Sustainable Risk Management Framework for Petroleum Storage Facilities: Integrating Bow-Tie Analysis and Dynamic Bayesian Networks

Abstract

Petroleum storage and transport systems necessitate robust safety measures to mitigate oil spill risks threatening marine ecosystems and sustainable development through ecological and socioeconomic safeguards. We aimed to gain a deeper understanding of the evolution patterns of accidents and effectively mitigate risks. An improved risk assessment method that combines the Bow-Tie (BT) theory and Dynamic Bayesian theory was applied to evaluate the safety risks of petroleum storage and transportation facilities. Additionally, a scenario modeling approach was utilized to construct a model of the event chain resulting from accidents, facilitating quantitative analysis and risk prediction. By constructing an accident chain based on fault trees, the BT model was converted into a Bayesian Network (BN) model. A Dynamic Bayesian Network (DBN) model was established by incorporating time series parameters into the static Bayesian model, enabling the dynamic risk assessment of an oil storage and transportation base in the Zhoushan archipelago. This study quantitatively analyzes the dynamic risk propagation process of storage tank leakage, establishing time-dependent risk probability profiles. The results demonstrate an initial leakage probability of 0.015, with risk magnitude doubling for the temporal progression and concurrent probabilistic escalation of secondary hazards, including fire or explosion scenarios. A novel risk transition framework for the consequences of petrochemical leaks has been developed, providing a predictive paradigm for risk evolution trajectories and offering critical theoretical and practical references for emergency response optimization.

1. Introduction

The petrochemical industry remains a cornerstone of global energy and industrial systems, underpinning modern economic development while simultaneously posing critical sustainability challenges due to its resource-intensive operations and environmental externalities [1]. In emerging economies like China, accelerated industrialization and urbanization have driven exponential growth in petrochemical demand, necessitating the urgent integration of decarbonization strategies with circular economy principles to reconcile sectoral expansion with planetary boundaries [2]. The efficient and safe development, extraction, and testing of offshore oil and gas resources are critical to ensuring energy security while driving socioeconomic development, especially in high-risk marine environments [3,4]. Coastal petrochemical industries typically feature extended supply chains and a diverse array of oil products, leading to heightened concentrations of hazardous materials [5]. Historical incidents, such as the 2015 Tianjin Port explosion in China (resulting in 165 deaths and an economic loss of CNY 6.866 billion) [6] and the 2020 Beirut Port explosion in Lebanon (with over 200 fatalities and USD 15 billion in damages), underscore the severity of such risks [7]. Therefore, it is essential to propose a safety framework tailored to coastal petrochemical cities to enhance overall urban safety and mitigate the damage caused by accidents.

In the domain of hazardous materials risk assessment, various models have been introduced to address safety concerns under different conditions. The dynamic risk assessment approach using Bayesian Networks (BNs), which continuously updates accident probabilities based on real-time data, was introduced by Wang et al. [8], enhancing accuracy. A multi-level dynamic framework was developed by integrating fuzzy logic and Markov chain models for the effective management of high-risk events in coastal areas [9], while a dynamic system capable of predicting accident trends and issuing early warnings based on historical and real-time port data was created through the combination of big data analysis with machine learning [10].

Qualitative approaches, while useful for initial screenings, lack precision in quantifying risks and conducting detailed analyses of complex systems and risk interactions [11]. Quantitative methods, including the Analytic Hierarchy Process (AHP) and BN, offer more detailed risk quantification [12,13]. AHP decomposes complex problems into hierarchical components, allowing experts to assign weights and prioritize risks; however, maintaining consistency in scoring is challenging, and AHP is not well suited for capturing dynamic risk changes [14]. In contrast, BN models have probabilistic dependencies between variables, making them particularly suitable for dynamic risk assessment in complex systems. Given the substantial scale of petrochemical enterprises in coastal cities, the complex and diverse risk factors involved, and the relatively limited ecological capacity, the consequences of hazardous chemical accidents significantly impact the sustainable development of these urban areas [5,15]. A quantitative risk assessment based on expert scoring exhibits high practicability and reliability, offering actionable insights for the enterprise-level risk evaluation and dynamic evolution processes of accident scenarios [16]. This methodology enhances managerial awareness of enterprise-specific risk categories and severity levels while facilitating the implementation of on-site safety protocols and emergency management strategies. In particular, it provides critical analytical value for understanding evolving risk consequences and predicting dynamic risk progression patterns, thereby supporting evidence-based decision-making in industrial safety governance.

This study aims to address the limitations of traditional risk analysis methods, such as fault tree analysis and static Bayesian models, which do not adequately meet the dynamic risk analysis needs of coastal oil storage and transportation facilities. To analyze the interconnections among risk factors and clarify the dynamic evolution of accidents, this research employs the Bow-Tie (BT) method to assess leakage risks and their consequences in storage tank areas. A Dynamic Bayesian Network (DBN) model is then established, incorporating temporal factors influencing leakage probabilities. This model seeks to outline the risk evolution of accidents, identify key hazardous factors, and provide rapid diagnostic and predictive capabilities, offering valuable insights for risk control and emergency response in coastal oil storage and transportation facilities.

2. Methods

BN, which are probabilistic graphical models, encapsulate random variables and their conditional dependencies, serving as a critical tool for assessing risks in complex systems characterized by uncertainty [17]. The BT analysis method is a highly visual and structured approach to risk analysis and management [18]. Utilizing the BT analysis method, the risks associated with incidents such as leaks, fires, and explosions at petroleum storage and transportation facilities can be analyzed. By developing an accident chain from a fault tree analysis, the BT model can be converted into a BN model. Building upon a static BN, the incorporation of the noise-or-gate model and time series parameters allows for the construction of a DBN model, thereby enabling the dynamic risk assessment of petroleum storage and transportation facilities. The flow chart of the research framework is shown in Figure 1.

2.1. BN Model Method

The development of a BN model encompasses several key steps [19]. Initially, it is essential to identify the pivotal nodes relevant to the research subject. This involves summarizing the core elements based on empirical knowledge and integrating significant factors from historical incidents. Subsequently, one must analyze the causal relationships among the variables, sequence the scenario in chronological order, arrange the identified factors according to their logical occurrence, link each node with directed edges, and thereby create the topology diagram for the research subject. Ultimately, the model’s parameters for each node must be quantified, including the node’s associated probabilities: prior probabilities, conditional probabilities, and posterior probabilities. Refer to Figure 2 for a detailed flow chart illustrating the process.

2.2. Network Parameter

After establishing the BN model, it is necessary to determine the parameters of the network, that is, the prior probabilities and conditional probabilities of the nodes [20]. Based on the criteria for determining expert weights established in

Table 1. Criteria for determining expert weights.

Stats	Category	Score
Position	Senior engineer	5
	Manager	4
	Engineer/researcher	3
	Technician	2
	Operator	1
Educational background	Learned scholar	5
	Master	4
	Undergraduate course	3
	Junior college	2
	Senior high school	1
Field experience	Firm	2
	Colleges and universities	0

, a weight analysis was conducted for four experts, and the weights of each expert were obtained, as shown in

Table 2. Expert rating weight.

Domain Expert	Weight
Senior engineer (E1)	0.3
Engineer (E2)	0.25
Front-line worker (E3)	0.2
Corporate safety officer (E4)	0.25

[21].

(1) Prior probability

Prior probabilities refer to the occurrence probabilities of each node. The main steps are given as follows:

Four industry experts, each possessing substantial fieldwork experience, were invited to evaluate and score the questionnaire. Different weights were assigned to the experts according to Table 2. The experts used their experience and referred to

Table 3. Fuzzy weight.

Language Evaluation	Evaluation Description	Fuzzy Number
very low (VL)	only happened once	(0, 0, 0.1)
low (L)	occurs once every 6 to 10 years	(0, 0.1, 0.3)
relatively low (RL)	occurs once every 1 to 5 years	(0.1, 0.3, 0.5)
middle (M)	occurs once every 10 to 12 months	(0.3, 0.5, 0.7)
relatively high (RH)	occurs once every 7 to 9 months	(0.5, 0.7, 0.9)
high (H)	occurs once every 4 to 6 months	(0.7, 0.9, 1)
very high (VH)	occurs once every 1 to 3 months	(0.9, 1, 1)

to assess the risk probabilities of the nodes in linguistic terms [20].

The expert’s language is then translated into a triangular fuzzy number format, and the fuzzy membership function is used to obtain the triangular fuzzy probability:

$$P_i^k=(a_i^k,b_i^k,c_i^k)$$

(1)

Triangular Fuzzy Probability Mean: The fuzzy probabilities given by the experts’ scores are averaged to obtain the fuzzy mean probability.

$$P_i^{″}={\displaystyle \sum _{j=1}^n\lambda P_{ij}^k}=(a_i^{″},b_i^{″},c_i^{″})$$

(2)

Defuzzification: The fuzzy mean probability is converted into a specific probability value using the area centroid method. First, the fuzzy possibility score (FPS) is calculated according to Equation (2). The FPS is determined by integrating the fuzzy membership function over the entire range of possible values and then finding the centroid of the area under the curve, which represents the most likely value or the mean of the fuzzy distribution.

$$P_i^{*}={\displaystyle \frac{a_i^{″}+2b_i^{″}+c_i^{″}}{4}}$$

(3)

Secondly, fuzzy probability (FP) is obtained according to Formulae (3) and (4):

$$FP=\left\{\begin{array}{c}{\displaystyle \frac{1}{{10}^K}},FPS\ne 0\\ 0,FPS=0\end{array}\right.$$

(4)

Among these, $K=2.301\times {\left({\displaystyle \frac{1-FPS}{FPS}}\right)}^{1/3}$.

(2) Conditional probability

Conditional probability is a combination of probabilities of child nodes corresponding to different states of parent nodes, and its quantity is a function of the exponential of the corresponding child nodes to each parent node [22]. When the structure of the BN is complex, determining the conditional probability table by experts is too labor-intensive and inconvenient to operate, and it may also increase the error rate of the results. In this study, a BN was established by combining the expert evaluation based on fuzzy theory and the noisy-or-gate model.

The conditional probability of risk probability is calculated by Equation (5).

$$P\left(Y\left|X_1,X_2,\cdots X_n\right.\right)=1-{\displaystyle \prod _{i:X_i\in X_T}\left(1-P_i^{*}\right)}$$

(5)

In the formula, P_i^* refers to the fuzzy possibility score, which represents the probability of a parent node occurring when only one of its child nodes occurs.

The node variables in the BN are binary. Probability importance indicates the degree of change in the probability of an event occurring due to changes in the state variables of factors; that is, the greater the probability’s importance, the greater the overall impact of the factor on the event, and the more likely it is to lead to the occurrence of a risk event. The probability importance of the root node in the BN is as follows:

$$I_i^{\mathrm{Pr}}(x_i)=P\left(X=1\left|x_i=1\right.\right)-P\left(X=1\left|x_i=0\right.\right)={\displaystyle \frac{P\left(X=1,x_i=1\right)}{P\left(x_i=1\right)}}-{\displaystyle \frac{P\left(X=1,x_i=0\right)}{P\left(x_i=0\right)}}$$

(6)

The critical importance of the root node indicates the rate of change in the probability of leaf nodes occurring due to changes in the occurrence probability of the root node:

$$I_i^{Cr}(A_i)={\displaystyle \frac{P\left(A_i=A_p\left|U=U_p\right.\right)}{P(U)}}{I}_i^{\mathrm{Pr}}(A_i)$$

(7)

where P_(U) represents the posterior probability of the leaf node.

If the probability of the leaf node is known, the posterior probabilities of each node can be obtained using the BN’s backward reasoning algorithm.

Given that the risk probability of the leaf node X in the BN is represented by X_p, then the posterior probability of the risk for the root node $x_i^p$ is the following:

$$P\left(x_i=x_p\left|X=X_p\right.\right)={\displaystyle \frac{P\left(x_i=x_p,X=X_p\right)}{P\left(X=X_p\right)}}={\displaystyle \frac{{\displaystyle \sum _{x_1,x_2,\cdots x_n}P\left(x_1,x_2,\cdots ,x_j=x_p,\cdots ,x_n,X=X_p\right)}}{P\left(X=X_p\right)}}$$

(8)

By integrating expert analysis with historical data, BNs can more accurately ascertain accident risk probabilities and the significance of risk sources within petroleum storage and transportation facilities, thereby offering theoretical underpinnings for the identification of safety hazards at these sites. This paper introduces a Markov process into the BN model, considering the temporal parameter, to conduct a preliminary investigation into the dynamics of risks associated with petroleum storage and transportation facilities.

2.3. Establishment of the DBN Model

A DBN is typically characterized as an extension of the BN model that incorporates a temporal dimension. The primary distinction between the DBN and traditional BN models lies in its composition, which includes an initial network B0 and a series of transition networks Bi. DBN models typically assume that the transition probability network parameters remain constant throughout the system’s changes. The probability parameters of nodes in the dynamic changes only consider the influence of the previous adjacent time period [17]. The method for determining the transition probability of any two adjacent nodes in a DBN is given by Equation (9).

$$P\left(X_t|X_{t-1}\right)={\displaystyle \prod _{i=1}^{N}P\left(X_t^i|P_a\left(X_t^i\right)\right)}$$

(9)

In the formula, $X_t^i$ represents the i_-th node at the t_-th time slice, and $P_a\left(X_t^i\right)$ represents the parent nodes of $X_t^i$.

In the DBN, the conditional probabilities of the transition network are the parameter values of the initial network. The method for calculating the joint probability of any node is given in Equation (10).

$$P\left(X_{1:N}^{0:T}\right)={\displaystyle \prod _{i=1}^N{P}_{B_0}\left(X_i^0|P_a\left(X_i^0\right)\right)}\times {\displaystyle \prod _{t=1}^T{\displaystyle \prod _{i=1}^N{P}_{B_{\to }}\left(X_i^t|P_a\left(X_i^t\right)\right)}}$$

(10)

In the formula, $X_{1:N}^{0:T}$ refers to all nodes of the system’s random variables from the initial moment to time T; $P_{B_0}$ is the initial state probability distribution of the system.

3. Evaluate the Application Results of the Model

This study employs accident analysis to pinpoint risk sources and elucidate the inherent interconnections among risk factors within defined scenarios. It constructs an event chain grounded in the patterns of these scenarios and establishes the BT model accordingly. Subsequently, the BT model is translated into a BN model, thereby finalizing the BN model’s construction.

3.1. Construction of BT Model

The historical accident analysis of petroleum storage and transportation facilities reveals that the tank farm is central to the facility’s risk profile and is the most commonly affected unit during incidents [23]. Using a petroleum storage and transportation base in Zhoushan as a case study and acknowledging the superior fire prevention features of floating roof tanks, it was observed that the majority of the oil storage tanks at the base are of the floating roof variety. This paper focuses on the leakage incidents of floating roof tanks, developing a fault tree and event tree analysis specific to such leaks. It conducts a comprehensive analysis of the factors associated with floating roof tank leakages, drawing from the actual conditions at the base, expert insights, historical incident data, and the pertinent literature. This analysis encompasses the principal sources of leakage risk, the event chains, and the secondary events that may be triggered by leaks. Subsequently, a BT model for leak incidents at the petroleum storage and transportation base was formulated.

3.2. Establishment of the BN

The systematic transformation of a fault tree analysis (FTA) into a BN framework requires rigorous ontological alignment between hierarchical events and multivariate causal dependencies in the FTA with the directed acyclic graph topology and conditional probability distributions of the BN nodes [17]. This methodological conversion preserves structural isomorphism through the probabilistic encoding of AND-OR gates as parent–child node relationships while enhancing dynamic risk inference capabilities via the Bayesian probability theory [20]. Such integration establishes a hybrid probabilistic risk assessment framework that enables the quantification of uncertainty and cross-temporal risk trajectory simulations unattainable through conventional static FTA paradigms. This conversion process is depicted in Figure 3. Specifically, key elements of the Bow-Tie model—basic events, intermediate events, top events, safety barriers, and accident consequences—are mapped to their corresponding nodes in the DBN framework: root nodes, intermediate nodes, leaf nodes, barrier nodes, and consequence nodes, respectively. The obtained BN model is shown in

Table 4. BN node information about oil storage and transportation base risk.

Series A	Series B	Series C	Series D	Series E
Top event A	B1 Oil spill	C1 Liquid level exceeds the safe height	D1 Level control and monitoring system failed (LC1)
			D2 Liquid level exceeded	E1 Operation error
				E2 Staff negligence
				E3 Safety valve failure
		C2 Emergency stop system failed
	B2 Floating plate sinking	C3 The strength of the floating roof decreases	D3 Accessory damage
			D4 Construction quality defect
			D5 Floating roof fatigue operation
			D6 Natural disaster
		C4 Operation management is not in place	D7 No strict implementation of the post responsibility system
			D8 The operation procedure is not strictly implemented
			D9 Devices are not properly managed during thunderstorms
	B3 Tank rupture	C5 Uneven settlement of foundation	D10 Improper foundation treatment
			D11 Strength design defect
			D12 The construction quality is not in place
			D13 Natural disaster
		C6 Settlement monitoring failure (LC1)
		C7 Corrosion or crack	D14 Corrosion
			D15 Quality defect
			D16 Inclement weather
			D17 Routine equipment maintenance is not in place
			D18 Insufficient knowledge of tank storage medium
		C8 External failure
		C9 Tank fatigue	D19 Temperature control and monitoring system (LC1) failure
			D20 Overpressure	E4 Safety devices are not complete
				E5 High ambient temperature

.

Following a leak, the potential consequences that may ensue due to the failure of safety barriers encompass the spread of the leak, ignition leading to combustion and explosions, jet fires, flashovers, the formation of toxic gas clouds, and vapor cloud explosions. The probabilities of safety barrier failure, as per the data, are presented in

Table 5. Probability of safety barrier failure.

Barrier	Failure Probability
Immediate ignition	0.031
Delayed ignition	0.025
Finite space	0.046

[24]. The accident consequences are categorized into four severity levels—C1, C2, C3, and C4—based on their seriousness, with further details provided in

Table 6. Criteria for grading the consequences of events.

Personal Injury	Economic Loss (Ten Thousand CNY)	Environmental Damage	Consequence Hierarchy
No casualties	<100	companies can solve it themselves	C1
Stay in hospital for more than 24 h	100~1000	the impact on the environment is serious and requires assistance from local authorities	C2
Long-term effects of injury	1000~5000	it has a great impact on the external environment of enterprises, which requires the intervention of the state	C3
Irreversible casualties	>5000	it has irreversible impact on the external environment of enterprises, which requires state intervention	C4

. [25] The enterprise safety risk assessment criteria for the evaluation model are established by the following information: initially, embedding risk probabilities within a matrix framework; subsequently, stratifying the risks into several grades based on their potential consequences; and ultimately, integrating these aspects to formulate the assessment criteria, as detailed in

Table 7. Consequences of events.

Consequence	Level
Fire explosion	C3
Jet fire	C2
Flash ignition	C2
Vapor cloud explosion	C4
Gas cloud	C4
leak	C1

and

Table 8. Risk probability level.

Probability Level	Risk Probability Level	Probability Range
low	I	$\left(0,\left.0.0003\right]\right.$
normal	II	$\left(0.0003,\left.0.03\right]\right.$
relatively high	III	$\left(0.03,\left.0.3\right]\right.$
high	IV	(0.3, 1)

.

Table 9. Risk level.

Risk Level			Risk Loss Level
			I	II	III	IV
			C1	C2	C3	C4
Risk probability level	I	low	1	1	2	2
	II	normal	1	2	3	3
	III	relatively high	2	3	3	4
	IV	high	2	3	4	4

indicates that risks are stratified into four levels, with the implications of different risk levels defined as follows: Level 1 indicates that no supervision or inspection is necessary; Level 2 necessitates regular supervision and inspection; Level 3 requires the implementation of measures to mitigate risk; Level 4 demands continuous supervision and inspection to avert accidents.

4. Accident Risk Analysis Based on BN

As an archipelagic port city, Zhoushan boasts a thriving petrochemical sector with significant advancements in the establishment of enterprises within its parks and industrial zones. Focusing on a petroleum storage and transportation hub within a chemical park in Zhoushan, equipped with a storage capacity of 2.56 million cubic meters for oil products and a theoretical peak throughput capacity of 42.205 million tons at the dock, therefore, represents considerable potential risks. A BN-based safety risk assessment methodology was employed to conduct a thorough analysis of the site.

4.1. Network Parameter Determination

The outcomes derived from the computation of network parameters were subsequently imported into the GeNIe software to determine the risk accident probability associated with the floating roof tank. It has been ascertained that the accident risk probability for the petroleum storage and transportation base is 0.015 (See Appendix A). The risk levels corresponding to various consequence events are graphically represented in Figure 4. In the diagram, the horizontal axis represents the risk severity levels (as defined in Table 6), while the color gradient corresponds to risk classification using a four-tiered chromatic scheme: green indicates acceptable risk, yellow denotes moderate risk, orange signifies elevated risk, and red represents the highest hazard level.

The risk level diagram for each consequence, as depicted, illustrates that the severity of each accident and the consequences it entails escalates with the progression of the event. Consequently, the optimal window for incident control is identified to be at the initial stage.

4.2. Critical Importance Analysis

The critical importance curves depicted in Figure 5 reveal that the primary root nodes, in order of significance, are C8, D14, E5, D15, and D17. Specifically, C8 signifies damage from external forces, D14 indicates corrosion, E5 denotes high ambient temperatures, D15 is associated with quality defects, and D17 corresponds to a lack of routine maintenance. Expert analysis has determined that the risk of leakage is considerably higher when uncontrollable external forces impact the tank, when there are inherent quality issues, and if the tank’s safety maintenance is inadequate. The escalation of systemic risk predominantly stems from inherent vulnerabilities in organizational governance mechanisms; notably, these include deficiencies in safety culture indoctrination programs and non-compliance with corrective action timelines, compounded by structural inadequacies such as suboptimal personnel allocation matrices and fragmented regulatory oversight frameworks. These anthropogenically amplifiable factors exhibit nonlinear interdependencies that exacerbate latent risks beyond conventional probabilistic thresholds, necessitating institution-level resilience and engineering interventions.

4.3. Risk Analysis of Oil Storage and Transportation Base Based on DBN

To conduct a dynamic assessment of the accident risks associated with petroleum storage and transportation facilities, we developed a DBN. For the inference learning process, GeNie 2.3 academic software was utilized. The system’s organizational management recovery rate was assumed to be 0.01, drawing from reference [26]. Additionally, the fuzzy probability values determined in the preceding section were employed in this analysis to substitute for the average likelihood of human error within a given time frame.

Figure 6 illustrates the accident risk probabilities for the petroleum storage and transportation base across 10 distinct time intervals. Employing the DBN risk assessment model for the facility, the dynamic progression of tank leakage was examined. Consequently, the dynamic probability change curve for tank leakage was derived, commencing with an initial leakage probability of 0.015. This probability progressively ascended with the elapse of time, signifying an ongoing accumulation of risks throughout the system’s operational phase. Within each time slice, the accident consequence probabilities were ranked as follows: C1 leak is more probable than C3 toxic gas cloud, which in turn is more likely than C2 jet fire, C2 flashover, C2 deflagration, and finally C2 vapor cloud explosion.

4.4. Discussion

The trend graph of dynamic risks over time demonstrates an increase in the probabilities of various risk types, though the rate of this increase differs. This pattern corresponds to observations in petrochemical hazardous material accidents, where minor risks, if neglected over an extended period, gradually escalate into larger risks, potentially resulting in catastrophic disasters with severe casualties [27]. Therefore, future research should prioritize dynamic risk assessment, disaster models for petrochemical hazardous material accidents, and the dynamic monitoring of risk safety trends. Such studies are essential for preventing and mitigating the escalation of accidents, quantifying their evolution over time, and understanding the trajectory of disasters, all of which are crucial for effective risk control and emergency response.

The evolution of hazardous chemical emergencies is characterized by an interplay of multiple complex event chains. During the development of petrochemical leakage incidents that lead to fires and explosions, typical nonlinear risk stages are often observed (Figure 7). A relatively minor initial event can trigger multiple, multi-layered secondary events, resulting in a chain reaction of accident progression [18]. If the leaked petrochemical products are promptly addressed through emergency response measures, subsequent consequences can be averted. In the absence of the conditions necessary for fires or explosions, the risk associated with the leakage, despite gradually increasing, remains at a relatively low level. However, once ignition or explosion conditions are met, the risk level can undergo a rapid nonlinear transition, as energy release during fires and explosions occurs over a very short time [28]. This brief interval often leaves insufficient time for emergency response. Therefore, during the emergency management of hazardous materials incidents, special attention must be given to the potential for risk transitions toward higher levels to prevent secondary accidents and casualties. The 2015 Tianjin Port explosion in the Binhai New Area serves as a classic example, where the emergency response resulted in significant casualties among rescue personnel [6]. Hence, understanding the properties of hazardous substances and the dynamic evolution of accidents is crucial for preventing secondary disasters and mitigating risks during rescue operations.

In extreme operational environments marked by elevated thermal conditions, hyperbaric states, and the presence of combustible/explosive material, the interplay of energy transfer dynamics and informational entropy disparities may induce cascading catastrophic events. Empirical evidence indicates that the synergistic interaction of these multidimensional risk factors generates nonlinear risk amplification phenomena during phase transition processes [16]. From a systems safety perspective, two critical operational imperatives emerge: primary containment through maintaining system risk parameters within established safety thresholds and secondary mitigation via the timely activation of preventive interventions to arrest incident escalation pathways. The former necessitates the continuous monitoring of thermodynamic equilibria and stochastic process variables, while the latter requires the implementation of adaptive control algorithms for emergency scenario management.

Furthermore, strategic prioritization in emergency response protocols must emphasize human capital preservation through optimized evacuation procedures following low-probability, high-consequence event triggers. This life-preservation calculus incorporates the spatial-temporal modeling of hazard propagation patterns and multi-agent evacuation route optimization, forming an essential component of catastrophic risk mitigation frameworks in industrial safety systems.

5. Conclusions

By developing an event chain model derived from accident scenarios and integrating it with a Dynamic Bayesian Network model, this study accomplishes a dynamic risk assessment of petroleum storage and transportation facilities, pinpointing critical risk points. The main conclusions are as follows:

(1) Based on the results of the statistical analysis of accidents, leak incidents have been identified as significant top events in the risk source hierarchy. To facilitate comprehensive examinations, a DBN model was utilized. The analysis revealed that external force damage, corrosion, high ambient temperatures, quality defects, and substandard routine maintenance are the predominant contributors to leakage occurrences. In terms of risk levels, aside from the toxic gas cloud being classified as a level three risk and leakage as a level-one risk, the remaining accident consequences are categorized as level-two risks.

(2) Employing the DBN risk assessment model for the petroleum storage and transportation base, an analysis of the dynamic process of tank leakage was conducted, resulting in the acquisition of the dynamic probability change curve for tank leakage. Accident risk transitions play a critical role in the escalation of consequences. Therefore, during incident management and emergency response, close attention must be paid to the risk evolution process to prevent secondary harm.