Introduction
Coalbed methane (CBM) is an unconventional gas stored in coal seams in the adsorbed state [1⇓⇓⇓-5]. The selection and evaluation of geological sweetspot for CBM development is the prerequisite and foundation for efficient exploration and development of CBM resources [1⇓⇓⇓-5], which refers to selecting favorable areas for CBM exploration and development by investigating key control factors for CBM enrichment, resource potential, mining technical conditions, and evaluation index [6-7]. Many countries such as the United States and Australia have achieved commercial exploitation of CBM. In addition, they have developed evaluation and development technologies suitable for their own reservoir strata according to the geological conditions in their CBM area [8-9].
In China, the main coal-bearing strata occur in diverse sedimentary environments, and have experienced long coal-forming period as well as later multiple-period structural movement and geological evolution. Therefore, the CBM reservoirs have obvious heterogeneity. That is, the permeability, gas content, and other reservoir parameters of the same coal seam vary greatly in different regions [10⇓-12]. At present, the main idea for area selection and evaluation of CBM reservoir is to select enrichment areas by combining static geology and dynamic development. However, the accurate selection of high-yield CBM areas from resource-rich ones is a major problem for CBM development [13-14].
Since the evaluation and selection of favorable areas for CBM development is fuzzy, uncertain and complex, this process can hardly be dealt with by conventional information-processing techniques effectively. Analytic hierarchy process (AHP), multi-level fuzzy synthetic judgment (MFSJ) and the mathematical method combining with these two are valuable for application. Yao et al. [15] built an AHP synthetic evaluation model based on the geographic information systems (GIS) and applied it to the evaluation of the Carboniferous-Permian coal seam resources in Qinshui Basin. Wei et al. [16] comprehensively evaluated the deep CBM resources and favorable areas of coal field in Panji District, Huainan City, with the aid of a MFSJ model considering geological factors and reservoir characteristics. These research results have been used widely and played an important role in CBM area evaluation [16-17]. Nevertheless, when AHP and MFSJ are used, it is difficult to avoid the impact of subjective factors in the determination of the weights of evaluation parameters for CBM area selection, resulting in uncertainty and variability in the evaluation results [18-19].
Fuzzy pattern recognition (FPR) can simplify the structure of recognition systems, simulate the thinking of human brains more widely and deeply, and classify and identify targets more effectively. It plays a very important role in fields including computer science, information science, management science, and engineering technology [20⇓-22]. In addition, FPR model can be used in recognition of given objects in complex systems [23-24]. The area selection and evaluation of geological sweetspot for CBM development, which can be regarded as a typical FPR process, is to identify and determine the evaluation level of target area by comparing evaluation parameters or indicators. In this study, from the perspective of geological selection area for CBM development, the geological and mining conditions that affect CBM development were classified in detail and evaluated. The optimal area selection and evaluation parameters were determined, and the area selection and evaluation index system was built. Besides, the FPR model of geological sweetspot for CBM development was established. Furthermore, the model was applied in the No.3 Coal Seam of Fanzhuang Block in southern Qinshui Basin to verify the rationality and effectiveness of the model.
1. FPR model of sweetspot
1.1. Evaluation parameters and evaluation level classification
According to The Procedure and Method of Coalbed Methane Play Evaluation and Selection (NB/T10013-2014 [25]), the evaluation parameters for selection of the geological sweetspot for coalbed methane development were optimized, and the evaluation level system for area selection was constructed (Table 1 ). Fifteen evaluation parameters including geological conditions and mining conditions were selected. The evaluation level system was divided into four levels, i.e., I, II, III, and IV, which indicates that the evaluated block has excellent, medium, and lower potential for CBM development and no CBM development potential, respectively.
Table 1. Evaluation parameters and level system of geological sweetspot selection for CBM development (medium-high rank coal) |
| Evaluation level | Regional geology | Reservoir recoverability | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Buried depth/m | Geologic structure | Hydrological condition | Gas saturation/ % | Ratio of critical desorption pressure to reservoir pressure | Permeability/ 10−3μm2 | ||||||||||
| I | <1000 | Simple structure, undeveloped folds and faults, weak transformation | Simple detention area with favorable water quality | >80 | >0.8 | >1.00 | |||||||||
| II | [1000, 1500) | Moderate structure, moderately developed folds and faults, and weak transformation | Complex detention area with favorable water quality | (60, 80] | (0.5, 0.8] | (0.10, 1.00) | |||||||||
| III | [1500, 2000] | Moderate structure, relatively developed folds and faults, and relatively strong transformation | Weak runoff area with relatively unfavorable water quality | (40, 60] | (0.2, 0.5] | (0.01, 0.10) | |||||||||
| IV | ≥2000 | Complex structure, developed folds and faults, and strong transformation | Runoff area with unfavorable water quality | ≤40 | ≤0.2 | ≤0.01 | |||||||||
| Parameter type | xnz | xqx | xqx | xpy | xpy | xpy | |||||||||
| Evaluation level | Transformability | ||||||||||||||
| Coal structure | Effective geostress/ MPa | Relation between coal seam and surrounding rock | Coal seam distribution area/km2 | Coal seam thickness/ m | Vitrinite content/ % | Ash production rate/% | Gas content/ (m3•t−1) | Methane content/ % | |||||||
| I | Primary- cataclastic | <10 | Simple relationship, small coal seam spacing | >500 | >6 | >75 | <15 | >15 | (90, 100) | ||||||
| II | Cataclastic | [10, 15] | Relatively simple relationship, relatively small coal seam spacing | (100, 500] | (4, 6] | (60, 75] | [15, 25) | (8, 15] | (85, 90) | ||||||
| III | Cataclastic- granulated | [15, 20] | Relatively complex relationship, with many interlayers and large spacing | (10, 100] | (2, 4] | (45, 60] | [25, 40) | (4, 8] | (80, 85) | ||||||
| IV | Granulated- mylonitic | ≥20 | Complex relationships, multiple interlayers, and large spacing | ≤10 | ≤2 | ≤45 | [40, 50] | ≤4 | ≤80 | ||||||
| Parameter type | xqx | xnz | xqx | xpy | xpy | xpy | xnz | xpy | xpy | ||||||
For the purpose of facilitating FPR for the four evaluation levels in the evaluation system, the evaluation level matrix Ye (e=I, II, III, IV) was built. In the matrix, yi,j is the element, and 0 and 1 are the standard values of evaluation parameters at a certain evaluation level:
${{Y}_{\text{I}}}=\left[ \begin{matrix} {{y}_{i,1}}=1 & {{y}_{i,2}}=0 & {{y}_{i,3}}=0 & {{y}_{i,4}}=0 \\ \end{matrix} \right]$
${{Y}_{\text{II}}}=\left[ \begin{matrix} {{y}_{i,1}}=0 & {{y}_{i,2}}=1 & {{y}_{i,3}}=0 & {{y}_{i,4}}=0 \\ \end{matrix} \right]$
${{Y}_{\text{III}}}=\left[ \begin{matrix} {{y}_{i,1}}=0 & {{y}_{i,2}}=0 & {{y}_{i,3}}=1 & {{y}_{i,4}}=0 \\ \end{matrix} \right]$
${{Y}_{\text{IV}}}=\left[ \begin{matrix} {{y}_{i,1}}=0 & {{y}_{i,2}}=0 & {{y}_{i,3}}=0 & {{y}_{i,4}}=1 \\ \end{matrix} \right]$
1.2. Normalization of evaluation parameters
In order to eliminate the impact of the dimension difference of different parameters on the evaluation results, it is necessary to normalize the evaluation parameters before FPR calculation [26].
As can be seen in Table 1 , evaluation parameters can be classified into qualitative parameters and quantitative parameters. Qualitative parameters include geological structure, hydrological conditions, coal structure, and the relation between coal seam and surrounding rock. Qualitative parameters (xqx) were normalized by assigning them values of 0 and 1 [27]. That is, when a parameter of the evaluation block is closest to a certain evaluation level in the evaluation system, a value of 1 in this evaluation level is assigned to this parameter; otherwise, a value of 0 is assigned. eqx is the result of assignment and normalizing of qualitative parameters (xqx).
Quantitative parameters can be divided into two categories. One is positive correlation quantitative parameters (xpy), including coal seam distribution area, coal seam thickness, vitrinite content, gas content, methane content, gas saturation, the ratio of critical desorption pressure to reservoir pressure, and permeability. Higher values of these parameters are more favorable for CBM exploitation. The other is negative correlation quantitative parameters (xnz), including buried depth, ash production rate and effective geostress. Higher values of these parameters are more unfavorable for CBM exploitation. The quantitative parameters are usually normalized by interval mapping [28], and the calculation formulas are as follows:
${{e}_{\text{py}}}=\left\{ \begin{matrix} \frac{{{x}_{\text{py}}}-a}{b-a} & \text{ }{{x}_{\text{py}}}\in \left( a,b \right] \\ 1 & \text{ }{{x}_{\text{py}}}\in \left( b,+\infty \right) \\ \end{matrix} \right.$
${{e}_{\text{nz}}}=\left\{ \begin{matrix} 1-\frac{{{x}_{\text{nz}}}-c}{d-c} & \text{ }{{x}_{\text{nz}}}\in \left[ c,d \right) \\ 0 & \text{ }{{x}_{\text{nz}}}\in \left[ d,+\infty \right) \\ \end{matrix} \right.$
After the normalization of all evaluation parameters, an evaluation parameter matrix can be obtained:
$E={{\left[ {{e}_{i,j}} \right]}_{15\times 4}}=\left[ \begin{matrix} {{e}_{1,1}} & {{e}_{1,2}} & {{e}_{1,3}} & {{e}_{1,4}} \\ \vdots & \vdots & \vdots & \vdots \\ {{e}_{15\text{,}1}} & {{e}_{15\text{,}2}} & {{e}_{15\text{,}3}} & {{e}_{15\text{,}4}} \\ \end{matrix} \right]$
1.3. Calculation of fuzzy nearness degree
FPR of geological sweetspot for CBM development aims to determine the evaluation levels of the blocks to be evaluated based on the vicinity principle, and to characterize the proximity quantitatively by calculating the fuzzy nearness degree between the evaluation parameter matrix E and the evaluation level matrix Ye.
Nearness degree is the measurement of similarity between two fuzzy subsets. The longer the distance between two fuzzy subsets is, the lower the nearness degree is, while the shorter the distance is, the higher the nearness degree is [23]. As the most common nearness degree, spatial cosine similarity can reflect the similarity between two objects under the influence of the same factors [29]. Since the recognition between the evaluation parameter matrix and the evaluation level matrix fits the characteristics of spatial cosine similarity, the spatial cosine similarity was selected as the nearness degree to determine the evaluation levels of blocks to be evaluated. For the purpose of enhancing the accuracy of the evaluation results, the impact of 15 evaluation parameters and 4 evaluation levels involved on the evaluation results should be considered in the selection of fuzzy nearness degree.
First, the evaluation parameter matrix and evaluation level matrix were converted into column vectors M and N, and then the nearness degree was calculated with spatial cosine similarity.
$M=\left[ {{e}_{i,j}} \right]=\left[ \begin{matrix} {{e}_{1,1}}\cdots {{e}_{15,1}} & {{e}_{1,2}}\cdots {{e}_{15,2}} & {{e}_{1,3}}\cdots {{e}_{15,3}} & {{e}_{1,4}}\cdots {{e}_{15,4}} \\ \end{matrix} \right]_{1\times 60}^{\text{T}}$
$N=\left[ {{y}_{i,j}} \right]=\left[ \begin{matrix} {{y}_{1,1}}\cdots {{y}_{15,1}} & {{y}_{1,2}}\cdots {{y}_{15,2}} & {{y}_{1,3}}\cdots {{y}_{15,3}} & {{y}_{1,4}}\cdots {{y}_{15,4}} \\ \end{matrix} \right]_{1\times 60}^{\text{T}}$
$\beta \left( E,{{Y}_{e}} \right)=\cos \theta =\frac{M\cdot N}{\left\| M \right\|\left\| N \right\|}=\frac{\sum\limits_{k=1}^{60}{{{M}_{k}}{{N}_{k}}}}{\sqrt{\sum\limits_{k=1}^{60}{{{M}_{k}}^{2}}}\sqrt{\sum\limits_{k=1}^{60}{{{N}_{k}}^{2}}}}$
1.4. FPR of evaluation levels
The higher the value of nearness degree β(E, Ye) is, the closer the two vectors are. By comparison of the value of β(E, Ye), the evaluation levels of blocks to be evaluated can be identified. The detailed schematic diagram of building and calculation of the FPR model of geological sweetspot for CBM development is presented in Fig. 1 .
Fig. 1. Schematic diagram of the FPR model of geological sweetspot and calculation flow. |
2. Application examples
The FPR model of geological sweetspot for CBM development was applied to the No.3 Coal Seam of Fanzhuang Block in Qinshui Basin to verify the rationality and effectiveness of the model.
2.1. Research objects and evaluation parameters
2.1.1. Geological structure and coal-bearing strata
The Fanzhuang Block is located in the horseshoe-shaped slope zone of the southern synclinorium in Qinshui Basin. In Fanzhuang Block, the strata are wide and gentle, and well preserved in complete sequence. In addition, normal faults and parallel folds are widely developed. The coal-bearing strata include the Upper Carboniferous Taiyuan Formation, the Lower Permian Shanxi Formation, the Upper Permian Lower Shihezi Formation and Upper Shihezi Formation. The Taiyuan Formation and the Shanxi Formation are two main coal-bearing strata. The Shanxi Formation is 40-110 m thick, consisting of sandstone, siltstone, and mudstone of land and littoral facies, with 3-6 coal seams. The Taiyuan Formation is 50-150 m thick, consisting of limestone, siltstone, and mudstone of paralic facies, with 7-10 coal seams. The floor and roof of the main mining coal seam, i.e., the No.3 Coal Seam of Shanxi Formation, are relatively stable, with the lithology of mudstone. In addition, the contact relation between the coal seam and the surrounding rock is rather simple, which is beneficial to CBM development.
In Fanzhuang Block, the coal seam is about 320 km2 in area. Influenced by tectonic movement, coal seams in different areas may differ from each other in continuity, integrity and spatial distribution, which will affect the difficulty of CBM development. Therefore, to facilitate the selection of the geological sweetspot for CBM development, it is necessary to divide the study area into different evaluation units. In accordance with the tectonic boundaries and the development characteristics of structures such as faults and folds, Fanzhuang Block was divided into four evaluation units (Fig. 2 ).
Fig. 2. Division of evaluation units in Fanzhuang Block, Qinshui Basin. |
2.1.2. Thickness and buried depth of the coal seam
The drilling data show that the No.3 Coal Seam in Fanzhuang Block is 4.00-8.00 m in thickness, with an average of 5.68 m, belonging to a thick to extra-thick coal seam. The thickness of the coal seam increases gradually from west to east (Fig. 3a ). Moreover, the buried depth of the No.3 Coal Seam is 100-1100 m and less than 800 m in most parts of the area, with an average of 580 m. The buried depth increases gradually from southeast to northwest. Due to the influence of topography and structure, the buried depth changes from deep to shallow alternately in some areas (Fig. 3b ).
Fig. 3. Isopleths of thickness, buried depth and gas content of the No.3 Coal Seam in Fanzhuang Block. |
2.1.3. Coal quality characteristics of the coal seam
In terms of macroscopic type, the majority of coals in the No.3 Coal Seam are semibright, and small parts are semidull, with blocky structure, vitreous luster, conchoidal fracture surface, and developed internal fractures. The vitrinite content of the No.3 Coal Seam is 71%-88%, with an average of 81%. The inertinite content is 9%-18%, with an average of 14%. The maximum ash production rate is 17.60%, and the minimum ash production rate is 9.04%, with an average of 13.72%, which means that the No.3 Coal Seam has a medium-low ash content. The vitrinite reflectivity is 2.43%, which means that coals in the coal seam are high-rank anthracite. The fixed carbon content is relatively high, being 72.55%-79.10%, with an average of 77.32%.
2.1.4. Permeability and reservoir pressure of the coal seam
According to the existing CBM well testing data, the No.3 Coal Seam has a permeability of (0.4-0.8)×10−3 μm2, indicating that it is a low-permeability coal seam. The reservoir pressure is 2.33-4.50 MPa, with an average of 3.49 MPa. The reservoir pressure gradient is 0.003 8-0.012 0 MPa/m, with an average of 0.006 9 MPa/m, which means that the coal seam is a low-pressure reservoir.
2.1.5. Gas content of the coal seam
The Fig. 3c indicates that in plane distribution, the gas content of the No.3 Coal Seam increases gradually from the periphery to the center, being 12.80-28.00 m3/t, with an average of 21.11 m3/t. The gas saturation is 66%-100%, with an average of 90%, which suggests that the coal seam is a highly saturated CBM reservoir. Moreover, according to the isothermal adsorption experiment, the Langmuir volume and Langmuir pressure of the No.3 Coal Seam are 52.41 m3/t and 3.68 MPa, respectively (dry ash-free basis).
2.2. Evaluation parameters
Based on the statistical analysis on the geological characteristics and reservoir parameters of the No.3 Coal Seam in Fanzhuang Block, the evaluation parameters of four evaluation units can be obtained through the following approaches: (1) The distribution area of the coal seam can be calculated based on the ratio of each evaluation unit area to the total area of the block. (2) Parameters such as the buried depth, thickness, and gas content of the coal seam can be obtained by the average value of isopleth of each evaluation unit. (3) Vitrinite content, ash production rate, and methane content can be obtained in the light of the borehole parameters in each evaluation unit. (4) The permeability and reservoir pressure can be obtained from the field water injection and pressure falloff test in each evaluation unit. (5) The ratio of critical desorption pressure to reservoir pressure and the gas saturation can be calculated by the measured gas content, reservoir pressure, the coal seam Langmuir volume and Langmuir pressure of each evaluation unit. (6) The effective ground stress can be calculated in line with the buried depth and ground stress gradient of the coal seam in each evaluation unit. (7) The type of coal structure can be determined by microscopic identification on samples from the field drilling sampling. (8) Qualitative parameters such as structure, hydrological conditions, and the relation between the coal seam and the surrounding rock can be obtained based on the geological characteristics of coal seam in each evaluation unit. The results of evaluation parameters of the four evaluation units are displayed in Table 2 .
Table 2. Evaluation parameters for each evaluation unit of No.3 Coal Seam in Fanzhuang Block |
| Evaluation unit | Buried depth/m | Geologic structure | Hydrological condition | Coal seam distribution area/km2 | Coal seam thickness/m | Vitrinite content/% | Ash production rate/% | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Unit 1 | 580 | Moderate tectonic, moderately developed folds and faults, and the transformation is not strong | Complex detention area with favorable water quality | 112.4 | 5.9 | 81 | 13.70 | ||||||
| Unit 2 | 670 | Moderate tectonic, moderately developed folds and faults, and the transformation is not strong | Complex detention area with favorable water quality | 87.8 | 6.3 | 88 | 11.24 | ||||||
| Unit 3 | 420 | Simple tectonic, undeveloped folds and faults, weak transformation | Complex detention area with favorable water quality | 43.4 | 5.5 | 76 | 14.50 | ||||||
| Unit 4 | 400 | Moderate tectonic, relatively developed folds and faults, and relatively strong transformation | Complex detention area with favorable water quality | 47.4 | 5.4 | 79 | 13.14 | ||||||
| Evaluation unit | Methane content/ % | Relation between coal seam and surrounding rock | Gas content/ (m3•t−1) | Gas saturation/ % | Ratio of critical desorption pressure to reservoir pressure | Permeability/ 10−3 μm2 | Coal structure | Effective geostress/ MPa | |||||
| Unit 1 | 89.73 | Relatively simple relationship and relatively small coal seam spacing | 20.1 | 84.0 | 0.68 | 0.59 | Primary- cataclastic | 11.66 | |||||
| Unit 2 | 92.73 | Relatively simple relationship and relatively small coal seam spacing | 26.6 | 91.4 | 0.65 | 0.59 | Primary- cataclastic | 13.47 | |||||
| Unit 3 | 83.52 | Relatively simple relationship and relatively small coal seam spacing | 12.1 | 66.3 | 0.49 | 0.51 | Primary- cataclastic | 8.82 | |||||
| Unit 4 | 84.03 | Relatively simple relationship and relatively small coal seam spacing | 14.3 | 72.6 | 0.55 | 0.54 | Cataclastic | 8.40 | |||||
2.3. Calculation process and evaluation results of the FPR model
The calculation of the FPR model can be conducted by four steps: (1) Carry out normalization on the evaluation parameters of the four evaluation units of No.3 Coal Seam in Fanzhuang Block in Table 2 (Table 3 ), and establish the evaluation parameter matrix E and the evaluation level matrix Ye. (2) Convert the matrices E and Ye into column vectors M and N with Eqs. (8)-(9), respectively. (3) Calculate the nearness degree between M and N with Eq. (10). (4) Conduct evaluation on each unit of the No.3 Coal Seam of Fanzhuang Block on the basis of the calculation results.
Table 3. Normalization results of evaluation parameters for each evaluation unit of No.3 Coal Seam in Fanzhuang Block |
| Evaluation unit | Evaluation result | Buried depth | Geologic structure | Hydrological condition | Coal seam distribution area | Coal seam thickness | Vitrinite content | Ash production rate | Gas content | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Unit 1 | Evaluation level | I | II | II | II | II | I | I | I | ||||||
| Calculation result | 0.60 | 1.00 | 1.00 | 0.03 | 0.94 | 0.24 | 0.09 | 1.00 | |||||||
| Unit 2 | Evaluation level | I | II | II | III | I | I | I | I | ||||||
| Calculation result | 0.47 | 1.00 | 1.00 | 0.86 | 1.00 | 0.52 | 0.25 | 1.00 | |||||||
| Unit 3 | Evaluation level | I | I | II | III | II | I | I | II | ||||||
| Calculation result | 0.83 | 1.00 | 1.00 | 0.37 | 0.77 | 0.04 | 0.03 | 0.59 | |||||||
| Unit 4 | Evaluation level | I | III | II | III | II | I | I | II | ||||||
| Calculation result | 0.86 | 1.00 | 1.00 | 0.42 | 0.70 | 0.16 | 0.12 | 0.90 | |||||||
| Evaluation unit | Evaluation result | Methane content | Gas saturation | Ratio of critical desorption pressure to reservoir pressure | Permeability | Coal structure | Effective geostress | Relation between coal seam and surrounding rock | |||||||
| Unit 1 | Evaluation level | II | I | II | II | I | II | II | |||||||
| Calculation results | 0.95 | 1.00 | 0.60 | 0.54 | 1.00 | 0.67 | 1.00 | ||||||||
| Unit 2 | Evaluation level | I | I | II | II | I | II | II | |||||||
| Calculation results | 0.17 | 1.00 | 0.50 | 0.54 | 1.00 | 0.31 | 1.00 | ||||||||
| Unit 3 | Evaluation level | III | II | III | II | I | I | II | |||||||
| Calculation results | 0.7 | 0.32 | 0.97 | 0.46 | 1.00 | 0.12 | 1.00 | ||||||||
| Unit 4 | Evaluation level | III | II | II | II | II | I | II | |||||||
| Calculation results | 0.81 | 0.63 | 0.17 | 0.49 | 1.00 | 0.16 | 1.00 | ||||||||
The calculation results of the nearness degree of the four evaluation units are shown in Table 4 . It can be seen from Table 4 that the nearness degree of evaluation level II corresponding to Unit 1 is 0.569 4, significantly higher than the nearness degree of corresponding evaluation levels I, III, and IV, which demonstrates that Unit 1 of the No.3 Coal Seam corresponds to the evaluation level of II. That is, it has a medium potential for CBM development. Similarly, the evaluation levels of units 2-4 are I, II, and II, respectively, with excellent, medium, and medium potential for CBM development. For evaluation units of the same level, the favorable development potential of the evaluation units can be selected by comparison of nearness degree. Hence, it can be concluded that the CBM development potentials of the No.3 Coal Seam in Fanzhuang Block from excellent to inferior are as follows: Unit 2, Unit 1, Unit 4, and Unit 3 (Fig. 4 ).
Table 4. Analysis results of nearness degree for each evaluation unit of No.3 Coal Seam in Fanzhuang Block |
| Evaluation unit | Nearness degree | Evaluation level | |||
|---|---|---|---|---|---|
| I | II | III | IV | ||
| Unit 1 | 0.332 5 | 0.569 4 | 0 | 0 | II |
| Unit 2 | 0.466 7 | 0.375 2 | 0.074 2 | 0 | I |
| Unit 3 | 0.284 2 | 0.389 6 | 0.191 9 | 0 | II |
| Unit 4 | 0.121 7 | 0.551 5 | 0.208 8 | 0 | II |
Fig. 4. Selection of CBM development units in the No.3 Coal Seam of Fanzhuang Block. |
3. Model reliability testing
3.1. Reliability of FPR model
Based on the aforementioned FPR results, the evaluation level of geological sweetspot for CBM development in Unit 2 of the No.3 Coal Seam in Fanzhuang Block is I, and those of the other evaluation units are all II. This indicates that the CBM development of this coal seam has an above-medium potential, which is consistent with the previous research results [30-31]. Since 2006, a total of 760 vertical wells and 50 horizontal wells have been put into production in the No.3 Coal Seam. The maximum single-well production is approximately 16 000 m3/d, and wells with a single-well production over 2000 m3/d make up 33% of total production wells [32]. Tao et al. [32] further analyzed the gas production of 79 wells in the No.3 Coal Seam of Fanzhuang Block, and found that the daily gas production of 10 wells exceeds 3000 m3 (account for 12.66%), that of 24 wells is 1000-3000 m3 (account for 30.38%), that of 39 wells is less than 1000 m3, and six wells do not produce gas (Fig. 4 ). For Unit 2, the daily gas production of 6 wells is over 3000 m3, and that of 16 wells is 1000-3000 m3, which means that Unit 2 has the largest number of wells with the aforementioned daily gas production among all units. Considering that the overall production of CBM wells in China is very low, the blocks with a daily single-well production of over 1000 m3 can generally be developed commercially, and wells with a daily gas production of 3000 m3 or more are defined as high-yield wells. Therefore, the above data show that the No.3 Coal Seam is qualified for CBM commercial development, which is consistent with the FPR results. Moreover, Wu et al. [33] explored favorable seepage channels in the coal seams and their influence on the distribution of high-yield areas. He found that high-yield wells in the No.3 Coal Seam are mostly located in Unit 2, followed by units 1 and 4. Zhao et al. [34] predicted the CBM high-yield area in Fanzhuang Block in accordance with the fluid-solid coupling production control mode. The prediction demonstrates that high-yield wells with a daily average single-well gas production of over 3000 m3 are mainly situated in western areas of the block. The prediction is basically consistent with the selection results of this study and thus further verifies the reliability of the selection results of our FPR model.
3.2. Comparison between the model in this study and other models
The advantage of AHP and MFSJ models lies in that they can combine qualitative and quantitative analysis, showing people’s subjective judgment in a quantitative form, and scientifically handle objective factors at different levels. The disadvantage is that researchers have different understandings regarding the importance of the same evaluation index, which can affect the determination of parameter weights and ultimately leads to diversity in evaluation results [35-36]. Therefore, it is necessary to analyze the influence of parameter weights on the evaluation results of geological sweetspot for CBM development when the two models are adopted.
The evaluation system of geological sweetspot for CBM development in Table 1 is comprised of 15 parameters, among which the gas content and permeability are the two most critical parameters. Cai et al. [30] considered the weight of gas content as 0.3 in the research on the evaluation of CBM development potential in southern Qinshui Basin, China. Yao et al. [15] took the weights of gas content and permeability as 0.7 and 0.4, respectively. Meng et al. [12] regarded the weights of gas content and permeability as 0.5 and 0.3, respectively, in the evaluation of CBM production potential in Liulin area of eastern Ordos Basin. Clearly, the values of parameter weights vary greatly. For the purpose of studying the impact of parameter weights on the evaluation results, Unit 1 of the No.3 Coal Seam was taken as an example. In accordance with the basic parameters in Table 2 and the normalization results in Table 3 , the weights of permeability and gas content were set to increase from 0.1 to 0.9, with a changing range of 0.1. Subsequently, the nearness degrees under different weight combinations of permeability and gas content were calculated by the method specified in The Procedure and Method of Coalbed Methane Play Evaluation and Selection (NB/T 10013-2014 [25]) (Fig. 5 ). On this basis, the impact of changes in permeability and gas content weights on the evaluation results was analyzed. In addition, it is worth noting that since the evaluation parameters of Unit 1 in Table 3 do not belong to evaluation levels III and IV, the nearness degrees of these two evaluation levels are zero, and only those of evaluation levels I and II are listed.
Fig. 5. Changes in the nearness degree under different weight combinations of permeability and gas content in Unit 1. |
The following results can be observed from Fig. 5 : (1) For evaluation level I, the weight of permeability is negatively linearly correlated with the nearness degree, and the weight of gas content exhibits a positive correlation with the nearness degree. (2) For evaluation level II, the weight of permeability has a positive linear correlation with the nearness degree, and weight of gas content is negatively correlated with the nearness degree. (3) When the weight of gas content is less than or equal to 0.3, the nearness degree of evaluation level I is lower than that of evaluation level II (Fig. 5a ); when the weight of gas content is 0.4-0.5, the curves of nearness degree of these two evaluation level intersect (Fig. 5b ); when the weight of gas content is more than or equal to 0.6, the nearness degree of evaluation level I is higher than that of evaluation level II (Fig. 5c ).
The evaluation results under different weight combinations of permeability and gas content are shown in Table 5 . As can be seen from Table 5 , evaluation level of Unit 1 of No.3 Coal Seam in Fanzhuang Block is level II under three combined conditions ((1) The weight of gas content is less than or equal to 0.3, and the weight of permeability is less than or equal to 0.4. (2) The weight of gas content is less than or equal to 0.4, and the weight of permeability is more than 0.4 and less than 0.8. (3) The weight of gas content is less than or equal to 0.5, and the weight of permeability is 0.8-0.9). Besides, the evaluation level of Unit 1 is evaluation level I under the other weight combinations of permeability and gas content. This demonstrates that the change in weights of gas content and permeability have a significant influence and bring about considerable uncertainty in the evaluation results.
Table 5. Evaluation results under different permeability and gas content weight combinations |
| Permeability weight | Evaluation level | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 0.1 | II | II | II | I | I | I | I | I | I |
| 0.2 | II | II | II | I | I | I | I | I | I |
| 0.3 | II | II | II | I | I | I | I | I | I |
| 0.4 | II | II | II | I | I | I | I | I | I |
| 0.5 | II | II | II | II | I | I | I | I | I |
| 0.6 | II | II | II | II | I | I | I | I | I |
| 0.7 | II | II | II | II | I | I | I | I | I |
| 0.8 | II | II | II | II | II | I | I | I | I |
| 0.9 | II | II | II | II | II | I | I | I | I |
| Gas content weight | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
In the above analysis, only the weights of two parameters at the same level were adjusted, but the evaluation system of geological sweetspot for CBM development consists of three levels and 15 parameters. It can be inferred that the evaluation results can be influenced more greatly under multiple levels or change in parameter weights. Hence, since scientific and reasonable weighting is challenging for users of AHP and MFSJ models, the usage of these two models to evaluate the geological sweetspot for CBM development can lead to errors due to subjective factors. Meanwhile, multi-level judgment matrices are required in AHP and MFSJ models, which means the calculation of these two models is much more complex than that of the FPR model in this paper.
4. Conclusions
Since the FPR model of geological sweetspot for CBM development does not involve parameter weighting, it overcomes the shortcomings of traditional AHP and MFSJ models which have uncertainty in evaluation results due to parameter weighting. Moreover, this model is much simple in calculation because it does not require building multi-level judgment matrices. The model was applied to evaluate four evaluation units of the No. 3 Coal Seam in Fanzhuang block in the southern part of the Qinshui Basin. The evaluation results are consistent with the actual development effect and consistent with the existing research results, verifying the rationality and reliability of the FPR model.
Through the practical evaluation and verification for CBM blocks, it has been confirmed that the prediction results of the FPR model are reliable, and can provide technical support for efficient CBM development.
Nomenclature
a, b—upper and lower limits of the classification interval of positive correlation quantitative parameters;
c, d—upper and lower limits of the classification interval of negative correlation quantitative parameters;
eqx, epy, enz—normalization results of qualitative parameters, positive correlation quantitative parameters, and negative correlation quantitative parameters;
E—evaluation parameter matrix;
ei,j—elements in the evaluation parameter matrix;
i, j—number of rows and columns of matrices;
k—column vector element sequence number;
M, Mk—column vectors and its elements of evaluation parameter matrix transformation;
N, Nk—column vectors and its elements of evaluation level matrix transformation;
xqx, xpy, xnz—qualitative parameters, positive correlation quantitative parameters, negative correlation quantitative parameters;
Ye—evaluation level matrix;
yi,j—elements in evaluation level matrix;
β—fuzzy nearness degree, dimensionless;
γ—gas content weight;
θ—space vector angle, (°).