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Chapter 9

Quantitative Methods for Natech Risk Assessment

V. Cozzani

E. Salzano Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna, Bologna, Italy

Abstract

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.

Keywords

Natech

QRA

software tool

risk analysis

individual risk

societal risk

ARIPAR-GIS

RISKCURVES

9.1. ARIPAR

9.1.1. Framework of the ARIPAR-GIS Natech Module

The Natech module of the ARIPAR-GIS software was developed to implement the specific procedure for the quantitative analysis of Natech events developed by Antonioni et al. (2009). The procedure is summarized in Fig. 9.1 and is actually a customization of the general framework presented in Fig. 7.3. The specific assumptions and steps introduced to implement the general methodology discussed in Chapter 7 are briefly summarized later in the chapter.

Figure 9.1 Flowchart of the Framework Proposed for Quantitative Risk Assessment of (A) Natech Scenarios and (B) Domino Effect Adapted from Cozzani et al. (2014).

The starting point in the quantitative assessment of Natech scenarios is the characterization of the frequency and severity of the natural event by a sufficiently simple approach, which is suitable for use in a risk-assessment framework (Steps 1–3 in Fig. 9.1A). Usually, in this step a limited number of “reference events” is identified, each having a given intensity and an expected frequency or return time. A set of impact vectors may thus be defined, the elements of the vectors being the intensity of the natural events characterized by one or more intensity parameters selected to describe the natural event. It should be noted that this step in no way is intended to provide a characterization of the natural hazard at the site, nor to provide data for a detailed analysis of the damage to structures, but only to obtain the input data necessary for use in simplified equipment damage models.

Simplified hazard-ranking criteria based on inventory and physical state of hazardous substances may be used to identify critical equipment items that should be included in the analysis (Step 4 in Fig. 9.1A) (Antonioni et al., 2009). The application of vulnerability models is then needed to assess the equipment damage probability (Step 5). These equipment vulnerability models are further discussed in Section 9.1.5. Consequence assessment of the single scenarios triggered by the natural event (Step 6) can be carried out by using conventional models, although a limited number of Natech-specific final outcomes may arise (Cozzani et al., 2010; Renni et al., 2010).

The final steps of the procedure (Steps 7–10) are aimed at risk recomposition. These steps require a dedicated approach for the identification of possible multiple and simultaneous accident scenarios and the calculation of their frequencies and consequences. This procedure, which is summarized in Table 9.1, was originally developed within the framework of the risk analysis of domino accidents presented in Fig. 9.1B (Cozzani et al., 2005, 2006). Actually, as shown in the figure, several steps needed in the quantitative analysis of risk due to either domino effects (cf. Section 7.3.2.2) or the impact of natural events on process equipment are similar, and similar mathematical procedures can be applied in the assessment process. The procedure used for Steps 7–10 is described in detail in Antonioni et al. (2007), Reniers and Cozzani (2013), and Cozzani et al. (2014).

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	—
N_k	Number of Natech-induced scenarios involving k different final outcomes	$N_{k} = (\begin{array}{l} k \\ n \end{array}) = \frac{n!}{(n - k)! k!}$ $N_{k} = (\begin{array}{l} k \\ n \end{array}) = \frac{n!}{(n - k)! k!}$
m	Index associated with a generic combination of k events	m = 1,…, N_k
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
$δ (i, J_{m}^{k})$ $δ (i, J_{m}^{k})$	Combination index	$δ (i, J_{m}^{k}) = 1$ $δ (i, J_{m}^{k}) = 1$ if i-th event triggered by flooding belongs to the vector $J_{m}^{k}; δ (i, J_{m}^{k}) = 0$ $J_{m}^{k}; δ (i, J_{m}^{k}) = 0$ if not.
Evaluation of Combinations Probability and Frequency
N_f	Number of different overall scenarios that may be generated by a single natural event	$N_{f} = \sum_{k = 1}^{n} (\begin{array}{l} n \\ k \end{array}) = 2^{n} - 1$ $N_{f} = \sum_{k = 1}^{n} (\begin{array}{l} n \\ k \end{array}) = 2^{n} - 1$
$P_{f}^{(k, m)}$ $P_{f}^{(k, m)}$	Probability of occurrence of the m-th combination involving the simultaneous damage of k equipment	$P_{f}^{(k, m)} = \prod_{i = 1}^{n} [1 - ψ + δ (i, J_{m}^{k}) (2 ψ - 1)]$ $P_{f}^{(k, m)} = \prod_{i = 1}^{n} [1 - ψ + δ (i, J_{m}^{k}) (2 ψ - 1)]$
$f_{f}^{(k, m)}$ $f_{f}^{(k, m)}$	Frequency of occurrence of the m-th combination involving the simultaneous damage of k equipment	$f_{f}^{(k, m)} = f \cdot P_{f}^{(k, m)}$ $f_{f}^{(k, m)} = f \cdot P_{f}^{(k, m)}$
Consequence Assessment Trough the Vulnerability Evaluation of Multiple Scenarios
V_f,i	Vulnerability calculated for the (k,m) scenario triggered by Natech
$V_{f}^{(k, m)}$ $V_{f}^{(k, m)}$	Vulnerability associated with the occurrence of the m-th combination involving the simultaneous damage of k equipment	$V_{f}^{(k, m)} = \min [\sum_{i = 1}^{m} V_{f, i}; 1]$ $V_{f}^{(k, m)} = \min [\sum_{i = 1}^{m} V_{f, i}; 1]$

Adapted from Antonioni et al. (2015).

9.1.2. The ARIPAR-GIS Software

The ARIPAR-GIS software was developed in the framework of the ARIPAR project (Egidi et al., 1995), which was one of the first applications of Quantitative Area Risk Analysis techniques in the evaluation of all hazards in an extended industrial area. The ARIPAR-GIS software allows the calculation of individual and societal risk originating from multiple risk sources due to both fixed installations and hazardous-materials transport systems. The software is supported by a geographical information system (GIS) platform that allows positioning of the different risk sources and producing risk maps as a result of the assessment. Spadoni et al. (2000, 2003) provide a detailed description of the software.

9.1.3. The Natech Package of the ARIPAR-GIS Software

A specific software package was developed and added to the ARIPAR-GIS software in order to allow the quantitative analysis of risk due to Natech events. The implemented procedure allows the automatic identification of all the possible overall scenarios that may be generated by the impact of a natural event (earthquake or flood) on a hazardous site of interest. A simplified layout needs to be implemented in a GIS environment. The procedure automatically generates all the overall events generated by equipment damage, calculates the expected overall frequencies and vulnerability maps, and performs the quantitative analysis of the risk in the area of interest.

9.1.4. Input Data and Calculation Procedure

The starting point of the procedure is the input of data on all the possible critical targets. The critical targets were defined in the present approach as all equipment items having a relevant inventory of hazardous substances (cf. Chapter 6). The GIS section of the ARIPAR-GIS software associates to a simplified layout (usually reporting only the equipment items and the main lines) the critical targets identified in the safety assessment of the plant. A single risk source is associated to each equipment item. In the Natech version, if the risk source is a possible target of the natural event, it may be associated to a vulnerability model, an equipment class, and to a secondary “Natech” event. Equipment involved only in Natech events, if present, may be represented by risk sources not associated to any primary scenario.

The default equipment classes in ARIPAR-GIS are atmospheric and pressurized tanks, elongated vessels, and auxiliary vessels, but further classes may be defined by the user. Specific equipment vulnerability models, yielding the equipment damage probability as a function of a severity vector used to quantify the severity of the natural event, are associated to each equipment class. Vulnerability models are usually defined in the software as probit equations, since this is the most common approach used in the literature. This issue will be further discussed in Section 9.1.5. Figure 9.2 shows an example of the equipment vulnerability model input interface provided by the software.

Figure 9.2 Management of Natech Equipment Vulnerability Models in the ARIPAR-GIS Software

A secondary event is also associated to all the identified domino targets. A single secondary event is considered, in order to limit the computational effort required. Typically, the most severe credible scenario should be selected as the secondary event. An occurrence probability associated to this event is also required by the software. The occurrence probability represents the probability of the selected secondary event to take place given the equipment damage. The occurrence probability may be used to take into account that the equipment damage may not always be followed by a relevant secondary accident (e.g., the ignition of a release is not certain). In the absence of specific data, the occurrence probability should be conservatively assumed equal to 1.

The expected frequency of each domino scenario and the vulnerability map of each scenario are then calculated. The standard procedure of the ARIPAR-GIS software is used to estimate the contribution to the risk indices of all the identified domino scenarios.

9.1.5. Equipment Vulnerability Models

The detailed quantitative approach to the assessment of Natech scenarios presented in the previous section is based on the availability of models for equipment vulnerability. As mentioned in Chapter 7, several types of models may be applied to assess the failure probability of an equipment item due to the impact of a natural event. Detailed vulnerability models based on structural analysis may be developed, although these are time consuming and require unaffordable efforts in a QRA context. Observational fragility curves are also available in the literature (Salzano et al., 2003; 2009; Campedel et al., 2008; Antonioni et al., 2009).

In the framework of QRA, simple models are needed to allow the swift assessment of a high number of scenarios. Thus, fragility curves or simplified probabilistic models were selected for the ARIPAR-GIS software procedure for Natech risk assessment.

In the case of Natech accidents triggered by earthquakes, fragility curves expressed in the form of a probit function were selected:

$Y = k_{1} + k_{2} \ln (PGA)$ $Y = k_{1} + k_{2} \ln (PGA)$

(9.1)

where PGA is the horizontal component of peak ground acceleration and the constants k₁ and k₂ are given in Table 9.2. With respect to floods, the equipment vulnerability models developed by Landucci et al. (2012, 2014) are compatible with the software. Tables 9.3 and 9.4 summarize these models which are based on the evaluation of the mechanical integrity of vessels under the action of the flood, which results in both a “static” external pressure component, due to the depth of the flooding, and in a “dynamic” external pressure component, due to the flood-water velocity and the associated kinetic energy. Considering this type of mechanical load, there is evidence that the vessel filling level is the most relevant parameter for the evaluation of the equipment integrity and associated fragility (i.e., its vulnerability). Thus, a critical filling level (CFL) was defined for each equipment item involved in a flood event of a specific intensity (e.g., having assigned flood-water velocity and depth) as the liquid level below which failure due to instability is possible. Further details are presented in Landucci et al. (2012, 2014).

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	k_1,i,j	k_2,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	$CFL = (\frac{ρ_{w} k_{w}}{2} v_{w}^{2} + ρ_{w} g h_{w} - P_{cr}) / ρ_{f} g H$ $CFL = (\frac{ρ_{w} k_{w}}{2} v_{w}^{2} + ρ_{w} g h_{w} - P_{cr}) / ρ_{f} g H$
P_cr	Vessel critical pressure evaluated with the proposed simplified correlation	P_cr = J₁C+J₂ in which J₁ = -0.199 J₂ = 6950
Ψ	Vessel vulnerability due to flooding	$ψ = \frac{CFL - φ_{\min}}{φ_{\max} - φ_{\min}}$ $ψ = \frac{CFL - φ_{\min}}{φ_{\max} - φ_{\min}}$
Input Parameters
C	Vessel capacity	Small capacity C < 5,000 m³ Medium capacity 5,000–10,000 m³ Large capacity > 10,000 m³
v_w	Flood-water velocity^a	0–3.5 m/s
h_w	Flood-water depth^a	0–4 m
ρ_w	Flood-water density	1,100 kg/m³
ρ_f	Stored liquid density	650–1,300 kg/m³
k_w	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
φ_min	Minimum operative filling level	0.01
φ_max	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
CFL_h	Critical filling level for horizontal vessels (pressurized or atmospheric)	$CF L_{h} = (ρ_{ref} \cdot A) / (ρ_{l} - ρ_{v}) \cdot (h_{w} - h_{c}) + (ρ_{ref} \cdot B - ρ_{v}) / (ρ_{l} - ρ_{v})$ $CF L_{h} = (ρ_{ref} \cdot A) / (ρ_{l} - ρ_{v}) \cdot (h_{w} - h_{c}) + (ρ_{ref} \cdot B - ρ_{v}) / (ρ_{l} - ρ_{v})$
v_w,c	Flooding critical velocity	$v_{w,c} = E \cdot {(h_{w} - h_{c} - h_{\min})}^{F}$ $v_{w,c} = E \cdot {(h_{w} - h_{c} - h_{\min})}^{F}$
Ψ	Vessel vulnerability due to flooding	If v_w ≥ v_w,c, Ψ = 1; If v_w < v_w,c, $ψ = (CFL - φ_{\min}) / (φ_{\max} - φ_{\min})$ $ψ = (CFL - φ_{\min}) / (φ_{\max} - φ_{\min})$
Input Parameters
C	Vessel capacity	Small capacity < 10 m³ Medium capacity 10–30 m³ Large capacity > 30 m³
W_t	Vessel tare weight^a	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 CFL_h correlation coefficient	$A = K_{1} \cdot D^{a}$ $A = K_{1} \cdot D^{a}$
B	Second CFL_h correlation coefficient	B = K₂ (W_t + K₃)^b
E	v_w,c correlation factor	$E = K_{4} \cdot L^{c}$ $E = K_{4} \cdot L^{c}$
F	v_w,c correlation exponent	F = K₅ ln (L/D) + K₆
K₁	Coefficient for A evaluation^a	1.339
K₂	Coefficient for B evaluation^a	−1.21
K₃	Coefficient for B evaluation^a	−374.4
K₄	Coefficient for E evaluation^a	5.497
K₅	Coefficient for F evaluation^a	−0.06
K₆	Coefficient for F evaluation^a	−0.375
a	Exponent for A evaluation^a	−0.989
b	Exponent for B evaluation^a	−0.107
c	Exponent for E evaluation	−0.692
v_w	Flood-water velocity^b	0–3.5 m/s
h_w	Flood-water depth^b	0–4 m
ρ_w	Flood-water density	1100 kg/m³
h_c	Height of concrete basement (flooding protection)	0.25 m
h_min	Minimum flooding height able to wet the vessel surface	h_min = 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)
ρ_l	Stored liquid density	500–1100 kg/m³
ρ_v	Stored vapor density	1.25–20 kg/m³
ρ_ref	Reference density used for the definition of CFL correlations	1000 kg/m³
φ_min	Minimum operative filling level	0.01
φ_max	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.

9.1.6. Output

ARIPAR-GIS provides a number of different outputs. Local individual-risk maps allow a detailed mapping of the individual risk. If data on the population distribution is available, individual-risk maps for specific population categories (e.g., resident population, workers, etc.) can be calculated. This also includes vulnerability centers (i.e., sites where the aggregation of a high number of persons is expected, such as schools, hospitals, or railway stations.). ARIPAR-GIS outputs societal risk in the form of F–N curves or I–N diagrams. The latter is a measure of the exposure of society to the risk that plots the number of persons N in the impact area exposed to an individual risk within a specific range, I.

With the implementation of the Natech module, ARIPAR-GIS is currently the only software tool that provides a correct calculation of societal risk by being able to include the scenarios resulting from the simultaneous failure of more than one equipment item. This feature is not present in conventional software for QRA.

ARIPAR-GIS also allows the disaggregation of risk components, providing risk maps for specific scenarios or risk sources, thus allowing a sensitivity analysis and the identification of the most important risk sources and scenarios. Impact areas for the different scenarios considered can also be obtained. Further details on the output of the ARIPAR-GIS software are provided in Spadoni et al. (2000, 2003).

A quantitative risk analysis of earthquake and flood impacts at a hazardous installation using ARIPAR-GIS is presented in Chapter 11.

9.2. RISKCURVES

RISKCURVES is a computer program package that was developed by the Netherlands Organization for Applied Scientific Research (TNO) in the late 1980s to perform a QRA of hazardous activities due to conventional causal factors of accidents. The software has since then been upgraded continuously to introduce several innovative concepts, such as full integration of consequence modeling, showing societal risk on a map, calculation of risk contours and allowing external consequence data to be used for the risk calculation. Considering that a QRA is a complex task, special attention is paid to the user friendliness of the software and its capabilities to easily integrate the results in office- and GIS environments (TNO, 2015a).

RISKCURVES is a tool that aims to quantify the risk from the storage and transport of hazardous materials to the surrounding population and the built environment in urban areas and at chemical facilities. The risk sources include both fixed installations but also equipment used in the transport of hazardous materials (e.g., pipelines, road and rail tankers, ships). The tool allows the definition of a QRA with an unlimited number of fixed or transport equipment types with all their associated accident scenarios. Similar to RAPID-N, which was introduced in Section 8.1, RISKCURVES aims to support the user by offering different levels of user interaction during the assessment process, ranging from standard user on the one end in which user input is minimal, to expert user on the other end in which all input data is provided by the user him/herself (van het Veld et al., 2007). This means that depending on the complexity level, either RISKCURVES’s internal assessment models will decide the analysis to various degrees or the user can fully customize the input data. This gives the user a maximum amount of flexibility in tailoring the assessment process, and it is a winning approach that has already shown its usefulness in the application of RAPID-N.

In order to support the consequence analysis, RISKCURVES includes the software package EFFECTS, also developed by TNO, which calculates the consequences of the accidental release of toxic and/or flammable chemicals. It includes models related to hazmat release, evaporation, and dispersion, as well as fire and explosion models (TNO, 2015b). Both RISKCURVES and EFFECTS are based on reference handbooks developed in the Netherlands, namely the Yellow Book, Green Book, Purple Book, and Red Book (VROM, 2005a,b,c,d), which are considered a standard reference for risk assessment by many risk-assessment practitioners.

The main output of RISKCURVES is individual and societal risk (F–N curves and societal-risk maps), as well as the consequence areas of the accident scenarios (Fig. 9.3). This includes the identification of the equipment and the scenarios that dominate the overall risk. By determining the area under the F–N curve, RISKCURVES also provides an estimate of the expected number of fatalities per year (van het Veld et al., 2007). This information can be used for risk management, decision-making, urban planning, and for any activity in support of compliance with criteria required by legislation.

Figure 9.3 Example of Iso-Risk Contours and Societal Risk Area Map for a QRA Using RISKCURVES
(Courtesy: TNO)

RISKCURVES was developed for the analysis of conventional risks associated with hazardous activities. It therefore does not contain any specific models or software modules that explicitly take into account the interaction of natural events with industrial equipment or more generally Natech risks. However, this problem can be overcome by customizing the tool for Natech-type applications. This involves the use of models for equipment vulnerability analysis that consider natural-hazard intensities and recognizing a local probability of occurrence in terms of exceedance probability for the given intensity, as discussed, for example, in Chapters 5 and 7, or in Campedel et al. (2008) and Salzano et al. (2009).

For the Natech case study in Chapter 12, new source terms expressed as risk states (RSs) were introduced in RISKCURVES for each independent natural event with a given intensity measure IM, and for three equipment categories (atmospheric tank, pressurized vessel, and large pipes). These risk states are directly linked to the Natech fragility function P and to the natural hazard. The overall probability of exceeding a given RS was then defined as:

$P [RS \geq R S_{i}] = \int_{IM} P [RS \geq R S_{i} | IM] \cdot h (IM) d IM$ $P [RS \geq R S_{i}] = \int_{IM} P [RS \geq R S_{i} | IM] \cdot h (IM) d IM$

(9.2)

In other words, the RS probability of any equipment conditional to the occurrence of a natural event may be assessed by considering the corresponding hazard h of the natural event. The annual rate of RS exceedance is then calculated by using the annual rate of occurrence.

The fragility functions in Eq. (9.2) were defined in a similar way as in ARIPAR-GIS (Section 9.1.5). For earthquakes, the same analysis and functions as shown in Table 9.2 (Campedel et al., 2008) were adopted for different equipment. For the evaluation of the seismic fragility of pipes, the data and functions reported in Lanzano et al. (2014, 2015) were used. The only seismic intensity parameter considered was PGA.

For the analysis of tsunami-triggered Natech risk, the fragility functions as defined in Basco and Salzano (2016) were adopted. In this case, the main intensity parameter is the energy flux expressed in J/m² of the tsunami wave. This is equivalent to ρ_wh_wv_w² (where ρ, h, and v are the density, the height, and the velocity of the water wave) or, in other terms, the combination of kinetic and potential (i.e., buoyancy) energy of the wave. For tsunami debris, the Johnson number was considered (Corbett et al., 1996).

A complete overview of all features and further details of the software are available at www.tno.nl/riskcurves. Additional information is provided in Chapter 12 in which a customized version of RISKCURVES was applied to a QRA of an oil refinery located in the Mediterranean Sea under both earthquake and tsunami effects.

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Table of Contents for Chapter 9: Quantitative Methods for Natech Risk Assessment

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