Coal sample adsorption and coal quality tests. Sample number

Mid-point depth, m

RGC m3/t

NDGC m3/t

LGC m3/t

GCR m3/t

τ d

Mad %

Ad %

Vdaf %

TD g/cm3

AD g/cm3

Cdaf

Hdaf

Odaf

Ndaf

W-1-1 W-1-2 W-1-3 W-1-4 W-1-5 W-1-6 W-1-7 W-1-8 W-1-9 W-1-10 W-1-11 W-1-12 W-2-13 W-2-14 W-2-15 W-2-16 W-2-17 W-2-18 W-2-19 W-2-20 W-2-21 W-2-22 W-2-23 W-3-24 W-3-25 W-3-26 W-3-27 W-3-28 W-3-29 W-3-30 W-3-31 W-3-32 W-3-33 W-3-34 W-3-35 W-3-36 W-3-37 W-4-38 W-4-39 W-4-40 W-4-41 W-4-42 W-4-43 W-4-44 W-4-45 W-4-46 W-5-47 W-5-48 W-5-49 W-5-50 W-5-51 W-5-52 W-5-53 W-5-54 W-5-55 W-5-56 W-6-57 W-6-58 W-6-59 W-6-60 W-6-61 W-6-62 W-6-63 W-6-64 W-6-65 W-6-66 W-6-67 W-6-68 W-6-69 W-6-70 W-6-71 Average

583.0 583.5 584.3 585.0 584.7 585.5 585.2 586.0 586.7 587.0 587.6 588.4 450.9 451.7 452.6 452.9 453.1 453.8 454.1 454.3 455.5 456.4 451.9 792.4 792.8 793.2 793.9 793.5 794.4 794.9 795.3 795.8 796.3 796.7 797.4 797.8 798.3 762.8 763.1 765.6 766.1 767.0 766.4 768.0 767.6 767.3 595.1 596.1 597.8 597.5 596.8 598.1 597.8 598.7 598.2 599.5 556 556.4 556.8 557.2 557.9 557.6 558.6 559.0 560 559.7 559.4 560.9 560.6 560.3 558.3 625.28

8.63 8.48 9.28 9.64 9.28 10.69 8.44 9.09 8.07 7.68 7.45 9.61 8.37 9.94 7.15 9.85 8.28 8.49 9.86 6.20 7.90 10.84 7.85 11.35 12.83 15.74 15.60 12.18 14.25 14.01 14.33 14.22 10.18 12.99 15.99 16.86 14.19 9.33 2.56 6.46 8.77 7.13 7.34 10.01 8.65 4.20 / / / / / / / / / / 8.61 5.42 3.20 7.97 8.62 8.13 8.65 4.55 6.56 9.36 10.07 5.50 11.71 6.83 8.63 9.41

8.17 7.99 8.67 9.40 8.86 10.10 8.20 8.67 7.63 7.21 7.10 8.95 8.21 9.81 6.87 9.67 8.00 8.18 9.74 5.77 7.49 10.71 7.75 10.79 12.50 15.29 15.30 11.79 13.67 13.39 13.90 13.90 9.83 12.52 15.53 16.14 13.91 8.43 2.16 6.24 8.52 6.91 7.06 9.79 8.32 3.90 5.68 5.75 10.30 5.10 6.10 7.13 7.08 8.29 6.52 7.01 8.22 5.10 3.03 7.72 8.35 7.81 8.40 4.36 6.38 9.05 9.68 5.29 11.47 6.41 8.39 8.75

0.26 0.14 0.18 0.05 0.12 0.25 0.10 0.09 0.22 0.14 0.20 0.37 0.12 0.08 0.07 0.07 0.24 0.14 0.07 0.13 0.15 0.09 0.10 0.14 0.28 0.21 0.21 0.19 0.37 0.25 0.21 0.19 0.16 0.21 0.24 0.37 0.12 0.70 0.21 0.10 0.18 0.15 0.19 0.19 0.23 0.10 / / / / / / / / / / 0.17 0.12 0.04 0.06 0.09 0.11 0.06 0.06 0.05 0.15 0.21 0.07 0.08 0.16 0.25 0.17

0.20 0.35 0.43 0.19 0.30 0.34 0.14 0.33 0.22 0.33 0.14 0.29 0.04 0.05 0.20 0.11 0.05 0.18 0.05 0.30 0.26 0.04 0.20 0.43 0.05 0.24 0.10 0.20 0.20 0.37 0.23 0.13 0.19 0.26 0.22 0.35 0.16 0.20 0.19 0.12 0.07 0.07 0.08 0.04 0.11 0.20 / / / / / / / / / / 0.21 0.20 0.14 0.19 0.19 0.21 0.19 0.12 0.14 0.16 0.17 0.14 0.16 0.26 0.20 0.19

12.47 37.09 9.23 9.08 10.19 10.18 9.13 9.04 8.95 9.20 9.06 8.29 57.08 59.57 59.17 59.90 59.36 59.43 58.27 59.43 59.46 57.07 57.78 35.37 32.32 34.35 39.67 25.88 45.63 47.29 37.10 43.56 38.06 35.02 34.52 26.35 25.83 10.12 30.14 38.95 34.03 33.81 35.20 31.14 27.59 10.25 / / / / / / / / / / 24.67 21.00 14.89 27.62 26.67 25.00 26.36 25.57 25.36 24.71 16.89 17.40 21.68 17.86 28.04 30.89

0.42 1.11 1.02 1.01 1.01 0.9 0.74 0.93 1.02 0.76 0.97 1.4 0.2 0.22 0.18 0.28 0.1 0.24 0.18 0.13 0.18 0.1 0.3 0.60 0.63 0.52 0.70 0.51 0.70 0.68 0.82 0.92 0.58 0.75 0.85 0.61 0.72 0.70 0.83 0.58 0.82 0.81 0.62 0.81 0.58 0.61 0.45 1.01 1.01 1.1 0.7 0.93 0.62 0.8 0.88 1.05 0.84 0.83 0.8 0.92 0.81 0.79 0.98 0.94 0.78 0.72 0.66 0.91 0.95 0.75 0.72 0.71

10.1 16.38 12.04 12.62 14.3 12.12 12.9 18.48 20.44 22.69 15.32 9.36 15.24 14.85 11.53 13.48 17.26 11.71 16.07 12.62 35.71 6.36 14.39 14.25 18.28 8.09 9.78 9.85 10.17 9.03 9.08 9.52 22.44 13.43 6.87 9.13 11.73 18.85 79.41 21.75 10.62 20.36 20.28 9.78 21.97 67.75 13.91 9.04 9.95 13.99 16.89 12.32 14.35 12.76 21.46 10.77 8.49 8.9 10.36 11.83 10.1 9.34 10.42 10.98 10.36 5.14 13.95 13.35 24.53 11.39 24.19 15.45

11.82 9.93 11.41 12.34 10.72 14.01 12.83 14.72 16.13 13.22 10.83 11.05 9.41 8.49 8.97 9.78 16.03 10.09 14.72 8.46 12.12 7.19 8.52 11.91 13.68 10.94 11.27 10.84 10.77 11.49 11.41 10.81 13.80 11.20 8.10 11.55 11.66 10.37 / 11.34 11.19 13.48 14.11 10.72 12.93

/ / 1.58 / / / / 1.60 / / / / / 1.55 / / 1.52 / / / / 1.43 / / 1.59 / / / / / 1.50 / / / / / / / 2.38 / 1.51 / / / / / / / / / 1.56 / / / 1.60 / / / / / / 1.46 / / / / 1.51 / / / / 1.60

/ / 1.50 / / / / 1.51 / / / / / 1.48 / / 1.46 / / / / 1.32 / / 1.49 / / / / / 1.42 / / / / / / / 2.18 / 1.42 / / / / / / / / / 1.48 / / / 1.52 / / / / / / 1.39 / / / / 1.44 / / / / 1.51

/ / 90.60 / / / / 88.27 / / / / / / / 91.84 / 90.25 / / / 92.5 / / / 90.94 / / / 90.49 / / / / / / / 91.40 / 90.57 / / / / / / / / / / 89.86 / / / 89.69 / / / / / / / 91.47 / / / / 91.62 / / / 90.73

/ / 4.20 / / / / 4.30 / / / / / / / 3.62 / 3.99 / / / 3.4 / / / 4.02 / / / 4.04 / / / / / / / 4.04 / 3.96 / / / / / / / / / / 4.34 / / / 4.30 / / / / / / / 3.64 / / / / 3.65 / / / 3.96

/ / 4.19 / / / / 6.29 / / / / / / / 3.48 / 4.7 / / / 3.08 / / / 3.97 / / / 4.39 / / / / / / / 3.49 / 4.39 / / / / / / / / / / 4.70 / / / 4.92 / / / / / / / 1.24 / / / / 1.23 / / / 3.85

/ / 1.01 / / / / 1.14 / / / / / / / 1.06 / 1.06 / / / 1.02 / / / 1.07 / / / 1.08 / / / / / / / 1.07 / 1.08 / / / / / / / / / / 1.10 / / / 1.09 / / / / / / / 3.65 / / / / 3.5 / / / 1.46

11.39 10.15 10.43 10.39 12.38 13.9 17.74 12.09 12.04 12.25 8.51 8.08 9.29 8.79 10.1 8.13 8.71 8.58 10.15 7.71 9.18 8.64 11.46 8.9 10.8 11.10

RGC — raw gas content, NDGC — naturally desorption gas content, LGC — lost gas content, GCR — residual gas content, τ — desorption time, Mad — moisture content (air-dried basis); Ad — ash content (dry basis), Vdaf — volatile content (dry ash free basis); TD — true density, AD — apparent density, Cdaf — carbon content (dry ash free basis), Hdaf — hydrogen content (dry ash free basis), Odaf — oxygenium content (dry ash free basis), and Ndaf — nitrogen content (dry ash free basis).

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

Gamma (API) 0

200

400

600

540 Gamma ray Log density Lab density

Lithology

560

A 580

B

Sandstone Coal seam #3

Raw gas content (RGC) (m3/ton)

20

20

RGC = -0.1113Ad + 11.165 R² = 0.19

15

10

5

0 0

20

40

60

80

100

Ash content (Ad) (%) 600

Depth (m)

Fig. 5. Relationship between ash content (dry basis) and raw gas content.

620

C Shale

640

660

D E 680

Coal seam #15 Limestone

700 0

1

2

3

Density (g/cm3) Fig. 3. Lithology of well W-1 defined from log GR and DEN (coal seam located at “B” and “E”; clean sandstone and limestone located at “A” and “D”; shale located at “C”).

Therefore these three faults are ignored when building the reservoir structure model. The study area is divided into 50 m × 50 m cells on the horizontal plane with a total number of cells of 148 × 240 = 35,520. In the vertical direction, the averaged 6-m CS-3 is sub-layered into 12 layers. Two reservoir structure models constructed using the CI method for the top structure and coal seam thickness are named as T-CI and T-SGSIM. Using the KCC distribution and the coal density distribution, the CBM resources are calculated based on these two types of reservoir structure models. 3.5. Distribution of KCC The distribution of KCC is related to structural activity, underground water condition, and sedimentology (He et al., 2009). But,

Ash content (Ad) (%)

100 80

Ad = 88.36ρ - 114.21 R² = 0.98

60 40

given that there is insufficient seismic data, the coal and KCC are converted into two facies and then the stochastic model is built using the objective modelling method. The distribution probability of KCC is calculated by the number of the KCC wells divided by the total drilled wells. Hence, a ratio of 4.3% (=6 KCC wells out of 137 drilled wells) is used to control the reservoir modelling. The dimensions of the KCC are assumed to be the half distance of the well spacing between the KCC and other wells which were drilled into CS-3. Using the well spacing in the study area, the dimensions of the KCC are set as a width of 50 m to 400 m with an average of 300 m and a length/width ratio of 0.8 to 1.2 with an average of 1.0. A thickness of 15 m is assigned to make the KCC through the CS-3 in the modelling. Coal is considered as the background facies and the KCC is modelled with ten realisations. Fig. 13 shows one realisation of the KCC and coal in the 3D reservoir model. 3.6. Distribution of coal density CS-3 was formed in a deltaic plain which consists of distributary channels and a flood plain (Liang et al., 2002). Comparing the variograms in four directions, 0° (N–S), 45° (N45E), 90° (E–W), and 135° (E45S), the 135° was selected as the major direction because this gives the longest variation range. Based on the distribution of logged wells (Fig. 1), the searching distance in the major and minor directions is set to be 6000 m. A spherical model is chosen to fit the sample variogram. Table 2 reports the results of semivariance, nugget and sills. The heterogeneous range of coal density in the major and minor directions is from 1300 m to 500 m, respectively. Nuggets in the major, minor, and z-directions are all assumed to be 0.327. Sills in major and minor directions are equal to 1.0. The vertical semivariogram range of coal thickness is 5.8 m. 3.6.1. Transformation In order to delete some data points with the highest and lowest frequencies and setting the data range of the properties, the data probability distribution used in reservoir modelling should be filtered by transformation. Fig. 14 shows both original and transformed density distributions. The density ranges from 1.8 to 2.7 g/cm 3 in the KCC regions and ranges from 1.1 to 1.8 g/cm 3 in the coal seam. Fig. 14(b) shows a bimodal histogram of density in the KCC wells which may have been caused by the presence of more than one lithology in these wells.

20 0 0.0

0.5

1.0

1.5

2.0

2.5

Coal bulk density (ρ) (g/cm3) Fig. 4. Relationship between ash content (dry basis) and coal bulk density.

3.6.2. Coal density distribution Based on the above analysis, the coal density distribution was modelled using the SGSIM method. The SGSIM method honours well data, input distributions, variograms and trends. In this study, ten realisations of coal density distribution were built based on each

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

21

Fig. 6. Relationship between ash content (dry basis) and raw gas content for individual wells (W-1, W-2, W-3, W-4 and W-6).

facies model. Total 100 realisations of coal density in each of the two reservoir structural models, the T-CI and T-SGSIM models, were built. 3.7. Estimation of CBM resources Based on the 200 realisations of coal density, Eqs. (1) and (3) are used to calculate the ash content and gas content in the 3D reservoir model. Then, Eq. (4) is used to calculate the gas volume in each cell — CBMR ¼ V b ⋅ρ⋅RGC

where CBMR is the gas volume of cells in m 3, Vb is the cells' bulk volume in m 3, ρ is the coal density of each cell in g/cm 3, and RGC is the gas content of cell in m 3/t. The calculated averages of CBM resources for the structure models T-CI and T-SGSIM are 8.173 × 10 9 m 3 and 8.133 × 10 9 m 3, respectively (Fig. 15). The T-CI model gives higher CBM resources than the TSGSIM model. This is because the coal seam thickness in the T-CI model is more homogeneous than that in the T-SGSIM model.

ð4Þ

25

By ash content and depth By ash content

3200

4000

4800

5600

3200

4000

4800

5600

1.6

2.4

3.2

Function: Spherical Sill : 0.242 m2 Nugget : 0.002 m2 Min range : 1,612 m Major Range : 3,430 m Max range/Min Range: 2.13 Min Orientation: E-W Major Orientation: N-S

0.8 0

0

5

2400

1.6

10

1600

0.8

15

800

2.4

Semivariance (m2)

0

3.2

Measured RGC (m3/t)

20

0

800

0 0

5

10

15

20

25

Calculated RGC (m3/t) Fig. 7. Comparison of calculated raw gas contents (RGCs) with the measured data.

1600

2400

Separation distance (m) N-S

E-W

Model

Fig. 8. Experimental semivariograms of well tops of coal seam #3 along the major (N–S) and minor (E–W) directions and their spherical fitting models.

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

1000

1500

375

2500m

475

450

300

275

W-7

2500m

Depth (m)

0

275

600 575 550 525 500 475 450 425 400 375 350 325 300 275 250

W-6

500

350

350

425

0

475

45 0

400

47 5

275

400

2000

300

375

1500

5 32

425

25 0

1000

400

35

325

275

250

500

0 30

625 600 575 550 525 500 475 450 425 400 375 350 325 300 275 250 225

W-6 300

0

Depth (m)

400

325

350

250

W-7

225

2000

375

500

425

0

525

22

5

575

550

52

425

350

W-5

W-4

5

400

350

300

575

475 450

475

5

42

400 425

W-2 W-1

W-1

500

475

W-2

52 555 5750 600

275

450

600

500

375

550

350

300

325

450

525

400

300 325 350

37 5

300

450 425

0

40

425

450

325

475

275

W-3

W-3

425

375

W-5

W-4

500

37

250 275

450

225

275

32

5

30

(a)

625

(b)

Fig. 9. Comparison of two structural contour maps conducted by (a) the CI method and (b) the kriging method, showing the elevation of the top of coal seam #3. The types of the wells are described in Fig. 1.

among four homogeneous scenarios. The difference between the maximum and minimum resources of the 8 scenarios is 0.129 × 109 m3, which suggests that the varying variograms have a negligible contribution to the uncertainty in CBM resource estimation.

4. Discussion 4.1. Effect of spatial heterogeneity on CBM resources Eight different heterogeneous scenarios for coal seam thickness were built based on the same structural and KCC distribution models. Fig. 16 shows the results. All the scenarios have the same sill and nugget data and a seed number of 25,000 (which controls the calculating path when using the SGSIM model). Fig. 17 shows that scenario (b) has the highest CBM resources (with 7.871× 109 m3) among four heterogeneous scenarios. By comparison, scenario (h) has the highest CBM resources (with 7.928 ×109 m3)

0

1600

2400

3200

4000

4800

5600

6400

2400

3200

4000

4800

5600

6400

2.5 2

2 1.5

1.5

2.5

1

Sill

0.5

0.5

1

Semivariance (m2)

800

Function: Spherical Sill: 1.33 m2 Nugget: 0.28 m2 Min. range: 2,250 m Major Range: 4,500 m Max range/Min Range: 2 Min Orientation: N45ºE Major Orientation: N45ºW

Nugget

0

0

0

800

1600

Separation distance (m) N45ºE

N45ºW

Model

Fig. 10. Experimental semivariograms of the thickness of coal seam #3 along the major (N45°W) and minor (N45°E) directions and their spherical fitting models.

4.2. Gas content log interpretation model The gas content can be calculated using different independent parameters (Fu et al., 2009). In this paper, the reason for the low correlation between the gas content and ash content is attributed to the fact that the samples are from 5 wells distributed in different parts of the study area (Fig. 1). In addition, heterogeneous coal properties likely scatter the test results. If Eq. (3) is used to calculate the RGC, the calculated average CBM resources are 7.55 × 10 9 m 3 and 7.49 × 10 9 m 3 in the structure models using the T-CI and T-SGSIM models, respectively (Fig. 18). The results show that the CBM resources based on the gas content obtained from the ash content are less than that when the gas content is obtained from the ash content and measured depth. Fig. 18 also shows that the histogram of CBM resources calculated based on Eq. (2) and CI-thickness are bimodal. This is because (1) the CBM resources are estimated based on the two parameters' distributions and (2) the CI-thickness distribution is smoothed unlike the stochastic-thickness distribution which is heterogeneous (see Fig. 11). Apart from the complexity of the gas content interpretation, the clay interlayer also causes some uncertainty. Fig. 19 shows three types of clay layers in the coal seam, thick clay layer, random and very thin clay layer and thin clay layer. Types (a) and (b) can be identified using well logging, but type (c) cannot. All these three types of clay layers have potential to increase the uncertainty in CBM resource estimation and CBM production.

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

0

500

1000

1500

2000

2500m

0

6.5

6

5

5.25

5

5.5

5

5.7

25 6.

6

5.5

6.2 6.5 5

5 6.2

5

5 6.7 6.5

5.75

6.2

5

6

6.5

W-3

7

6.2

5

7.25

5

7

7

6.5

6.75

6.75

W-2

W-1

6.2

5

5

6.2

6.75

6.25

5 6.2

25

5.75

5 6.

6

6.

W-1

6 6.5 .25

5

6.7

6.

6.25

6.5

W-2

6.5

6.5

5

5

6.75 7

6.7

7.25

6.5

6

5.5

6.

7

6.75

W-3

W-5

5.75

7.5

6

6.5

6.75

W-4

6

7

6.5

6.5

6.5

6.5

5 6.7

6.2

4.75

5 5.25

6.25

6

5

6.5

4.5

5.5 5.75

5

4.75

6

5

5.25

5.7

5 6.

6.25

6.5

6.2

5

5.5

6.2

W-5

6

5.7

5.7 5 5 .5

6.25

5.7

5

25

6

6.25

6.2 5

5.7

6.2 5

5

W-6

6

7

2500m

7.75 7.5 7.25 7 6.75 6.5 6.25 6 5.75 5.5 5.25 5 4.75 4.5 4.25

5.7 5

6

6.2

5 6.2

6

6

6.5

6.

6

6

6.25

2000

Thickness

6.25

6.25

W-6

W-4

6.5

1500

6.25

6.5

6.5

6.5

6.5

1000

6.5

6.5

6

6

500

6

6.25

6

6

5

Thickness 7.5 7.25 7 6.75 6.5 6.25 6 5.75 5.5 5.25 5

W-7

5 .7

6.25

W-7

23

(a)

(b)

Fig. 11. Comparison of coal seam thickness (except for KCC wells) modelled by (a) the CI method and (b) the SGSIM method. The types of the wells are described in Fig. 1.

calculations. The equation used in the calculation of CBM resources is given by —

4.3. Comparison with Monte Carlo simulation Monte Carlo simulation models the phenomena that have significant uncertainty in input variables. In this study, the coal seam thickness, coal distribution area (affected by the distribution of KCC), RGC and coal density are uncertain parameters in the CBM resource

CBMR ¼ ASA ⋅ð1−P AKCC Þ⋅h⋅RGC⋅ρ

ð5Þ

KCC A1 CS-3 Top

A2

KCC

Coal

(1) (2) CS-3 bottom

(3)

(4)

Fig. 12. Structural model building process; 1 — make the top surface based on the well top of coal seam #3 using the CI method, 2 — construct the coal seam thickness distribution using the CI and SGSIM methods, 3 — make the bottom surface based on the top of the underlying formation and coal seam thickness, and 4 — identify the top and bottom depths in KCC wells and make a zone of 12 layers.

Fig. 13. One realisation of coal seam and KCC distribution using the object modelling method.

24

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

14

Table 2 Variogram parameters of coal density. Degrees

Range (m)

Fitting type

Nugget

Sill (m )

135 45 /

1300 500 5.8

Spherical Spherical Spherical

0.327 0.327 0.327

1 1 1

Frequency

Major direction Minor direction Vertical

(a)

Mean= 8.173 S.d.= 0.179 Min= 7.870 Max= 8.349

12 2

10 8 6 4

5. Conclusions

6

This study has used 71 data sets obtained from 6 wells, 22 well logs and 137 well tops in log interpretation, variogram analysis, structure modelling and stochastic modelling to determine the CBM

5 4

8.4

8.36

8.32

8.28

8.2

8.24

8.16

8.12

8.08

8

8.04

7.96

7.92

7.88

7.8

7.84

0

CBM resources (109m3) 16

(b)

Mean= 8.133 S.d.= 0.162 Min= 7.778 Max= 8.282

14 12 10 8 6 4 2

8.28

8.2

8.24

8.16

8.12

8.08

8

8.04

7.96

7.92

7.88

7.84

7.8

7.76

0

CBM resources (109m3) Fig. 15. Comparison of the CBM resources histogram based on two structural models obtained using (a) the CI method and (b) the SGSIM method. The gas content is only related to ash content.

resources and study the uncertainty involved in these calculations. The following conclusions are drawn, • The results show that spatial heterogeneity is an important parameter in uncertainty assessment. Geostatistics (e.g., variogram, object modelling and sequential Gaussian simulation) can be applied effectively to study the spatial heterogeneities. • The distributions of karst collapse column, coal seam thickness, coal quality and gas content are the main sources of the uncertainty in CBM resource estimation. The density variogram and top structure contribute less to the uncertainty in CBM resource estimation. • KCC can be considered in the calculation of CBM resource estimation using the stochastic object modelling.

2

3

N

0

1

Probability(%)

Mean:1.39 S.d.: 0.16 Max.:1.8 Min.:1.1

(a) Coal

2

Frequency

where ASA is the study area (88.8 km 2), PAKCC is the area fraction of the KCC in the study area, h is the coal thickness in m, RGC is the raw gas content in m 3/t, and ρ is the coal bulk density in t/m 3. Based on the experiment and previous analysis, the distributions in Table 3 are used for PAKCC, h, RGC and ρ. Fig. 20 shows the cumulative probability of CBM resources after 5000 trials of Monte Carlo simulations. The calculated CBM resources at P90, P50 and P10 levels of confidence are 5.0 × 10 9 m 3, 7.0 × 10 9 m 3, and 10.2 × 10 9 m 3, respectively. These compare well with the results obtained using the reservoir modelling. This comparison shows that the mean CBM resource of 7.32 × 10 9 m 3, obtained from the Monte Carlo simulations, is close to the minimum CBM resources obtained using the reservoir modelling, 7.38 × 10 9 m 3. In order to understand the contribution of each coal property to the CBM resource, the 5000 CBM resources obtained using Monte Carlo simulations were ranked from highest to lowest. A ranking correlation coefficient for each property was calculated based on the procedure described in Appendix B. Fig. 21 shows a chart of the normalised contribution of each coal property to the CBM resource. The contributions of RGC, coal density, coal seam thickness, and KCC to the variance of CBM resources are 67.6%, −24.9%, 7.4% and −0.2%, respectively. This suggests that the RGC has the highest impact on CBM resources, followed by the coal density, coal seam thickness and the KCC.

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(b) KCC

4 2

3

Mean:2.43 S.d.: 0.23 Max.:2.7 Min.:1.8

E

0

1

Probability(%)

5

6

Density (g/cm3)

1.8

2

2.2

2.4

2.6

Density (g/cm3) Fig. 14. Transformation of density in (a) coal and (b) KCC. The curves are those used in the modelling of density distribution.

Fig. 16. Setting for the heterogeneity of density variogram in facies (coal). (a) The major direction = 135°, the major range = 1300 m, the minor range = 500 m; (b) the major direction = 45°, the major range = 1300 m, the minor range = 500 m; (c) the major direction = 135°, the major range = 3000 m, the minor range = 1000 m; (d) the major direction = 45°, the major range = 3000 m, the minor range = 1000 m; (e) ranges in all directions = 500 m; (f) ranges in all directions = 1300 m; (g) ranges in all directions = 3000 m; and (h) ranges in all directions = 6000 m.

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

25

CBM resources (109m3)

7.95 7.90 7.85 7.80 7.75

(a)

7.70 a

b

c

d

e

f

g

Thick clay layers Coal Random and thin clay layers

Scenarios Fig. 17. Comparison of CBM resources for different scenarios which are generated based on different variograms of coal density shown in Fig. 16. a-d: heterogeneous realisations, and e-h: homogeneous realisations.

• Well logs can be used to calculate the ash content. The raw gas content has a better relationship with the ash content and measured depth than with the ash content only. • The mean CBM resource obtained using Monte Carlo simulations is lower than the minimum CBM resource determined by the reservoir modelling.

Acknowledgements

7.4 7.42 7.44 7.46 7.48 7.5 7.52 7.54 7.56 7.58 7.6 7.62 7.64 7.66 7.68 7.7

Frequency

Frequency

= density log = multiple in regression = area, km 2 = probability, % = volume, m 3

This work was carried out in the context of the China–Australia Joint Coordination Project supported by the Department of Resources, Energy and Tourism, Australia, the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGL100249) and funds of TPR-2010-15, and the Cooperative Research Centre for Greenhouse Gas Technologies. The financial support is greatly acknowledged. The authors thank the China United CBM Co. for permission to publish the paper. Appendix A. Semivariogram The semivariogram, γ(h), of stationary and intrinsic random variables, Z(x), is calculated by —

(b)

Mean= 7.49 S.d.= 0.050 Max= 7.59 Min= 7.38

5

8

7.6

7.58

7.56

7.54

7.5

7.52

7.48

7.46

7.44

7.4

7.42

0 7.38

γðhÞ ¼

ðA:1Þ

where h is the separation distance, N(h) is the number of pairs with a distance of h, and xi is the head value of the pair i. The experimental semivariograms of the top structure of coal seam #3 and the coal seam thickness were fitted using the spherical model and a nugget component as follows —

10

7.36

1 X 2 ½Z ðxi þ hÞ−Z ðxi Þ 2NðhÞ i¼1 N ðhÞ

25

15

10cm

Fig. 19. Three types of clay layers described by an outcrop from a coal mine. (a) Thick clay layers; (b) a thin clay layer; and (c) random and very thin clay layers.

CBM resources (109m3)

20

0

Subscript ad = air dry base daf = dry and ash free

(a)

Mean= 7.55 S.d.= 0.046 Max= 7.66 Min= 7.44

(b)

DEN R A P V

Nomenclature Mad = moisture content (air-dried basis), % Ad = ash content (dry basis), % Vdaf = volatile content (dry ash free basis), % RGC = raw gas content, m 3/t SGSIM = sequential Gaussian simulation CI = convergent interpolation ρ = coal bulk density, g/cm 3 τ = desorption time, days Depth = buried depth, m h = thickness, m GR = gamma, API DLL = dual laterlog 20 18 16 14 12 10 8 6 4 2 0

(c)

h

 3   h h γ ðhÞsph ¼ c 1:5 −0:5 a a

ðh≤aÞ

ðA:2Þ

CBM resources (109m3) Fig. 18. Comparison of the CBM resource histograms from two structural models using (a) the CI method and (b) the SGSIM method. The raw gas content is related to ash content and depth.

γ ðhÞsph ¼ c

ðh≥aÞ

c ¼ Sill−Nugget

ðA:3Þ ðA:4Þ

26

F. Zhou et al. / International Journal of Coal Geology 99 (2012) 16–26

Table 3 Input distribution of assumptions. Properties

Min

Max

Mean

Std. dev.

Mid point

Scale

Deg. freedom

P95

Distribution

RGC (m3/t) ρ (g/cm3) h (m) PAKCC (fraction)

0 1.27 0 0.006

50 2.80 12 0.200

9.41 1.51 / 0.044

3.11 0.16 / /

/ / 6.23 /

/ / 0.3 /

/ / 2 /

/ / / 0.006

Lognormal Lognormal Student's t Normal

where a is the range in the major or minor direction, h is the separation distance, c is the sill–nugget component which is shown in Fig. 10, and γ(h) is the fitted semivariogram. Appendix B. Assessing the contribution of coal properties to CBM resource estimation Monte Carlo simulation calculates the contribution of each variable to the estimation by squaring the rank correlation coefficients and normalising them. The contribution of each variable to the estimation is given by
3 C xi ¼ γ xi

1 ,0  X n
2   @γ x  γx A i

ðB:1Þ

j

j¼1


.

 2 2 γ ¼ 1− 6∑d m m −1

ðB:2Þ

100

4,000

80 60 20

40

2,000

P 50

0

P 10

Cumulative Frequency

P90

0

Cumulative probability (%)

where Cxi is the contribution of coal seam properties to the variance of CBM resources, xi is the ith variable, γ is the Spearman's rank correlation coefficient (Spearman, 1904), j is the variable, n is the total number of variables, d is the rank difference and m is the pair of sampled variable and its forecast. A positive value of Cxi shows an increase in

1

3

5

7

9

11

13

CBM resources (109m3) Fig. 20. Cumulative probability of CBM resources. P10 is the CBM resource in low confidence (10.2 × 109 m3); P50 is the CBM resource in median confidence (7.0 × 109 m3); P90 is the CBM resource in high confidence (5.0 × 109 m3); and the mean CBM resource is 7.32 × 109 m3.

Contribution of variables 0%

30%

60%

RGC (m 3 /t) Coal bulk density (g/cm 3) Coal seam thickness (m) KCC area percent (%)

Fig. 21. Normalised contribution of coal seam properties to the CBM resource.

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