Dynamic process simulation of accident scenarios: the role of safety barriers

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Tesi di Laurea magistrale

Dynamic Process Simulation of Accident Scenario:

the role of safety barriers

Relatori

Candidato

Prof. Ing. Gabriele Pannocchia

Alessio Pupillo

Dott. Ing. Gabriele Landucci

Controrelatore

Prof. Ing. Leonardo Tognotti

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Abstract

Safety of industrial installations storing and handling hazardous materials is a major concern. Technical standards and legislation ask for detailed studies such Quantitative Risk Assessment (QRA) in order to guarantee safety for workers, population, environment and asset.

QRA is based on the identification of accidents (Hazard Identification), the estimation of the related frequencies (Frequency Assessment) and the associated severity (Consequence Assessment). Specific and well developed tools are currently available to support each part of QRA.

Since conventional models used for Consequence Assessment are strongly conservative and consider accidents as steady-state phenomena without taking in account their transient evolution neglecting the intervention of preventive or mitigation barriers such as alarm and shut down systems, to perform a more accurate consequence assessment, the dynamic evolution of industrial equipment given process deviations and accident scenarios should be taken into account

In this work, dynamic and automatic tools for Consequence Assessment developed in an earlier work have been implemented in a real facility simulation: these tools have the form of templates for the dynamic process simulator UniSim®_{Design, which can be inserted by the user in existing process plant} UniSim®_{Design dynamic simulations, treating them like built-in unit operations.}

In particular two accidental scenarios have been evaluated with the developed tool: Pool Fire and Jet Fire. The first considering a leakage of flammable liquid subsequent to an overpressure event in an atmospheric storage tank while the second considering a release of flammable pressurized gas from a three-phase separator.

The tool has been implemented in a simulated plant to estimate how the above-mentioned dynamic process behavior affects the accident scenarios and to evaluate the role of safety barriers in mitigating loss of containment events. In addition, both the templates have been modified to estimate the heat flux absorbed by a target located at a known distance and improved by adding a tool for the evaluation of the vulnerability with the probit model.

A qualitative analysis of dynamic results has been provided highlighting the difference between the mitigated and the non-mitigated case.

Further developments of this work include the development of other specific templates (one for each accidental scenario),their unification in one unique template for Dynamic Consequence Assessment and the estimation of possible domino effects.

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List of figures

Figure 2.1 Quantitative Risk Analysis flow diagram ... 13

Figure 2.2 Post- release Event tree for a liquid leak ... 19

Figure 2.3 View Factor scheme ... 25

Figure 2.4 Pool Fire schematization ... 26

Figure 2.5 Pool Fire schematization considering wind effects ... 27

Figure 2.6 Relationship between probit and percentage (adapted from ) ... 35

Figure 3.1 Structure of a commercial simulation process software and solving steps ... 40

Figure 3.2 Sequential Modular Approach Concept ... 41

Figure 3.3 Holdup Model scheme ... 43

Figure 3.4 UniSim®_{Design Template ... 47}

Figure 3.5 Pool Fire Template View ... 48

Figure 3.6 Life-phases of a pool fire ... 50

Figure 3.7 Rate of Heat Release ... 51

Figure 3.8 Pool fire geometry for Fview factor ... 55

Figure 3.9 Pool Flame Tilt ... 56

Figure 3.10 Flame Basis Displacement ... 56

Figure 3.11 Jet Fire Template view ... 59

Figure 3.12 Punctual source model for gaseous jet flames ... 61

Figure 3.13 Conversion from c⟂,high to c⟂,ground for vertical jet fires ... 62

Figure 3.14 Effects of the wind on c⟂, vertical jet fire ... 62

Figure 3.15 Effects of the wind on c//, vertical jet flames ... 63

Figure 3.16 Conversion from c⟂,high to c⟂,ground for horizontal jet fires ... 64

Figure 4.1Flowchart of the methodology adopted ... 68

Figure 4.2 Event Scheduler Structure (adapted from [add source]) ... 69

Figure 4.3 Pressure relief valves sizing criteria ... 70

Figure 5.1 Probit evaluation in the Pool Fire template ... 77

Figure 5.2 Probit evaluation in the Jet Fire template ... 77

Figure 5.3 Probit evaluation tool spreadsheet ... 79

Figure 5.4 Actuator Tab for Valve Unit Operation ... 80

Figure 5.5 Cause and Effect Matrix for Shut-Down System Design for the condensate storage tank .. 81

Figure 5.6 PROTEGO®_{UB/SF-80 ... 82}

Figure 5.7 Confrontation between real curve and calculated curve ... 83

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Figure 5.9 Spreadsheet for the calculation of control valve set point ... 84

Figure 5.10 Confrontation between different controller parameters, high integral time ... 86

Figure 5.11 Confrontation between different controller parameters, low integral time ... 86

Figure 5.12 Pool Fire template ... 87

Figure 6.1 Process Block Diagram ... 92

Figure 6.2 Plant Layout ... 94

Figure 6.3 Condensate storage tank process flow diagram ... 95

Figure 6.4 Condensate storage tank UniSim®_{Design process flow diagram ... 96}

Figure 6.5 Three-phase separator process flow diagram ... 98

Figure 6.6 Three-phase separator UniSim®_{Design process flow diagram ... 99}

Figure 7.1 Event Tree For a flammable liquid release ... 101

Figure 7.2 Mitigated and Non-mitigated pool radius and flame radius ... 102

Figure 7.3 Pool Mass Variation in the Non-mitigated case ... 102

Figure 7.4 Mitigated and Non- mitigated Pool Fire downwind damage distances ... 103

Figure 7.5 Mitigated and Non-Mitigated Heat Flux ... 103

Figure 7.6 Threshold values representation in plant layout... 105

Figure 7.7 Vulnerability curves for the mitigated case ... 105

Figure 7.8 Vulnerability curves for the non-mitigated case in plant layout ... 106

Figure 7.9 Separator pressure and valve opening ... 107

Figure 7.10 Mitigated and Non-Mitigated Jet Fire Damage distances ... 108

Figure 7.11 Heat flux for mitigated and non-mitigated case compared to the steady state approach . 108 Figure 7.12 Jet Fire downwind direction for mitigated and non-mitigated scenario... 109

Figure 7.13 Vulnerability curves for jet fire ... 110

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Lyst of symbols

Symbol Description Scenario

𝐴 Pool surface Pool Fire

𝑎 Flame height for view factor

calculation

Pool Fire

𝐴 Surface area of the frustum, including end discs

Jet Fire 𝐴𝑖𝑔𝑛𝑖𝑡𝑒𝑑 Ignited surface of the pool Pool Fire

𝑏 Flame radius for view factor

calculation

Pool Fire

𝑏 Flame lift-off Jet Fire

𝑐 Distance from the target at the ground level for view factor calculation

Pool Fire

𝑐// Distance from the target, down-wind direction

Both

𝑐⊥ Distance from the target, cross-wind direction

Both

𝐶0 Discharge coefficient for vapours Jet Fire

𝐶𝑑 Discharge coefficient for liquids Both

𝑐𝑝 Specific heat capacity, constant pressure

Both

𝑐𝑝,𝑙 Rain-out specific heat capacity Pool Fire

𝑐𝑣 Specific heat capacity, constant volume

Jet Fire

𝐷 Pool diameter Pool Fire

𝑑𝑒𝑞 Equivalent pool diameter Pool Fire

𝐷𝑓 Diameter of the ignited part of the pool

Pool Fire

𝐷𝑓′ Flame diameter Pool Fire

𝐷𝑠 Effective source diameter for jet fires Jet Fire 𝐸 Evaporating mass flow (generic pool) Pool Fire

𝐸𝑐𝑜𝑛𝑣 Evaporating mass flow due to

convection, evaporating pools

Pool Fire

𝐸𝑟𝑎𝑑 Evaporaing mass flow due to solar radiation

Pool Fire 𝐸𝑣𝑎𝑝 Evaporating mass flow (boiling pools) Pool Fire

𝐹 Frequency for a given event -

𝐹𝑠 Radiation fraction Both

𝐹𝑣𝑖𝑒𝑤 or 𝐹 View factor Both

𝐹𝑟10 Froude number at 10 m Pool Fire

𝐻𝑓 Flame height Pool Fire

ℎ𝑓 Flame side length Pool Fire

ℎℎ𝑜𝑙𝑒 Leakage elevation from the ground Both

ℎ𝑚𝑖𝑛,𝑝𝑜𝑜𝑙 Minimum pool thickness Pool Fire

ℎ Pool thickness Pool Fire

𝑘𝑠 Soil thermal conductivity Pool Fire

𝐿𝑏 Length of the jet flame from the flame tip to the centre of the exit plane

Jet Fire 𝐿𝑏0 Length of the jet flame in still air Jet Fire

𝐿𝑏𝑟 Pool fire burn rate length Jet Fire

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Symbol Description Scenario

𝑚 Pool mass Pool Fire

𝑚̇ Leakage mass flow rate Jet Fire

𝑚̇ See m'_rain-out Pool Fire

𝑚′′ Pool burning rate Pool Fire

𝑚̇𝑒𝑛𝑡𝑟𝑎𝑖𝑛𝑒𝑑 Entrained mass flow, i.e. droplets of liquid entrained by the released vapour

Pool Fire

𝑚̇𝑒𝑣𝑎𝑝 Evaporated mass flow, after the expansion of the leakage

Pool Fire

𝑀𝑗 Mach number of the jet Jet Fire

𝑚̇𝑙𝑖𝑞 Liquid mass flow, after the expansion of the leakage

Pool Fire

𝑚̇𝑙𝑖𝑞,𝑡𝑜𝑡 Liquid mass flow coming out from the vessel

Pool Fire

𝑚𝑚𝑎𝑥′′ Maximum pool burning rate Pool Fire

𝑚̇𝑟𝑎𝑖𝑛−𝑜𝑢𝑡 Rain-out mass flow, i.e. liquid falling on the ground and forming the pool

Pool Fire

𝑀𝑊 Molecular weight Both

𝑃𝑎𝑡𝑚 Atmospheric pressure Both

𝑃𝑐 Static pressure at the hole exit plane Jet Fire

𝑃𝑟𝑒𝑙 Relative pressure in the vessel Pool Fire

𝑃𝑠𝑎𝑡 Vapour pressure Both

𝑞 Heat flux in a specified point Both

𝑄′ Released heat per unit time Jet Fire

𝑄𝑏𝑜𝑖𝑙 Rate of heat input for boiling pools Pool Fire 𝑄𝑐𝑜𝑛𝑑 Rate of heat related to soil conduction

(boiling pools)

Pool Fire

𝑄𝑐𝑜𝑛𝑣 Rate of heat related to atmospheric convection (boiling pools)

Pool Fire

𝑄𝑟𝑎𝑑 Rate of heat related to solar radiation (boiling pools)

Pool Fire

𝑄𝑠𝑜𝑙 Rate of heat related to solution of the leakage in water (boiling pools)

Pool Fire

𝑄𝑠𝑝𝑖𝑙𝑙 Rate of heat related to the sensible heat of the leakage (boiling pools)

Pool Fire

𝑅 Risk related to an accident -

𝑟 Pool radius Pool Fire

𝑅𝑙 Frustum length Jet Fire

𝑅𝑤 Ratio of wind speed to jet velocity Jet Fire

𝑅𝐻𝑅 Rate of Heat Release Pool Fire

𝑅𝐻𝑅𝑚𝑎𝑥 Rate of Heat Release when the flame has covered the whole pool

Pool Fire

𝑅𝑖 Richardson number Jet Fire

𝑠 Distance at which the rain-out reaches the ground

Pool Fire

𝑆 Solar heat flux Both

𝑆𝐸𝑃 Surface Emissive Power Both

𝑆𝐸𝑃𝑡ℎ𝑒𝑜𝑟 Theoretical SEP, considering the whole RHR

Pool Fire

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Symbol Description Scenario 𝑡0.7 𝑇𝐹𝐿 Time at which 70% TFL of the pool

has been consumed

Pool Fire

𝑇𝑎𝑡𝑚 Atmosperic temperature Both

𝑇𝑏 Pool boiling temperature Pool Fire

𝑡𝑑𝑒𝑐𝑎𝑦,𝑠𝑡𝑎𝑟𝑡 Time at which decay phase begins (confined pools)

Pool Fire 𝑡ℎ𝑜𝑙𝑒 𝑐𝑟𝑒𝑎𝑡𝑖𝑜𝑛 Time at which the hole occurs Pool Fire 𝑡𝑖𝑔𝑛𝑖𝑡𝑖𝑜𝑛 Time at which ignition occurs Pool Fire

𝑇𝑗 Temperature of the expanding jet Jet Fire

𝑇𝑙𝑒𝑎𝑘 Leakage temperature Pool Fire

𝑡𝑁𝐹𝑆 Time at which the leakage is detected and blocked

Pool Fire

𝑇𝑝𝑜𝑜𝑙 Pool temperature Pool Fire

𝑇𝑠 Initial soil temperature Pool Fire

𝑇𝑠 Initial gas temperature Jet Fire

𝑡𝑡𝑜𝑡 Time at which the fire is totally extinguished

Pool Fire

𝑡𝑡𝑟𝑎𝑛𝑠 Time at which flame propagation phase is completed

Pool Fire

𝑇𝐹𝐿 Total Fire Load Pool Fire

𝑢∗ _{Scaled wind velocity} _{Pool Fire}

𝑢𝑗 Exit velocity of the expanding jet Jet Fire

𝑢𝑤 Wind velocity at a height of 10 m Pool Fire

𝑊1 Frustum base width Jet Fire

𝑊2 Frustum tip width Jet Fire

𝑥𝑝, 𝑦𝑝 Confinement pool dimensions Pool Fire

𝛼′ Tilt angle between hole axis and

frustum axis

Jet Fire

𝛼𝑠 Soil thermal diffusivity Pool Fire

𝛾 Poisson constant Jet Fire

𝛥𝐻𝑐 Low heating value Pool Fire

𝛥𝐻𝑣 Heat of vaporization Pool Fire

𝛥𝑡 Integration time step Pool Fire

𝜁 Soot fraction Pool Fire

𝜃′ Angle between frustum axis and

vertical

Jet Fire

𝜃𝑗𝑣 Angle between hole axis and the horizontal in the direction of the wind

Jet Fire

𝜇𝑎 Atmospheric air dynamic viscosity Pool Fire

𝜉𝑅 Rain-out fraction Pool Fire

𝜉𝑇 Entrainment fraction Pool Fire

𝜉𝑉 Vaporization degree Pool Fire

𝜌𝑎 Atmospheric air mass density Pool Fire

𝜏𝑎 Atmospheric transmissivity Both

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Lyst of acronyms

Acronym Description

BLEVE Boiling Liquid Expanding Vapour Explosion

CA Consequence Assessment

DCA Dynamic Consequence Assessment

EPA Environmental Protection Agency

ETA Event Tree Analysis

FA Frequences Assessment

FTA Fault Tree Analysis

HazOp Hazard and Operability analysis

HazId Hazard Identification

HSE Health, Safety and Environment

LNG Liquefied Natural Gas

LPG Liquefied Petroleum Gas

NFS No Feed Starts

OLE Object Linking and Embedding

PSV Pressure Safety Valve

PVC Polyvinyl Chloride

QRA Quantitative Risk Assessment

SEP Surface Emissive Power

TNO Netherlands Organization for Applied Scientific Research

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Chapter 1 Introduction

The realization of safer chemical facilities is one of the major concerns during the preliminary design stage of a chemical process. The technological progress leads towards more complex chemical processes that need equally complex and advanced safety tools to reduce risk and give inherently safe processes.

Inside any industrial activity, it is possible to locate multiple preventive or protective barriers that contain components to prevent hazardous events or to protect equipment and mitigate effects resulting from accident scenario.

Since a growing attention is given to the performance of existing safety barriers and their adequacy, this work aims point out the effectiveness of the protective layers in mitigating the effects of relevant accidents in the chemical industry since the conventional quantitative risk assessment approach does not takes them in account.

This is done recreating an accident scenario occurring in a real facility with the process simulator

UniSim® Design Design Suite in dynamic mode ad calculating the effects with the tool developed

by Alessio Mencaroni in his thesis work.

The above-mentioned tool evaluates the effects of a pool fire caused by a leak of flammable liquid and of a jet flame from a high-pressure gas release. The results are presented by mean of the conventional threshold model and with the probit model to estimate the probability of injury. For this purpose, the tool itself was modified and new features for the evaluation of the heat flux absorbed by a target placed in a fixed location and for the calculation of the probability of injury were added.

In chapter 2 is reported an overview of quantitative risk assessment in the chemical industry and a presentation of models and tools adopted for conventional consequence assessment.

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Chapter 3 focuses on process simulators, first outlining the difference between steady state and dynamic mode and how calculations are performed in both modes, and then making a literature review of their adoption in safety studies. Moreover, Mencaroni’s thesis work is summarized in the last section of the chapter.

The aim of the work and the methodology adopted are described in chapter 4, giving an overview of the steps followed to perform calculations and to set up the simulated scenarios in the software. In chapter 5 are reported and described the new features of the consequence assessment tool developed during this thesis work and the emergency shut-down system, implementation of which was necessary to evaluate how the safety system can mitigate the effects. In addition, it is described the modeling of the vacuum valve mounted on the atmospheric storage tank.

The reference process and the case studies are outlined in chapter 6 with a generic description of the gas treatment operations followed by a detailed analysis of the process units subject of study. A layout adaptation is provided both to show the location of the equipment and to pinpoint some sensitive targets or locations.

The results are then presented in chapter 7 showing how mitigation barriers can reduce the effects of an accident scenario and discussing about how powerful a dynamic process simulator is in performing advanced and more realistic consequence assessment.

In chapter 8 the conclusions of the work are reported as well as further development that can be achieved in future works.

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Chapter 2 Consequence assessment in process safety studies:

state of the art and research needs

2.1 Overview of quantitative risk assessment methods

In the 1960s, the developments of the chemical, oil, and petrochemical industry lead to larger facilities with more severe operating conditions, close to the limits of safety. The use of larger items of equipment for process operations, increased the mass and the energy involved and, consequently, the potential for loss.

The adoption of strategies aiming to prevent accidents and/or to mitigate the extent of damages using proper design and technologies became a priority.

At the same time, the effects of industry operations both on people and the environment with a special focus on the possible hazards and the reduction of emissions and noise, became of major concern. The industry had to take steps to show that its operations were conducted with due regard to safety.

By the 1970s, these problems forced the senior management to assign to their solution many senior and capable people as well as other resources: risk analysis and evaluation techniques set up in the aeronautical and nuclear sector were applied in the process industry too.

Chemical process quantitative risk analysis is a methodology designed to provide management with a tool to help evaluate overall process safety in the chemical process industry. The basis of Quantitative Risk Analysis is to identify incident scenarios and evaluate the risk by defining the probability of failure, the probability of various consequences and the potential impact of those consequences. It is made by many activities linked each other and can be applied to different risk types.

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The risk is a measure of human injury, environmental damage or economic loss in terms of both the incident likelihood and the magnitude of the loss or injury. Mathematically, it is defined as a function of probability and magnitude of damage of an accident scenario:

𝑅 = 𝑓(𝑀, 𝐹) (2.1)

- M is the estimated magnitude of damage of the accident scenario

- F is the estimated frequency of the scenario generally expressed as number of occurrences of an event per unit of time.

At this point, it must be noticed that the term “risk” has a different definition from the term “hazard”: a hazard is any condition that has the potential for causing damage to people, property, or the environment and it is defined as a function of the magnitude of the specific scenario. The steps that must be followed in order to achieve an effective analysis are illustrated in Figure 2.1 and discussed below.

• Hazard Identification: the definition of the potential accident scenario and hazard identification is of fundamental importance in loss prevention and it is the starting point of each Quantitative Risk Analysis. Many techniques can be used and each of them can be applied in different stages of a project. These techniques and methods include checklists, hazard index techniques, what-if analysis, hazard and operability (HAZOP) analysis, failure modes and effects analysis (FMEA), experience both about earlier incidents and equipment failure. There are a number of codes available to assist in the conduct of the various techniques for hazard identification.

• Frequency Evaluation: once the hazards have been identified, the analysis focuses on the likelihood estimation of the event. Such estimation may be obtained by historical incident data on failure frequencies or, when such data are not available, by the fault tree and event

tree analysis.

• Consequences Evaluation: by this methodology, the potential for damage or injury from specific incidents can be determined. Once the incident has been outlined and described with a source term model, its outcomes may be determined performing an Event tree

Analysis and its effects estimated using the proper model (dispersion, fire or explosion),

depending on the released material. Effect models, in the end, convert these incident specific results into effects on people and structures.

• Risk recomposition: the results of the previous steps are combined to provide one or more measures of risk.

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HAZARD

IDENTIFICATION

FREQUENCY

EVALUATION

CONSEQUENCES

EVALUATION

RISK

RECOMPOSITION

RISK EVALUATION

Figure 2.1 Quantitative Risk Analysis flow diagram

The results from a risk analysis are used to make decisions either through relative ranking of risk reduction strategies or through comparison with specific risk targets: this step is crucial for the adoption of measures to reduce the global risk of the system.

2.2 Consequence assessment: methods and tools

As briefly described in the previous section, consequence evaluation is a necessary step in the risk management process. In order to manage risk effectively, consequences must be estimated. The steps forming the procedure are:

• Schematization and description of the release scenario by the source term models, • Incident outcome list through the event tree analysis,

• Selection of fire/explosion model or toxic effects model.

Sometimes mitigation factors, e.g. people escape, emergency response, containment dikes, shall be considered for the consequence assessment in order to provide a more realistic result to be used in risk calculations.

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2.2.1 Source term models

Source term models are used to quantitatively define the release scenario by estimating discharge rates, total quantity released (or total release duration), extent of flash and evaporation from a liquid pool, and aerosol formation.

An accident always starts with the release of flammable or toxic material from its normal containment. When a release takes place, a distinction must be made to classify the type of release:

- Instantaneous release - Continuous release

When the release of the substance is instantaneous, the entire inventory of the equipment is released very quickly.

On the other side, in case of a continuous release, distinction must be made between release from the venting system and accidental release: in the first case the source diameter is known while in the latter case the leak may occur either from a small diameter source, i.e. a small crack in a pipe or a flange connected to the process unit, or from a full-bore rupture of the pipe. Hypothesis about the diameter based on well-known methodologies are required to perform the calculations. Such leaks may be gas, liquid or two-phase flashing liquid-gas releases and each of these has the appropriate discharge model

In conclusion the source term considered can be summarized as follows: • Liquid Discharges

- Hole in atmospheric storage tank or other atmospheric pressure vessel or pipe under liquid head

- Hole in vessel or pipe containing pressurized liquid below its normal boiling point

• Gas Discharges

- Hole in equipment (pipe, vessel) containing pressurized gas - Relief valve discharge (of vapor only)

- Relief valve discharge from top of pressurized storage tank • Two-Phase Discharges

- Hole in pressurized storage tank or pipe containing a liquid above its normal boiling point

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When the release is quantified, the results constitute the input for the consequences models’ calculations.

The models implemented in the tool for the dynamic consequence assessment are described below.

Two-Phase Discharge

When released to atmospheric pressure, any pressurized liquid above its normal boiling point is subjected to an adiabatic expansion and starts to flash with part of the liquid that breaks up forming droplets. Bigger droplets fall onto the ground forming the so-called rain-out while the smaller ones are entrained with the vapor forming a disperse phase.

Considering the following energy balance:

𝑚̇𝐻̂0= 𝑚̇𝐿𝐻̂𝐿+ 𝑚̇𝑉𝐻̂𝑉 (2.2)

𝐻̂0= 𝑐̂𝑃𝐿⋅ (𝑇𝑎𝑚𝑏− 𝑇𝑒𝑏) (2.3)

𝐻̂𝐿= 𝑐̂𝑃𝐿⋅ (𝑇𝑒𝑏− 𝑇𝑒𝑏) = 0 (2.4)

𝐻̂𝑉= 𝛬 (2.5)

𝑚̇ ∙ 𝑐̂𝑃𝐿⋅ (𝑇𝑎𝑚𝑏− 𝑇𝑒𝑏) = 𝑚̇𝑉∙ 𝛬 (2.6)

it is possible to evaluate the fraction of released liquid that vaporizes:

ξ𝑉= 𝑚̇𝑉 𝑚̇ = 𝑐̂𝑃𝐿 Λ (𝑇𝑎𝑚𝑏− 𝑇𝑒𝑏) (2.7) Considering: 𝑚̇𝐿= 𝑚̇𝑅+ 𝑚̇𝑇 (2.8) it results: ξ𝑅= 𝑚̇𝑅 𝑚̇ (2.9) ξ𝑇 = 𝑚̇𝑇 𝑚̇ (2.10)

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In this work the it is assumed that:

ξ𝑉 < 0.15 ξ𝑅= 1 − ξ𝑉 ξ𝑇 = 0

0.15 < ξ𝑉 < 0.30 ξ𝑅 = 1 − 2ξ𝑉 ξ𝑇 = ξ𝑉

ξ𝑣> 0.30 ξ𝑅 = 0 ξ𝑇 = 1 − ξ𝑉

Pool vaporization models

The rain-out may form a pool that can be:

• Evaporating if the liquid released was stored at atmospheric condition

• Boiling if the released substance is normally gaseous at atmospheric condition

The liquid can be released either in a confinement basin or can spread on the ground assumed flat and non-porous.

The pool material balance for a continuous release is:

{ 𝑑𝑚(𝑡)

𝑑𝑡 = 𝑚̇(𝑡) − 𝐸(𝑡)

𝑚(𝑡0 = 𝑡ℎ𝑜𝑙𝑒 𝑐𝑟𝑒𝑎𝑡𝑖𝑜𝑛) = 𝑚0 = 0

(2.11)

Note that for evaporating pools 𝐸(𝑡) ≪ 𝑚̇𝑒(𝑡)

The heat balance for a pool spreading onto the ground:

𝑄𝑛𝑒𝑡= 𝑄𝑐𝑜𝑛𝑑+ 𝑄𝑐𝑜𝑛𝑣+ 𝑄𝑟𝑎𝑑+ 𝑄𝑠𝑝𝑖𝑙𝑙− 𝑄𝑒𝑣𝑎𝑝 _(2.12)

Where 𝑄𝑐𝑜𝑛𝑑 is the heat flow rate from conduction,𝑄𝑐𝑜𝑛𝑣 is the heat flow rate from convection,

𝑄𝑟𝑎𝑑 is the heat flow rate from solar radiation, 𝑄𝑠𝑝𝑖𝑙𝑙 is the heat flow rate from spilled liquid and

𝑄𝑒𝑣𝑎𝑝 is the heat flow rate from evaporation.

The parameters are evaluated with the following equations:

𝑄𝑐𝑜𝑛𝑑=

𝑘𝑠∙ (𝑇𝑠− 𝑇𝑏)

√π ⋅ α𝑠⋅ 𝑡 (2.13)

Convective heat flux, 𝑄𝑐𝑜𝑛𝑣 is modelled as if it took place over a flat plate of length 𝐿 in the

downwind direction. In these condition, two types of boundary may occur i.e. laminar or turbulent flow. Considering the Reynolds number defined as follows:

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𝑅𝑒 =𝑢𝑤⋅ ρ𝑎⋅ 𝐷

μ𝑎 (2.14)

the Nusselt number is calculated by:

𝑁𝑢 = {

0.664 ⋅ 𝑃𝑟1/3⋅ 𝑅𝑒1/2, 𝑅𝑒 ≤ 320000

0.037 ⋅ 𝑃𝑟1/3⋅ [𝑅𝑒0.8− 15200], 𝑅𝑒 > 320000 (2.15)

with the Prandtl number

𝑃𝑟 =𝑐𝑝,𝑎⋅ 𝜇𝑎

𝑘𝑠 (2.16)

So the convective heat is calculated by:

𝑄𝑐𝑜𝑛𝑣= 𝑘𝑠∙ 𝑁𝑢 ∙

π ∙ r_pool2

𝐿 ∙ (𝑇𝑎− 𝑇𝑝𝑜𝑜𝑙) (2.17)

Another term to be considered is heat gained by the pool from solar radiation. The rate of heat input is calculated as:

𝑄𝑠𝑜𝑙𝑎𝑟= π ∙ rpool2 ∙ 𝑆 (2.18)

where 𝑆 is the solar heat flux with an assumed typical value of 400 𝑊/𝑚2. A small contribution can come from long wave radiation:

𝑄𝑙𝑜𝑛𝑔= 𝜀 ∙ 𝜎 ∙ (𝑇𝑎4− 𝑇𝑝𝑜𝑜𝑙4 ) ∙ 𝜋 ∙ 𝑟𝑝𝑜𝑜𝑙2 (2.19)

And so, the total rate of heat input is:

𝑄𝑟𝑎𝑑= 𝑄𝑠𝑜𝑙𝑎𝑟+ 𝑄𝑙𝑜𝑛𝑔 _(2.20)

The heat flow rate from spilled liquid, due to the fact that leaking liquid is at temperature different from that of the pool can be calculated considering:

𝑄𝑠𝑝𝑖𝑙𝑙= 𝑚̇𝑟𝑎𝑖𝑛−𝑜𝑢𝑡⋅ [𝑐𝑝𝐿(𝑇𝑙𝑒𝑎𝑘) ⋅ (𝑇𝑙𝑒𝑎𝑘− 𝑇𝑝𝑜𝑜𝑙)] _(2.21)

Once the release has ended, 𝑄𝑠𝑝𝑖𝑙𝑙 becomes zero

The evaporating mass flow must be determined with the proper approach. If the pool is evaporating, the mass flow 𝐸(𝑡) is determined considering the empirical equations presented in (1):

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For round pools _{𝐸 = 𝐾}′_{∙ 𝑢} 𝑤 2−𝑛

2+𝑛_{∙ 𝑟}4+𝑛_2+𝑛 _(2.22)

For rectangular pools _{𝐸 = 𝐾 ∙ 𝑢}

𝑤 2−𝑛 2+𝑛_{∙ 𝑥} 𝑝 2 2+𝑛_{∙ 𝑦} 𝑝 (2.23) where 𝐾′ = 𝑎′⋅ 𝑥𝑜 _(2.24) 𝐾 = 𝑎 ⋅ 𝑥𝑜 (2.25) 𝑥𝑜 = 𝑃𝑎𝑡𝑚𝑃𝑀 𝑅𝑇 𝑙𝑛 (1 + 𝑃(𝑇) 𝑃𝑎𝑡𝑚 ) _(2.26)

The values for 𝑛, 𝑎 and 𝑎′ are reported in Table 2.1.

Table 2.1 Evaporating pool equation parameters

Atmosphere n a a'

Unstable 0.20 1.278 × 10−3 3.846 × 10−3

Neutral 0.25 1.579 × 10−3 4.685 × 10−3

Stable 0.30 1.786 × 10−3 _{5.285 × 10}−3

The found value must be added to the evaporating mass flow due to the solar radiation 𝑄𝑟𝑎𝑑.

If the pool temperature is equal to the boiling point of the liquid, then the pool is assumed to be boiling with a rate of heat input given by:

𝑄𝑏𝑜𝑖𝑙 = 𝑄𝑐𝑜𝑛𝑑+ 𝑄𝑐𝑜𝑛𝑣+ 𝑄𝑟𝑎𝑑+ 𝑄𝑠𝑜𝑙+ 𝑄𝑠𝑝𝑖𝑙𝑙 _(2.27)

The resulting vaporization rate is calculated considering:

𝐸𝑣𝑎𝑝(𝑡) =

𝑚𝑎𝑥{𝑄𝑏𝑜𝑖𝑙, 0}

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2.2.2 Event Tree Analysis

Event trees are used to study or model event sequences which can result in different consequences. Given an initiating event i.e. the release (continuous or instantaneous) of a dangerous substance, it can develop into several outcomes depending on the occurrence of one or more intermediate events. An event tree always starts with an initiating event and it can be recognized from the fact that the various heading events can occur only after occurrences of the initiating event. An example of a post-release event tree is shown in Figure 2.2.

Every heading event matches a node and from every node starts one or more branches: the upper branch is associated to the happening of the event while the lower one represents the unhappening of the same event.

Post-release event trees are useful for flammable and flammable/toxic substances releases as it allows to identify all the possible scenarios that may occur. In this case the final scenarios are:

- Jet-fire - Pool-fire - Fireball - Flash-fire

- Vapor Cloud Explosion or VCE - Toxic Cloud

- No effects

Figure 2.2 Post- release Event tree for a liquid leak

Making an event tree is useful if:

• a specific event can result in more than one outcome;

• one is interested in the probability of occurrence of each of the different outcomes.

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Implementing the quantification of the probability of intermediate events returns a complete event

tree. It is possible to consider the activation of safety systems as an intermediate event with a

modification both on type and frequency of occurrence of the final scenario.

2.2.3 Consequence evaluation models

Every plausible outcome resulting from the Event tree analysis must be quantified with the adoption of a specific model. Final scenarios can be grouped in three categories:

1. Explosion models

- Boiling liquid expanding vapor explosion or BLEVE - Vapor Cloud Explosion or VCE

- Confined Explosion - Physical Explosion 2. Dispersion models

3. Fire models

- Pool Fire/Tank Fire - Jet Fire

- Flash-Fire - Fireball Explosion models

An explosion can be thought of as a rapid release of a high-pressure gas into the environment. This release must be rapid enough that the energy is dissipated as a pressure or shock wave. Explosions can arise from strictly physical phenomena such as the catastrophic rupture of a pressurized gas container or from a chemical reaction such as the combustion of a flammable gas in air. These latter reactions can occur within buildings or vessels or in the open in potentially congested areas.

Explosions from combustion of flammable gas are of two kinds: (1) deflagration and (2) detonation.

In a deflagration the flammable mixture burns at subsonic speeds. For hydrocarbon-air mixtures the deflagration velocity is typically of the order of 300 m/s. A detonation is quite different. In a detonation the flame front travels as a shock wave followed closely by a combustion wave which releases the energy to sustain the shock wave. At steady state the detonation front reaches a velocity equal to the velocity of sound in the hot products of combustion; this is much greater

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A detonation generates greater pressures and is more destructive than a deflagration. A deflagration may turn into a detonation, particularly when travelling down a long pipe.

Many types of outcomes are possible for a release. This includes:

• Vapour cloud explosions (VCE): When a large amount of flammable vaporizing liquid or gas is rapidly released, a vapor cloud forms and disperses with the surrounding air. The release can occur from a storage tank, process, transport vessel, or pipeline. If this cloud is ignited before the cloud is diluted below its lower flammability limit (LFL), a VCE or flash fire will occur. For QRA modeling the main consequence of a VCE is an overpressure that results while the main consequence of a flash fire is direct flame contact and thermal radiation.

• Confined explosions: this type of explosion occurs in congested enclosures and represents an in-plant threat more than a hazard to the community.

• Physical explosions: it comes from the rupture of a vessel containing a pressurized gas. The release of the stored energy can produce a shock wave and accelerate vessel fragments that constitute the major threat for this type of scenario.

• Boiling liquid expanding vapour explosion (BLEVE): is a sudden release of a large mass of pressurized superheated liquid to the atmosphere. The primary cause is usually an external flame impinging on the shell of a vessel above the liquid level, weakening the container and leading to sudden shell rupture.

Dispersion models

Typically, the dispersion calculations provide an estimate of the area affected and the average vapor concentrations expected. The simplest calculations require an estimate of the release rate of the gas (or the total quantity released), the atmospheric conditions (wind speed, time of day, cloud cover), surface roughness, temperature, pressure and perhaps release diameter. More complicated models may require additional detail on the geometry, discharge mechanism, and other information on the release.

Three kinds of vapor cloud behavior and three different release-time modes can be defined: Vapor Cloud Behavior:

• Neutrally buoyant gas • Positively buoyant gas

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Duration of Release:

• Instantaneous (puff)

• Continuous release (plumes) • Time varying continuous

The well-known Gaussian models describe the behavior of neutrally buoyant gas released in the wind direction at the wind speed. Dense gas releases will mix and be diluted with fresh air as the gas travels downwind and eventually behave as a neutrally buoyant cloud. Thus, neutrally buoyant models approximate the behavior of any vapor cloud at some distance downwind from its release. Neutrally or positively buoyant plumes and puff have been studied for many years using Gaussian models. These studies have included especially the dispersion modeling of power station emissions and other air contaminants used for air pollution studies.

Fire models

When flammable liquids and gases are released, there is the possibility of a fire after ignition. In this case the damage to people and surroundings to be evaluated is the heat flux from the fire. This heat flux is estimated through several models that provide the distribution of the thermal radiation in space and time.

The different types of fire are:

• Pool Fire: it occurs when a flammable liquid spills onto the ground and is ignited. If the fire occurs in a liquid storage tank it can be treated as a pool fire and is named tank fire. A pool fire may also occur on the surface of flammable liquid spilled onto water. They are mainly of concern in establishing the potential for domino effects and employee safety zones, rather than for community risk. The primary effects of such fires are due to thermal radiation from the flame source;

• Jet Fire: typically results from the combustion of a material as it is being released from a pressurized process unit. The main concern, similar to pool fires is in local radiation effects.

• Flash Fire: is the nonexplosive combustion of a vapor cloud resulting from a release of flammable material into the open air. Major hazards from flash fires are from thermal radiation and direct flame contact.

• Fireball: is the atmospheric burning of a fuel-air cloud in which the energy is mostly emitted in the form of radiant heat. It occurs when a given amount of flammable vapor or gas, previously confined at relevant pressure, is suddenly released into the atmosphere

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Except for the case of impinging fires, heat radiation is the most relevant contribute in heat transfer. In case of an impinging fire, also heat convection and heat conduction through the vessel wall must be taken into account.

The heat radiated to objects in the surroundings of a fire is determined by the dimensions and shape of the surface area of the fire, the heat generated due to combustion, the fraction of heat which is emitted as heat radiation, produced soot which screens the luminous parts of the flame, water vapour and carbon dioxide in the air which absorbs the radiation, and the position of the object.

The models reported in literature for the evaluation of the heat radiated by a flame and can be divided into three classes:

- Semi-empirical models - Field models

- Integral models

Semi-empirical modelling is a relatively simple technique for providing models for predicting the

heat flux at a distance, associated with jet flames and pool fires. Because of their simplicity, semi-empirical models are usually designed only to predict quantities such as flame shape and radiative, rather than to provide a detailed description of the fire itself.

There are two types of models:

1. Point source models, which assume that the source of the heat radiation is a point 2. Surface emitter models, which assume that heat is radiated from the surface of a solid

object (i.e. tilted cone or cylinder)

Semi-empirical models are ideally suitable for routine hazard assessment purposes because they are mathematically simple, and hence easily understood.

Field models are based on solutions of the time-averaged Navier-Stokes- equations of fluid flow

and are, therefore, mathematically complex, embodied in large computer programs and have significant run times on large computer systems

Integral models are a compromise between semi-empirical models and field models. The models

that incorporate a more rigorous description of the physics permit them to be used over a wider range of circumstances than semi-empirical models. Integral models are formulated mathematically in the same way as field models. They solve equations that describe the conservation of mass, momentum and scalar quantities within a flow, and can in principle contain sub-models of the turbulence structure and combustion and heat transfer process. These equations

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are, expressed in a simplified form, namely in integral models, such that their solution is demanding far less computer time than for field models.

In this work, the models adopted both for the pool fire and for the jet fire belong to the surface

emitter models type included in the semi-empirical model category. Therefore, an introduction to

the concept of the Surface Emissive Power is necessary.

The surface emissive power is defined as the heat rate from a radiating surface of a flame and can be calculated with the Stefan-Boltzmann equation.

𝑆𝐸𝑃 = 𝜖𝜎(𝑇_𝑓4− 𝑇𝑎4) (2.29)

Since the flame temperature is difficult to determine, the “solid flame approach” is used, which means that part of the combustion heat is radiated through the visible flame surface area of the flame.

SE𝑃𝑡ℎ𝑒𝑜𝑟 can be estimated from the combustion energy generated per second and the surface of

the flame

𝑆𝐸𝑃𝑡ℎ𝑒𝑜𝑟= 𝑄′/𝐴 (2.30)

SE𝑃𝑚𝑎𝑥 can be calculated from SE𝑃𝑡ℎ𝑒𝑜𝑟 and the fraction of the heat radiated from the flame

surface:

𝑆𝐸𝑃𝑚𝑎𝑥 = 𝐹𝑠 𝑆EP𝑡ℎ𝑒𝑜𝑟 (2.31)

The heat flux at a certain distance from the fire can be calculated by:

𝑞 = 𝑆𝐸𝑃𝑚𝑎𝑥∙ 𝐹𝑣𝑖𝑒𝑤∙ 𝜏𝑎 (2.32)

The view factor 𝐹𝑣𝑖𝑒𝑤 is defined as the ratio between the received and the emitted radiation energy

per unit area and depends on the flame shape and dimensions, distance of the target from the flame and shape and the angular orientation of the source and the target.

The geometric view factor is mathematically defined by:

𝐹𝑣𝑖𝑒𝑤 𝑑𝐴2,𝑑𝐴1= 1 𝜋∫ ∫ ( 𝑐𝑜𝑠𝛽1𝑐𝑜𝑠𝛽2 𝑥2 ) 𝑑𝐴2 𝐴2 (2.33) where x is the distance between the centers of 𝑑𝐴1 and 𝑑𝐴2, 𝛽1 is the angle of the normal vector

to plane 𝑑𝐴1and the line connecting 𝑑𝐴1and 𝑑𝐴2and 𝛽2 is the angle of the normal vector to plane

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Figure 2.3 View Factor scheme

Several methods have been developed for the evaluation of view factors including direct integration, contour integration or short-cut method. In this work the view factor is estimated with the interpolation method developed in (2) that will be outlined in the following chapters.

The atmospheric transmissivity 𝜏𝑎 accounts for the fact that emitted radiation is partyl absorbed

by the air present between the radiator and the radiated object. The factor is equal to 1 minus the absorption factor, the value which depends on the absorbing properties of the components of the air in relationship to the emission spectrum of the fire. Since water vapour and carbon-dioxide are the main absorbing components within the wave length area of the heat radiation, the following approximating expression can be given:

𝜏𝑎= 1 − 𝛼𝑎− 𝛼𝑐 (2.34)

As well as for the view factor, since the transmissivity depends both on distance and on vapour pressure the following equation was used and implemented in the tool.

𝜏𝑎= 2.02 (𝑝𝑤⋅ 𝑐)−0.09 (2.35)

Follows a description of the theoretical background of the models implemented in the tool for the dynamic consequence assessment of pool fire and jet fire.

Pool fire model description

The SEPmax for a pool fire is calculated as follows

𝑆𝐸𝑃𝑚𝑎𝑥= 𝐹𝑠 𝑆𝐸𝑃𝑡ℎ𝑒𝑜𝑟 =

𝐹𝑠 𝑚′′𝛥𝐻𝐶

1 + 4_𝑑ℎ𝑓

𝑓

(2.36)

For a pool fire, however the heat flux equation does not consider the SEPmax since the presence

of soot may reduce this value, so, the 𝑆𝐸𝑃𝑚𝑎𝑥 value must be actualized.

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The equation for the evaluation of the SE𝑃𝑎𝑐𝑡 is:

𝑆𝐸𝑃𝑎𝑐𝑡= 𝑆𝐸𝑃𝑚𝑎𝑥(1 − 𝜁) + 𝑆𝐸𝑃𝑠𝑜𝑜𝑡 (2.37)

As can be seen in (2.36), to evaluate the pool fire 𝑆𝐸𝑃𝑚𝑎𝑥 it is necessary to calculate the geometry

of the liquid pool and the burning rate of the liquid spilled.

Starting from the source term models the equivalent diameter of the pool can be calculated. The use of an equivalent diameter is due to the difficulty of evaluation of the pool diameter with an irregular shape. The equivalent diameter is derived from the thickness of the pool, considered constant in case of a non-confined pool, and the released liquid volume. In case of a confined pool, the pool surface is equal to that of the confinement basin.

The burning rate of the liquid material is calculated by:

𝑚𝑚𝑎𝑥′′ = 10−3 Δ𝐻̂𝐶 Δ𝐻̂𝑉+ 𝐶𝑃(𝑇𝑏− 𝑇𝑎) (2.38) 𝑚′′_{(𝑡) = 𝑚} 𝑚𝑎𝑥 ′′ _{(1 − 𝑒} 𝐷_𝑓(𝑡) 𝐿𝑏𝑟 ) (2.39)

In stagnant conditions, that is with no wind effects, the flame diameter is equal to the pool diameter and the height can be evaluated as follows.

ℎ𝑓 𝑑𝑓 = 42 ( 𝑚 ′′ 𝜌_{𝑎√𝑔 D}) 0.61 (2.40)

Figure 2.4 Pool Fire schematization

On the contrary, with strong wind effects, the flame tilts and new equations are required to

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𝐻𝑓 𝑑𝑓 = 55 ( 𝑚 ′′ 𝜌_{𝑎√𝑔 𝐷}) 0.61 (𝑢∗₎−0.21 _(2.41)

where 𝑢∗ is the scaled wind velocity calculated by:

𝑢∗= 𝑢𝑤

(𝑔 𝑚_𝜌′′𝐷

𝑎 )

0.33 _(2.42)

Figure 2.5 Pool Fire schematization considering wind effects

And 𝐻𝑓 is the length of the tilted flame:

𝐻𝑓 = ℎ𝑓⋅ 𝑐os(𝜃) = ℎ𝑓

1

ℎ𝑓 (2.43)

Due to the presence of wind, the flame elongates, and the flame basis will have a kind of elliptical shape. This elongated diameter of the flame basis can increase the surface area of the flame on one side and can be calculated as follows:

𝐹𝑟10=

𝑢𝑤2

𝑔 ⋅ 𝐷 (2.44)

𝐷′= 𝐷 𝑎𝑝⋅ (𝐹𝑟10)𝑏𝑝 (2.45)

where ap and bp are parameters that depend on the flame shape, i.e. conical or cylindrical.

Jet Fire model description

The model adopted is that developed by Chamberlain, also called “Thornton model”. This model represents the flame as a frustum of a cone, radiating as a solid body with a uniform surface emissive power.

For the evaluation of the heat radiated from a jet fire, as well as already seen for the calculations of a pool fire, the first step is the estimation of the geometrical dimensions of the flame.

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From the output of the source terms, the exit velocity of the expanding jet can be determined as follows: 𝑢𝑗= 𝑀𝑗 (γ ∙ 𝑅𝐶∙ 𝑇𝑗 𝑊𝑔 ) 1 2 (2.46)

As can be seen, several terms are required to evaluate the exit velocity.

The mass fraction of flammable material in a stoichiometric mixture with air 𝑊

𝑊 = 𝑊𝑔

15.816 ⋅ 𝑊𝑔+ 0.0395 (2.47)

The Poisson constant

γ =𝑐𝑝

𝑐𝑣 (2.48)

The temperature of the expanding jet

𝑇𝑗= 𝑇𝑠(

𝑃𝑎𝑖𝑟

𝑃𝑖𝑛𝑖𝑡

) (γ − 1

γ ) (2.49)

The Mach Number for choked and non-choked flow

𝑀𝑗 = √(γ + 1) ∙ (_𝑃𝑃_𝑎𝑖𝑟𝑐 ) (γ−1_{γ )} − 2 γ − 1 (2.50) 𝑀𝑗= √ √1 + 2(γ − 1)𝐹2_{− 1} γ − 1 (2.51)

with 𝐹 calculated by the following equation

𝐹 = 3.6233 × 10−5𝑚̇ 𝑑02

√ 𝑇𝑗 γ ⋅ 𝑊𝑔

(2.52)

where 𝑚̇ is the leakage mass flow rate and 𝑑0 is the hole diameter.

The equations hereafter reported, are used to calculate the flame position and dimensions, required to calculate both the lift-off and the angle of the flame with respect to the object and the view factor as well as the surface area of the flame.

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Air density determination:

ρ𝑎𝑖𝑟 = 𝑃𝑎𝑖𝑟⋅

𝑊𝑎𝑖𝑟

𝑅𝑐⋅ 𝑇𝑎𝑖𝑟

(2.54)

Determination of combustion effective source diameter. The concept of effective source diameter is widely used in combustion modelling and represents the throat diameter of an imaginary nozzle releasing air at a mass flow rate 𝑚′

𝐷𝑠(𝑚) = √4

𝑚′

π ρ𝑎𝑖𝑟 𝑢𝑗

(2.55)

For the calculation of the length of the jet flame in still air, an auxiliary term 𝑌 is needed and it is calculated by: 𝑓(𝑌) = 𝐶𝑎⋅ 𝑌 5 3_{+ 𝐶}_𝑏_{⋅ 𝑌} 2 3_{− 𝐶}_𝑐 _{= 0} (2.56) in which: 𝐶𝑎= 0.024√𝑔 𝐷𝑠 𝑢_𝑗2 3 (2.57) 𝐶𝑏= 0.2 (2.58) 𝐶𝑐= 0.024√𝑔 𝐷𝑠 𝑢_𝑗2 3 (2.59)

In the tool developed, the auxiliary term is calculated by performing five steps of Newton’s

tangents method in the same spreadsheet

𝑌𝑛+1= 𝑌𝑛−

𝑓(𝑌𝑛)

𝑓′_(𝑌 𝑛)

(2.60) where 𝑓′_{is the derivative function of the polynomial 𝑓}

𝑓′(𝑌𝑛) = 5 3𝐶𝑎⋅ 𝑌𝑛 2 3₊2 3𝐶𝑏⋅ 𝑌𝑛 −1₃ (2.61) The auxiliary parameter is then used to evaluate the jet flame length in still air 𝐿𝑏0

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This value is used to determine the length of the jet flame measured from the flame tip to the centre of the exit plane

𝐿𝑏 = 𝐿𝑏0(0.51𝑒

−0.4𝑢_𝑤_{+ 0.49)[1.0 − 6.07 × 10}−3_(θ

𝑗𝑣− 90°)] (2.63)

in which θ𝑗𝑣 is the angle between hole axis and the horizontal in the direction of the wind.

For the calculations of the tilt angle α′ between the hole axis and the frustum axis, the Richardson’s number as a function of 𝐿𝑏₀ is needed

𝑅𝑖(𝐿𝑏₀) = ( 𝑔 𝐷𝑠2𝑢𝑗2 ) 1 2 𝐿𝑏₀ (2.64)

The next steps involve the distinction between two cases, determined by the value of 𝑅𝑤.

The two cases are:

1. Jet dominated flame 2. Wind dominated flame

If 𝑅𝑤 ≤ 0.05 then the flame is jet dominated and the tilt angle is given by:

α′[°]_{= (θ}

𝑗𝑣− 90°) ⋅ (1 − 𝑒−25.6⋅𝑅𝑤) +

8000𝑅𝑤

𝑅𝑖(𝐿𝑏0)

(2.65) If 𝑅𝑤 > 0.05 then the flame tilt becomes increasingly dominated by wind forces:

α′[°] _{= (θ} 𝑗𝑣 − 90°) ⋅ (1 − 𝑒−25.6⋅𝑅𝑤) + 134 + 1726(𝑅𝑤− 0.026) 1 2 𝑅𝑖(𝐿𝑏0) (2.66)

The following equation gives the value of the lift-off of the flame

𝑏 = 𝐿𝑏

𝑠𝑖𝑛 𝐾𝛼′

sin 𝛼′ (2.67)

in which:

K = 0.185e−20Rw_{+ 0.015} _(2.68)

Furthermore, 𝑏 = 0.2 ⋅ 𝐿𝑏 in still air (α′ = 0°) while for the ‘lazy’ flames pointing directly into

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𝑅𝑖 = [𝐿𝑏2− 𝑏2⋅ 𝑠𝑖𝑛2(𝛼′)] 1

2_{− 𝑏 ⋅ 𝑐𝑜𝑠(𝛼}′₎ (2.69)

To evaluate the frustum width both of the base and the tip, the ratio between the air and the jet density, the Richardson’s number as a function of the effective source diameter and the factor 𝐶′_,

must be determined: 𝜌𝑎𝑖𝑟 𝜌𝑗 = 𝑇𝑗𝑊𝑎𝑖𝑟 𝑇𝑎𝑖𝑟𝑊𝑔 (2.70) 𝑅𝑖(𝐷𝑠) = ( 𝑔 𝐷𝑠2𝑢𝑗2 ) 1 2 𝐷𝑠 (2.71) 𝐶′ = 1000𝑒−100𝑅𝑤_{+ 0.8} _(2.72)

The frustum base width is, therefore, given by:

𝑊1= 𝐷𝑠 (13.5𝑒−6𝑅𝑤+ 1.5) ∙ [1 − (1 − 1 15√ 𝜌𝑎𝑖𝑟 𝜌𝑗 ) 𝑒−70(𝑅𝑖(𝐷𝑠))𝐶′𝑅𝑤_] _(2.73)

while the frustum tip width can be calculated by:

𝑊2= 𝐿𝑏 (0.18𝑒−1.5𝑅𝑤+ 0.31) ∙ (1 − 0.47𝑒−70𝑅𝑤) (2.74)

The surface area of frustum, including end discs is determined with:

𝐴 =π 4(𝑊1 2_{+ 𝑊} 22) + π 2(𝑊1 2_{+ 𝑊} 22) × √𝑅𝑙2+ ( 𝑊2− 𝑊1 2 ) 2 (2.75)

or, as an alternative considering a cylinder with an average width, the surface area can be calculated as follows: 𝐴 =π 2( 𝑊1+ 𝑊2 2 ) 2 + π𝑅1 𝑊1+ 𝑊2 2 (2.76)

The following equations are used to evaluate the surface emissive power of the jet flame considering the net heat of combustion of the flammable gas, the fraction of that part of the heat radiated and the surface area of the frustum.

The net heat per unit time released is given by: 𝑄′ _{= 𝑚̇ ⋅ Δ𝐻}

𝑐 (2.77)

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𝐹𝑠= 0.21𝑒−0.00323⋅𝑢𝑗+ 0.11 (2.78)

Considering the surface area obtained with eq. (2.75), the Surface emissive power can be evaluated: 𝑆𝐸𝑃𝑚𝑎𝑥[ 𝐽 𝑚2_𝑠] = 𝐹𝑠 𝑄′ 𝐴 (2.79)

In this case, as well as for the pool fire, the SEP value must be actualized to take into account the presence of soot

𝑆𝐸𝑃𝑎𝑐𝑡[

𝑘𝑊

𝑚2] = 𝑆𝐸𝑃𝑚𝑎𝑥⋅ (1 − ζ) + 𝑆𝐸𝑃𝑠𝑜𝑜𝑡⋅ ζ (2.80)

where 𝑆𝐸𝑃𝑠𝑜𝑜𝑡 = 20 kW/m2 and ζ depending on the case.

So, to calculate damage distances the following heat flux equation has been considered in the tool developed.

𝑞 = 𝑆𝐸𝑃𝑎𝑐𝑡⋅ 𝐹𝑣𝑖𝑒𝑤⋅ τ𝑎 (2.81)

The details about the evaluation of the distance at which threshold values for heat fluxes are obtained are reported in section Description of the “UniSim® Design - Consequence Assessment

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2.2.4 Vulnerability models

The output of consequence evaluation models can be used to calculate vulnerability. The

vulnerability in QRA is defined as the probability of death, in the case of damage to persons, or

equipment damage probability in the case of equipment items.

Threshold models

The threshold models assume that above a selected threshold, a prefixed consequence is assumed to occur. On the contrary below the selected threshold the consequence is assumed to not occur. This kind of approach may be qualitative but defining, for each category of effects, a reference vulnerability it can be considered as a quantitative approach.

The threshold values are quoted in a number of codes and standards and in numerous papers. Many limits are given for the purposes of plant design and layout. Generally, such sets of limits include both limits related to damage and others related to injury.

The heat flux threshold values that are commonly used in Quantitative Risk Assessment, and that are, therefore used in this work are summarized in Table 2.2.

Table 2.2 Common heat flux threshold values

Threshold value Lethality grade Damage grade

12.5 kW/m2 _{High lethality level} _{Highly severe damage to structures} 7 kW/m2 _{First lethality level} _{Severe damage to structures} 5 kW/m2 _{Pain to unsheltered people} Minor damages to unprotected

structures

3 kW/m2 _{Reversible/nonsevere effects} _{No significant damage to structures}

Probit model

In this work, however, the threshold values are used only to assess the damage on equipment and building, since the probit model was adopted to evaluate the probability of death.

The estimation of the injury or damage caused by a physical effect such as heat radiation intensity, overpressure, or toxic concentration requires the use of injury or damage relations. The method to formulate can be divided in three stages:

• The determination of the causative factor which best correlates the data. It consists basically in the individuation of the physical effect that cause a specified degree of injury on people. The correlation between the physical effect and the probability of injury may

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or may not be direct: i.e. considering the eardrum rupture probability it is directly correlated with explosion overpressure, but probability of burn death correlates whit the radiation intensity time.

• The second stage is the determination of the probability distribution of the injury factor. The distribution usually considered first is the log-normal distribution since that this distribution fits the case where the population contains a proportion of individuals who are unusually resistant.

• The last stage is the transformation of the injury distribution in a more convenient and useable form, i.e. a probit equation.

The probit 𝑌 is an alternative way of expressing the probability 𝑃 of injury. It is defined with the following cumulative distribution function:

𝑃 = 1 √2𝜋∫ 𝑒 −𝑡2/2 𝑌−5 −∞ 𝑑𝑡 (2.82)

The probit is a random variable with a mean 5 and variance 1. The probability range (0-1) is generally replaced in probit work by a percentage range (0-100). The percentage values as a function of probit are reported in Table 2.3 with a graphical representation in Figure 2.6Figure 2.1.

Table 2.3 Transformation of percentages to probit

% 0 1 2 3 4 5 6 7 8 9 0 - 2.67 2.95 3.12 3.25 3.36 3.45 3.52 3.59 3.66 10 3.72 3.77 3.82 3.87 3.92 3.96 4.01 4.05 4.08 4.12 20 4.16 4.19 4.23 4.26 4.29 4.33 4.36 4.39 4.42 4.45 30 4.48 4.50 4.53 4.56 4.59 4.61 4.64 4.67 4.69 4.72 40 4.75 4.77 4.80 4.82 4.85 4.87 4.90 4.92 4.95 4.97 50 5.00 5.03 5.05 5.08 5.10 5.13 5.15 5.18 5.20 5.23 60 5.25 5.28 5.31 5.33 5.36 5.39 5.41 5.44 5.47 5.50 70 5.52 5.55 5.58 5.61 5.64 5.67 5.71 5.74 5.77 5.81 80 5.84 5.88 5.92 5.95 5.99 6.04 6.08 6.13 6.18 6.23 90 6.28 6.34 6.41 6.48 6.55 6.64 6.75 6.88 7.05 7.33 - 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 99 7.33 7.37 7.41 7.46 7.51 7.58 7.6 7.75 7.88 8.09

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Figure 2.6 Relationship between probit and percentage (adapted from )

For an injury factor 𝑥 which fits the log-normal distribution the probit equation has the form.

𝑌 = 𝑘1+ 𝑘2𝑙𝑛 𝑥 (2.83)

Since this work is focused on the consequence assessment of fire events, the injury factor considered for the vulnerability evaluation is the thermal dose defined as the product of the thermal radiation intensity and time. The level of thermal radiation for a particular effect, is often correlated in terms of the thermal dose. The empirical correlation for the injury factor which best fits the data is:

𝑡𝐼𝑛 = constant (2.84)

where 𝐼 is the intensity of thermal radiation expressed in 𝑊/𝑚2, 𝑡 is the time of exposure in seconds and 𝑛 is an index.

Eq, (2.84) has been given by Eisenberg et al. for the correlation of data on burn fatalities with a value of the index 𝑛 = 4/3 = 1.33. For non-fatal burn injuries these authors use the slightly different exponent n = 1.15, It has been proposed by Hymes that the data for fatal and non-fatal injury are adequately correlated using a value of 𝑛 = 1.33 for both.

So, from now on, the thermal load L instead of thermal dose 𝐷 = 𝑡𝐼 is used in the evaluation of

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𝐿 = 𝑡𝐼1.33 (2.85)

Since the practice of use an intensity expressed in 𝑊/𝑚2_{gives rise to thermal loads which are}

large numbers, it is convenient to define also an alternative thermal load 𝐿′, defined as:

𝐿′₌𝑡𝐼 1.33

104 (2.86)

The probit value is therefore evaluated using the following equation:

𝑌 = −14.9 + 2.56 ln(𝑡𝐼1.33_{× 10}−4₎ _(2.87)

Since eq.(2.87) is based on burn injuries to people going about their normal affairs, it applies to persons who are clothed.

2.3 Conventional approaches for consequence assessment

The more diffused software packages applied in QRA studies are, among others:

• CAMEO Aloha, freeware software developed by American Enviromental Protection

Agency;

• EFFECTS, developed by TNO; • PHAST™_{developed by DNV GL’s.}

DNV GL PHAST™ is one of the commonly adopted software for Quantitative Risk Assessment and it is the one adopted in this thesis work to compare the results obtained with the tool developed. It is an industry hazard analysis software tool and it is used to analyze situations which present hazards to life, property and the environment and to quantify their severity.

It is used to estimate, understand and visualize the effects from loss of containment scenarios in several types of chemical industry. Its applications range from plant layout to pollution control as well as emergency plan development. In addition, it is widely accepted by governments and regulatory authorities to verify law compliance of chemical facilities.

In PHAST™ are implemented the models presented in the previous sections (3) for the selected fire scenarios (i.e. Pool Fire and Jet Fire models) as well as:

• Other flammable models, that is Fireball and Flash Fire giving related radiations effects; • Discharge and dispersion models, including DNV GL’s proprietary Unified Dispersion

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• Explosion Models to calculate overpressure and impulse effects. Available models include Baker Strehlow, TNO Multi-Energy and TNT explosion models;

• Toxic hazards, including indoor toxic dose calculations.

The results from the analysis can be displayed in tabular & graphical form, so the extent of the impact can be seen, and the effect of the release on the population and environment assessed; also technical reports are automatically generated for each simulation case.

2.3.1 Limitations of conventional approaches

The consequences evaluated using the models proposed in literature or commercial software, are the result of many conservative estimations. These estimations are necessary to treat the uncertainties that arise during a consequence assessment procedure: to name a few, the uncertainties can derive from an incomplete understanding of the geometry of the release, unknown or poorly characterized physical properties, a poor understanding of the chemical or release process, and unknown or poorly understood mixture behavior.

To illustrate conservative modeling, consider a problem requiring an estimate of the gas discharge rate from a hole in a storage tank. This discharge rate will be used to estimate the downwind concentrations of the gas, with the intent on estimating the toxicological impact. The discharge rate is dependent on several parameters, including the hole area the pressure within and outside the tank the physical properties of the gas, and the temperature of the gas. A conservative approach consists in assuming steady state conditions for all the unknowns mentioned above: for example, it is usual to calculate the mass discharge rate at the instant the leak occurs, assuming a fixed temperature and pressure within the tank equal to the initial temperature and pressure. The actual discharge rate at later times will always be less and so the downwind concentration. In summary, the calculations are made without taking into account the dynamic behavior of the accident itself, ignoring how the conditions differ from their initial value. The conditions may vary because of:

• the already mentioned intrinsic phenomenology of the release;

• the material, momentum and energy balances across the process units; • the intervention of either the control system or the operators

• the feedbacks from the accident

The existing tools can account for a release variability that can be modeled a priori from the initial condition of the equipment according to a given law, but the intervention of the control system and the presence of some additional inlet/outlet streams to/from the damaged process unit are not supported by those programs. Moreover, they cannot account for any interactions between the process dynamics and the accident event.

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Combining dynamic simulators with dynamic accident simulator allows the simultaneous evaluation of the dynamics of the process and the accident, as well as their mutual feedbacks.

Dynamic process simulation of accident scenarios: the role of safety barriers

Tesi di Laurea magistrale