Asma Amira*
| Fares Innal
© 2025 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
OPEN ACCESS
The storage and handling of hazardous substances in industrial environments present a significant risk of catastrophic accidents, particularly due to domino effects, where an initial incident triggers a cascade of secondary events. Such scenarios can result in severe consequences for personnel, the environment, and infrastructure. This paper introduces a systematic methodology based on Petri net modeling to analyze and predict domino effects in industrial layouts. It is worth noting that Petri nets present a high-level modeling power able to capture potential dynamics such as sequential and competitive activities, synchronization, resource sharing, mutual exclusion (conflict situations), and complex stochastic processes. Unlike conventional risk assessment approaches that often fail to capture the dynamic and stochastic nature of cascading failures, the proposed framework enables the simulation of accident propagation by modeling process units and safety states as “places” and failure events as “transitions” in the Petri nets. The quantification is achieved using established probabilistic vulnerability functions, such as probit models for escalation vectors, and event frequencies derived from historical data or fault tree analysis, allowing the estimation of escalation path frequencies thanks to Monte Carlo simulation. This quantification offers enhanced insight into risk evolution and identifies critical escalation paths, thereby providing a robust decision support tool to safety managers for domino effect prevention and mitigation. The proposed approach was illustrated on a gasoline tank farm, where the considered primary event is a large bund fire. The obtained results are identical to those derived from some traditional approaches. The main limitation of Petri nets compared to traditional approaches is the difficulty of model validation, especially in the case of multiple escalation scenarios.
cascading events, domino effect, dynamic risk assessment, Monte Carlo simulation, Petri nets modeling, process safety, probabilistic vulnerability models, quantitative risk assessment
Industrial facilities frequently store and process large quantities of flammable, toxic, and explosive substances, inherently exposing them to the risk of catastrophic accidents. A single initiating event, such as a fire, explosion, or toxic release, can trigger a domino effect, where the initial incident propagates to adjacent equipment, causing a cascade of secondary events with combined consequences far exceeding those of the primary event. Such low-frequency but high-consequence domino effects have historically been responsible for some of the most devastating accidents in the process industries [1].
The definition of domino effects remains nuanced within safety engineering, despite broad acknowledgment in industrial risk literature. Following Kadri and Chatelet [2], a domino accidental event is “an accident in which a primary event propagates to nearby equipment, triggering one or more secondary events, resulting in overall consequences more severe than those of the primary event”. This propagation embodies complex, stochastic, and dynamic interactions among equipment and hazards.
The inherent complexity of domino effects arises from several factors: the probabilistic nature of escalation pathways, temporal evolution of accident scenarios, and synergistic interactions where multiple events concurrently amplify risk [3]. These complexities pose significant challenges for risk modeling and management. Many existing methodologies rely on static, threshold-based escalation models or simplified event chains valuable for screening but limited in capturing the true dynamism and uncertainty of domino effects.
A rich body of literature has developed numerous analytical and computational methods for domino effect modeling, each with distinct strengths and limitations. For example, early influential works [4-9] established empirically validated escalation thresholds and conditional probability models using Probits that remained benchmarks for estimating escalation likelihoods based on physical hazard intensities such as thermal radiation, blast overpressure, fragment projection, and toxic gas dispersion. Although these models are computationally efficient and grounded on physical phenomena, they generally neglect temporal dynamics since they assess static aspects and often do not adequately capture synergistic effects arising from simultaneous hazards or from the ways different hazards might combine or reinforce each other dynamically over time.
Qualitative approaches, such as MICADO [10] and Delvosalle’s method [11], represented a simple methodology for preliminary analysis of domino effect hazards. However, they lack quantitative rigor for comprehensive risk evaluation. Khan and Abbasi [12] and Khan et al. [13] integrated deterministic and probabilistic approaches in software frameworks like DOMIFFECT, enabling systematic scenario treatment and decision support. More recently, Agent-Based Modeling (ABM) techniques have been employed to model installations as autonomous agents with behaviors and interactions evolving over time [14, 15]. Several researchers have used Computational Fluid Dynamics (CFD) tools that provide detailed, high-resolution physical modeling of fire, explosion, and toxic dispersion phenomena driving escalation [16]. Although they offer unparalleled accuracy for risk intensity and spatial distribution mapping, they are often difficult to dynamically integrate into probabilistic risk models. Approaches based on matrix and graph enumeration methods, as proposed by Zhou and Reniers [17] and Zhou and Reniers [18], systematically represented escalation influence among units and simulate accident propagation using iterative numerical techniques. These methods efficiently handle multi-vector and synergistic escalations and scale well computationally. However, the temporal evolution and nonlinear feedback inherent in domino effect scenarios are often oversimplified. Bayesian Networks (BNs) and Dynamic Bayesian Networks (DBNs) approach was introduced to offer graphical probabilistic models because they are capable of representing complex causal dependencies and updating event probabilities dynamically [19]. DBNs extend this capability by incorporating temporal dynamics and barrier performance assessment [20].
Despite the fact that each of these approaches contributes uniquely to the understanding of domino effects, a critical analysis reveals several gaps that hamper a comprehensive risk assessment, particularly for dynamic and complex scenarios. In fact, many predominant methods, including those relying on static escalation thresholds and simplified event trees [9, 13] fail to adequately capture the unfolding temporal nature and time-dependent vulnerabilities essential for realistic domino risk assessment. These models provide static snapshots rather than dynamic risk evolution. In addition, the integration of synergistic effects involving multiple physical phenomena (e.g., concurrent fire, explosion, and toxic releases) remains uncommon in most risk assessment methods, resulting in an incomplete understanding of combined consequences. Although fault tree-based approaches have improved the representation of such complexities, as shown in the study [21], significant challenges remain. High-fidelity models such as ABM and CFD offer detailed insights but are computationally expensive and data-intensive, limiting their application to large-scale or real-life scenarios and complicating their integration into dynamic probabilistic frameworks. Besides the abovementioned limitations, the non-consideration of input data uncertainty, due to incomplete or imprecise data on equipment characteristics, hazardous substances, and initiating events, may influence the robustness of the results.
Table 1. Comparative analysis of domino effect modeling approaches
|
Criterion |
Level |
Justification |
|
Temporal Dynamics |
Excellent |
SPNs explicitly model concurrency and stochastic timings, enabling realistic, dynamic propagation representation [22] |
|
Good |
ABM and CFD simulate accident progressions over time, capturing dynamics [15, 23] Bayesian Networks (BN/DBN): explicitly model temporal dependencies [24] |
|
|
Limited |
Methods like Probit models and DOMIFFECT assess static or snapshot probabilities without detailed temporal evolution [25] ETA: static sequential event modeling; less suited for dynamic evolution [26] |
|
|
Synergistic Effects |
Excellent |
SPNs inherently capture concurrent escalations and synergistic feedback pathways by specifying and analysing the behaviour of complex, distributed, and concurrent systems [26, 27] |
|
Good |
ABM, CFD, and BN incorporate some interdependencies but may lack full systemic coupling [28, 29] |
|
|
Limited |
DOMIFFECT: handles multiple escalation vectors but has less focus on dynamic evolution [26] ETA: mainly linear sequences, limited in handling multiple interacting events [26] |
|
|
Computational Cost |
Low / Moderate |
Probit and DOMIFFECT models: have efficient computations suited for large-scale assessments [25] ETA: well-established analytical approach with low resources [26] SPNs balance model detail and resource demands via state-space reduction techniques [22, 30] Bayesian Networks (BN/DBN): computationally intensive for large networks [24] |
|
High |
ABM and CFD require substantial computational power, limiting practical use [15, 23] |
|
|
Data Requirements |
Moderate |
SPNs: reduce pure data dependence by integrating physical models with stochastic processes [22] DOMIFFECT: uses probit and threshold models [25] ETA: Needs probabilities for event branches [26] |
|
High |
ABM, CFD, BN: need detailed operational, physical, and statistical inputs [14, 25, 31] |
|
|
Scalability |
Excellent |
SPNs: use modular Petri nets efficiently, managing complexity and enabling large-scale modeling [22] |
|
Good |
ETA: can be scaled for large, complex systems [25] Bayesian Networks (BN/DBN): can efficiently handle large-scale problems involving many variables and time slices through strategies like divide-and-conquer for structure learning or parameter sharing to reduce model complexity [31, 32] DOMIFFECT: Designed for typical chemical plant sizes [26] |
|
|
Limited |
ABM and CFD: scale poorly due to computational complexity [15, 24] |
|
|
Interpretability |
Excellent |
ETA: simple graphical and tabular presentation [25] SPNs’ graphical, rigorously defined structure clarifies system behavior and dependencies [22] |
|
Good |
Probit, BN: are structured and understandable by experts [29, 33] DOMIFFECT: practical tool with user-oriented interface [25] |
|
|
Poor |
Complex ABM and CFD models are difficult to interpret [15], they generate complex simulation outputs requiring expert analysis [26] |
For a more detailed comparison, Table 1 summarizes the main differences between existing modeling approaches based on a literature review.
To address the aforementioned limitations, this work proposes a novel and systematic methodology based on Stochastic Petri Nets (SPNs) for the dynamic modeling and prediction of domino effects in industrial plants. Indeed, SPNs provide a mathematically rigorous and graphical framework inherently well suited for modeling concurrent, asynchronous, and stochastic system behaviors, ideal for capturing the intrinsic timing characteristics of domino effects [34, 35]. The developed SPN-based framework is able to integrate deterministic and stochastic time delays and the different potential interdependencies, far beyond the capabilities of classical models. This methodology explicitly identifies critical accident escalation pathways and accurately quantifies their propagation likelihood based on probabilistic vulnerability functions (probit models), thereby facilitating stakeholders' understanding and communication, and providing actionable information for risk management. Unlike computationally intensive high-fidelity models, the SPNs solution is dynamic yet relatively simple, making it more practical for real-world industrial applications.
The remainder of this paper is organized as follows. Section 2 introduces the Petri nets' elementary structure and the respective modeling approach. Section 3 details the steps of the proposed methodology. Section 4 illustrates this methodology through a case study and provides the obtained results. A summary of the presented work, together with future research directions, is given in Section 5.
Petri nets are now widely used in system safety. They offer a powerful tool that allows accounting for the various relationships that may exist. Sequential and competitive activities, synchronization, resource sharing, and mutual exclusion (conflict situations) can be easily represented. It is worth noting their ability to easily consider the temporal aspect in the model.
Petri nets were developed in 1962 by Carl Adam Petri [33], based on automata theory. A Petri net is a graphical notation with an underlying mathematical structure suitable for modeling discrete event systems. In the following, the presentation of Petri nets is deliberately limited to the necessary elements used in the context of this work. For more details, the reader can refer to references [36, 37].
2.1 Petri nets’ structure
The structure of a Petri net can contain the following elements (Figure 1):
Figure 1. Petri nets elements
2.2 Petri nets modeling approach
The different steps to model and evaluate a system with Petri nets are depicted in Figure 2 and described in the following.
Figure 2. Petri nets modeling steps
1. Randomly generate a value for each of the model parameters (according to their distributions).
2. Place the parameter values representing durations (transitions firing times) in a schedule according to an ascending order.
3. Evolve the system marking based on these times and update the schedule (transitions firing times) iteratively, and return to the first step if necessary.
4. Continue the simulation (previous steps) until the first instant of the schedule exceeds the observation period for which the calculations are to be performed. A history is created.
5. Repeat steps 1 to 4 a large number of times (e.g., 10,000) to gather a statistically representative sample of what we are trying to evaluate.
In this study, we propose an advanced methodology based on SPNs, building upon the dynamic risk assessment framework presented in the study [22]. Our approach also incorporates recent advances in the quantification of synergistic effects, as emphasized by the Fire Synergistic Effect Model (FSEM) [38], which highlights the importance of temporal escalation and cumulative impacts on equipment time-to-failure (TTF) and escalation probability. The different steps of the proposed methodology are depicted in Figure 3. A brief presentation of these steps is given hereafter.
Figure 3. Steps of the proposed methodology
4.1 System description
To demonstrate the proposed methodology, we apply it to a hypothetical case study of a gasoline tank farm. For the sake of simplicity, the studied scenario is demonstrated in a facility containing three identical atmospheric storage tanks (Tank 1, Tank 2, and Tank 3). Each tank has a diameter of 40 m and a height of 20 m, enclosed within an 80 m × 80 m retention bund. The tanks are arranged with 40 m spacing between Tank 1 and Tank 2, and between Tank 2 and Tank 3 (Figure 4). This configuration represents a common industrial layout where domino effects can propagate through HR or blast impacts.
This simplified layout provides a controlled environment to test and validate the proposed methodology, allowing clear observation of domino effect pathways and escalation probabilities.
Figure 4. Schematic of the gasoline tank farm
We assume that a loss of containment (LOC) occurs in Tank 1, followed by an ignition (in our case, ignition probability of = 0.7), which causes a fire in Tank 1. The potential escalation scenarios relating to fire spreading to the neighboring tanks (Tanks 2 and 3) are presented in Figure 5. We will also examine which scenario is most likely to occur, while considering synergistic effects: the simultaneous burning of two tanks could increase the impact on the third tank. Through this process, we want to test whether our approach can help improve the safety system by enhancing our understanding and management of domino effect phenomena.
4.2 Estimation of escalation vectors
For each primary event, escalation vectors, specifically HR intensities, are calculated at neighboring tanks. The generic formula of the heat flux (thermal radiation) emitted by a pool fire and received by a target located at x meters from the center of the flame is given by Eq. (1) [39]:
$\emptyset(x)=\emptyset_0 \cdot F(x) \cdot \tau(x)$ (1)
where,
$\emptyset(x)$: heat flux at a certain distance $x$ (received heat flux) (kW/m2).
$\emptyset_0$: flame surface emissive power (kW/m2).
$F(x)$: view factor. It is the fraction of the radiation falling directly on the receiving target.
$\tau(x)$: atmospheric transmissivity to thermal radiation.
There are several correlations for calculating these quantities. More details are given in the Purple Book [27]. The following considerations are taken into account during the calculation process: air relative humidity 70%, ambient temperature 15℃, wind speed 5 m/s, air density 1.161 Kg/m3, gasoline mass burning rate per unit area 0.055 Kg/(m2 s).
The resulting HR against distance is plotted in Figure 6.
Figure 5. Potential escalation scenarios
Figure 6. Heat flux versus distance
4.3 Time-to-failure calculation
Using the HR intensity, the TTF for each exposed Tank is calculated with the following correlation [39]:
$\ln \mathrm{TTF}_{T a \rightarrow T b}=-1.13 \cdot \ln \left(\mathrm{HR}_{T a \rightarrow T b}\right)-2.67 \cdot \frac{V}{10^5}+9.9$ (2)
where, HR is the heat radiation intensity (kW/m²) emitted from tank a to tank b, and V is the tank volume (m³). This formula captures the dynamic vulnerability of tanks exposed to thermal radiation, reflecting how longer exposure reduces structural integrity [39]. Note that HRT1→T2 = 17.11 KW/m2 (for a distance of 20 m between the bund wall of Tank 1 and the wall of Tank 2) and HRT1→T3 = 10.87 KW/m2 (for a distance of 36 m between the bund wall of Tank 1 and the wall of Tank 3).
4.4 Probit model for escalation probability
Once the value of ln TTF is calculated, it is possible to estimate the probability of escalation (PES) using the probit function. In this paper, only HR is considered as escalation vector. The corresponding probit function is given by Eq. (3) [39]:
$\left\{\begin{array}{c}Y=12.54-1.847 \cdot \ln \mathrm{TTF}_{T a \rightarrow T b} \\ P E S=\frac{1.005}{\left(1+\exp \left(\frac{-Y}{0.6120}+\frac{5.004}{0.6120}\right)\right)}\end{array}\right.$ (3)
Eq. (3) allows us to quantify the likelihood that the heated Tank will fail and propagate the accident, integrating both intensity and duration of exposure [39]. The different PES related to the case study and the other relevant data are given in Table 1.
4.5 Construction of the Petri nets model
The Perti net of Figure 7 depicts the studied scenario, which addresses the potential fire propagation from Tank 1 to the neighboring Tanks 2 and 3. The GRIF software (Petri module) has been used for the establishment and simulation of the Petri net [41]. The different parameters used within the Petri net are gathered in Table 1. Note that equations of Table 2 were inserted in the Petri net module, and the quantities related to ln TTF and PES were automatically determined.
Table 2. Used parameters
|
Parameter |
Definition |
Value |
Unit |
|
V |
Basic data |
2500 |
m3 |
|
F_LOC |
Basic data |
5E-6 |
y-1 |
|
P ignition |
Basic data |
0.7 |
- |
|
HR_T12 |
Curve of Figure 4 |
17.11 |
KW/m2 |
|
HR_T13 |
Curve of Figure 4 |
10.87 |
KW/m2 |
|
HR_T23 |
HR_T12 + HR_T13 |
27.98 |
KW/m2 |
|
HR_T32 |
2 × HR_T12 |
34.22 |
KW/m2 |
|
ln TTF_T12 |
Eq. (2) with HR_T12 |
6.023 |
ln(s) |
|
ln TTF_T13 |
Eq. (2) with HR_T13 |
6.536 |
ln(s) |
|
ln TTF_T23 |
Eq. (2) with HR_T23 |
5.468 |
ln(s) |
|
ln TTF_T32 |
Eq. (2) with HR_T32 |
5.240 |
ln(s) |
|
YT12 |
Eq. (3) with ln TTF_T12 |
1.414 |
- |
|
YT13 |
Eq. (3) with ln TTF_T13 |
0.467 |
- |
|
YT23 |
Eq. (3) with ln TTF_T23 |
2.441 |
- |
|
YT32 |
Eq. (3) with ln TTF_T32 |
2.861 |
- |
|
PEST12 |
Eq. (3) with YT12 |
2.842E-3 |
- |
|
PEST13 |
Eq. (3) with YT13 |
6.062E-4 |
- |
|
PEST23 |
Eq. (3) with YT23 |
0.015 |
- |
|
PEST32 |
Eq. (3) with YT32 |
0.030 |
- |
Places 1, 7, and 10 represent the normal states of Tank 1, Tank 2, and Tank 3, respectively (each place has 1 token). Initially, the transition Tr1 is the sole enabled transition. This transition characterizes the event related to the Tank 1 LOC with a stochastic delay F_LOC = 5E-6 y-1. During the simulation, this delay is generated randomly according to the exponential law: d = -ln z /F_LOC, where z is a random number. After firing Tr1, the token is removed from place 1, and a token is added to place 2 corresponding to the LOC of Tank 1. The transition Tr2, relating to ignition possibility, becomes then enabled and triggered instantaneously (delay = drc 0, drc for Dirac law) according to a solicitation law (sol Pignition), where Pignition refers to the ignition probability = 0.7. During the simulation, a random number between 0 and 1 is generated. If this number is between 0 and 0.7, the token moves from place 2 to place 3, indicating that Tank 1 is on fire. In the contrary case, the token ends up in place 4, and therefore the LOC is controlled. If Tank 1 is on fire (place 3), there will be a possibility for Tank 2 and Tank 3 to be impacted. Thus, Transition Tr5 is immediately fired, and places 5 and 6 get one token each, making transitions Tr4 and Tr6 enabled, indicating a potential escalation for Tank 2 and Tank 3, respectively. These potential escalations are calculated according to Eq. (3). The triggering principle for transitions Tr4 and Tr6 is the same as for Tr2 (solicitation law according to the respective probability). If the fire propagates from Tank 1 to Tank 2 (according to the probability PEST12 = 2.842E-3), a token appears in each place 15 and 16. Note that place 15 is added to address the propagation of fire from Tank 2 to Tank 3 (same thing for place 11: to address the propagation of fire from Tank 3 to Tank 2). In case there is no direct propagation from Tank 1 to Tank 2 (marking of place 17 with one token), Tank 2 is still subject to fire propagation if Tank 3 is on fire. This reflects the synergic aspect of fire propagation. In fact, Tank 3 on fire (place 11) contributes with Tank 1 to the propagation of fire toward Tank 2: Tank 2 receives HR from the two tanks (HR_T32 = 34.22 kW/m2). This results in a probability of escalation PEST32 = 0.03. Tank 2 may catch fire according to this probability by the firing of transitions Tr8 and Tr10, leading to the marking of place 16 with one token. The same explanations can be made regarding the spread of fire from Tanks 1 and 2 to Tank 3.
Figure 7. Petri net model for escalation paths
4.6 Petri nets simulation and numerical results
In the GRIF software, Petri nets are coupled with the Monte Carlo technique to simulate the model and statistically extract the quantities of interest. 1E+10 history has been performed over an observation period of 1E+3 years. The different transition frequencies related to escalation events (domino effects) are grouped in Table 2. In addition to these results and for comparison and validation purposes, Table 2 also presents the frequencies of the different scenarios obtained from other modeling approaches, namely: Bow-Tie (BT), Fault Tree (FT), and Bayesian Network (BN). The associated models are presented in Figures 8-10, respectively. The BT and FT models were created using GRIF software [41], while the BN model was developed using Netica software [42]. It should be noted that with the FT and BN approaches, it was necessary to build two separate models to capture the different escalation scenarios. This limits their ability to provide a holistic picture of the potential scenarios, and the modeling becomes unmanageable in case of several escalations. In contrast, BT and Petri nets offer a full and clear graphical representation of these escalations.
Moreover, the underlying mathematical expression of the BN does not allow for directly calculating the scenario frequencies, since the BN is a probability-based approach and the algorithm for frequency calculation is not yet available. Hence, in Table 2, the probabilities and frequencies are presented for each scenario, where the different frequencies were simply derived by multiplying the corresponding probabilities by the LOC frequency (5E-6 y-1). This is not the case with the FT technique, for which frequency calculation codes have been available for a long time.
It should be noted that the BT formalism implemented in the GRIF software has a higher modeling power than traditional BT. This explains the relative simplicity of the model in Figure 8, thanks to the use of the AND gate.
The inspection of Table 3 reveals the following statements:
Figure 8. Bow-tie model for escalation paths
Figure 9. Fault tree model for escalation paths
Figure 10. BN model for escalation paths
Table 3. Domino effects sequences frequencies (y-1)
|
Escalation Scenarios |
Approaches |
|||||
|
SPNs |
BT |
FT |
BN |
|||
|
Probability |
Frequency |
|||||
|
Tank 1 on fire |
Tr5 |
3.4999E-06 |
3.5000E-06 |
3.5000E-06 |
7.0000E-01 |
3.5000E-06 |
|
Tank 1 → Tank 2 |
Tr4 |
9.9507E-09 |
9.9470E-09 |
9.9470E-09 |
1.9894E-03 |
9.9470E-09 |
|
Tank 1 → Tank 3 |
Tr6 |
2.1249E-09 |
2.1217E-09 |
2.1217E-09 |
4.2434E-06 |
2.1217E-09 |
|
Tank 1 → Tank 2 → Tank 3 |
Tr12 |
1.5100E-10 |
1.4912E-10 |
1.4912E-10 |
2.9823E-05 |
1.4912E-10 |
|
Tank 1 → Tank 3 → Tank 2 |
Tr10 |
6.3300E-11 |
6.3470E-11 |
6.3470E-11 |
1.2694E-05 |
6.3470E-11 |
The direct escalation from Tank 1 to Tank 2 is more likely (9.95E-09 y-1) than that from Tank 1 to Tank 3 (2.125E-09 y-1). This is explained by the greater distance between the bund of Tank 1 and the wall of Tank 3 (36.6 m) compared to that between the bund of Tank 1 and the wall of Tank 3 (20 m).
This paper emphasizes the effectiveness of Petri net modeling as a powerful tool for representing, predicting, and managing domino effects within industrial layouts. By providing a rigorous and dynamic framework, the proposed methodology enhances our ability to analyze complex accident propagation scenarios, thereby contributing significantly to the development of safer and more resilient industrial environments. Incorporating the Petri nets-based approach into safety management practices enables more accurate identification and quantification of escalation risks associated with hazardous substances. Consequently, it supports informed decision-making aimed at minimizing potential domino effect incidents, ultimately fostering greater protection for both communities and the environment. The proposed methodology uniquely integrates both physical (HR intensities) and probabilistic (probit) models together with the outstanding modeling capabilities of Petri nets animated by Monte Carlo Simulation. It was successfully illustrated on a gasoline tank farm, where the obtained results in terms of escalation frequencies were found to be identical to those derived from some traditional and established approaches, providing valuable information for process safety management.
To further strengthen this methodology, several improvements could be implemented to capture full domino effect complexity and ensure applicability and robustness. This may include: considering parametric uncertainty based on Monte Carlo sampling to increase the accuracy of the model output, Conducting sensitivity analysis to study how the variation in model output can be apportioned to changes in the input parameters, integrating more escalation vectors beside HR (blast, fragments, and toxic release), adopting hierarchical and modular Petri nets to ensure scalability and easier model validation and maintenance, integrating safety barriers and emergency response allowing evaluation of risk reduction strategies. It is worth noting that the GRIF software could account for the above-stated enhancements in an easy manner.
|
TTF |
Time to failure (s) |
|
HR |
Heat radiation (kW/m2) |
|
D |
Diameter (m) |
|
d |
Distance (m) |
|
H |
Height (m) |
|
LOC |
Loss of containment |
|
F_LOC |
Loss of containment frequency (y-1) |
|
P_Ignition |
Probability of Ignition |
|
PES |
Probability of escalation |
|
Y |
Probit function |
|
Tr |
Transition |
|
V |
Volume (m3) |
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