Quantitative risk assessment is a powerful but complex and time-consuming task, which requires a significant amount of information and sophisticated models for the analysis of a very high number of scenarios even for rather simple plant layouts. The availability of software tools that support the risk analyst is therefore crucial. In this chapter, two tools that support the quantitative analysis of Natech risk are presented. The risk figures resulting from the application of these tools can then be used for comparison with quantitative risk-acceptability criteria.
Table 9.1
Summary of Steps 7–10 for the Identification of Credible Combinations of Events and of the Resulting Frequencies and Consequence Evaluation, Taking Into Account Multiple Simultaneous Failures
Item | Definition | Value/Equation |
Input Parameters |
||
n | Total number of target equipment | — |
k | Number of target equipment simultaneously damaged by a Natech scenario | — |
Nk | Number of Natech-induced scenarios involving k different final outcomes | |
m | Index associated with a generic combination of k events | m = 1,…, Nk |
Ψ | Vessel vulnerability | See Tables 9.2–9.4 |
f | Overall expected frequency of the Natech scenario affecting the industrial facility | Evaluated according to specific models for the natural event of interest |
Combination index | if i-th event triggered by flooding belongs to the vector if not. | |
Evaluation of Combinations Probability and Frequency |
||
Nf | Number of different overall scenarios that may be generated by a single natural event | |
Probability of occurrence of the m-th combination involving the simultaneous damage of k equipment | ||
Frequency of occurrence of the m-th combination involving the simultaneous damage of k equipment | ||
Consequence Assessment Trough the Vulnerability Evaluation of Multiple Scenarios |
||
Vf,i | Vulnerability calculated for the (k,m) scenario triggered by Natech | |
Vulnerability associated with the occurrence of the m-th combination involving the simultaneous damage of k equipment |
Adapted from Antonioni et al. (2015).
Table 9.2
Values of the Probit Constants for Equipment Vulnerability Models Expressing Damage Probability Following an Earthquake
Type of Equipment | Damage State | Filling Level | k1,i,j | k2,i,j |
Anchored atmospheric tanks | ≥2 | Near full | 7.01 | 1.67 |
≥2 | ≥50% | 5.43 | 1.25 | |
3 | Near full | 4.66 | 1.54 | |
3 | ≥50% | 3.36 | 1.25 | |
Unanchored atmospheric tanks | ≥2 | Near full | 7.71 | 1.43 |
3 | Near full | 5.51 | 1.34 | |
3 | ≥50% | 4.93 | 1.25 | |
Horizontal pressurized storage tanks | ≥1 | Any | 5.36 | 1.01 |
≥2 | Any | 4.50 | 1.12 | |
3 | Any | 3.39 | 1.12 | |
Pressurized reactors | ≥1 | Any | 5.46 | 1.10 |
≥2 | Any | 4.36 | 1.22 | |
3 | Any | 3.30 | 0.99 | |
Pumps | ≥2 | — | 5.31 | 0.77 |
3 | — | 4.30 | 1.00 |
Adapted from Campedel et al. (2008).
Different vulnerability models are provided as a function of equipment category, damage state, and filling level.
Table 9.3
Vulnerability Model and Input Parameters for Atmospheric Cylindrical Tanks Involved in Flood Events Based on the Critical Filling Level (CFL)
Item | Definition | Value/Equation |
Vulnerability Model Equations |
||
CFL | Critical filling level | |
Pcr | Vessel critical pressure evaluated with the proposed simplified correlation | Pcr = J1C+J2 in which J1 = -0.199 J2 = 6950 |
Ψ | Vessel vulnerability due to flooding | |
Input Parameters |
||
C | Vessel capacity | Small capacity C < 5,000 m3 Medium capacity 5,000–10,000 m3 Large capacity > 10,000 m3 |
vw | Flood-water velocitya | 0–3.5 m/s |
hw | Flood-water deptha | 0–4 m |
ρw | Flood-water density | 1,100 kg/m3 |
ρf | Stored liquid density | 650–1,300 kg/m3 |
kw | Hydrodynamic coefficient | 1.8 |
H | Vessel height | Small capacity 3.6–18 m Medium capacity 3.6–16.2 m Large capacity 3.6–7.2 m |
g | Gravity acceleration | 9.81 m/s2 |
φmin | Minimum operative filling level | 0.01 |
φmax | Maximum operative filling level | 0.75 |
Adapted from Landucci et al. (2012).
a Parameters can be derived from the hydrogeological study of the analyzed area or provided by local competent authorities.
Table 9.4
Vulnerability Model and Input Parameters for Horizontal Cylindrical Tanks Involved in Flood Events Based on the Critical Filling Level (CFL)
Item | Definition | Value/Equation |
Vulnerability Model Equations |
||
CFLh | Critical filling level for horizontal vessels (pressurized or atmospheric) | |
vw,c | Flooding critical velocity | |
Ψ | Vessel vulnerability due to flooding | If vw ≥ vw,c, Ψ = 1; If vw < vw,c, |
Input Parameters |
||
C | Vessel capacity | Small capacity < 10 m3 Medium capacity 10–30 m3 Large capacity > 30 m3 |
Wt | Vessel tare weighta | 900–2,200 kg (Small capacity) 3,000–7,200 kg (Medium capacity) 9,900–63,000 kg (Large capacity) |
D | Vessel diameter | 1.3–1.6 m (Small capacity) 1.6–2.4 m (Medium capacity) 2.3–3.8 m (Large capacity) |
L | Vessel length | 3–3.5 m (Small capacity) 4.5–11.1 m (Medium capacity) 8–24 m (Large capacity) |
A | First CFLh correlation coefficient | |
B | Second CFLh correlation coefficient | B = K2 (Wt + K3)b |
E | vw,c correlation factor | |
F | vw,c correlation exponent | F = K5 ln (L/D) + K6 |
K1 | Coefficient for A evaluationa | 1.339 |
K2 | Coefficient for B evaluationa | −1.21 |
K3 | Coefficient for B evaluationa | −374.4 |
K4 | Coefficient for E evaluationa | 5.497 |
K5 | Coefficient for F evaluationa | −0.06 |
K6 | Coefficient for F evaluationa | −0.375 |
a | Exponent for A evaluationa | −0.989 |
b | Exponent for B evaluationa | −0.107 |
c | Exponent for E evaluation | −0.692 |
vw | Flood-water velocityb | 0–3.5 m/s |
hw | Flood-water depthb | 0–4 m |
ρw | Flood-water density | 1100 kg/m3 |
hc | Height of concrete basement (flooding protection) | 0.25 m |
hmin | Minimum flooding height able to wet the vessel surface | hmin = λ–D/2 |
λ | Saddle height parameter which indicates the vessel axis height with respect to the ground anchorage point | 0.98 m (Small capacity) 0.98–1.38 m (Medium capacity) 1.38–1.98 m (Large capacity) |
ρl | Stored liquid density | 500–1100 kg/m3 |
ρv | Stored vapor density | 1.25–20 kg/m3 |
ρref | Reference density used for the definition of CFL correlations | 1000 kg/m3 |
φmin | Minimum operative filling level | 0.01 |
φmax | Maximum operative filling level | 0.90 |
Adapted from Landucci et al. (2014).
a Value evaluated for 2 MPa design pressure.
b Parameters can be derived from the hydrogeological study of the analyzed area or provided by local competent authorities.