A novel approach for domino effects modeling and risk analysis based on synergistic effect and accident evidence
Introduction
Domino effect is a low-frequency high consequence chain of accidents, where a primary accident occurs and spreads to adjacent units, causing secondary accidents and the total consequences much severer than the consequence of the primary accident [1]. Chemical industrial parks have infrastructures, such as fuel tanks and pipelines, high complexity and growing interdependencies make infrastructures increasingly vulnerable to domino effects [2]. The need for risk analysis of domino effects in chemical industrial parks has been recognized [3], [4], [5], [6]. In the past, the studies on risk analysis of domino effects focused on four main tasks: the identification of domino scenarios, the assessment of escalation frequencies, the calculation of loss of life in complex domino scenarios and the assessment of equipment vulnerability [7].
In most of the early studies, such as [3,4,6], simple "domino chains" were considered and secondary accidents were considered as independent accidents. The over-simplification of studies loses a fundamental characteristic of real-world domino effects, which is the spatial-temporal evolution of domino effects. As a result, the early studies considered the risk of a particular independent accident rather than the risk of domino effects. The spatial evolution of domino effect refers to the escalation route in which the primary accident propagates to adjacent units. For example, if a storage tank is on fire, spatial evolution means which adjacent tank could be the secondary accident unit, the tertiary accident unit and so on. To address the over-simplification problem, some studies aimed to model the spatial evolution of domino effects, such as determination of the most likely propagation route given a primary accident. Cozzani et al. [8] introduced a methodology based on the binomial distribution, the methodology considered all possible accident scenarios triggered by a primary accident to handle the uncertainty arisen from the lack of knowledge about the likely units involved in a domino effect. Khakzad et al. [9] applied ordinary Bayesian network (BN) to model the spatial evolution of domino effects and to determine the most likely propagation route given a primary accident. There are similar studies based on different approaches, such as game theory [10], Monte Carlo simulation [11], and event tree [12], [13], [14]. However, these studies did not take the temporal evolution of domino effects into account.
Since domino effects are quite complicated due to probabilistic propagation, synergistic effects (synergistic effect refers to the collaboration of concurrent primary and secondary accidents to trigger another accident in a tertiary unit and so forth, making an already started domino effect continues [2]), dynamic evolution and behavior of target unit (adjacent/neighboring unit) [15], therefore, a domino effect is a time-dependent process, not only spatial evolution of involved units but also temporal evolution of involved units should be identified. The temporal evolution of domino effect refers to the escalation time at which the primary accident propagates to adjacent units. For example, if a storage tank is on fire, temporal evolution means when the adjacent tanks will be destroyed and be the secondary accident unit, the tertiary accident unit and so on. More importantly, nearly half domino effects are caused by fire [16], [17], [18], and since the escalation caused by fire is delayed concerning the start of fire, foreseeing the temporal evolution of domino effects and predicting the most likely sequence of accidents with timeline could guide the allocation of preventive and mitigative safety measures [2].
To address the drawbacks of previous studies, modeling the spatial-temporal evolution of domino effects has been studied recently. The spatial-temporal evolution of domino effect refers to the escalation route and escalation time the primary accident propagates to adjacent units. Khakzad [2] proposed a methodology based on dynamic Bayesian network (DBN) to model the spatial-temporal evolution of domino effects and also to obtain the most likely sequence of accidents in a potential domino effect. However, the approach is unable to model the temporal dependency quantitatively and obtain accident propagation time considering the synergistic effect. Later, Khakzad et al. [19] introduced a methodology based on graph theory which models a domino effect as a directed graph, graph centrality measures such as out-closeness and betweenness scores were used to identify the units playing a pivotal role in initiating and propagating domino effect. Zhang et al. [15] proposed an agent-based modeling and simulation approach to study the spatial-temporal evolution of domino effects, which explains a domino effect from a bottom-up perspective. Zhou and Reniers [20] proposed a matrix-based approach to model the spatial-temporal evolution of fire-induced domino effects, the approach uses a simulation-based algorithm to calculate accident probability. Chen et al. [21] proposed a methodology involving a Domino Evolution Graph (DEG) model and a Minimum Evolution Time (MET) algorithm to model the spatial-temporal evolution of domino effects.
In these works, fire-induced domino effects were studied, and the synergistic effect [9] of fires was considered by superimposing heat radiations. However, the synergistic effect was dealt with statically, and the superimposed escalation vector on a target unit was compared with an empirical threshold value to determine whether a target unit is damaged or not, as a result, consideration of synergistic effect lacks detailed modeling of time dependency. In studies [2,19,20], if the intensity of the escalation vector is below the threshold value, the likelihood of accident propagation is neglected. Thus, accumulated heat energy or strength loss of tank wall due to the escalation vectors which are below the threshold value is overlooked. For example, consider two fuel storage tanks T1 and T2 as shown in Fig. 1, and a threshold value of 15 kW/m2. If the thermal radiation T2 received from T1 is 14 kW/m2, since it is below the threshold value, therefore it is deemed the primary accident in T1 could not propagate to T2 no matter how long the fire in T1 lasts. From the viewpoint of heat energy accumulation, the radiation intensity threshold value method is inappropriate. However, it should be noted that there are different radiation thresholds commonly used (e.g. 12 kW/m2 or even 7.5 kW/m2) because of the theoretical possibility that after a sufficient amount of time, if the radiation received is constant and below a given threshold, the target unit cannot fail because a sort of steady-state can be reached in which heat received through radiation is balanced by heat dispersed through convection with ambient air.
More accurately, whether a target unit loses its structural integrity in a fire depends on the received thermal dose which decides the thermal stress temperature that can cause failure [22,23]. In this work, the fire synergistic effect model (FSEM) [24] is used to model the spatial-temporal evolution of domino effects considering accident evidence and synergistic effect quantitatively. The FSEM based approach models the escalation route of accidents and predicts escalation time and probability through modeling time-dependent synergistic effect. Besides, from the viewpoint of energy accumulation, the receivable thermal dose is adapted as the failure criterion to consider heat energy accumulation of escalation vectors which are below the threshold value. The FSEM based approach could deliver a macroscopic image of the domino effect evolution route with a microscopic evolution time.
The present work aims to examine the capability of FSEM in spatial-temporal evolution modeling and risk analysis of domino effects in chemical plants. The remainder of this paper is organized as follows: Preliminaries of FSEM are firstly recapitulated in Sections 2. The proposed methodology is presented in Section 3. In Section 4, the application of the methodology to a hypothetic chemical storage plant is illustrated. Finally, the conclusions of the present work are drawn in Section 5.
Section snippets
Preliminaries of FSEM
FSEM [24] is an approach to model the contribution of the synergistic effect of fires for a domino effect, and it is based on the API method [25]. For a fire accident, when the entire target unit surface area is not engulfed in the fire and only exposed to thermal radiation, the thermal radiation received by a target unit is calculated by Ding et al. [24]:
In the case of n concurrent fires, considering the synergistic effect,
Approach overview
Since fire synergistic effect exists when there are at least two fires, to make the modeling process concise and straightforward, consider a tank farm that has three fuel storage tanks, as shown in Fig. 1(a). Once a tank catches fire, the released thermal radiation will affect all the nearby tanks, and a tank will receive thermal radiation released from all the nearby tanks, as shown in Fig. 1(b).
The longer a target unit exposed to fire, the higher its failure probability due to received heat
Application scenario
The proposed approach is applied to an illustrative chemical storage tank farm to demonstrate the capability for modeling domino effects. The layout of the tank farm is shown in Fig. 5. The tank farm refers to Chen's work [21], one reason is a simplification of the case study, and another reason is a verification of the approach compared with Chen's results. Features of tanks are summarized in Table 1. Table 2 lists heat radiation intensity released by tank i on tank j, i.e. EV. Strictly, the
Conclusions
In the present study, a novel approach based on FSEM is proposed to study the spatial-temporal evolution of domino effects and to analyze associated risk in chemical plants. The proposed approach has considered fire accident evidence, the synergistic effect of burning units and heat energy accumulation during the accident to model the accident propagation process. The domino effect evolution results include escalation path, escalation times and escalation probabilities of involved units. This
CRediT authorship contribution statement
Long Ding: Methodology, Software, Writing - original draft, Validation. Faisal Khan: Writing - review & editing. Jie Ji: Conceptualization, Supervision, Project administration, Funding acquisition.
Declaration of Competing Interest
None.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51904284, the National Key Research & Development (R&D) Plan of China under Grant No. 2016YFC0800100, and the Opening Project of Jiangsu Key Laboratory of Hazardous Chemicals Safety and Control under Grant No. HCSC201902. Faisal Khan thankfully acknowledges the support provided by the Natural Science and Engineering Council of Canada and the Canada Research Chair (CRC) Program to enable
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