A Risk Assessment Model of Coalbed Methane Development Based on the Matter-Element Extension Method

Abstract

Coalbed methane development represents a complex system engineering operation that involves complex technology, many links, long cycles, and various risks. If risks are not controlled in a timely and effective manner, project operators may easily cause different levels of casualties, resource waste and property loss. To evaluate the risk status of coalbed methane development projects, this paper constructs a coalbed methane development risk assessment index system that consists of six first grade indexes and 45 second grade indexes. The weight of each index is calculated based on the structure entropy weight method. Then, a theoretical model for risk assessments of coalbed methane development is established based on the matter-element extension method. Finally, the model is applied to analyze a coalbed methane development project in the southern Qinshui Basin of China. The results show that the overall risk level of the coalbed methane development project is Grade II, indicating that the overall risk of the project is small, but the local risk of the project needs to be rectified in time. The assessment results are consistent with the actual operation of the project, indicating that the established risk assessment model has good applicability and effectiveness.

1. Introduction

With the rapid development of the global economy and the continuous advancement of urbanization, national dependence on black fossil energy, such as coal and oil, has increased. However, this increased dependence has caused excessive emissions to the atmosphere of toxic and harmful substances, such as carbon dioxide, sulfur dioxide, carbon monoxide and soot. These problems have caused environmental pollution problems, such as greenhouse effects, acid rain and haze, which have seriously affected the quality of life and health of residents. The above situation has received the attention of many actors, including the Chinese government. To achieve a balance between economic development and environmental protection, China’s energy use structure is changing to a pattern of “high efficiency, low energy consumption, low pollution and low emissions” under the leadership of the government [1].

In this context, coalbed methane (CBM) has become a prominent resource. CBM is mainly composed of methane that is stored in coal seams, adsorbed on the surface of coal matrix particles, partially free in coal pores or dissolved in coal seam water hydrocarbon gas. It is an associated mineral resource of coal and unconventional natural gas, and it is also a clean and high-quality energy source. China is a large coal mining country that experiences frequent gas explosions [2]. Since 1949, 126 severe gas explosion accidents (defined as killing 30 or more people in one accident) have occurred, and 7502 people have died [3]. These accidents have not only caused serious casualties and property losses, but have also had a serious negative impact on society [4,5]. The development of CBM can not only improve environmental pollution [6], but also fundamentally reduce the methane content in the coal seam, which is beneficial to reducing the occurrence of coal mine gas explosions [7,8,9]. These advantages have driven CBM development as a component of the new energy industry and ushered it into a golden development period [1]. However, CBM development represents a complex system engineering operation that involves complex technology, many links, long cycles, and various risks. CBM development is highly susceptible to various risks, such as economic, legal, technological, and management risks, and risk control failure can result in casualties, resource waste and property losses. To avoid these risks and promote the steady development of the CBM industry, it is necessary to first understand and perceive the risks throughout the life cycle of CBM development via risk assessment research.

At present, achievements have been made in the research on CBM development risk assessment. Roadifer et al. [10] evaluated the future trends and risks of CBM development and identified the key factors affecting CBM reserves and productivity by combining experimental and mathematical-statistical methods. Senthi et al. [11] used Monte Carlo simulations and the hypercube model to evaluate the economic risks faced by the CBM industry. Chen et al. [12] also used the Monte Carlo simulation method to establish a risk transformation process model of the main uncertain factors in the CBM economy. Zhang et al. [13] determined the optimal index weights using the optimized combination entropy method and the triangular fuzzy number method and established a CBM development potential assessment model. Acquah-Andoh et al. [14] explored the best schemes for optimizing a company’s revenue share for CBM development contracts based on factor analysis, discounted cash flow and parameter sensitivity analysis and found that the best scheme can distribute the economic risks of CBM development between governments and contractors. Luo et al. [15] used the net present value method to evaluate the economics of CBM production in China and found that the CBM price, productivity and operating costs are the three main factors affecting the economic feasibility of CBM development. Mares et al. [16] found that the uncertainty of adsorption capacity and desorption capacity were two important factors affecting the commercial development of CBM development, and their study provides a reference for the economic risk assessment of CBM development. Mu et al. [17] believed that three aspects are of great significance for avoiding CBM development risks: Pre-evaluation of CBM development, geological and gas reservoir engineering research and engineering technological innovation. Kirchgessne et al. [18] believed that safety and environmental factors also affect the economic benefits of CBM recovery. Su et al. [19] improved the discounted cash flow method by performing a hierarchical differentiation evaluation, staged evaluation and dynamic evaluation. It is also believed that production has the greatest impact on the economics of CBM development.

In summary, although scholars have made some achievements in the research on CBM development risks, the following shortcomings are observed:

(1)

Most studies focus on economic risk factor analyses of the national CBM industry. At present, risk assessment research for CBM development projects has not provided a reference for investors, insurance companies and CBM development operators.

(2)

Although several researchers have studied the risk of CBM development projects, the research depth was insufficient because the studies only determined the weight of the CBM risk assessment indicators. These studies used the weights to identify the main risk factors of CBM development, but failed to quantitatively measure the overall risk levels of CBM development projects and calculate the membership degree of each bottom index.

(3)

In terms of the construction of the indicator system, the above studies lack a systematic and comprehensive indicator selection process and did not cover the life cycle of CBM development, including geological exploration, drilling, gathering, and market applications. Therefore, the research results have a certain one-sidedness.

To fill the above gaps and achieve a reasonable assessment of the risk status of coalbed methane development projects, this paper will construct a risk assessment model for coalbed methane development. First, this paper seeks to construct a complete risk assessment index system for CBM development, including the laws, regulations and policies, resource characteristics, engineering technology and organizational management, according to the risk characteristics involved in the life cycle of CBM development.

Second, to scientifically determine the weight of each index, the weight calculation method should be chosen reasonably. The AHP, Delphi method and expert experience are commonly used methods to determine the index weights in risk assessment, and the AHP is the most widely used method [20]. However, the disadvantage of AHP is that if the index system contains a large number of indexes, it will greatly increase the workload of experts, which affects the acquisition of the judgment matrix, and thus, affects the accuracy of the weight calculation. Compared with the AHP, the structure entropy weight method (SEWM) can reduce a large amount of the computational workload and obtain more accurate results in the case of a large number of indexes. The SEWM combined the methods of subjective and objective assignments, as well as qualitative and quantitative analysis [21]. The main steps of the SEWM include: (1) Collecting experts’ comments and forming the typical order; (2) analyzing the blind degree (uncertainty) of indexes; (3) normalized treatment of indexes; and (4) determining the index weight of each layer. Please refer to Section 2.2 for the specific calculation process.

Third, scientifically assess the risk of CBM development, and the assessment method should be rationally selected. The risk assessment method in this paper is based on the matter-element extension method (MEEM). Because MEEM is a method for multi-index comprehensive assessment and mainly based on the extrinsic matter-element model, extension set and correlation function theory [22], the method can judge the membership level of things according to different characteristics of the elements and less data and can avoid the randomness and subjectivity of the evaluation process to a certain extent. It is a combination of qualitative and quantitative methods. At present, this method has achieved good results in risk assessment in many fields, such as oil exploitation [23], tailings pond [24], and building fire [25]. The main steps of the MEEM include the following: (1) Determining the classical domains, joint domains, and matter elements; (2) calculating the correlation degrees; (3) assessing multi-level extension; and (4) classifying risk. Please refer to Section 2.3 for the specific calculation process. Finally, this paper will conduct a case study to verify the feasibility of the risk assessment model.

The main contents of this paper include the following parts: Section 1 introduces the research significance, research purposes, literature review and current deficiencies in the field of coalbed methane development risk research. Section 2 introduces the research steps of the article, constructs the risk assessment index system of coalbed methane development, introduces the calculation steps of the structural entropy weight method and uses this method to calculate the index weight, and then introduces the calculation process of the matter-element extension method. Section 3 conducts a case study to verify the validity of the evaluation model. Section 4 analyses and discusses the assessment results. Section 5 summarizes the conclusions of the article.

2. Methodology

This study follows four steps: (1) The key risk factors involved in the life cycle of CBM development were identified through literature analysis, field investigation, legal norm inquiry and expert consultations. Thus, the risk assessment index system of CBM development was determined; (2) The SEWM was used to determine the weight of each index; (3) Based on the MEEM, a theoretical model of risk assessment was constructed. The risk classification rules were determined; (4) A case study was implemented. The main research steps involved in this paper are shown in Figure 1.

The four steps are described as follows:

Step 1: Build a targeted risk assessment index system for CBM development. First, the status quo of risk assessment and the key influencing risk factors of CBM development were achieved through on-site investigation, reading relevant literature and visiting the insurance company and a third-party risk assessment institution. On this basis, a preliminary risk assessment index system was established. Some experts from consulting organizations, management departments, and research institutions engaged in CBM development were invited to evaluate the preliminary index system. According to the experts’ suggestions, this system mainly focused on the risks involved in geological resource exploration, drilling and drainage, gathering and transportation and market operations. Six main aspects, namely, laws and policies, resource characteristics, engineering technology, economic operation, organization and management, and safety and emergency protection, were covered. Finally, the first-level indexes were refined to the second-level indexes; thus, the risk assessment index system used in the CBM development was established.

Step 2: After the index system was determined, an index weight was assigned to all indexes in each layer. However, using the traditional analytic hierarchy process (AHP) method to assign the index weights would greatly increase the experts’ workload. Therefore, this paper introduced a new method, the SEWM, to assign the index weights. This method combines the methods of subjective and objective assignments via qualitative and quantitative analyses. The detailed principles and application method of the SEWM will be explained in Section 2.2.1.

Step 3: For quantitative risk assessment, this paper established a theoretical model of risk assessment based on the MEEM. The model covers four parts: (1) Determining classical domains, sections, and matter elements; (2) calculating correlation degrees; (3) assessing multi-level extension; and (4) classifying risk. The detailed calculation steps will be described in Section 2.3.

Step 4: Case study. A CBM development project in the southern part of the Qinshui Basin in China was chosen for the case study to verify the feasibility of the assessment system.

2.1. Construction of the CBM Development Risk Assessment Index System

2.1.1. Principle

To reflect the risks of CBM development accurately and objectively, the scientific basis, guidance, operability, systematic process, comparability and comprehensiveness were considered to establish the index system in this paper.

2.1.2. Construction of Index System

Life cycle theory has been widely used in many fields, such as economics [26], environmental research [27], and management research [28]. The basic meaning of the life cycle can be understood as the whole process from “cradle to grave”. For a product, the life cycle is the process of returning to nature from nature, which includes not only raw material collection and processing, but also the product storage, transportation and sales. According to the above definition, this paper divides the life cycle of CBM development into three main stages: Resource exploration, resource exploitation, and gathering and market operation. The risk characteristics of these three stages were analyzed, and the risk factors were summarized into the following six categories: (1) Risks of laws, regulations and policies; (2) risks of resource characteristics; (3) risks of engineering and technology; (4) risks of economic operations; (5) risks of organization and management; and (6) risks of safety and emergency protection.

Second, these six types of risks are used as first grade indexes, which are then refined to second grade indexes through an on-site investigation and a literature review [10,11,12,13,15,16,17,18,19,29,30,31,32,33,34,35,36,37] and related laws and regulations. The laws and regulations include the “Mineral Resources Law of the People’s Republic of China” [38], “Coalbed Methane Industry Policy” [39], “Safety Production Law of the People’s Republic of China” [40], and “Hazardous Chemicals Safety Management Regulations” [41]. Third, the index system was revised through expert consultation. Finally, the assessment index system of CBM development risk was determined (Figure 2), and it consisted of six first grade indexes and 45 s grade indexes. For a detailed index analysis, please refer to Appendix A.

2.2. Determination of Index Weights

To accurately calculate the weight of each index, a reasonable weight calculation method should be selected. The AHP, Delphi method and expert experience are commonly used methods to determine the index weights in risk assessment, and the AHP is the most widely used method [20]. Because many indexes are included in the proposed index system, the use of the AHP to determine the index weight would entail a large workload, which would not be conducive to acquiring the judgement matrix. Therefore, this paper introduced the SEWM to determine the index weight of the CBM development risk assessment system. The SEWM combines subjective and objective assignment methods, as well as qualitative and quantitative analyses. This method can reduce the calculation workload and achieve higher accuracy, especially for the many indexes in the CBM development risk assessment system.

2.2.1. Principle of the SEWM

The basic idea of the SEWM is to analyze the indexes of the assessment system and the interrelationship between them and then to classify the indexes into independent hierarchical grades. The execution steps are as follows.

(1) Collection of experts’ comments

Several experts were invited to complete the questionnaire form (

Table 1. Collection of experts’ comments.

	Index1	Index2	Index3	Index4	Index5	…
Expert1
Expert2
Expert3
Expert4
…

) in accordance with the procedure and requirements of the Delphi method [42]. The experts ranked the importance of each index independently according to their own knowledge and experience. The indexes were ranked from high to low according to their importance; for example, mark ‘‘1” represented ‘‘most important”, mark ‘‘2” represented ‘‘more important”, mark ‘‘3” represented ‘‘important”, and so on. Some indexes could be recognized as equally important, and the final rank of the indexes could be discussed by the experts.

(2) Blind degree (uncertainty) analysis

The potential deviation and uncertainty of the experts’ comments on the index ranks might arise, due to noisy data. To eliminate noisy data and reduce uncertainty, the qualitative judgement conclusion from the experts should be statistically analyzed and addressed. To reduce the uncertainty of the experts’ ranking, the entropy value was calculated by the entropy theory. The execution steps are shown below [21,43].

Supposing that k experts were invited to take the questionnaire survey, then k questionnaire forms would be returned, and every form would be recognized as an index set and marked as R={r₁, r₂,…r_k}; where r_i refers to the expert ranking array denoted by {a_i1, a_i2,…a_in}(i=1, 2,…k) and a_i1, a_i2,…a_in can be any natural number from {1, 2,…n}. As previously mentioned, ‘‘1” represents the highest level of importance. The index sort matrix obtained from the k table is shown as matrix A.

$$A=\left[\begin{array}{ccccc}{a}_{11}& a_{12}& a_{13}& \cdots & a_{1n}\\ a_{21}& a_{22}& a_{23}& \cdots & a_{2n}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ a_{k1}& a_{k2}& a_{k3}& \cdots & a_{\mathrm{kn}}\end{array}\right]$$

(1)

where a_ij represents the ith expert’s evaluation of the jth index.

The qualitative ranking result could be transformed into quantitative results by a membership function, which can be defined as follows:

$${\chi \left(I\right)=-\lambda p}_n{\left(I\right)\mathrm{lnp}}_n\left(I\right),$$

(2)

where $p_n\left(I\right)=\frac{m-I}{m-1},\lambda =\frac{1}{\ln (m-1)}$, which can be input into Equation (2):

$$\chi \left(I\right)=-\frac{1}{\ln (m-1)}(\frac{m-I}{m-1}\left)\ln \right(\frac{m-I}{m-1}).$$

(3)

Dividing both sides by (m-I)/(m-1), assume that 1-χ(I)/(m-I)/(m-1)=μ(I). Then,

$$\mu \left(I\right)=\frac{\ln (m-I)}{\ln (m-1)},$$

(4)

where I is defined as the qualitative ranking number of a certain index evaluated by an expert. For example, a set of qualitative ranking numbers 5, 2, 3, 4, 1 for the five indexes r₁, r₂, r₃, r₄, r₅ was evaluated by one expert. Thus, index r₅ was the most important, because I = 1. M is the transformation parameter and defined as m = j + 2, and j is the number of indexes.

The qualitative ranking number I is input into Equation (4) to obtain the quantitative transformation value of b_ij. B_ij = μ(a_ij) is the membership degree of the qualitative ranking number I, and the matrix B = (b_ij)_k*n is defined as the membership degree matrix. A new parameter, average understanding degree b_j, was introduced to present the consistency degree of the evaluation of index r_j by k experts; its calculation is as follows:

$$b_j=\frac{b_{1j}{+b}_{2j}+\cdots {+b}_{\mathrm{kj}}}{k}.$$

(5)

Blind understanding degree σ_j is defined as the uncertainty of the evaluation of index r_j by k experts,

$${\sigma }_j=\left|\left\{\left[\max \left(b_{1j}{,b}_{2j},\cdots b_{\mathrm{kj}}\right){-b}_j\right]+\left[b_j{-\min (b}_{1j}{,b}_{2j},\cdots b_{\mathrm{kj}})\right]\right\}/2\right|.$$

(6)

The global understanding degree X_j is defined as the degree of the evaluation of every index r_j by all k experts invited,

$$X_j=b_j(1-{\sigma }_j).$$

(7)

(3) Normalized treatment

To obtain the weight of index r_j, Equation (7) needs further normalized treatment,

$${\omega }_j{=\chi }_j/{{\displaystyle \sum }}_{j=1}^k{\chi }_j.$$

(8)

Obviously, ω_j > 0 and ${\displaystyle \sum }_{j=1}^k{\omega }_j$=1. The ω=(ω₁, ω₂,…ω_j) was expressed as the weight vector of the index set R=(r₁, r₂,…r_j).

2.2.2. Calculation of the Index Weight

In this study, a total of 12 experts who have worked in the CBM development industry for a long time, including three experts in CBM resource exploration, three experts in CBM mining technology, two experts in coal economy, two experts in energy policy, and two managers of CBM development enterprises. To more comprehensively formulate risk assessment criteria from multiple perspectives, the experts were randomly divided into four groups, each with three persons. In this way, the diverse understandings of various research fields could be fully explored, and different knowledge and experience could be used to perform a qualitative evaluation of each assessment index.

The weight determination of the indexes in the first grade was taken as an example:

(1)

The rank results from the four groups of experts were collected in

Table 2. Expert ranking results.

	Index r 1	Index r 2	Index r 3	Index r 4	Index r 5	Index r 6
Group A	4	1	2	3	6	5
Group B	3	1	1	2	5	4
Group C	3	1	2	3	5	4
Group D	4	2	1	3	6	5

:

(2)

The obtained rank matrix A:

$$A=\left[\begin{array}{cccccc}4& 1& 2& 3& 6& 5\\ 3& 1& 1& 2& 5& 4\\ 3& 1& 2& 3& 5& 4\\ 4& 2& 1& 3& 6& 5\end{array}\right]$$

(3)

The calculated membership matrix B was based on Equation (4) and rank matrix A, and m was set as 8.

$$B=\left[\begin{array}{cccccc}0.712& 1.000& 0.921& 0.827& 0.356& 0.565\\ 0.827& 1.000& 1.000& 0.921& 0.565& 0.712\\ 0.827& 1.000& 0.921& 0.827& 0.565& 0.712\\ 0.712& 0.921& 1.000& 0.827& 0.356& 0.565\end{array}\right]$$

(4)

The average degree of understanding of a particular dimension from all experts:

$$b_j=\frac{b_{1j}{+b}_{2j}{+b}_{3j}{+b}_{4j}}{4}=(0.770,0.980,0.960,0.851,0.460,0.638).$$

(5)

Based on the previous results and Equations (5) and (6), the blind understanding degree σ_j for the indexes from all experts could be obtained. Then, the evaluation vector X could be calculated according to the blind understanding degree σ_j and Equation (7). Finally, the weight of each index could be achieved by the normalized treatment method. The calculated result of each parameter is shown in

Table 3. Weight distribution of the first grade index.

	Index r1	Index r2	Index r3	Index r4	Index r5	Index r6
Group A	4	1	2	3	6	5
Group B	3	1	1	2	5	4
Group C	3	1	2	3	5	4
Group D	4	2	1	3	6	5
Average cognition degree bj	0.770	0.980	0.960	0.851	0.460	0.638
bjmax	0.827	1.000	1.000	0.921	0.565	0.712
bjmax- bj	0.057	0.020	0.040	0.070	0.104	0.074
bjmin	0.712	0.921	0.921	0.827	0.356	0.565
bj- bjmin	0.057	0.059	0.040	0.023	0.104	0.074
σj	0.057	0.040	0.040	0.047	0.104	0.074
1-σj	0.943	0.960	0.960	0.953	0.896	0.926
Xj	0.726	0.941	0.922	0.811	0.412	0.591
Weight	0.165	0.214	0.209	0.184	0.094	0.134

. Similarly, the weight distribution of the second grade indexes can be obtained by refining. The index distribution is shown in

Table 4. Index weights and actual scores.

First Grade Indexes (ri)	Weight (ωi)	Second Grade Indexes (rik)	Weight (ωik)	Total Score	Actual Score (vik)
Laws, regulations and policies (r1)	0.165	Mineral rights and gas rights conflict (r11)	0.226	100	91
		Major licenses and approvals (r12)	0.235	100	88
		Foreign cooperation franchise (r13)	0.113	100	48
		Government financial subsidies (r14)	0.188	100	83
		Resource tax reform (r15)	0.118	100	86
		New energy policy (r16)	0.120	100	84
Resource characteristics (r2)	0.214	Gas content (r21)	0.160	100	79
		Permeability (r22)	0.173	100	82
		Reservoir pressure (r23)	0.160	100	89
		Porosity (r24)	0.124	100	76
		Hydrogeological conditions (r25)	0.124	100	86
		Coal seam area (r26)	0.075	100	74
		Coal seam thickness (r27)	0.067	100	81
		Buried depth (r28)	0.118	100	87
Engineering technology (r3)	0.209	Geological evaluation technique (r31)	0.170	100	86
		Extraction technology (r32)	0.158	100	74
		Development process technology (r33)	0.134	100	77
		Gas gathering technology (r34)	0.121	100	82
		Treatment technology (r35)	0.111	100	81
		Transportation technology (r36)	0.073	100	68
		Dynamic monitoring and analysis (r37)	0.098	100	78
		Drainage system (r38)	0.136	100	75
Economic operation (r4)	0.184	CBM price fluctuation (r41)	0.087	100	83
		Project cost (r42)	0.147	100	78
		Return on investment (r43)	0.134	100	76
		CBM production (r44)	0.145	100	72
		Macroeconomics (r45)	0.086	100	84
		Funds recovery (r46)	0.104	100	86
		External market resources (r47)	0.086	100	56
		External network resources (r48)	0.057	100	82
		Market demand (r49)	0.155	100	78
Organizational management (r5)	0.094	Organizational structure adaptability (r51)	0.270	100	85
		Management coordination and communication (r52)	0.181	100	79
		Process management (r53)	0.205	100	73
		Organizational management quality (r54)	0.115	100	82
		Resource allocation capability (r55)	0.229	100	74
Safety and emergency protection (r6)	0.134	Safety technology and equipment (r61)	0.151	100	75
		Hidden danger investigation and treatment (r62)	0.133	100	78
		Safety training and education (r63)	0.133	100	56
		Safety culture (r64)	0.062	100	72
		Safety investment (r65)	0.141	100	82
		Emergency plan (r66)	0.098	100	74
		Emergency drill frequency (r67)	0.088	100	54
		Emergency supplies reserve (r68)	0.095	100	63
		Emergency rescue team (r69)	0.100	100	76

. The detailed calculation processes are shown in Appendix B (

Table A2. Weight distribution of the second grade indexes of r _1.

	Index r 11	Index r 12	Index r 13	Index r 14	Index r 15	Index r 16
Group A	1	2	6	3	5	4
Group B	2	1	5	4	3	6
Group C	2	1	5	3	4	4
Group D	2	1	4	3	6	5
bj	0.941	0.980	0.549	0.798	0.615	0.586
bjmax	1.000	1.000	0.712	0.827	0.827	0.712
bjmax- bj	0.059	0.020	0.163	0.029	0.212	0.126
bjmin	0.921	0.921	0.356	0.712	0.356	0.356
bj- bjmin	0.020	0.059	0.193	0.086	0.259	0.230
σj	0.040	0.040	0.178	0.058	0.236	0.178
1-σj	0.961	0.961	0.822	0.943	0.765	0.822
Xj	0.904	0.941	0.451	0.752	0.470	0.482
Weight	0.226	0.235	0.113	0.188	0.118	0.120

,

Table A3. Weight distribution of the second grade indexes of r _2.

	Index r 21	Index r 22	Index r 23	Index r 24	Index r 25	Index r 26	Index r 27	Index r 28
Group A	2	1	3	4	5	7	7	6
Group B	3	1	2	5			8	6
Group C	3	2	1	6	4	8	7	5
Group D	1	2	3	4	6	7	8	5
bj	0.929	0.973	0.929	0.749	0.749	0.454	0.408	0.682
bjmax	1.000	1.000	1.000	0.815	0.815	0.500	0.500	0.732
bjmax- bj	0.071	0.027	0.071	0.067	0.067	0.046	0.092	0.051
bjmin	0.886	0.946	0.886	0.631	0.631	0.315	0.315	0.631
bj- bjmin	0.044	0.027	0.044	0.118	0.118	0.138	0.092	0.051
σj	0.057	0.027	0.057	0.092	0.092	0.092	0.092	0.051
1-σj	0.943	0.973	0.943	0.908	0.908	0.908	0.908	0.949
Xj	0.876	0.947	0.876	0.680	0.680	0.412	0.370	0.647
Weight	0.160	0.173	0.160	0.124	0.124	0.075	0.067	0.118

,

Table A4. Weight distribution of the second grade indexes of r _3.

	Index r 31	Index r32	Index r 33	Index r 34	Index r 35	Index r 36	Index r 37	Index r 38
Group A	1	2	4	5	3	7	6	4
Group B	1	3	2	6	4	8	7	5
Group C	2	1	3	4	7	6	5	3
Group D	1	2	5	4	3	7	6	3
bj	0.987	0.945	0.845	0.749	0.772	0.487	0.624	0.830
bjmax	1.000	1.000	0.946	0.815	0.886	0.631	0.732	0.886
bjmax- bj	0.013	0.055	0.101	0.067	0.114	0.144	0.109	0.056
bjmin	0.946	0.886	0.732	0.631	0.500	0.315	0.500	0.732
bj- bjmin	0.040	0.059	0.113	0.118	0.272	0.171	0.124	0.097
σj	0.027	0.057	0.107	0.092	0.193	0.158	0.116	0.077
1-σj	0.972	0.943	0.893	0.908	0.807	0.842	0.884	0.923
Xj	0.960	0.891	0.755	0.680	0.623	0.410	0.551	0.766
Weight	0.170	0.158	0.134	0.121	0.111	0.073	0.098	0.136

,

Table A5. Weight distribution of the second grade indexes of r _4.

	Index r 41	Index r42	Index r 43	Index r 44	Index r 45	Index r 46	Index r 47	Index r 48	Index r 49
Group A	8	2	4	3	7	5	6	9	1
Group B	6	1	2	3	8	7	4	5	1
Group C	5	1	3	2	4	6	7	8	2
Group D	7	3	4	2	6	5	8	9	1
bj	0.639	0.964	0.887	0.929	0.656	0.714	0.656	0.464	0.989
bjmax	0.778	1.000	0.954	0.954	0.845	0.778	0.845	0.778	1.000
bjmax- bj	0.139	0.036	0.067	0.0256	0.189	0.064	0.189	0.314	0.011
bjmin	0.477	0.903	0.845	0.903	0.477	0.602	0.477	0.301	0.954
bj- bjmin	0.162	0.061	0.042	0.026	0.179	0.112	0.179	0.163	0.034
σj	0.151	0.048	0.055	0.026	0.184	0.088	0.184	0.239	0.023
1-σj	0.850	0.952	0.945	0.974	0.816	0.912	0.816	0.761	0.978
Xj	0.543	0.918	0.838	0.905	0.535	0.651	0.535	0.354	0.966
Weight	0.087	0.147	0.134	0.145	0.086	0.104	0.086	0.057	0.155

,

Table A6. Weight distribution of the second grade indexes of r _5.

	Index r 51	Index r 52	Index r 53	Index r 54	Index r 55
Group A	1	3	4	5	2
Group B	1	2	3	4	2
Group C	2	4	1	5	3
Group D	1	4	2	5	3
bj	0.975	0.725	0.821	0.443	0.836
bjmax	1.000	0.898	0.898	0.613	0.898
bjmax- bj	0.025	0.174	0.077	0.170	0.062
bjmin	0.898	0.613	0.613	0.387	0.774
bj- bjmin	0.076	0.111	0.208	0.057	0.062
σj	0.051	0.143	0.143	0.113	0.062
1-σj	0.949	0.857	0.857	0.887	0.938
Xj	0.925	0.621	0.704	0.393	0.784
Weight	0.270	0.181	0.205	0.115	0.229

and

Table A7. Weight distribution of the second grade indexes of r _5.

	Index r 61	Index r62	Index r 63	Index r 64	Index r 65	Index r 66	Index r 67	Index r 68	Index r 69
Group A	1	2	4	8	3	5	6	7	7
Group B	2	3	4	8	1	5	5	7	6
Group C	1	4	2	9	3	7	8	6	5
Group D	1	3	2	8	1	7	6	5	4
bj	0.989	0.901	0.900	0.433	0.952	0.690	0.663	0.670	0.731
bjmax	1.000	0.954	0.954	0.477	1.000	0.778	0.778	0.778	0.845
bjmax- bj	0.011	0.053	0.055	0.044	0.048	0.088	0.115	0.108	0.114
bjmin	0.954	0.845	0.845	0.301	0.903	0.602	0.477	0.602	0.602
bj- bjmin	0.034	0.056	0.055	0.132	0.048	0.088	0.186	0.068	0.129
σj	0.023	0.055	0.055	0.088	0.048	0.088	0.151	0.088	0.122
1-σj	0.977	0.945	0.945	0.912	0.952	0.912	0.850	0.912	0.878
Xj	0.966	0.852	0.851	0.395	0.905	0.629	0.563	0.611	0.642
Weight	0.151	0.133	0.133	0.062	0.141	0.098	0.088	0.0953	0.100

.).

2.3. Assessment Model Construction

The goal of the MEEM is to use the degree of association of the extension set to determine the assessment level of the matter element feature. The MEEM is a method for comprehensive multi-index assessments, and it is mainly based on the extrinsic matter-element model, extension set and correlation function theory [22]. This method can judge the subordinate level of items according to their different characteristics with low data requirements and can avoid the randomness and subjectivity of the evaluation process to a certain extent. The MEEM combines qualitative and quantitative analyses and has achieved good results in risk assessment in many fields, such as oil exploitation [23], tailings pond [24], and building fire [25]. Based on the above advantages, this method is applied to research CBM development risk assessments.

The MEEM includes the following steps [44,45]: (1) According to the development of things and relevant reference materials, the characteristics of things are analyzed, the things are divided into several grades according to certain rules, the numerical range of each level is clarified, and a multi-index MEEM is established; (2) Using the correlation function to calculate the degree of association between the things to be evaluated and each assessment level; (3) Things have the highest degree of relevance to one of the levels, indicating that they are most consistent with that level. Next, the calculation process of the CBM development risk assessment model will be described in detail.

2.3.1. Determination of the Classical Domain, Joint Domain and Matter-Element Evaluation

The matter element uses the ordered triplet M = {C, R, V} as the basic element to describe things, where C is the name of the thing, R is the name of the feature, and V is the value taken by C for R [25].

(1) Determining the classical domain M_j

Let M_j be the classic domain of matter-element M:

$$M_j=\left(U_j{,R,V}_j\right)=\left(\begin{array}{ccc}{U}_j& r_1& \left(a_{j1}{,b}_{j1}\right)\\ & r_2& \left(a_{j2}{,b}_{j2}\right)\\ & ⋮& ⋮\\ & r_i& \left(a_{ji}{,b}_{ji}\right)\end{array}\right),$$

(9)

where U_j is the j risk level in the risk level domain U, V_j is the range of assessment index set R about the risk level U_j, and a_ji and b_ji are the lower and upper limits of the index r_i at the jth risk level, respectively.

(2) Determining the joint domain M_c

Let M_c be the joint domain of matter-element M:

$$M_c=\left(U,R,V_c\right)=\left(\begin{array}{ccc}U& r_1& (a_{c1},b_{c1})\\ & r_2& \left(a_{c2}{,b}_{c2}\right)\\ & ⋮& ⋮\\ & r_i& \left(a_{ci}{,b}_{ci}\right)\end{array}\right),$$

(10)

where V_c is the range of evaluation index set R about the risk level domain U, and a_ci and b_ci are the lower and upper limits of the index r_i at all risk levels, respectively.

(3) Determining the matter-element evaluation M_i

Let M_i be the matter-element evaluation of matter-element M:

$$M_i=(S_i,R_i,V_i)=\left(\begin{array}{ccc}{S}_j& r_{i1}& v_{i1}\\ & r_{i2}& v_{i2}\\ & ⋮& ⋮\\ & r_{ip}& v_{ip}\end{array}\right),$$

(11)

where S_i is the ith first grade index to be evaluated, R_i={ r_i1, r_i2, …, r_ip} is the second grade assessment index set for S_i, r_ip is the pth second grade assessment index of the ith first grade index, and V_i is the value of the second grade index R_i for S_i.

2.3.2. Calculating the Correlation Degree

By introducing the concept of distance in classical mathematics, the correlation function of the second grade index r_ik of the CBM development risk assessment on the risk level U_j is established. Therefore, the correlation degree K_j(r_ik) of the kth second grade index in the ith first grade index with respect to the risk level U_j is determined.

$$K_j\left(r_{ik}\right)=\{\begin{array}{cc}\frac{{\rho (v}_{ik}{,V}_j)}{\rho \left(v_{ik}{,V}_c\right){-\rho (v}_{ik}{,V}_j)}& \rho \left(v_{ik},V_c\right)-\rho (v_{ik},V_j)\ne 0\\ -\rho \left(v_{ik},V_j\right)-1& \rho \left(v_{ik}{,V}_c\right)-\rho \left(v_{ik}{,V}_j\right)=0\end{array},$$

(12)

where ρ$\left(v_{ik}{,V}_j\right)=\left|v_{ik}-\frac{a_{ji}+b_{ji}}{2}\right|-\frac{1}{2}\left(b_{ij}-a_{ji}\right)$, $\rho \left(v_{ik}{,V}_c\right)=\left|v_{ik}-\frac{a_{ci}{+b}_{ci}}{2}\right|-\frac{1}{2}\left(b_{cj}-a_{ci}\right)$, a_ci and b_ci are the lower and upper limits of the index r_i at all risk levels, respectively, and v_ik is the expert score for the second grade index r_ik.

2.3.3. Multi-Level Extension Assessment

(1) Primary assessment

Calculate the correlation matrix K(r_i) of the first indexes for each risk level:

$${K(r}_i)=({\omega }_{i1}{,\omega }_{i2},\cdots {,\omega }_{ip})\left[\begin{array}{cccc}{k}_1\left(r_{i1}\right)& k_2\left(r_{i1}\right)& \cdots & k_m\left(r_{i1}\right)\\ k_1\left(r_{i2}\right)& k_2\left(r_{i2}\right)& \cdots & k_m\left(r_{i2}\right)\\ ⋮& ⋮& & ⋮\\ k_1\left(r_{ip}\right)& k_2\left(r_{ip}\right)& \cdots & k_m\left(r_{ip}\right)\end{array}\right]=(k_j\left(r_i\right)),$$

(13)

where ω_i = (ω_ik) is the weight vector of the second grade indexes, and the calculation method is shown in Formulas (1)~(8); and K(r_ik) = (k_j(r_ik)) is the correlation degree matrix of the second grade indexes for each risk level.

(2) Secondary assessment

Determine the correlation degree matrix K(S) of the CBM development safety for each risk level.

$$K\left(S\right)=\left({\omega }_1{,\omega }_2,\cdots {,\omega }_j\right)\left[\begin{array}{cccc}{k}_1\left(r_1\right)& k_2\left(r_1\right)& \cdots & k_m\left(r_1\right)\\ k_1\left(r_2\right)& k_2\left(r_2\right)& \cdots & k_m\left(r_2\right)\\ ⋮& ⋮& & ⋮\\ k_1\left(r_p\right)& k_2\left(r_p\right)& \cdots & k_m\left(r_p\right)\end{array}\right]=(k_j\left(S\right)),$$

(14)

where ω = (ω_j) is the weight vector of the first grade indexes, and the calculation method is shown in formulas (1)~(8); a^®K(r) = (k(r_i)) is the correlation degree matrix of the first grade indexes for each risk level.

(3) Determining the risk level

According to the principle of maximum membership degree, the risk level corresponding to the maximum correlation degree in the correlation degree matrix K(S) of the CBM development for each risk level is the risk level of the assessment object. That is, when $max{k}_j{\left(S\right)=k}_j\left(S\right)$, with j = (1,2,3…n), the risk level of the assessment object is at level j.

2.3.4. Risk Classification

To scientifically measure the risk of CBM development and ensure the systematic nature and accuracy of the assessment results, this paper divides the risk level of CBM development into five grades according to the actual CBM development situation and the risk classification rules in the literature [25,46], as shown in

Table 5. Risk levels.

Risk Level	Score Range	Basic Characteristics
Ⅰ	(85, 100]	System operation condition is very good, risk is very low
Ⅱ	(70, 85]	System operation condition is good, risk is lower
Ⅲ	(50, 70]	System operation condition is mediocre, risk is mediocre
Ⅳ	(25, 50]	System operation condition is poor, risk is higher
Ⅴ	[0, 25]	System operation condition is very poor, risk is very high

. Notably, when the established risk assessment model has been tested by a large number of empirical tests, the risk classification criteria can be corrected by data feedback to make the criteria more sensitive.

3. Case Study

The southern part of the Qinshui Basin is one of the earliest areas for CBM exploration and development in China, and it has also attracted the most investment and research in CBM exploration and development in China [47]. The CBM storage conditions in this area are stable and have good development potential [48,49]. As a key breakthrough area for CBM exploration and development, many experts have carried out exploration and research work here, leading to the accumulation of a wealth of test and production data [50]. The experts have a deeper understanding of the characteristics of reservoir CBM accumulation, reservoir geological conditions and gas layer distribution. Therefore, this paper takes a CBM development project in this area as the research object and invited 5 experts, including 1 CBM exploration expert, 2 CBM mining technical experts, 1 energy policy expert and 1 project manager, to participate. Based on the engineering practice data of the project, the experts anonymously scored the actual operation status of each second grade index. The total score for each index is 100. In this paper, the actual scores of the second grade indexes of the CBM development project are obtained by calculating the average value, as shown in Table 4.

3.1. Determination of the Classical Domain, Joint Domain and Matter-Element Evaluation

Take the first grade index laws, regulations and policies (r₁) as an example to establish the matter-element M and determine its classical domain M_j, joint domain M_c and matter-element evaluation M_i. Similarly, classical domains, joint domains and matter-element evaluations of other first grade indexes can be obtained.

(1) Determining the classical domain M_j

The classical domains for each risk level are determined by Formula (9):

$$M_{\mathrm{I}}=(\begin{array}{ccc}{U}_{\mathrm{I}}& r_{11}& (85,100)\\ & r_{12}& (85,100)\\ & r_{13}& (85,100)\\ & r_{14}& (85,100)\\ & r_{15}& (85,100)\\ & r_{16}& (85,100)\end{array})M_{\mathrm{II}}=(\begin{array}{ccc}{U}_{\mathrm{II}}& r_{11}& (70,85)\\ & r_{12}& (70,85)\\ & r_{13}& (70,85)\\ & r_{14}& (70,85)\\ & r_{15}& (70,85)\\ & r_{16}& (70,85)\end{array}),$$

$$M_{\mathrm{III}}=(\begin{array}{ccc}{U}_{\mathrm{III}}& r_{11}& (50,70)\\ & r_{12}& (50,70)\\ & r_{13}& (50,70)\\ & r_{14}& (50,70)\\ & r_{15}& (50,70)\\ & r_{16}& (50,70)\end{array})M_{\mathrm{IV}}=(\begin{array}{ccc}{U}_{\mathrm{IV}}& r_{11}& (25,50)\\ & r_{12}& (25,50)\\ & r_{13}& (25,50)\\ & r_{14}& (25,50)\\ & r_{15}& (25,50)\\ & r_{16}& (25,50)\end{array}),$$

$$M_{\mathrm{V}}=(\begin{array}{ccc}{U}_{\mathrm{V}}& r_{11}& (0,25)\\ & r_{12}& (0,25)\\ & r_{13}& (0,25)\\ & r_{14}& (0,25)\\ & r_{15}& (0,25)\\ & r_{16}& (0,25)\end{array}),$$

(2) Determining the joint domain M_c

The joint domain M_c is determined by Formula (10):

$$M_c=\left(\begin{array}{ccc}U& r_{11}& (0,100)\\ & r_{12}& (0,100)\\ & r_{13}& (0,100)\\ & r_{14}& (0,100)\\ & r_{15}& (0,100)\\ & r_{16}& (0,100)\end{array}\right).$$

 (3) Determining the matter-element evaluation M_i

The matter-element evaluation M₁ of indexes r_1i is determined by Formula (11):

$$M_1=\left(\begin{array}{ccc}{S}_1& r_{11}& v_{11}\\ & r_{12}& v_{12}\\ & ⋮& ⋮\\ & r_{1p}& v_{1p}\end{array}\right)=\left(\begin{array}{ccc}{R}_1& r_{11}& 91\\ & r_{12}& 88\\ & r_{13}& 48\\ & r_{14}& 83\\ & r_{15}& 86\\ & r_{16}& 84\end{array}\right).$$

3.2. Calculating the Correlation Degree

Taking the correlation degree of the second grade index r₁₁ of the first grade index r₁ as an example, the calculation steps of the correlation degrees of the second grade indexes are obtained by Formula (12).

ρ(v₁₁,V₁)=|91 − (85 + 100)/2| − (100 − 85)/2 = − 6; ρ(v₁₁,V₂) = |91 − (70 + 85)/2| − (85 − 70)/2 = 6;

ρ(v₁₁,V₃) = |91 − (50 + 70)/2| − (70 − 50)/2 = 21; ρ(v₁₁,V₄)=|91 − (25 + 50)/2| − (50 − 25)/2 = 41;

ρ(v₁₁,V₅) = |91 − (25 + 0)/2| − (25 − 0)/2 = 66; ρ(v₁₁,V_c) = |91 − (0 + 100)/2| − (100 − 0)/2 = − 9;

k₁(r₁₁) = ρ(v₁₁,V₁)/[ ρ(v₁₁,V_c)− ρ(v₁₁,V₁)] = −6/(−9 + 6) = 2;

k₂(r₁₁) = ρ(v₁₁,V₂)/[ ρ(v₁₁,V_c) − ρ(v₁₁,V₂)] = 6/(−9−6) = −0.4;

k₃(r₁₁) = ρ(v₁₁,V₃)/[ ρ(v₁₁,V_c) − ρ(v₁₁,V₃)] = 21/(−9−21) = −0.7;

k₄(r₁₁) = ρ(v₁₁,V₄)/[ ρ(v₁₁,V_c) − ρ(v₁₁,V₄)] = 41/(−9−41) = −0.82;

k₄(r₁₁) = ρ(v₁₁,V₅)/[ ρ(v₁₁,V_c) − ρ(v₁₁,V₅)] = 66/(−9−66) = −0.88;

Similarly, the correlation degrees of the second grade indexes under other first grade indexes can be calculated. The calculation results are shown in

Table 6. The relevance of second grade indexes.

First Grade Indexes	Second Grade Indexes	Relevance of Second Grade Indexes					Risk Level
		Ⅰ	Ⅱ	Ⅲ	Ⅳ	Ⅴ
Laws, regulations and policies (r1)	Mineral rights and gas rights conflict (r11)	2.000	−0.400	−0.700	−0.820	−0.880	Ⅰ
	Major licenses and approvals (r12)	0.333	−0.200	−0.600	−0.760	−0.840	Ⅰ
	Foreign cooperation franchise (r13)	−0.435	−0.314	−0.040	0.043	−0.324	Ⅳ
	Government financial subsidies (r14)	−0.105	0.133	−0.433	−0.660	−0.773	Ⅱ
	Resource tax reform (r15)	0.077	−0.067	−0.533	−0.720	−0.813	Ⅰ
	New energy policy (r16)	−0.059	0.067	−0.467	−0.680	−0.787	Ⅱ
Resource characteristics (r2)	Gas content (r21)	−0.222	0.400	−0.300	−0.580	−0.720	Ⅱ
	Permeability (r22)	−0.143	0.200	−0.400	−0.640	−0.760	Ⅱ
	Reservoir pressure (r23)	0.571	−0.267	−0.633	−0.780	−0.853	Ⅰ
	Porosity (r24)	−0.273	0.333	−0.200	−0.520	−0.680	Ⅱ
	Hydrogeological conditions (r25)	0.077	−0.067	−0.533	−0.720	−0.813	Ⅰ
	Coal seam area (r26)	−0.297	0.182	−0.133	−0.480	−0.653	Ⅱ
	Coal seam thickness (r27)	−0.174	0.267	−0.367	−0.620	−0.747	Ⅱ
	Buried depth (r28)	0.182	−0.133	−0.567	−0.74	−0.826	Ⅰ
Engineering technology (r3)	Geological evaluation technique (r31)	0.770	−0.067	−0.533	−0.720	−0.813	Ⅰ
	Extraction technology (r32)	−0.297	0.182	−0.133	−0.480	−0.653	Ⅱ
	Development process technology (r33)	−0.258	0.438	−0.233	−0.540	−0.693	Ⅱ
	Gas gathering technology (r34)	−0.143	0.200	−0.400	−0.640	−0.760	Ⅱ
	Treatment technology (r35)	−0.174	0.267	−0.367	−0.620	−0.747	Ⅱ
	Transportation technology (r36)	−0.347	−0.059	0.067	−0.360	−0.573	Ⅲ
	Dynamic monitoring and analysis (r37)	−0.241	0.467	−0.267	−0.560	−0.707	Ⅱ
	Drainage system (r38)	−0.286	0.250	−0.167	−0.500	−0.667	Ⅱ
Economic operation (r4)	CBM price fluctuation (r41)	−0.105	0.133	−0.433	−0.660	−0.773	Ⅱ
	Project cost (r42)	−0.241	0.467	−0.267	−0.560	−0.707	Ⅱ
	Return on investment (r43)	−0.273	0.333	−0.200	−0.520	−0.68	Ⅱ
	CBM production (r44)	−0.317	0.077	−0.067	−0.440	−0.627	Ⅱ
	Macroeconomics (r45)	−0.059	0.067	−0.467	−0.680	−0.787	Ⅱ
	Funds recovery (r46)	0.077	−0.067	−0.533	−0.720	−0.813	Ⅰ
	External market resources (r47)	−0.397	−0.214	0.158	−0.120	−0.413	Ⅲ
	External network resources (r48)	−0.143	0.200	−0.400	−0.640	−0.760	Ⅱ
	Market demand (r49)	−0.241	0.467	−0.267	−0.560	−0.707	Ⅱ
Organizational management (r5)	Organizational structure adaptability (r51)	0.000	0.000	−0.500	−0.700	−0.800	Ⅰ, Ⅱ
	Management coordination and communication (r52)	−0.222	0.400	−0.300	−0.580	−0.720	Ⅱ
	Process management (r53)	−0.308	0.125	−0.100	−0.460	−0.640	Ⅱ
	Organizational management quality (r54)	−0.142	0.200	−0.400	−0.640	−0.760	Ⅱ
	Resource allocation capability (r55)	−0.297	0.182	−0.133	−0.480	−0.653	Ⅱ
Safety and emergency protection (r6)	Safety technology and equipment (r61)	−0.286	0.250	−0.167	−0.500	−0.667	Ⅱ
	Hidden danger investigation and treatment (r62)	−0.241	0.467	−0.267	−0.560	−0.707	Ⅱ
	Safety training and education (r63)	−0.397	−0.241	0.158	−0.120	−0.413	Ⅲ
	Safety culture (r64)	−0.317	0.077	−0.067	−0.440	−0.627	Ⅱ
	Safety investment (r65)	−0.143	0.200	−0.400	−0.640	−0.760	Ⅱ
	Emergency plan (r66)	−0.297	0.182	−0.133	−0.480	−0.653	Ⅱ
	Emergency drill frequency (r67)	−0.403	−0.258	0.095	−0.080	−0.387	Ⅲ
	Emergency supplies reserve (r68)	−0.373	−0.159	0.233	−0.260	−0.507	Ⅲ
	Emergency rescue team (r69)	−0.273	0.333	−0.200	−0.520	−0.680	Ⅱ

. The calculation process is shown in Appendix C.

3.3. Multi-Level Extension Assessment

(1) Primary assessment

Taking the first grade index r₁ as an example, the correlation degree matrix K(r₁) is determined according to the weight calculation result in Table 4 and Formula (13).

$$\begin{array}{c}\hfill K(r_1)=({\omega }_{11},{\omega }_{12},{\omega }_{13},{\omega }_{14},{\omega }_{15},{\omega }_{16})(k_j(r_1))=\hfill \\ \hfill (0.226,0.235,0.113,0.188,0.118,0.120)\left[\begin{array}{ccccc}0.200& -0.400& -0.700& -0.820& -0.880\\ 0.333& -0.200& 0.600& -0.760& -0.840\\ -0.435& -0.314& -0.040& -0.043& -0.324\\ -0.105& 0.133& -0.433& -0.660& -0.773\\ 0.077& -0.067& -0.533& -0.720& -0.813\\ -0.059& 0.067& -0.467& -0.680& -0.787\end{array}\right]\hfill \\ =(0.463,-0.148,-0.504,-0.650,-0.769)\hfill \end{array}$$

In the same way, the correlation degree matrixes of other first grade indexes are calculated. The detailed calculation processes are shown in Appendix B.

K(r₂)=(−0.006, 0.105, −0.411, −0.647, −0.765); K(r₃)=(−0.075, 0.205, −0.276, −0.566, −0.711); K(r₄)=(−0.204, 0.200, −0.260, −0.540, −0.694); K(r₅)=(−0.188, 0.163, −0.286, −0.572, −0.714); K(r₆)=(−0.295, 0.114, −0.103, −0.414, −0.610).

(2) Secondary assessment

According to formula (14), the comprehensive correlation degree matrix of the research object for each risk level is determined.

$$\begin{array}{c}\hfill K(S)=({\omega }_1,{\omega }_2,{\omega }_3,{\omega }_4,{\omega }_5,{\omega }_6)K_i(r_i)=\hfill \\ \hfill (0.165,0.214,0.209,0.184,0.094,0.134)\left[\begin{array}{ccccc}0.463& -0.148& -0.504& -0.650& -0.769\\ -0.006& 0.105& -0.411& -0.647& -0.765\\ -0.075& 0.205& -0.276& -0.566& -0.711\\ -0.204& 0.200& -0.260& -0.540& -0.694\\ -0.188& 0.163& -0.286& -0.572& -0.714\\ -0.295& 0.114& -0.103& -0.414& -0.610\end{array}\right]\hfill \\ =(-0.035,0.108,-0.317,-0.573,-0.716)\hfill \end{array}$$

(3) Determining the risk level

According to the principle of maximum membership degree, the risk level corresponding to the maximum correlation degree in correlation degree matrix K(S) of CBM development for each risk level is the risk level of the assessment object. Because $max{k}_j\left(S\right)$=0.108=K₂(S), the risk level of the CBM development project is Grade II.

4. Results and Discussion

(1).

The correlation degree of comprehensive risk of the research object is 0.108, and the overall risk level of the CBM development project is judged to be Grade II according to the principle of maximum membership degree. This finding shows that the overall risk of the project is small and within an acceptable range, but the local risk of the project needs to be rectified in a timely manner.

(2).

According to the calculation results of the correlation degree of the second grade indexes in Table 6, it is possible to determine the links with higher risks in the second grade indexes. The following is an analysis of the indexes with risk levels greater than Grade II.

(1)

According to the investigation, the operators of the project did not obtain the right to cooperate with foreign countries, which indicates that the project cannot be assisted by foreign companies in terms of technology and management. Therefore, the project is at a higher risk in foreign cooperation franchises.

(2)

The transportation technology of this project is relatively backwards, and mainly relies on tank trucks for CBM transportation, and there is no long-distance pipeline network for the system. Therefore, the transportation technology risk of this project is high. It is recommended that the project operator regularly check the reliability of the tank truck equipment and conduct safety training for the tank truck driver.

(3)

Because the project operators are affiliated with private enterprises, and the enterprises have been established only for a short period, a well-known corporate image or reputation in the CBM industry have not been established. For these reasons, the project’s external market resource risk is high.

(4)

The project is not doing well in safety training and education. According to the survey, not all employees have participated in safety training, which will cause high risks to the daily operation of the project. CBM leakage and explosion accidents caused by human error are not uncommon; therefore, project operators should pay more attention to this aspect.

(5)

The number of daily emergency drills of the project is not up to standard. During the investigation of the emergency drill record, it was found that the project conducted only one accident emergency drill every year, which did not meet the standards of China’ China’s Safe Production Law stipulates that emergency drills be performed at least once every six months for firms involved in the production, filling, storage, supply and sales of flammable and explosive chemicals and the emergency plan is to be continuously improved in light of the actual situation. Therefore, to reduce the project risk, the project operators should add at least one more accident emergency drill every year.

(6)

The project’s emergency supplies were not adequately prepared and did not include gas masks and explosion-proof emergency lights. The main component of CBM is methane, which is a flammable, explosive, toxic and corrosive gas. If a CBM leak accident occurs during the production process, rescue personnel are required to have a gas mask; otherwise, death, due to suffocation, is likely. Moreover, project operators should be equipped with a sufficient number of explosion-proof emergency lights. Other lighting equipment may cause methane explosion accidents, due to static electricity during use.

(7)

The risks of other second grade indexes are very small, and their risk levels reached the first or second level. First, the risks of laws, regulations and policies faced by the project are minimal. The current new energy policies and financial subsidy policies are conducive to the development of the CBM industry. Second, there is no conflict between mining rights and air rights in the block where the project is located. In addition, the major licensing and approval procedures for the project are also complete. Third, the coal reservoirs in the block where the project is located have good porosity, high permeability, high gas content and gas saturation, which are conducive to the development of CBM. Finally, the economic operational risks of the project are also small. The project’s return on investment and CBM production are at a high level.

(8)

In summary, the overall risk of the project is small and within an acceptable range, indicating that the project has development value. The assessment results are in good agreement with the actual operation of the project, indicating that the established risk assessment model is feasible and effective.

5. Conclusions

With the development of the CBM industry in various countries around the world, a mature and complete risk assessment system is needed to accurately determine the overall risk level and local risk weakness of CBM development projects. This paper provides a reference for government policy formulation, investor project feasibility analyses, insurance company insurance premium rate determination, and project operator risk perception improvement ability. This study fills the gap in the literature concerning the above requirements. The main contributions of this paper are as follows:

(1)

Taking a CBM development project as the research object and considering the risk characteristics of exploration, mining, gathering and market application involved in the project life cycle, a CBM development risk assessment index system consisting of six first grade indexes and 45 second grade indexes is constructed.

(2)

Based on the SEWM, the weights of the risk assessment indexes are calculated. Then, the MEEM is used to construct the theoretical model of CBM development risk assessment.

(3)

A case study of a CBM development project in the southern Qinshui Basin of China was carried out using the established CBM development risk assessment model. The results show that the overall risk level of the CBM development project is Grade II, indicating that the overall risk of the project is small and within an acceptable range, although the local risk of the project needs to be rectified in a timely fashion. The assessment results are in good agreement with the actual operation of the project, indicating that the established risk assessment model has good applicability and effectiveness.

(4)

The study makes three contributions. First, the research results can help relevant government departments formulate policies to reduce the risks faced by the CBM industry. Second, this work can provide a reference for investors to evaluate the feasibility of CBM development projects and for insurance companies to determine the insurance rate of CBM development projects. Finally, the research results are also conducive to improving the risk awareness and risk perception of CBM project operators. Therefore, the accuracy of managers’ risk aversion decisions can be improved, and the waste of resources and property loss caused by the failure of risk management and control in the daily production process of the project can be reduced.