Dynamic Risk Assessment of Equipment Operation in Coalbed Methane Gathering Stations Based on the Combination of DBN and CSM Assessment Models

Abstract

The operational risks of equipment in coalbed methane (CBM) gathering stations exhibit dynamic characteristics. To address this, a dynamic risk assessment method based on Dynamic Bayesian Networks (DBNs) is proposed for CBM station equipment. Additionally, a comprehensive safety management evaluation model is established for gathering station equipment. This approach enables accurate risk assessment and effective implementation of safety management in CBM gathering stations. This method primarily consists of three core components: risk factor identification, dynamic risk analysis, and comprehensive safety management evaluation. First, the Bow-tie model is applied to comprehensively identify risk factors associated with station equipment. Next, a DBN is constructed based on the identified risks, and Markov theory is employed to determine the state transition matrix. Finally, a Comprehensive Safety Management (CSM) evaluation model for gathering station equipment is established. The feasibility of the proposed method is validated through case study applications. The results indicate that during the operation of equipment at CBM gathering stations, priority should be given to strengthening maintenance for medium-hole and enhancing prevention and emergency measures for jet fires. Temperature-controlled spiral-wound heat exchangers, skid-mounted circulating pumps, and pipelines have been identified as critical factors affecting accident occurrence at CBM gathering stations. Enhanced daily inspection and maintenance of this equipment should be implemented. Furthermore, compared to other safety evaluation indicators, the Emergency Preparedness and Response indicator has the most significant impact on the operational safety of CBM gathering station equipment. It requires high-priority attention, thorough implementation of relevant measures, and continuous improvement through targeted actions.

1. Introduction

Coalbed methane (CBM), also known as “gas,” primarily consists of methane. As a hydrocarbon gas in coal seams, it offers advantages such as high calorific value and clean combustion products, and is now widely developed and utilized [1]. With growing national policy support and market demand, China’s CBM industry has flourished, with exploration and development technologies reaching international advanced levels [2]. CBM gathering stations serve as critical facilities for CBM processing, performing collection, treatment, storage, and transportation to ensure efficient utilization and sustainable development [3]. These stations operate numerous pieces of equipment over extended periods, with CBM typically maintained at high temperatures and pressures. The gas exhibits hazardous properties, including flammability, explosiveness, and toxicity. Leakage incidents can severely threaten personnel and equipment safety. For example, in 2019, a CBM leakage incident at Shanxi Tongyu CBM Transmission & Distribution Co., Ltd. caused an explosion and fire covering over 8000 m², resulting in direct economic losses of approximately RMB 815,962. Dynamic risk assessment of CBM gathering station equipment is therefore crucial to prevent casualties and property damage.

Recent studies on risk assessment of coalbed methane (CBM) primarily focus on two aspects: industry-wide risk analysis and project-specific risk evaluation, covering socio-environmental impacts, geological hazards, and economic factors. Wang Wanqing et al. established a risk index system for coalbed methane development projects, determined the index weights by using the structural entropy weight method, and completed the risk assessment combined with the gray clustering analysis method [4]. Barbara Uliasz-Misiak et al. established an environmental risk assessment framework for coalbed methane exploration and exploitation, determined the likelihood and consequence weightings based on expert knowledge and literature, and completed the risk assessment by using a modified hazard/probability matrix method [5]. Jiang Qiuxia established a risk assessment system for CBM development by combining subjective and objective weighting methods, and designed a decision support system for risk evaluation [6]. Runzhi Li et al. established an explosion risk assessment framework for low-concentration oxygen-bearing coalbed methane in low-temperature environments, determined the key risk factors by combining experimental analysis and numerical simulation, and completed the risk evaluation by using the cusp catastrophe theory [7].

Most existing studies focus on qualitative risk assessments of the coalbed methane (CBM) industry as a whole. Research on risk assessment for the operation of equipment in CBM gathering stations remains relatively insufficient. Furthermore, the risks faced by the equipment are not fixed; instead, they evolve continuously with factors such as the passage of time, fluctuations in operating conditions, changes in the environment, equipment aging, and operational behaviors. These risks exhibit dynamic characteristics of “uncertainty, timeliness, and correlation”—in other words, the risks are dynamic in nature. Dynamic Bayesian Network (DBN) offers an effective solution to this problem by combining static network structures with temporal information, creating a stochastic model capable of processing time-series data. This method has been widely applied in the petrochemical industry for scenario simulation and countermeasure evaluation of fire accidents in oil and gas storage and transportation [8]. Qingqing Xu et al. established a dynamic risk assessment index system for underground gas storage facilities, determined the prior probability of basic events by using fuzzy numbers, and completed the risk evaluation by combining the dynamic DBN and failure tree analysis [9]; Ming Liu et al. established a risk index system for the gasifier system, determined the weights of each risk index by using the entropy weight method, and completed the risk prediction evaluation by combining the dynamic cloud DBN and the cloud model [10]; Jing Wen et al. established a risk index system for submarine pipeline stoppers, determined the failure probability of basic events by using the fuzzy comprehensive evaluation method, and completed the reliability and safety evaluation by combining the dynamic Bayesian network (DBN) and fault tree analysis [11].

This study addresses the dynamic characteristics of equipment operation in coalbed methane (CBM) gathering stations by establishing a dynamic risk assessment model based on Dynamic Bayesian Network (DBN). It predicts risk evolution trends to provide a scientific reference for the safe operation and risk management of CBM gathering stations.

2. Material and Methods

The spatial layout of a CBM gathering station consists of multiple functional zones and equipment arrangements. Based on functional characteristics, it can be divided into four operational units: separation unit, dehydration unit, Boosting Unit, and pipelines/auxiliary equipment. A field photo of the CBM gathering station is shown in Figure 1.

The separation unit functions to remove impurities carried in the CBM, thereby improving gas purity; The Boosting Unit increases the transmission pressure to ensure stable gas supply. The dehydration unit removes water content from the CBM to lower its water dew point, preventing water condensation during transportation or processing that could negatively impact gas quality and transmission efficiency. Pipelines and other auxiliary equipment serve as supporting facilities for the production process units.

A comprehensive identification of risk factors and potential accident consequences during the operation of equipment and facilities in CBM gathering stations was conducted. Based on this analysis, a bow-tie(BT) model for CBM station accidents was established. Subsequently, a Dynamic Bayesian Network (DBN) model for the CBM gathering station was developed by integrating Markov theory. Finally, a comprehensive safety management evaluation model was constructed to calculate and assess safety management performance scores. Through case study applications, this research investigates the temporal evolution patterns of equipment risks under different operational states. The overall framework is illustrated in Figure 2.

2.1. Establishing the BT Model for CBM Gathering Stations

Field investigations at the CBM gathering station revealed a high degree of equipment automation. Consequently, the risk factors and accident consequences of CBM leakage were analyzed and categorized primarily from the perspective of equipment systems, leading to the establishment of a BT model for CBM leakage accidents. The bow-tie analysis method, also known as the cause-consequence diagram method—Cause-and-Effect Diagram Method (Ishikawa Diagram Method), is a qualitative risk assessment technique that visually represents the causes, pathways, and consequences of hazardous events along with their logical relationships during the evolution process [12,13]. As shown in Figure 3, the left side of the BT model illustrates the potential causes of CBM leakage, while the right side displays the possible accident consequences under different conditions.

The BT model diagram comprises 8 intermediate events, 12 basic events, and 4 types of accident consequences. The event node information is presented in

Table 1. Events of BT model.

Symbol	Event	Symbol	Event
M1	Equipment failure	X3	Temperature-controlled spiral-wound heat exchanger failure
M2	Unit failure	X4	Reciprocating surge drum failure
M3	Separation unit failure	X5	Skid-mounted circulating pump failure
M4	Dehydration unit failure	X6	Reciprocating compressor failure
M5	Pressure boosting unit failure	X7	Pipeline failure
M6	Pipeline and auxiliary equipment failure	X8	Valve failure
M7	Safety barrier failure	X9	Emergency shutdown system failure
M8	Detection system failure	X10	Grounding system failure
X1	Filter separator failure	X11	Gas detector failure
X2	Reciprocating separator failure	X12	Signaling device failure

.

2.2. DBN Model for CBM Gathering Station Accidents

Bayesian Network (BN) are probabilistic graphical models that represent complex variable relationships using sample data and domain knowledge to support uncertainty reasoning and predictive inference [14,15]. Dynamic Bayesian Network (DBN) extend BN by incorporating temporal dynamics, enabling the analysis of time-series data and making them particularly suitable for industrial applications [16,17,18].

Given the dynamic risk characteristics of equipment in CBM gathering stations, DBN effectively capture real-time risk evolution. Based on the BT model for CBM leakage, a corresponding DBN model is constructed, as shown in Figure 4. The boxes in the figure represent events and results, and the arrows indicate the causal relationships among the events.

2.2.1. Determination of Bayesian Network Parameters

Determination of Node Prior Probabilities

The RBI methodology is adopted to determine prior probabilities for equipment failure nodes. The generic failure frequencies for various equipment under different failure modes are obtained from API RP 581. These frequencies are then adjusted by both equipment-specific and management system modification factors based on actual operating conditions to determine the final equipment failure probability. For other nodes, prior probabilities can be determined based on the station’s hazard registry and relevant statistical records. The failure rates and repair rates for event nodes under small-bore leakage conditions are presented in

Table 2. Failure rate and repair rate of each node.

Event Node	Failure Rate /Times × a−1	Mean Repair Rate /h−1	Event Node	Failure Rate /Times × a−1	Mean Repair Rate /h−1
Pipeline	1.87 × 10−6	0.2	Skid-mounted circulating pump	3.45 × 10−6	0.0833
Filter separator	1.78 × 10−7	0.0833	Emergency shutdown system	2.32 × 10−6	0.0018
Reciprocating surge drum	1.56 × 10−6	0.0208	Grounding system	3.56 × 10−6	0.0003
Reciprocating separator	1.78 × 10−7	0.0833	Signaling device	3.78 × 10−6	0.0017
Temperature-controlled spiral-wound heat exchanger	7.88 × 10−6	0.0208	Gas detector	2.64 × 10−6	0.0007
Reciprocating compressor	1.78 × 10−7	0.0833

.

Determination of Conditional Probabilities

The establishment of node conditional probabilities follows two principal methodologies. The first approach derives probabilities through the logical relationships of AND-gates and OR-gates in fault tree analysis(FTA). The second method combines expert experience with fuzzy set theory, where invited experts provide scores represented by fuzzy numbers that are converted into fuzzy linguistic terms, ultimately determining the conditional probabilities through computation. The conditional probabilities for nodes associated with equipment and device failures all adhere to the logical “OR-gate” rule. The conditional probabilities for “accident consequence” nodes are provided in

Table 3. Conditional probability of the “accident consequence” node.

Coal Seam Gas Leakage	Yes
Ignition Source	Existence
Ignition Modes	Direct Ignition		Indirect Ignition
Leakage Modes	Instantaneous Release	Instantaneous Release	Instantaneous Release	Continuous Leak
Jet fire	0	1	0	0
VCE	0	0	1	1
Fireball	1	0	0	0

.

2.2.2. Determination of State Transition Matrices

To determine the probability of accidents at different time steps in a DBN structure, it is necessary to establish the state transition probabilities of nodes from one time step to the next, i.e., the transition matrix. Markov models have characteristic to handle uncertainty by modeling the probabilities of transitioning from current state to next state [19,20].

The root nodes corresponding to equipment and device failures in the DBN model are defined with four operational states: Fully Operational (N), Degraded but Functional (D1), Severely Damaged (D2), and Failed (F). The transitions between these states are depicted in Figure 5, with λ representing the equipment failure rate and μ denoting the repair rate.

A complete repair restores the system to the N state from the F state, while an incomplete repair improves the condition but only achieves the D1 state.

To establish the state transition matrix, probabilistic assumptions are made regarding the transitions between the four states (N, D1, D2, F), as formalized in Equation (1.1) [21].

$$\begin{array}{l}{\lambda }_{ND1}={\lambda }_{D1D2}={\lambda }_{D2F}\\ {\lambda }_{ND2}={\lambda }_{D1F}\\ {\lambda }_{ND1}+{\lambda }_{ND2}+{\lambda }_{NF}=\lambda \\ {\lambda }_{ND1}:{\lambda }_{ND2}:{\lambda }_{NF}=1:2:7\\ {\mu }_{D1N}={\mu }_{D2D1}={\mu }_{FD2}\\ {\mu }_{D2S}={\mu }_{FD1}\\ {\mu }_{ND1}+{\mu }_{FD2}+{\mu }_{FN}=\mu \\ {\mu }_{ND2}:{\mu }_{FD1}:{\mu }_{FN}=1:3:6\end{array}$$

(1.1)

To enable precise assessment of dynamic risks in CBM gathering station equipment across time sequences, time slices are incorporated into the DBN model. The transition probabilities between adjacent time slices under varying maintenance levels are provided in

Table 4. State transition probability without maintenance.

T	T + ΔT
State	N	D1	D2	F
N	$e^{-\lambda }$	$0.2(1-e^{-\lambda })$	$0.7(1-e^{-\lambda })$	$0.1(1-e^{-\lambda })$
D1	0	$e^{-0.9\lambda }$	${\displaystyle \frac{7(1-e^{-0.9\lambda })}{9}}$	${\displaystyle \frac{2(1-e^{-0.9\lambda })}{9}}$
D2	0	0	$e^{-0.2\lambda }$	$1-e^{-0.2\lambda }$
F	0	0	0	1

,

Table 5. State transition probability under incomplete maintenance condition.

T	T + ΔT
State	N	D1	D2	F
N	$e^{-\lambda }$	$0.2(1-e^{-\lambda })$	$0.7(1-e^{-\lambda })$	$0.1(1-e^{-\lambda })$
D1	0	$e^{-0.9\lambda }$	${\displaystyle \frac{7(1-e^{-0.9\lambda })}{9}}$	${\displaystyle \frac{2(1-e^{-0.9\lambda })}{9}}$
D2	0	0	$e^{-0.2\lambda }$	$1-e^{-0.2\lambda }$
F	$0.6(1-e^{-\mu })$	$0.3(1-e^{-\mu })$	$0.1(1-e^{-\mu })$	$e^{-\mu }$

and

Table 6. State transition probability under complete maintenance condition.

T	T + ΔT
State	N	D1	D2	F
N	$e^{-\lambda }$	$0.2(1-e^{-\lambda })$	$0.7(1-e^{-\lambda })$	$0.1(1-e^{-\lambda })$
D1	0	$e^{-0.9\lambda }$	${\displaystyle \frac{7(1-e^{-0.9\lambda })}{9}}$	${\displaystyle \frac{2(1-e^{-0.9\lambda })}{9}}$
D2	0	0	$e^{-0.2\lambda }$	$1-e^{-0.2\lambda }$
F	$1-e^{-\mu }$	0	0	$e^{-\mu }$

. The parameter T denotes the initial time of equipment or device states, while T + ΔT marks the time of state transition completion. In this study, the time slice interval (ΔT) is standardized as one month, with all tabulated probabilities representing the likelihood of state transitions occurring within this monthly timeframe.

2.3. Comprehensive Safety Management Evaluation Model for CBM Gathering Station Equipment Operations

2.3.1. Establishment of a Comprehensive Safety Management Evaluation Index System for CBM Gathering Station Equipment Operations

The safety management assessment system for CBM gathering station equipment is a multi-level framework, structured into four tiers: Group Company—Company—Subsidiary—Field Operators, which incorporates diverse data sources across multiple elements. Based on the operational and structural features of the equipment, along with relevant regulations and standards, the evaluation index system is organized into 4 primary and 11 secondary indicators, as shown in

Table 7. Comprehensive evaluation system of operation safety management of CBM plant and station equipment.

Tier-1 Indicators		Tier-2 Indicators
Project Performance Indicators	Project Code	Project Performance Indicators	Project Code
Basic management	B1	Integrity of management systems Implementation of safety accountability Personnel training and education Equipment availability rate	C11 C12 C13 C21
Equipment condition	B2	Equipment failure rate Maintenance status	C22 C23
Work environment	B3	Workplace safety conditions Hazard identification and risk assessment	C31 C32
Emergency preparedness and response	B4	Emergency plan development Emergency drills resources and equipment	C41 C42 C43

.

2.3.2. Determination of Subjective Weighting Factors for Indicators Using AHP

AHP is one of the common methods used in multi-criteria decision-making processes, which is considered to be a decision method that decomposes a complex multi-criteria decision problem into a hierarchy using experts as the objects of a questionnaire survey [22,23]. In this study, three university experts were specially invited to form an evaluation panel. All of these experts have long been committed to scientific research and teaching in the field of oil and gas safety, with an average of more than ten years of professional experience. They possess profound theoretical foundations and rich academic accumulations in this field, which ensures the reliability and scientificity of this study.

The procedural steps for determining subjective weights of indicators using the AHP are as follows:

(1)

Construct the judgment matrix

Experts construct an $n\ast n$ judgment matrix $\mathit{A}$ through pairwise comparisons of evaluation indicators.

$$\mathit{A}=\left[\begin{array}{cccc}1& a_{12}& \dots & a_{1n}\\ {\displaystyle \frac{1}{a_{12}}}& 1& \dots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\displaystyle \frac{1}{a_{1n}}}& {\displaystyle \frac{1}{a_{2n}}}& \dots & 1\end{array}\right]$$

(2.1)

The element $a_{ij}$ represents the importance score of element $i$ relative to element $j$.

(2)

Calculate the weight vector

Normalization processing:

$$a_{ij}^{’}={\displaystyle \frac{a_{ij}}{\sum _{i=1}^n{a}_{ij}}}$$

(2.2)

The calculation formula for the weight $w_i$ is:

$$w_i={\displaystyle \frac{1}{n}}{\sum _{j=1}^n{a}_{ij}}^{’}$$

(2.3)

(3)

Consistency verification

The formula for calculating the Consistency Index (CI) is shown below, where $\mathit{A}$ is the judgment matrix, $\mathit{w}$ is the weight vector, $n$ is the order of the matrix, and ${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum eigenvalue of the judgment matrix.

$${\lambda }_{max}={\displaystyle \frac{\sum {\left(\mathit{A}\mathit{w}\right)}_i}{n{w}_i}}$$

(2.4)

$$CI={\displaystyle \frac{{\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}-n}{n-1}}$$

(2.5)

$$CR={\displaystyle \frac{CI}{RI}}$$

(2.6)

2.3.3. Determination of Objective Weighting Factors for Indicators Using Entropy Method

The entropy method is an objective weighting technique that assigns weights based on the information entropy derived from data distributions. It ranks indicators by relative importance, measures ranking uncertainty using entropy, and computes weights through deviation analysis.

The procedural steps for determining objective weights of indicators using the entropy method are as follows:

(1)

The evaluation of operational safety management indicators for CBM field station equipment was conducted using the expert scoring method, with corresponding assessment sets as shown in the

Table 8. Evaluation set correspondence table.

Safety Assessment Remark	Extremely Safe	Safe	Moderately Safe	Hazardous	Extremely Hazardous
Assessment Interval	[9, 10]	[8–9)	[7–8)	[6–7)	[0–6)
Interval Median Value	9.5	8.5	7.5	6.5	3

:

This study quantifies the evaluation results of each factor using the median values of assessment intervals from the evaluation set.

(2)

Normalization of indicators

The entropy method requires maximizing positive indicators and minimizing negative indicators.

Normalization formula for positive indicators:

$$X_{ij}={\displaystyle \frac{X_{1J}-\min \left(X_{ij},X_{2j},\dots ,X_{nj}\right)}{\max \left(X_{IJ},X_{2J},\dots X_{nj}\right)-\min \left(X_{1j},X_{2j},\dots X_{nj}\right)}}$$

(2.7)

Normalization formula for negative indicators:

$$X_{ij}={\displaystyle \frac{\max \left(X_{ij},X_{2j},\dots X_{nj}\right)-X_{ij}}{\max \left(X_{ij},X_{2j},\dots X_{nj}\right)-\min \left(X_{1j},X_{2j},\dots X_{nj}\right)}}$$

(2.8)

(3)

Non-negative Data Translation

The adjustment formula is as follows:

$$X_{ij}=X_{ij}+a$$

(2.9)

To avoid altering the original data, the value of a should be kept as small as possible.

(4)

Calculate the proportion

To calculate the proportion $p_{ij}$ of the $i$-th sample under the $j$-th indicator, the following formula is applied:

$$p_{ij}={\displaystyle \frac{x_{i{j}^{’}}}{{\sum }_{i=1}^m{x}_{i{j}^{’}}}}$$

(2.10)

where $m$ denotes the sample size.

(5)

Compute the entropy value

$$E_j=-k{\sum }_{i=1}^m{p}_{ij}\ln \left(p_{ij}\right)$$

(2.11)

where $k={\displaystyle \frac{1}{\mathit{ln}\left(m\right)}}$ serves as the normalization constant, and $E_j$ denotes the entropy value of the $j$-th indicator.

(6)

Determine the redundancy degree

$$d_j=1-E_j$$

(2.12)

(7)

Derive the weight vector

$$w_j={\displaystyle \frac{d_j}{{\sum }_{j=1}^n{d}_j}}$$

(2.13)

where $w_j$ represents the weight of the $j$-th indicator, and $n$ denotes the total number of indicators.

2.3.4. Game Theory-Based Determination of Combined Weights

In the indicator weighting process, weights can be assigned based on either correlation or difficulty. To balance the influence of both approaches, game theory-based combined weighting is applied to integrate them. This method minimizes weight deviation as its optimization objective, resulting in optimal combined weights that overcome the limitations of single-method weighting. The specific calculation steps are as follows.

(1)

Assuming L distinct weighting methods are applied to the indicators, yielding L sets of weight vectors:

$$w\left(k\right)=\left[w_{k1},w_{k2},\dots ,w_{kn}\right],k=\mathrm{1,2},\dots ,L.$$

(2.14)

Any linear combination of the L weights is as follows, where ${\alpha }_k$ is the linear combination coefficient, ${\alpha }_k>$0.

$$w={\sum }_{k=1}^L{\alpha }_k{w}_K^T$$

(2.15)

(2)

By minimizing the deviations between $w$ and each $w_k$, the L weight combination coefficients in Equation (2.15) are optimized to obtain the most ideal weight values in $w$. The objective function is defined as:

$$\mathrm{m}\mathrm{i}\mathrm{n}{‖{\sum }_{k=1}^L{\alpha }_k{w}_K^T-w_K‖}_2,k=\mathrm{1,2},\dots ,L.$$

(2.16)

Based on the properties of matrix differentiation, the system of linear equations for the first-order derivative condition of Equation (2.15) optimization is:

$$\left[\begin{array}{ccc}{w}_1\cdot w_1^T& \dots & w_1\cdot w_L^T\\ ⋮& \ddots & ⋮\\ w_L\cdot w_1^T& \dots & w_L\cdot w_1^T\end{array}\right]\left[\begin{array}{c}{\alpha }_1\\ ⋮\\ {\alpha }_2\end{array}\right]=\left[\begin{array}{c}{w}_1\cdot w_1^T\\ ⋮\\ w_L\cdot w_L^T\end{array}\right].$$

(2.17)

(3)

Combined Weight Calculation.

After normalizing ${\alpha }_k$, the combined weights $w^{*}$ for operational indicators of CBM field station equipment are determined as follows:

$$w^{\mathrm{*}}={\sum }_{k=1}^L{\alpha }_k{w}_K^T,k=\mathrm{1,2},\dots ,L.$$

(2.18)

2.3.5. Fuzzy Comprehensive Evaluation

(1)

Constructing Fuzzy Evaluation Matrices for Secondary Indicators

After obtaining the combined weight vector $\mathit{A}$ through combined weighting, the fuzzy evaluation matrix $\mathit{R}$ is constructed as follows:

$$\mathit{R}=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \dots & r_{1m}\\ r_{21}& r_{22}& \dots & r_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ r_{n1}& r_{n2}& \dots & r_{nm}\end{array}\right]$$

where $r_{ij}$ denotes the membership degree of the $i$-th indicator under the $j$-th evaluation grade.

(2)

Deriving Fuzzy Comprehensive Evaluation Results

The fuzzy comprehensive evaluation result $Y$ is calculated using the weighted average fuzzy operator $M(\cdot ,+)$, where the membership degrees are derived and subsequently normalized.

$$M\left(\cdot ,+\right):Y_K=\mathrm{m}\mathrm{i}\mathrm{n}\left(1,\sum _{j=1}^m{a}_j{r}_{jk}\right),k=\mathrm{1,2},\dots ,n$$

(2.19)

$$Y=\mathit{A}\cdot \mathit{R}$$

(2.20)

(3)

Composite Score Calculation

The composite score $P_{score}$ is obtained by multiplying the membership degrees with their corresponding evaluation grade scores, as expressed in the following formula:

$$P_{score}=\sum _{j=1}^m\left(b_j\times v_j\right)$$

(2.21)

where $b_j$ and $v_j$ represent the normalized membership degree of the $j$-th evaluation grade and its assigned numerical score, respectively.

3. Case Application

3.1. Case Overview

Taking a CBM gathering station in Shanxi Province as a case study, we applied the proposed methodology to perform dynamic risk analysis. The gas gathering station is part of a pilot production project for tight gas exploration and development with 200 million cubic meters of geological reserves. It adopts a fully skid-mounted design, with a design capacity of 4.9 × 10⁴ Nm³/d, an operational flexibility range of 10–120%, and an automation level classified as “attended operation with centralized monitoring.” The process flow primarily consists of separation, pressurization, dehydration, and metering and export units, which treat incoming wellhead gas through separation and dehydration processes. The processed tight gas complies with Type II commercial natural gas standards and is sold to downstream users after custody transfer metering within the station.

3.2. Dynamic Risk Outcome Analysis

The relevant parameters were input into the dynamic Bayesian network (DBN) for updating, and the time slice was set to 240 (corresponding to 20 years). The relevant results obtained are as follows. For different failure types, the probability of CBM leakage under different maintenance states varies over time, as shown in Figure 6. As shown in the figure, medium-hole leaks exhibit the highest probability, followed by small-hole leaks, with large-hole leaks being the least probable. Both partial repair and complete repair effectively reduce the probability of coalbed methane (CBM) leakage, achieving a maximum reduction of 6.44 × 10⁻⁴. For small-hole leaks, complete repair demonstrates more significant risk mitigation. Compared with other studies in this field, the results of this study focus on CBM collection stations, with an emphasis on leak aperture and the probability of accident types. In contrast, other studies concentrate on the laws of gas loss [24]. Although the two differ in their focuses, both are important components of research on coalbed methane leakage prevention and control.

Under the no-repair condition, the evolution of probabilities for jet fires, fireballs, and vapor cloud explosions (VCE) triggered by CBM leakage over a 20-year period is illustrated in Figure 7, with quantitative data provided in

Table 9. Probabilities of different accident consequences under different failure types.

Failure Type	Small-Hole Leak		Medium-Hole Leak		Large-Hole Leak
Time	T = 0	T = 240	T = 0	T = 240	T = 0	T = 240
Jet Fire	2.05 × 10−9	1.11 × 10−5	2.05 × 10−9	1.77 × 10−5	2.05 × 10−9	7.02 × 10−6
Fireball	1.10 × 10−9	5.98 × 10−6	1.10 × 10−9	9.54 × 10−6	1.10 × 10−9	3.78 × 10−6
VCE	7.88 × 10−10	4.27 × 10−6	7.88 × 10−10	6.81 × 10−6	7.98 × 10−10	2.70 × 10−6

. As shown in the figure, jet fires exhibit the highest probability of occurrence, followed by fireballs, with VCE being the least probable. As equipment service life increases, the probabilities of these incidents rise correspondingly. After 20 years, the maximum probability increase reaches 1.77 × 10⁻⁵.

Figure 8 presents the probability variations in coalbed methane (CBM) leakage, jet fires, fireballs, and vapor cloud explosions (VCEs) under different failure types and maintenance states. As shown in the figure, complete repair demonstrates significantly greater effectiveness in reducing accident probabilities for small-hole leaks compared to partial repair, while the difference between the two repair strategies is marginal for other failure types. Compared with other studies, this research obtains the probability of CBM accidents by modifying maintenance methods and infers the relationship between them, while some other studies in this field link the correlation of corrosion defects with failure probability to deduce their relationship [25]. Although both methods involve research on gas facility leakage risks, the former is a comparative analysis of post-maintenance effects, and the latter is a modeling study of pre-failure causes; they differ in research dimensions and focus elements, but both contribute to the study of accident failures in this field.

Under the no-repair condition, with the “accident consequence” set as the evidence node and the jet fire probability fixed at 1 for T = 240, Bayesian network reverse reasoning was performed to derive the posterior probabilities of basic events, as shown in Figure 9. As shown in the figure, X₃ is the most critical factor influencing accidents at the CBM gathering station, exhibiting the highest contribution rate. This is followed by X₅ and X₇, which are also key contributing factors that cannot be overlooked.

3.3. Comprehensive Evaluation Results of Equipment Operational Safety Management

Based on the established safety management evaluation index system, the 1–9 ratio scale method and random consistency index (RI) were applied to conduct pairwise comparisons of all Tier-1 and Tier-2 indicators. Separate judgment matrices were constructed, and the consistency ratio (CR) was calculated for both Tier-1 and Tier-2 indicators. Among them, the work environment data forms a second-order matrix, for which the CR cannot be calculated. However, all second-order matrices inherently satisfy consistency tests, and the derived weights are consistent. Analysis confirms that all judgment matrices meet the consistency requirements.

Table 10. The CR values of each indicator.

Project Code	CR
B1	0.009
B2	0.009
B3	/
B4	0.024
Objective Layer	0.017

presents the CR values for the primary indicators and their respective secondary indicators.

The subjective weight allocation results for the operational safety management of CBM gathering station equipment are presented in

Table 11. The subjective weight of safety management of CBM plant equipment operation.

Objective Layer	Tier-1 Indicators	Tier-1 Indicator Weights	Tier-2 Indicators	Tier-2 Indicator Weights	Synthetic Weights
Operational Safety Management of Equipment in CBM Gathering Stations	Basic management	0.157	Integrity of management systems	0.164	0.0262
			Implementation of safety accountability	0.298	0.0475
			Personnel training and education	0.539	0.0862
	Equipment condition	0.247	Equipment availability rate	0.539	0.1348
			Equipment failure rate	0.297	0.0743
			Maintenance status	0.164	0.0410
	Work environment	0.094	Workplace safety conditions	0.750	0.0675
			Hazard identification and risk assessment	0.250	0.0225
	Emergency preparedness and response	0.502	Emergency plan development	0.334	0.1670
			Emergency drills	0.568	0.2840
			Resources and equipment	0.098	0.0490

. Among the tier-1 indicators, Emergency Preparedness and Response holds the highest weight (0.50), while Work Environment ranks lowest (0.09), demonstrating a significant disparity. The prioritized ranking of first-level indicators is: Emergency Preparedness and Response > Equipment Status > Basic Management > Work Environment. The weight distribution analysis of tier-2 indicators reveals that Emergency Drills (C42) under the Emergency Preparedness and Response category carries the highest weight coefficient of 0.29, followed by Emergency Plan Development (C41) at 0.17, while Integrity Of Management Systems (C21) under Equipment Status ranks third with a weight of 0.14. All remaining tier-2 indicators demonstrate relatively minor influence with weights below 0.10. Therefore, Emergency Preparedness and Response constitutes the most critical aspect of equipment operational safety management at CBM gathering stations, with particular emphasis on emergency drills.

Based on the expert scoring method, the data for each Tier-2 indicator was obtained. Following the procedures outlined in Section 2.2, the entropy values and objective weights of all Tier-2 indicators were calculated, with detailed results presented in

Table 12. Objective weight of safety management of CBM plant equipment operation.

Indicator Layer	Specific Indicators	Entropy Values	Weights	Tier-1 Indicator Weights
Basic management	Integrity of management systems	0.8340	0.0771	24.62%
	Implementation of safety accountability	0.8093	0.0886
	Personnel training and education	0.8268	0.0805
Equipment condition	Equipment availability rate	0.8340	0.0771	22.61%
	Equipment failure rate	0.8414	0.0737
	Maintenance status	0.8381	0.0753
Work environment	Workplace safety conditions	0.6791	0.1492	22.45%
	Hazard identification and risk assessment	0.8381	0.0753
Emergency preparedness and response	Emergency plan development	0.8381	0.0753	30.32%
	Emergency drills	0.8268	0.0805
	Resources and equipment	0.6828	0.1474

. As evidenced in Table 12, Emergency Preparedness and Response carries the highest weight (30.27%) in the operational safety management system of CBM gathering station equipment, followed by Basic Management (24.59%). Equipment condition and Work Environment demonstrate comparable yet minimal weight differences, registering 22.72% and 22.42%, respectively. The Emergency Preparedness and Response indicator constitutes a critical factor influencing equipment operational safety management at CBM gathering stations. It quantifies the station’s emergency readiness capability and response speed when confronting unforeseen incidents, ensuring rapid and effective action implementation during emergencies. Therefore, in the operational safety management of equipment at CBM gathering stations, priority attention must be given to the development of this indicator, with systematic enhancement of emergency preparedness and response protocols.

Based on the integration of subjective and objective weights for equipment operational safety management in CBM gathering stations, the combined optimization coefficients were calculated following the procedures outlined in Section 2.3.4. After normalization processing, the results yielded ${\mathsf{\alpha }}_1=0.772$ and ${\mathsf{\alpha }}_2=0.228$. Utilizing Equation (2.16), the comprehensive weights derived from game theory-based combination weighting are presented in

Table 13. Combined weights for equipment operational safety management in coalbed methane gathering stations.

Tier-1 Indicators	Tier-1 Indicator Weights	Tier-2 Indicators	Subjective Weights	Objective Weights	Combined Weights	Ranking
Basic management B1	0.1796	Integrity of management systems C11	0.0262	0.0771	0.0378	10
		Implementation of safety accountability C12	0.0475	0.0886	0.0569	8
		Personnel training and education C13	0.0862	0.0805	0.0849	5
Equipment condition B2	0.2446	Equipment availability rate C21	0.1348	0.0771	0.1216	3
		Equipment failure rate C22	0.0743	0.0737	0.0742	6
		Maintenance status C23	0.0410	0.0753	0.0488	9
Work environment B3	0.1200	Workplace safety conditions C31	0.0675	0.1492	0.0861	4
		Hazard identification and risk assessment C32	0.0225	0.0753	0.0345	11
Emergency preparedness and response B4	0.4551	Emergency plan development C41	0.1670	0.0753	0.1461	2
		Emergency drills C42	0.2840	0.0805	0.2376	1
		Resources and equipment C43	0.0490	0.1474	0.0714	7

. In order to visually represent the weight distribution of each secondary indicator in the comprehensive evaluation of equipment operation safety management at coalbed methane gathering stations, the results of subjective and objective weights as well as combined weights were integrated to generate Figure 10.

The fuzzy evaluation matrix can be derived from the combined weights:

$$R=\left(\begin{array}{ccccc}0.2945& 0.2421& 0.2634& 0.2000& 0\\ 0.4388& 0.3612& 0.2000& 0& 0\\ 0.2572& 0.4000& 0.3428& 0& 0\\ 0.4314& 0.2956& 0.1686& 0.1044& 0\end{array}\right)$$

The fuzzy comprehensive evaluation results are as follows:

$$\begin{gathered} Y=\left(\begin{array}{cccc}0.1796& 0.2446& 0.1200& 0.4551\end{array}\right)\left(\begin{array}{ccccc}0.2945& 0.2421& 0.2634& 0.2000& 0\\ 0.4388& 0.3612& 0.2000& 0& 0\\ 0.2572& 0.4000& 0.3428& 0& 0\\ 0.4314& 0.2956& 0.1686& 0.1044& 0\end{array}\right) \\ =\left(\begin{array}{ccccc}0.3874& 0.3144& 0.2141& 0.0834& 0\end{array}\right) \end{gathered}$$

$$\mathrm{Comprehensive}\mathrm{Score}=\left(\begin{array}{ccccc}0.3874& 0.3144& 0.2141& 0.0834& 0\end{array}\right)\left(\begin{array}{c}9.5\\ 8.5\\ 7.5\\ 6.5\\ 3\end{array}\right)=8.50055$$

In accordance with the evaluation criteria presented in Table 8, the calculated score is 8.50055. Therefore, the safety level of the operation and safety management for the coalbed methane (CBM) gathering station equipment is determined as “Safe”.

3.4. Section Summary

Although this study has conducted risk assessment on the operational status of equipment in CBM gathering stations, it has not yet carried out systematic classification based on the structural characteristics and functional attributes of the equipment. As a result, it fails to generate more targeted and detailed assessment conclusions. Future research will focus on this direction, optimizing the assessment framework through equipment classification to further improve the accuracy of risk assessment and its practical guiding value.

Furthermore, compared with other traditional Analytic Hierarchy Process (AHP) methods [26,27], this study introduces a combined weighting method integrating the entropy weight method and game theory, which reduces the interference of subjective factors on the evaluation results. However, there is still room for optimization in terms of improving the objectivity. In subsequent work, it is necessary to further explore weighting methods more suitable for this research scenario, so as to more effectively achieve the goals of reducing the subjectivity of evaluation and enhancing the scientificity and reliability of evaluation results.

4. Conclusions

As the service life of equipment extends, the associated risk of accidents also increases. In the context of CBM leakage, medium-hole leaks are the most frequent, with an occurrence probability roughly double that of large-hole leaks, which are the least common. Among leakage-related accidents, jet fires are the most prevalent, exhibiting a probability about three times higher than VCE. Consequently, it is recommended that CBM gathering stations enhance maintenance protocols focused on medium-hole leaks and reinforce prevention and emergency preparedness measures for jet fires.

In the event of medium or large-hole leaks, the difference in effectiveness between complete and incomplete maintenance for reducing accident risks is minimal. However, for small-hole leaks, complete maintenance proves most effective in mitigating the likelihood of accidents. Therefore, priority should be given to complete maintenance during equipment servicing and repair.

Temperature-controlled spiral-wound heat exchangers, skid-mounted circulating pumps, and associated pipelines are key factors influencing accident risks in CBM gathering stations. It is therefore essential to enhance inspection and maintenance activities for such equipment during routine operations.

Subjective and objective weights for each indicator were derived using the Analytic Hierarchy Process (AHP) and the entropy method, respectively. These weights were then integrated through game theory to obtain combined weights, which subsequently served as input for a fuzzy comprehensive evaluation. Among all Tier-1 indicators, Emergency Preparedness and Response received the highest combined weight (0.4551), highlighting its critical importance. Consequently, enhancing management focus on this aspect is recommended during the operation of the CBM gathering station equipment.