1. Introduction
Chemical industrial parks usually have a large number of flammable and explosive hazardous substances, and large chemical installations are densely distributed in these locations [
1,
2]. Once a major accident occurs, it is likely to destroy adjacent plants or enterprises, leading to the occurrence of domino effects [
3], which may have a serious negative impact on the sustainable development of chemical industrial parks [
4]. Due to worldwide climate change and industrialization, technological accidents triggered by natural events have occurred frequently in recent years, which are commonly called Natech events (an abbreviation for natural disaster-induced technological accidents) [
5,
6,
7,
8]. Natural disasters can lead to the simultaneous destruction of multiple dangerous installations in chemical industrial parks, damage or destroy safety barriers, and block the lifelines required for emergency rescue [
9,
10,
11]. A series of major accidents show that once a Natech event occurs, it will lead to more serious consequences than conventional accidents and is more likely to result in domino effects. For example, the 2011 Great East Japan earthquake caused serious damage to oil and gas storage tanks and other hazardous chemical facilities in some chemical industrial parks [
12]. According to the investigation of the Fire and Disaster Management Agency (FDMA), a total of 3324 hazardous chemical facilities were damaged, and 42 fire accidents and 122 leakage accidents happened after the earthquake [
13].
In recent decades, the increasing risk of domino effects and Natech events have attracted extensive attention from scholars, and the academic community has carried out a series of studies on domino effects and Natech events. In the field of domino effects, the current research mainly focuses on the following four aspects: statistical analysis of historical accidents [
14,
15,
16], equipment vulnerability assessment model [
17,
18,
19,
20], risk assessment [
21,
22,
23,
24,
25,
26,
27], and accident prevention and control [
28,
29,
30,
31]. For example, Darbra et al. analyzed 225 domino accidents and found that about 33% of domino accidents were caused by fire, explosion, lightning, flood, earthquake, and other external disasters [
16]. Similarly with domino effects, the research on Natech events mainly focuses on the statistical analysis of historical accidents [
32,
33], equipment vulnerability assessment model for natural disasters [
34,
35,
36], risk assessment [
37,
38,
39], and risk mitigation [
40,
41]. Previous studies of accident statistics reported that floods and lightning have the highest frequency, while earthquake-related Natech events caused the most serious consequences of accidents among Natech accidents [
42]. However, the above studies considered domino effects and Natech events separately and did not comprehensively study domino effects caused by natural disasters, which should be taken into account for a more realistic and comprehensive estimation.
Recently, some scholars have paid more attention to possible domino effects triggered by Natech events. Using a Bayesian Network, Yang et al. proposed a prediction method to evaluate the probability of domino effects triggered by lightning [
43], while Misuri et al. carried out a quantitative risk assessment method for domino effects triggered by lightning [
44]. However, the assessment method for lighting only considers a single primary accident scenario, but it is not suitable for assessing how earthquakes, floods, and other disasters may lead to multiple primary accident scenarios. Huang et al. developed a usable probabilistic analysis methodology for earthquake-induced domino effects based on a Monte Carlo simulation [
45], while Zeng et al. proposed a novel methodology for quantitative risk analysis of domino effects triggered by floods [
46]. Lan et al. used a network-based approach to carry out a Natech-related domino effects simulation involving a case study on a coastal oil storage base with respect to hurricanes and secondary flooding [
47]. Khakzad developed a fire-spread model to obtain spread probabilities showing the most probable path of wildfire in wildland-industrial interfaces based on a dynamic Bayesian network [
48]. The above research efforts have put forward solid ideas and have laid a strong foundation for the domino effects caused by natural disasters. However, these studies could not accurately identify the accident propagation paths of Natech-related domino effects, and quantitative risk assessment research has not been carried out, even though it plays an important role in effective accident prevention and control.
In order to solve the above shortcomings, Men et al. proposed an event-driven probabilistic methodology to simulate the spatial-temporal evolution of domino chains triggered by natural hazards, and the proposed method can quickly identify the critical system units and temporal intervals [
49]. Chen et al. developed a three-dimensional visualization system for domino effects triggered by Natech events in oil-gas depots, which can be used to calculate the probability and evolution path of the accident chain [
50]. However, these methods could not identify all the possible propagation paths and did not carry out quantitative risk assessment, which would thus lead to underestimated results. Yang et al. proposed a method for assessing all the propagation paths and probabilities of domino effects triggered by Natech events [
51], but this method is only applicable to vapor cloud explosions, and not to fires or other scenarios.
The present work focuses on two research topics to fill the gap mentioned in the current research, which is divided into two parts. Part I (current paper) develops a probability calculation method to obtain all possible propagation paths and their probabilities and to identify the most dangerous equipment units and propagation paths of domino effects triggered by Natech events, which provides data support for the quantitative risk assessment and prevention and control methods presented in Part II of this work. Part II (accompanying paper) proposes an individual risk and social risk assessment model for domino effects triggered by Natech events, and a full-life cycle prevention and control system is studied considering the influence of natural disasters and multi-level domino effects simultaneously. The individual risks and social risks of natural disasters and multi-level domino effects are compared and analyzed through a case study, to reveal the propagation principles of natural disasters and domino effects for increased risk in chemical industrial parks, and to quantify the effects of accident prevention and control with the proposed risk assessment models, so as to provide a theoretical basis for optimizing prevention and control strategies. Therefore, the current work can not only improve the safety level of chemical industrial parks and protect the safety of humans and property, but also simultaneously improve the sustainable production of chemical industrial parks, producing a double benefit [
4,
52]. The rest of the current paper is organized as follows: The propagation rules of domino effects triggered by Natech events are stated in
Section 2. The methodology procedures and corresponding equations and algorithms are demonstrated in
Section 3. The application of the proposed methodology to a case study is illustrated in
Section 4. Finally, the conclusions drawn from the present work are formulated in
Section 5. This work includes additional
Supplementary Materials. Some models proposed by other authors, alongside tables of some calculations. are available in the
Supplementary Materials.
2. Propagation Rules of Domino Effects Triggered by Natech Events
Natural disasters have a wide range of impacts and are highly destructive, usually destroying multiple equipment units [
6]. In addition to the direct damage caused by natural disasters, other infrastructure such as communication and power grids, pipelines, and road transport infrastructure are oftentimes also damaged, which hinders emergency response actions, thus aggravating the severity of the consequences and resulting in domino effects [
38]. According to the type of equipment and stored hazardous substances, damaged equipment may potentially lead to fires or explosions, which are escalation vectors resulting in domino effects. When a primary equipment unit is damaged by a natural disaster, the fire or explosion generated by the primary unit may lead to the destruction of adjacent target equipment units, thus triggering an accident chain of domino effects.
The domino effects triggered by natural disasters are essentially propagated by taking the dangerous equipment units as the carrier, and the domino effects escalation vectors as the medium, such as fires and explosions generated by the damaged equipment units. The propagation rules are mainly divided into two parts: the interaction relationship between equipment units and the synergistic effects between escalation vectors [
3]. For illustrative purposes, the accidental chains of domino effects among four tanks affected by natural disasters are illustrated in
Figure 1.
2.1. Interaction between Equipment Units
The primary accident scenarios caused by natural disasters are uncertain. When the primary equipment unit is undetermined, there are three possible interaction relationships between the two dangerous equipment units:
- (i)
Bidirectional-acting relationship. The intensity of the escalation vector generated by an equipment unit is larger than the escalation threshold of the target equipment unit, as is shown by T1 and T3 in
Figure 1a. When T1 first occurs in an accident, it may damage T3, and when T3 first occurs in an accident, it may cause T1 to be damaged.
- (ii)
Single-acting relationship. The intensity of the escalation vector generated by one equipment unit is larger than the escalation threshold of the target equipment unit, while the intensity of the escalation vector generated by the other equipment unit is less than the escalation threshold of the target equipment unit, as is shown by T1 and T4 in
Figure 1a. When T1 occurs first in an accident, it may damage T4, while when T4 occurs first in an accident, it will not lead to the destruction of T1.
- (iii)
No interaction relationship. The intensity of the escalation vector generated by the two equipment units is less than the escalation threshold of the target equipment unit. For example, T1 and T2 in
Figure 1a cannot damage each other in the case of an accident.
In the propagation process, the first damaged equipment unit will affect the target equipment unit as the primary equipment unit, and the later damaged equipment unit will not affect the already damaged equipment unit. For example, as shown in
Figure 1b, if T1 and T2 are assumed to be the primary equipment units that are damaged by natural disasters, then T1 may affect T3 after T1 is damaged, but T3 cannot have an impact on T1.
From the above analysis, it can be seen that due to the uncertainty in accident propagation, the propagation process of domino effects has many possible propagation paths. For example, as shown in
Figure 1b, both T3 and T4 have the possibility of failure. However, when the first-level domino effect is propagated to
Figure 1c, only T3 has a fire accident after becoming damaged, and T4 is still not damaged. Therefore, for the analysis of accident propagation process, in addition to the most possible propagation paths, all other possible propagation paths should also be considered.
2.2. Synergistic Effects
During the propagation process of domino effects, the thermal radiation of fires may have synergistic effects, which may strengthen the resulting impacts on the target equipment. For example, a fire usually lasts for a long time (usually lasting for hours or even days). If multiple equipment units are subject to fire accidents simultaneously, the generated thermal radiation will act on the same target equipment unit at the same time, resulting in an increase in the damage probability of the target equipment unit. For example, as shown in
Figure 1c, both T1 and T3 are subject to fire accidents, and the generated thermal radiation acts together on T4. At this time, the thermal radiation effects of T1 and T3 need to be considered simultaneously; that is, the thermal radiation intensity of T4 is the superposition of thermal radiation intensity from T1 and T3.
4. Case Study
4.1. Overview of the Case Study
The proposed method is demonstrated by a case study with a tank farm located in a coastal area of China, and the layout of the tank farm is shown in
Figure 4. Since the filling coefficient of the storage liquid in the tank constantly varied during the operation stage, the filling coefficient of the storage liquid in this case is a randomly assumed parameter in accordance with standard specifications. The characteristic parameters and storage liquid parameters of each tank are shown in
Table 2. According to the predominant meteorological conditions in the chemical industrial park, the wind speed is selected as 5 m/s with stability class B from the northwest, while the ambient temperature is 22 °C, and relative humidity is 0.67. The chemical industrial park is located in a flood-prone area; thus the catastrophic flood scenario with a return period of 200 years (i.e., the flood frequency is 0.005 times/year), having last occurred in 1915, is selected as the referenced natural disaster event. The maximum flood submergence depth is about 3.5 m, and the flood velocity is about 0.5 m/s. In the case study, the vulnerability assessment model for flooding proposed by the author is adopted (See
Supplementary Material S3 for detailed model) [
34], and the failure probability of each tank due to flooding is shown in
Table 2.
4.2. Accident Consequence Analysis and Accident Escalation Probability
Due to the great uncertainty of equipment damage and leakage intensity caused by natural and technical disasters, on the premise of ensuring safety, this paper adopts the worst-case accident scenario, assuming that the equipment failure caused by natural and technical disasters is catastrophic failure, and the leakage scenario is instantaneous leakage.
Gasoline and naphtha are volatile and flammable liquids, according to the event tree analysis, which may result in pool fire or vapor cloud explosion. Crude oil is a non-volatile flammable liquid, which may cause pool fire. The accident consequence can be calculated by the PHAST 8.21 software, which is one of the most famous and widely used software tools available in the field of risk analysis [
58], and the intensities of thermal radiation and overpressure received by the target tank from the primary tank are listed in
Supplementary Material S4.
The equipment escalation probability of a single accident scenario can be calculated by the probit model in
Supplementary Material S1. The escalation probability of the target equipment unit after the primary equipment unit is damaged can be calculated by Equation (4), and the equipment escalation probability matrix is shown in Equation (12), which takes into account the tank failure probabilities due to overpressure and thermal radiation in the subsequent calculations based on the probit model in
Supplementary Material S1 and accident consequences in
Supplementary Material S4.
4.3. Primary Failure State Assessment
Natural disasters may destroy multiple primary equipment units simultaneously. For the tank farm of eight tanks in this case study, there are 255 different failure state combinations. The failure state combinations and their identifications are shown in
Supplementary Material S5. The probability of each primary failure state combination can be calculated by Equation (2). Since a failure state combination with a probability of less than 10
−10 is considered almost impossible and its impact on risk can be neglected [
38], this paper only considers the failure state combinations with primary failure probabilities larger than 10
−10. There are thirty-five primary accident scenarios with probabilities larger than 10
−10, and the top ten most likely primary failure state combinations are shown in
Table 3. It can be seen from
Table 3 that the most likely primary failure state combination is S24. In this combination, T3 and T6 have the highest probability of being damaged by flood, so T3 and T6 being simultaneously damaged has the highest probability, which is
. Among the top ten most likely primary accident scenarios, the probability ranges from 10
−3 to 10
−7, and most of the combinations have T3 or T6 tanks, indicating that these two tanks have a large impact on the primary failure scenario, which can be considered as the most likely primary equipment unit.
4.4. Propagation Path Analysis
4.4.1. Most Likely Propagation Path
Analyzing the propagation path probability of domino effects caused by natural disasters can identify the most likely propagation path and probability and provide a data basis for quantitative risk assessment and mitigation.
Table 4 lists the top ten most likely propagation paths with probability ranges from
to
. The primary failure state combination of these ten propagation paths is S24 or S6, indicating that a primary failure state combination with high occurrence probability is most likely to trigger domino effects.
4.4.2. Propagation Paths at All Levels
Table 5 lists the number and probability of propagation paths at each level to analyze the impact of domino effects at different levels.
It can be seen from
Table 5 that the number of paths with single-level domino effects is the smallest, and the number of domino effect paths at 3–6th levels is up to the tens of thousands, but their cumulative probabilities are less than that of the first and second levels. The maximum path probability at each level decreases gradually from
to
with the increase of levels, indicating that the occurrence probability of the high-level domino effect cannot be ignored. The minimum path probability of each level gradually decreases from
to
, and these path probabilities are less than the cutoff value of 10
−10.
4.4.3. Failure Probability Distribution of Tanks at All Levels
Figure 5 shows the total failure probability and cumulative failure probability of tanks at different levels, and the total failure probability of T7 and T5 is the highest due to how they are adjacent to the T3 and T6 tanks that are susceptible to natural disasters, followed by T1, T4, T8, and T2. However, the failure probability of the above tanks is similar, at about 89–90% of the failure probability of T7. The total failure probability of T3 and T6 is the lowest, which is 28% and 2.8% of the failure probability of T7, respectively, because these two tanks are served as primary equipment units and are less affected by the domino effects of other tanks. The failure probability of the T2, T3, T6, and T7 tanks at the first level of domino effects is larger than that of other levels, because these four tanks are adjacent to the most likely primary equipment unit T3 or T6. Therefore, those tanks are susceptible to the influence of T3 or T6. However, the T1, T4, T5, and T8 tanks are susceptible to the domino effects of the T2, T3, T6, and T7 tanks, resulting in a high probability of a second level of domino effects. The proportion of domino effects occurring at or above three levels in these tanks is less than 20%, and the impact on the overall domino effect is relatively small compared to accidents at other levels.
4.5. Accident Scenario Analysis
In order to analyze the impact of different scenarios on the failure probability of each tank, four situations are analyzed: (a) Natech events and conventional accident scenarios; (b) multi-level domino effects triggered by Natech events and conventional accident scenarios; (c) single-level domino effects triggered by Natech events and conventional accident scenarios; (d) only conventional accident scenarios.
Table 6 lists the combination of different accident scenarios, and
Figure 6 shows the failure probability of each tank under different accident scenarios.
By the comparative analysis of failure probability of A and D accident scenarios, it is shown that when considering the Natech scenario, the failure probability of T2, T3, and T6 is significantly increased compared with the conventional accident scenario, by about two to three orders of magnitude, and the increased risk for other tanks is less than one order of magnitude. It shows that natural disasters can significantly increase the failure probability of some tanks, such as T2, T3, and T6 in this case, and ignoring the impact of natural disasters will cause the risk to be underestimated.
- 2.
Impact of domino effects
Comparing the failure probability of accident scenarios A and B, it can be seen that the failure probability of the T1, T2, T4, T5, T7, and T8 tanks increases by about three orders of magnitude when considering multi-level domino effects, which indicates that the occurrence of domino effects have a great impact on the failure probability of these tanks. Due to the impact of natural disasters, the other tanks are mostly served as primary equipment units and are relatively less affected by domino effects. It shows that domino effects will also lead to the destruction of tanks that are less affected by natural disasters, significantly increasing the risk for the chemical industrial park.
- 3.
Impact of multi-level domino effects
In order to compare and analyze the impact of multi-level domino effects and single-level domino effects, the failure probabilities of B and C accident scenarios are shown in
Figure 6. It can be seen that multi-level domino effects will lead to the most significant increase in the failure probability of T8, at about three orders of magnitude. The failure probability of T1, T2, T4, and T5 also increased significantly, with an increase range of about one to three times. It shows that considering multi-level domino effects can have a larger impact on the failure probability of some tanks and ignoring multi-level domino effects will cause the risk of some tanks to be underestimated.
5. Conclusions
This paper presents a probability analysis method for predicting all the possible propagation paths of Natech domino effects, which considers multiple primary equipment units and multi-level domino effects simultaneously. A chemical tank farm located in a flood prone area of China is selected as a case study to demonstrate the application of the proposed method, and the case application shows that this method can effectively identify all possible propagation paths and calculate their probabilities.
In the case study, the probability analysis of primary failure state combinations shows that the probability of the top ten most likely primary accident scenarios decreases from 10−3 to 10−7, and most of the top ten primary failure state combinations contain T3 or T6 tanks, indicating that these two tanks can be considered as the most likely primary equipment unit. The probability analysis of the propagation path of the domino effects induced by natural disasters in the case study shows that the primary failure state has the greatest impact on the propagation probability of domino effects, and the cumulative failure probability of each tank is greatly affected by the primary failure state. The number of propagation paths of the single-level domino effect is the least, but the cumulative failure probability is the largest, and the influence of the multi-level domino effect cannot be ignored. The failure probability analysis of each tank in different scenarios shows that Natech events and multi-level domino effects have a significant impact on the failure probability of tanks, even resulting in the failure probability of some tanks increasing by several orders of magnitude. Ignoring the impacts both of natural disasters and the multi-level domino effect will lead the failure probability of tanks to be underestimated.
The equipment failure probability calculated in this paper can be used for quantitative risk assessment, and the most dangerous propagation path and equipment unit identified can provide a reference for the optimizing risk mitigation measures proposed in Part II of the present work. It can be concluded that the results and mitigation measures proposed in this work play a critical role in safety production in chemical industrial parks, and improving safety performance will produce two-pronged benefits: reducing the safety risks of chemical industrial parks and simultaneously improving sustainability performance.
Nonetheless, it should be remarked that this paper only considers the possibility of the spatial propagation of domino effects and does not focus on the temporal evolution of domino effects. However, equipment failure caused by fire may take some time, and safety barriers and fire rescue actions have a delayed or even eliminative effect on the evolution of domino effects. Therefore, the accuracy of results may increase by considering the temporal factor of domino effects caused by fire, and future research should comprehensively consider the spatio-temporal evolution law of accident propagation and dynamic risk assessment method.