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Abstract

The recognition criteria of credible degree in uncertainty measure theory are improved based on the concept of distance discriminant and used to evaluate the potential for exploration and development of coalbed methane. This paper uses a systematic approach to establish a mathematical model based on entropy weight and improved uncertainty measure theory. In this model, uncertainty influence factors were analyzed qualitatively and quantitatively using data for the Muli coalfield of Qinghai province, China. The uncertainty measure function is based on experimental data, and the weight of index is determined by entropy weight theory. Optimization credible degree recognition criteria were used to evaluate the potential for coalbed methane exploration and development of six mines in the Muli coalfield. These data indicate that evaluation results obtained using entropy weight and improved uncertainty measure theory have practical application and can effectively assess the exploration and development potential of coalbed methane in a coal basin.

Keywords

Coalbed methane Muli coalfield entropy weight improved uncertainty measure evaluation potential

Introduction

Coalbed methane (CBM) is a hydrocarbon gas, with methane being the main component. It occurs in coal seams adsorbed onto the surface of coal matrix particles and in coal pore space or dissolved in coalseam water. This associated mineral resource of coal is an unconventional natural gas, a clean and high-quality energy source, and a chemical raw material that has gained increasing use worldwide during the last two decades (Fu et al., 2007; Hu, 2004; Lei et al., 2007; Singh, 2011; Xing, 2014; Zhao and Qin, 2010). A significant transformation of CBM development industry in recent years has reduced the loss of resources, reduced the project development costs, and maximized the economic benefits of implementing CBM projects. Yet it is important to continue improving the process of exploring and evaluating prospective ground in different mining areas of a coal basin to develop CBM projects.

The exploration and development of CBM is strongly influenced by geological factors (Singh, 2011). The complex geology of prospective ground and the interplay of different geological factors introduce uncertainties into the evaluation and development of CBM. A comprehensive analysis of different factors is necessary to make a systematic and reliable evaluation. Each evaluation index must be combined with subjective estimations and objective calculations to obtain robust scientific results. There are many methods to evaluate the exploration and development potential of CBM. However, the present study identified two problems in the evaluation process. One is the lack of a systematic approach and only performing a single analysis of the different factors, which yields a qualitative evaluation result. The second is using an average and not comprehensive weighting for subjective and objective information. Therefore, the evaluation index difference is not clear and this reduces the reliability of evaluation results (Clarkson et al., 2010; Connell et al., 2010; Han et al., 2008; He et al., 2016; Shao et al., 2008; Shi et al., 2014; Si et al., 2010; Tian et al., 2008; Wang et al., 2006). In order to make a systematic comprehensive evaluation of CBM exploration and development potential, uncertainty measure theory is an ideal method. Among them, the uncertainty measure theory can comprehensively consider the uncertainty factors such as fuzziness, complexity, etc. affecting CBM exploration and development potential, so that the evaluation results are more realistic and the prediction results are more accurate. However, at present, when using uncertainty measure to evaluate the grades of the objects to be measured, the recognition criteria of credible degree are mostly used for the attribute recognition. Because the credible degree $λ$ is artificially determined, the different researchers often have the different $λ$ values. This will lead to the different discriminant results, and even get the opposite result.

A comprehensive model using entropy weight and improved uncertainty measure to evaluate CBM exploration and development potential is presented in this paper. The model determines the weight of different factors based on entropy weight theory and the potential for CBM exploration and development based on optimization credible degree recognition criteria. This reduces the randomness in the evaluation to achieve a reasonable combination of subjective and objective measures, thereby yielding both accurate and reliable evaluation results. This novel systematic and comprehensive evaluation method provides a new idea for the evaluation of CBM exploration and development potential.

Geological background

The Muli coalfield occurs in the upstream portion of the Datong River basin at the junction of the Haibei Tibetan autonomous prefecture and the Haixi Mongolian Tibetan autonomous prefecture in Haibei and Haixi counties, respectively. The main part to the west of the Jiangcang River is in Muli village of Tianjun county ∼450 km from Xining city, the capital of the Qinghai province. This is the only coking coal resource-integrated exploration area in the Qinghai province. Total coal reserves and existing resources are 3.54 billion tons in the mining area, which represents the largest coal basin in Qinghai province. These coal reserves account for 8% of the total reserves in the Qinghai province. The Muli coalfield is found in the middle of the Central Qilian Depression Belt and is hosted by three synclines: the northern Dongku–Zhilongkou–Mole, central Hushan–Jiangcang–Riganshan–Haideer, and southern Juhugeng–Nurisi–Wailihada–Reshui synclines. The Muli coalfield can be divided into three sections by the westnorth and eastnorth faults, of which the western section has Juhugeng, Xuehuoli, Gushan, and Duosuogongma mining areas; the middle section has Dongku and Jiangcang mining areas; the eastern section has Wailihada, Reshui, Haideer, and Mole mining areas (Figure 1). The coalfield is an intracontinental-depression-type basin deposit and sedimentary rocks have characteristics of lake facies. Muli coalfield stratigraphic division belongs to Qilian division in Qilian formation area. The strata that exist in this area from old to new are: Lower Proterozoic, Middle Proterozoic, Ordovician, Silurian, Carboniferous, Permian, Triassic, Jurassic, Cretaceous, Paleogene, Neogene, Quaternary, etc. Among them, the most widely distributed strata are Triassic and Jurassic, and the sediments are completely preserved. Coal formed in the middle Jurassic and coal seams in the Muli coalfield are 7.94–95.51 m thick. Microscopic examination of samples indicates that the coal is mainly vitrinite, mostly between 40% and 80%. Coal is characterized by low and middle ash, high volatiles, and low to ultra-low sulfur contents. The coal is classified as medium and low rank.

Figure 1.

Sketch map showing distribution of different mining areas in the Muli coalfield, Qinghai Province (Shao et al., 2011; Liang, 2015).

Structures in the coal are mainly original, whereas granulated coal in the Wailiheda and Reshui mining areas is the result of fragmentation. Bright coal and clarain cleat developed in the area due to movement on faults and densities range from 3 to 30 pieces/5 cm, mainly in isolation net-cleat combination. Exogenous fractures serve to increase permeability of the coal seams. Permeability resulting from small holes and micro-pores is conducive to the adsorption of methane and creation of a gas reservoir. Porosity of the coal is generally high, mainly due to large and medium voids. A combination of good porosity and permeability allows for the exploitation of CBM. The Muli coalfield has a high capacity for gas storage as indicated by values of 17.25–24.04 m³/t for the Langmuir's Volume of balance water (Shao et al., 2008, 2011).

Methodology

Entropy weight theory

Thermodynamics defines entropy as an irreversible phenomenon in terms of the flow of energy and increasing randomness to the motion of ions or molecules. Entropy can represent uncertainty of different experimental results and characterize the disorder of a system in information theory. The entropy weight method determines weight of each evaluation index according to information contained in each index (Huang et al., 2012, 2014; Li et al., 2005; Zhang et al., 2012; Zhao and Zhang, 2016). As such, calculations are relatively simple and effectively use the data for all indices. This method is widely utilized for weight determination.

The initial evaluation matrix composed of $m$ evaluation indices and $n$ evaluation objects is $X_{ij} = [\begin{matrix} x_{11} & x_{12} & \dots & x_{1 n} \\ x_{21} & x_{22} & \dots & x_{2 n} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ x_{m 1} & x_{m 2} & \dots & x_{m n} \end{matrix}]$ (1)

All index values of $x_{i j}$ in the matrix $X_{i j}$ are normalized as follows $x_{i j}^{'} = \frac{x_{i j}}{\sum_{j = 1}^{n} x_{i j}}$ (2)

Therefore, the entropy of each evaluation index can be obtained as follows $E_{i} = \frac{\sum_{j = 1}^{n} x_{i j}^{'} \ln x_{i j}^{'}}{\ln n}$ (3)

The weight of each evaluation index can be calculated as follows $w_{i} = \frac{1 - E_{i}}{\sum_{i = 1}^{m} (1 - E_{i})}$ (4)

In formula (4), $w_{i}$ is the weight of the index and when $\sum_{i = 1}^{m} w_{i} = 1$ , this result illustrates that the greater the entropy weight, the greater the effect of the index. Therefore, an index that contains and transmits greater amounts of information will have a greater impact on the final evaluation decision.

Uncertainty measure theory and its optimization

Uncertainty measure of a single index

The index space $X = {x_{1}, x_{2}, \dots, x_{n}}$ is made up of $n$ objects (e.g., $x_{1}$ , $x_{2}$ ,…, $x_{n}$ ) to be classified, or that have been classified. There are $m$ single evaluation index spaces for each object, with $I = {I_{1}, I_{2}, \dots, I_{m}}$ and $x_{i}$ can be represented as a m-dimensional vector $x_{i} = {x_{i 1}, x_{i 2}, \dots, x_{i m}}$ . The factor $x_{i}$ has $p$ assessment degrees and the assessment degree space $U = {C_{1}, C_{2}, \dots, C_{p}}$ , where $C_{k}$ expresses the $k$ degree. The $k$ degree is higher than the $k + 1$ degree, as $C_{k}$ > $C_{k + 1}$ , and ${C_{1}, C_{2}, \dots, C_{p}}$ is labeled an ordered partition class of the evaluation space $U$ .

The single index measure function $μ_{i j k} = μ (x_{i j} \in C_{k})$ $(i = 1, 2, \dots, n; j = 1, 2, \dots, m; k = 1, 2 \dots, p)$ is constructed according to the definition of uncertainty measure. This function is used to calculate each index measure value $μ_{i j k}$ of the evaluation factor $x_{i}$ . The matrix ${(μ_{i j k})}_{m \times p}$ is labelled a single index evaluation matrix, and ${(μ_{i j k})}_{m \times p} = [\begin{matrix} μ_{i 11} & μ_{i 12} & \dots & μ_{i 1 p} \\ μ_{i 21} & μ_{i 22} & \dots & μ_{i 2 p} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ μ_{i m 1} & μ_{i m 2} & \dots & μ_{i m p} \end{matrix}]$ (5)

Multiple indices comprehensive measure

By using the index weight determined by entropy weight theory, the multi-index comprehensive measure of evaluating object, $μ_{i k} = \sum_{j = 1}^{m} ϖ_{j} μ_{i j k}$ $(i = 1, 2, \dots, n; j = 1, 2, \dots, m; k = 1, 2 \dots, p)$ is obtained. When $0 \leq μ_{k} \leq 1, \sum_{k = 1}^{p} μ_{i k} = 1$ , then $μ_{i k}$ is an uncertainty measure. The factor ${μ_{i 1}, μ_{i 2}, \dots, μ_{i p}}$ is a multi-index comprehensive evaluation measure vector of $x_{i}$ .

Recognition criteria of credible degree

If $C_{1} > C_{2} > \dots > C_{p}$ , this introduces credible degree recognition criteria. Credible degree is represented by $λ$ and when $λ \geq 0.5$ , and a value of $λ = 0.6$ or 0.7 is assigned. Then the factor $k_{0} = \min (k : \sum_{l = 1}^{k_{p}} μ_{i l} \geq λ, 1 \leq l \leq k)$ is considered to belong to $C_{k_{0}}$ (He et al., 2013, 2014, 2015; Liu et al., 1997, 1999).

From the above theory, it can be seen that $λ$ is artificially determined within a given range, and the artificial subjective factors have a greater influence on result. Through the study of literatures that adopts recognition criteria of credible degree as an attribute recognition criterion, it is found that when the $λ$ values are different, the discriminant results are not same, and sometimes even the opposite judgment or classification results are obtained.

Improved recognition criteria of credible degree

In order to reduce the error caused by artificial selection of $λ$ , the recognition criteria of credible degree are optimized by distance discriminant. The basic idea of distance discriminant analysis is to compare the minimum distance between the sample and the population and determine which population it belongs to. $Q_{1} = (1, 0, \dots, 0), Q_{2} = (0, 1, \dots, 0), \dots Q_{k} = (0, 0, \dots, 1)$ is set the uncertainty measure of each classification level in the hierarchical space $U$ , $d_{k}$ is the Euclidean distance from the multiple indices comprehensive measure $μ_{i k}$ to the classification level $Q_{k}$ , and ${\begin{matrix} d_{1} = \sqrt{{(u_{i 1} - 1)}^{2} + {(u_{i 2} - 0)}^{2} + \dots + {(u_{i k} - 0)}^{2}} \\ d_{2} = \sqrt{{(u_{i 1} - 0)}^{2} + {(u_{i 2} - 1)}^{2} + \dots + {(u_{i k} - 0)}^{2}} \\ \begin{matrix} ⋮ & ⋮ & ⋮ \end{matrix} \\ d_{k} = \sqrt{{(u_{i 1} - 0)}^{2} + {(u_{i 2} - 0)}^{2} + \dots + {(u_{i k} - 1)}^{2}} \end{matrix}$ (6)

The classification level of the objects $x_{i}$ to be evaluated is $K = \min d_{i} (1 \leq i \leq k; k = 1, 2, \dots, p)$ (He et al., 2017; Jin et al., 2017; Wan, 2004).

Order arranging

The assignment of $x_{i}$ to an evaluation level may require ordering $x_{i}$ based on its degree of importance. If $C_{1} > C_{2} > \dots > C_{p}$ , the command value of $C_{l_{0}}$ is $n_{l_{0}}$ . Then $n_{l_{0}} > n_{l + 1}$ and $q_{x_{i}} = \sum_{l = 1}^{p} n_{l} μ_{i l}$ , where $q_{x_{i}}$ is the uncertainty importance degree of evaluation, and the factor $x_{i}$ , $q = {q_{x_{1}}, q_{x_{2}}, \dots, q_{x_{p}}}$ is labelled the uncertainty-importance vector. The importance of $x_{i}$ activity is ordered according to the value of $q_{x_{i}}$ .

Determination of evaluation indices

CBM is the gas associated with coal that occurs, adsorbed onto the surface of coal matrix particles and within micro-pores of coal. Different physical and chemical functions are involved in the process of coalbed gas generation, migration, enrichment, and accumulation. These factors and the local geology create complexity in geological indices affecting the development of coalbed gas. A comparison of coalbed gas indicates the gas content in high-rank coal is greater than in medium- and low-rank coal. The gas content of the low-rank coal is generally low and its pure gas content no longer really reflects the coal reservoir. Therefore, the gas content is not used as an evaluation parameter of CBM resource potential in medium- and low-rank coal.

Multiple indices related to the enrichment and high production of CBM in the Muli coalfield are considered in the following evaluation (Busch and Gensterblum, 2011; Chattaraj et al., 2016; Faiz et al., 2007; Han et al., 2008; Shao et al., 2008). Each index is subdivided into three aspects, which are gas generation potential, reservoir physical properties, and capping performance. Individual aspects are determined by multiple parameters. Qualitative indices are evaluated by semi-quantitative methods, and quantitative indices are evaluated using measured values. The criteria used for the classification and valuation are presented in Table 1. Finally, the evaluation indices are assigned levels: I (very favorable block), II (more favorable block), III (favorable block), IV (unfavorable block), and V (extremely unfavorable block). The CBM geological characteristics in different mining areas of the Muli coalfield are presented in Table 2.

Table 1.

Classification standards for evaluation indices used in determining the exploration and development potential of coalbed methane resources.

Evaluation parameter	Evaluation index	Favorable grades
Evaluation parameter	Evaluation index	Very favorable ( $C_{1}$ )	More favorable ( $C_{2}$ )	Favorable ( $C_{3}$ )	Unfavorable ( $C_{4}$ )	Extremely unfavorable ( $C_{5}$ )
Gas generation potential	Accumulated coal thickness (m)	>30	20–30	10–20	5–10	<5
	Stability of coal seam	Very stable (5)	More stable (4)	Stable (3)	Unstable (2)	Very unstable (1)
	Maceral (content of vitrinite in) (%)	>90	70–90	50–70	30–50	<30
	Thermal maturity of coal seam R_omax (%)	>2.0	1.0–2.0	0.5–1.0	0.3–0.5	<0.3
	Resource abundance of coalbed methane (10⁸m³·km⁻²)	>2.0	1.0–2.0	0.5–1.0	0.3–0.5	<0.3
Reservoir physical properties	Cleat development level	Extremely developed (5)	More developed (4)	Developed (3)	Undeveloped (2)	Extremely undeveloped (1)
	Porosity (%)	>20	15–20	10–15	0–10	<0
	Permeability (mD)	>0.5	0.4–0.5	0.3–0.4	0.1–0.3	<0.1
	Langmuir's Volume (m³/t)	>20	15–20	10–15	4–10	<4
	Langmuir's Pressure (KPa/m)	>3	2–3	1–2	0–1	<0
Capping performance	Burial depth (m)	>1500	1000	500–1000	200–500	<200
	Caprock Lithology	Good: mainly mudstone or argillaceous limestone, fractures in the rock are poorly developed	Medium: mainly interlayered sand and mudstone, some fractures in the rock are developed	Medium: mainly and stone powder, some fractures in the rock are developed	Poor: mainly fine sandstone, some fractures are relatively developed	Extremely poor: mainly sandstone, coarse sandstone, gravel, and carbonate with developed fractures
	Geological Structure	Simple structure, few faults in the area and faults are mainly closed	Medium structure and fewer faults in the area	Structure is more complex and faults in the area are better developed	Complex structure, faults in the area are relatively developed and igneous rocks are present	Structure is extremely complex: the strata are inverted, faults in the area are very well developed, and igneous rocks are widespread
	Hydrogeology	Simple	Medium	General	Complex	Extremely complex, with better connectivity between the aquifer and coal seam

Table 2.

Data for CBM geological characteristics in different mining areas of the Muli coalfield.

Evaluation parameter	Evaluation index	Mining areas
Evaluation parameter	Evaluation index	Juhugeng	Jangcang	Wailihada	Reshui (Caidaer Minefield)	Haideer	Mole
Gas generation potential	Accumulated coal thickness (m)	32.59	95.51	7.83	56.70	27.69	7.94
	Stability of coal seam	More stable (3)	More stable (3)	Unstable (2)	More stable (3)	Unstable (2)	Unstable (2)
	Maceral (content of vitrinite in %)	62.23	76.15	70.70	55.75	52.14	46.55
	Thermal maturity of coal seam R_omax (%)	0.96	1.03	1.55	1.47	0.50	0.51
	Resource abundance of coalbed methane (10⁸m³·km⁻²)	0.69	1.04	0.80	1.46	1.97	1.02
Reservoir physical properties	Cleat development level	Developed (4)	Developed (4)	Not developed (2)	Not developed (2)	More developed (3)	More developed (3)
	Porosity (%)	3.58	4.70	10.43	10.43	13.70	13.70
	Permeability (mD)	0.78	3.33	0.14	0.14	10.60	10.60
	Langmuir's Volume (m³/t)	20.97	18.75	21.44	21.44	21.17	21.17
	Langmuir's Pressure (KPa/m)	3.49	3.35	2.34	2.34	13.33	13.33
Capping performance	Burial depth (m)	725	975	920	650	460	700
	Caprock lithology	Good (5)	Good (5)	Poor (2)	Poor (2)	Medium (4)	Medium (4)
	Geological structure	Structure is more complex (3)	Medium structure (4)	Structure is more complex (3)	Structure is more complex (3)	Structure is extremely complex (1)	Medium structure (4)
	Hydrogeology	Simple (5)	Simple (5)	Simple (5)	Simple (5)	Medium (4)	Medium (4)

Result analysis and discussion

Single index measure function

When an uncertainty measure set describes the phenomenon of uncertainty, it is necessary to construct a reasonable uncertainty measure function. According to the definition of single index measure function established by the classification standard in Table 1 and quantitative values presented in Table 2, single index measure functions are constructed to obtain the measure value of each evaluation index. Although there are many methods used to construct uncertainty measure function, this study utilizes the linear measure function. The specific single index measure functions are presented in Figures 2 to 10.

Figure 2.

Single index measure function of qualitative indices.

Figure 3.

Single index measure function of accumulated coal thickness.

Figure 4.

Single index measure function of maceral (content of vitrinite).

Figure 5.

Single index measure function of thermally matured coal seam and resource abundance of coalbed methane.

Figure 6.

Single index measure function of porosity.

Figure 7.

Single index measure function of permeability.

Figure 8.

Single index measure function of Langmuir's Volume.

Figure 9.

Single index measure function of Langmuir’s Pressure.

Figure 10.

Single index measure function of burial depth.

By using the single index measure functions presented in Figures 2 to 10 and data from Table 2, the single index evaluation matrix for six mining areas is calculated. The Juhugeng mining area serves as a case study for this paper, and the single index evaluation matrix is $μ_{A_{1}} = [\begin{matrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0.11 & 0.89 & 0 & 0 \\ 0 & 0.23 & 0.77 & 0 & 0 \\ 0 & 0 & 0.72 & 0.28 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0.72 & 0.28 \\ 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0.94 & 0.06 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \end{matrix}]$ (7)

Multiple index measure evaluation matrix calculation

When entropy weight theory is used to determine evaluation index weights, the weight of the evaluation index for the Juhugeng mining area is $ϖ_{1} = [\begin{matrix} 0.08 & 0.08 & 0.06 & 0.05 & 0.05 & 0.08 & 0.05 \end{matrix}$ $\begin{matrix} 0.08 & 0.08 & 0.08 & 0.07 & 0.08 & 0.08 & 0.08] \end{matrix}$ . Then considering the single index measure matrix and multiple-index calculation formula, the multiple index vector is $μ_{1} = ϖ_{1} \cdot μ_{A_{1}} = [\begin{matrix} 0.48 & 0.10 & 0.36 & 0.05 & 0.01 \end{matrix}]$ . The same process is used to calculate multiple index vectors for five other mining areas and the results are presented in Table 3.

Table 3.

Comparison of evaluation results between original and improved uncertainty measure model.

Mining areas	Comprehensive uncertainty measure					Discriminant of original credible degree recognition criteria				Optimization uncertainty measure distance					Discriminant results	Actual level
Mining areas	$C_{1}$	$C_{2}$	$C_{3}$	$C_{4}$	$C_{5}$	$λ = 0.6$	$λ = 0.7$	$λ = 0.8$	$λ = 0.9$	$d_{1}$	$d_{2}$	$d_{3}$	$d_{4}$	$d_{5}$	Discriminant results	Actual level
Juhugeng	0.48	0.10	0.36	0.05	0.01	$C_{3}$	$C_{3}$	$C_{3}$	$C_{3}$	0.64	1.08	0.81	1.13	1.16	$C_{1}$	$C_{1}$
Jiangcang	0.43	0.33	0.16	0.07	0.01	$C_{2}$	$C_{2}$	$C_{3}$	$C_{3}$	0.68	0.82	1.00	1.09	1.14	$C_{1}$	$C_{1}$
Wailihada	0.20	0.16	0.25	0.34	0.05	$C_{3}$	$C_{4}$	$C_{4}$	$C_{4}$	0.92	0.96	0.86	0.75	1.07	$C_{4}$	$C_{4}$
Reshui	0.26	0.22	0.28	0.21	0.03	$C_{3}$	$C_{3}$	$C_{4}$	$C_{4}$	0.85	0.89	0.82	0.91	1.09	$C_{3}$	$C_{3}$
Haideer	0.34	0.20	0.21	0.17	0.08	$C_{3}$	$C_{3}$	$C_{4}$	$C_{4}$	0.74	0.91	0.90	0.95	1.04	$C_{1}$	$C_{1}$
Mole	0.24	0.27	0.28	0.19	0.02	$C_{3}$	$C_{3}$	$C_{4}$	$C_{4}$	0.87	0.84	0.83	0.93	1.10	$C_{3}$	$C_{3}$

Credible degree recognition

In order to verify feasibility and accuracy of the model, credible degree $λ$ is taken 0.6, 0.7, 0.8, and 0.9 and compare with the attribute recognition optimization model by a distance discriminant. The results are shown in Table 3. From Table 3, when the credible degree $λ$ is taken 0.6, two groups of discriminant results are consistent with the actual situation; when the credible degree $λ$ is taken 0.7, three groups of discriminant results are consistent with the actual situation; when the credible degree $λ$ is taken 0.8 or 0.9, only one group of discriminant results is consistent with the actual situation. The results show that when the credible degree $λ$ is different, it has a great influence on the accuracy of the discriminant results. Comparing the improved method with the original method in Table 3, it can be seen that when the credible degree is not the same, the discriminant results have a large fluctuation. Therefore, the discriminant results of the recognition criteria of credible degree are largely influenced by the subjective selection.

After using the distance discriminant to improve, the distance between the multiple indices comprehensive measure and the discriminant level is used to divide the attribution of the sample to be measured, so as to avoid the influence of human factors on the discriminant results, and make the model more objective. All the results are consistent with the actual situation by the improved model. The accuracy of discriminant results is better than that of the model using recognition criteria of credible degree as the attribute recognition.

Order arranging of favorable grade

As indicated by the order formula, and because $C_{1} > C_{2} > C_{3} > C_{4} > C_{5}$ , take $n_{l} = 12 - 2 q$ , $1 \leq q \leq 5$ , then $q = [\begin{matrix} q_{1} & q_{2} & q_{3} & q_{4} & q_{5} & q_{6} \end{matrix}] = [\begin{matrix} 7.98 & 8.2 & 6.24 & 6.94 & 7.1 & 7.04 \end{matrix}]$ . This allows for a comparative ranking of the favorable grade calculated to represent the exploration and development potential of CBM in six mining areas. The Jiangcang mining area has the highest favorable grade, followed in descending order by the Juhugeng, Haideer, Mole, Reshui, and Wailihada mining areas. Evaluation results indicate that the Jiangcang, Juhugeng, and Haideer mining areas are the most favorable areas; the Mole and Reshui mining areas are favorable areas; and the Wailihada mining area is an unfavorable area. Prediction results on the exploration and development potential of CBM in Muli coalfield are shown in Figure 11. These results indicate that the Jiangcang mining area of the Muli coalfield may be prioritized for the exploration and development of CBM.

Figure 11.

Prediction on the exploration and development potential of CBM in the Muli coalfield.

Conclusions

In the uncertainty measure model, the attribute recognition using the credible degree criteria is easily affected by the subjective factors, which leads to large difference in the classification or evaluation results. The original attribute recognition criterion is optimized by the idea of distance discriminant method, and the optimization uncertainty measure model is established.

A mathematical model, based on entropy weight and improved uncertainty measure theory, was developed using influence factors and classification criteria to determine the exploration and development potential for CBM. In this model, the uncertainty measure function was established using uncertainty measure theory, evaluation index weights are based on entropy weight theory, and optimization credible degree recognition criteria were used to assess the potential for CBM exploration and development. Favorable grades for different mining areas were calculated using all of these data.

The Jiangcang, Juhugeng, and Haideer mining areas of the Muli coalfield are a priority area for the exploration and development of CBM. Favorable areas are the Mole and Reshui mining areas, but the Wailihada mining area is an unfavorable area.

The results of this study indicate that the entropy weight and improved uncertainty measure evaluation model is more scientific, objective, and reasonable than previous approaches. This provides a new method for assessing CBM exploration and development potential.

Footnotes

Acknowledgements

We gratefully acknowledge the thorough and constructive feedback provided by the editor and the anonymous reviewer.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This work was financially supported by the Natural Science Foundation of Shaanxi Province (2016JM4001) and the Special Fund for Basic Scientific Research of Central Colleges (310827173702),the open fund for State Key Laboratory of Water Resources Protection and Utilization in Coal Mining (SHJT-16–30.19),and China State Scholarship Fund ([2017]3105).

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The evaluation of potential for the exploration and development of coalbed methane resources based on an improved uncertainty measure optimization model

Abstract

Keywords

Introduction

Geological background

Methodology

Entropy weight theory

Uncertainty measure theory and its optimization

Uncertainty measure of a single index

Multiple indices comprehensive measure

Recognition criteria of credible degree

Improved recognition criteria of credible degree

Order arranging

Determination of evaluation indices

Result analysis and discussion

Single index measure function

Multiple index measure evaluation matrix calculation

Credible degree recognition

Order arranging of favorable grade

Conclusions

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

References