Fragility Assessment Methodology of Storage Tanks in

Fragility Assessment Methodology of

Storage Tanks in NaTech Events

Oscar Javier Ramirez Olivar

Universidad de los Andes Faculty of Engineering, Department of Chemical Engineering

Bogotá, Colombia 2018


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Fragility Assessment Methodology of Storage Tanks in NaTech Events


Thesis or research work presented as a requirement to apply for the title of: Master in Chemical Engineering

Director: Professor Felipe Muñoz Giraldo

Investigation Topic: Process Safety

Investigation Group: Design of Products and Processes

Universidad de los Andes Faculty of Engineering, Department of Chemical Engineering

Bogotá, Colombia 2017

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Abstract During the last decades, there has been a growing concern in the chemical and petrochemical industry regarding losses of containment of storage materials caused by different extreme natural phenomena. These events have the potential to cause significant damage, especially in areas where large quantities of hazardous substances are stored. The threat grows because the increase on extreme events of natural origin by 200% in the last 4 decades, reaching almost 350 billion dollars (US) lost only in 2017 worldwide. The release of these substances may lead to fires, explosions, or the emission of toxic clouds into the atmosphere; such releases might have a significant impact on the population located in neighbor urban areas and on the environment. When industrial accidents are triggered by natural events such as earthquakes, floods and storms, or any other extreme natural event, these chemical accidents are known as NaTech events (Natural Hazard Triggering Technological Accidents). The present study will focus on the assessment of fragility and vulnerability associated to extreme wind events, floods and earthquakes in industrial storage areas. A methodology is proposed for the quantification of fragility associated with extreme winds, floods and earthquakes in parameterized vertical storage tanks according to API-650/620. This methodology integrates mathematical models, which allows to estimate the 5 types of damage probability of an API-650 tank due to the impact of floods, extreme winds and earthquakes. The damage by the impact of an extreme natural event can cause are shell buckling, floatation, rigid sliding and tank overturning. The proposed methodology is used in a computational tool developed in conjunction with the department of civil and environmental engineering of Universidad de los Andes and allows the user to perform a fragility assessment on a storage tank. The tool exposes a storage tank to the impact of a natural hazard, in which the resistance of the equipment is calculated from physical and mechanical properties of the tank and then related to the solicitation or intensity of the natural hazard. Furthermore, the fragility assessment, as a function of damage probability, takes into account the uncertainty of the involved variables, given its natural behavior. The reduction in variables uncertainty is necessary for probability calculation considering that this is an input parameter in a classical operational risk analysis. Finally, the methodology ends with the calculation of the loss of containment of hazardous material once the storage tank has failed. The proposed methodology calculates the probability of damage, estimates the probability of failure and estimate the volume of loss of containment as a consequence of natural hazard, such as floods, extreme winds and earthquakes, taking into account the design parameters of storage tanks under API-650 and API-620 standard. Key Words: Fragility, vulnerability, risk, probability, damage, failure, storage tank, NaTech.

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Content

Abstract .............................................................................................................................. 5

1. Introduction ................................................................................................................ 13

2. History of NaTech Events ......................................................................................... 15

3. Methodology for fragility and vulnerability assessment of storage tanks

associated with NaTech events generated by different natural phenomena. ........... 20

3.1. Natural Hazards ........................................................................................................................ 21

3.2. Vertical Storage Tank Characterization .................................................................................. 23

3.2.1. Storage Tank Shell ............................................................................................................. 24

3.2.2. Storage Tank Roof .............................................................................................................. 25

3.2.3. Storage Tank Base ............................................................................................................. 26

3.3. Definition of Possible Accidental Scenarios .......................................................................... 26

3.4. Structural and Natural Hazard Analysis. ................................................................................ 29

3.4.1. Storage Tank Damage by Floods ........................................................................................ 29

3.4.2. Storage Tank Damage by Extreme Winds .......................................................................... 34

3.4.3. Storage Tank Damage by Earthquakes .............................................................................. 41

3.4.4. Definition of Limit State Equations (LSE)............................................................................. 44

3.5. Storage Tanks Fragility Analysis in NaTech Events. ............................................................. 45

3.5.1. Fragility Curves ................................................................................................................... 45

4. Case Study ................................................................................................................. 53 4.1. Storage Tank TK-201 Characterization ................................................................................... 54

4.2. Wind Hazard Characterization................................................................................................. 56

4.3. TK-201 Fragility Curves ........................................................................................................... 57

Conclusions ..................................................................................................................... 62

References ....................................................................................................................... 64

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Objectives General Objective Evaluate the fragility of industrial storage equipment that may be subject to NaTech events caused by natural hazards. Specific Objectives

Propose a methodology for fragility assessment of industrial storage equipment impacted by a natural hazard.

Develop a computational tool to perform a basic fragility assessment on industrial storage equipment affected by extreme natural events.

Identify an applied method for the treatment of uncertainty in the calculation of the damage probability in storage equipment in NaTech events.

Implement the computational tool on a case study representing a real system.

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Figures: Figure 1. Natural disasters in Europe between 1975 and 2008 [10]. ................................................................ 15

Figure 2. Distribution of the NaTech accident events identified in the analysis of the available chemical

accident databases: (a) flood events (272 records, 1960-2007), (b) seismic events (78 records, 1930-

2007) [9]. ...................................................................................................................................................................... 16

Figure 3. a) Industrial Equipment mainly involved in accidents triggered by flood events. b) Industrial

Equipment mainly involved in accidents triggered by seismic events) [9]. ........................................................ 16

Figure 4. Substances commonly involved in NaTech accidents [9]. ................................................................. 17

Figure 5. Storage tanks impacted by different natural hazards. a) Flood. b) Wind load. c) Lightning d)

Earthquake [6]. ........................................................................................................................................................... 17

Figure 6. Factors that aggravate or mitigate risk in a NaTech event. ............................................................... 18

Figure 7. State of the art for the a priori analysis of NaTech events [19]–[27]. ............................................... 19

Figure 8. Methodology for fragility and vulnerability assessment of the storage tanks associated with

NaTech events generated by different natural hazards. ...................................................................................... 20

Figure 9. Relevant natural loss events worldwide (1980-2017) [28]. ................................................................ 21

Figure 10. Overall and insured losses worldwide in US$ (1980-2017) [28]. .................................................... 22

Figure 11. Configuration of a storage tank based on API-620/650 standards. ................................................ 24

Figure 12. Basic configuration of a storage tank. a) open-top tank, b) Cone-roof tank, c) Dome-roof tank.

....................................................................................................................................................................................... 25

Figure 13. Types of floating roof in a storage tank: a) External floating roof, b) Internal floating roof. ........ 26

Figure 14. Tank anchor detail. ................................................................................................................................. 26

Figure 15. Structure of the event tree [42]. ............................................................................................................ 27

Figure 16. Event tree for the sequence of events due to the impact of a natural events on vertical storage

tanks. ............................................................................................................................................................................ 28

Figure 17. Event tree to identify the events sequence of a storage tank impacted by a wind load

depending on the wind speed. ................................................................................................................................. 28

Figure 18. Damage due to natural danger. ........................................................................................................... 29

Figure 19. Types of damage to a storage tank impacted by a flood [6]. ........................................................... 29

Figure 20. Schematic of the load-resistance forces considered for shell buckling. ........................................ 30

Figure 21. Schematic of the load-resistance forces considered for tank floatation. ....................................... 31

Figure 22. Schematic of the load-resistance forces considered for rigid sliding. ............................................ 32

Figure 23. Schematic of the load-resistance forces considered for rigid sliding. ............................................ 33

Figure 24. Types of damage to a storage tank exposed to high wind speeds. ............................................... 34

Figure 25. Schematic of the load-resistance forces considered for shell buckling produce by wind. .......... 35

Figure 26. External wind pressure coefficients along the circumference of cylinders. ................................... 36

Figure 27. a) Wind pressure distribution around shell circumference, b) equivalent axisymmetric pressure

distribution around shell circumference [49]. ......................................................................................................... 36

Figure 28. Wind pressure distribution around shell circumference at different velocities. ............................. 37

Figure 29. Schematic of load-resistance forces considered the overturning by a wind load. ....................... 38

Figure 30. Schematic of the load-resistance forces considered for impact of debris drag by the wind. ...... 39

Figure 31. Impact of a projectile (fragment) on a target (a plate) [54]. .............................................................. 41

Figure 32. Types of damage to a storage tank exposed to an earthquake. ..................................................... 42

Figure 33. Schematic of the load-resistance forces considered for shell buckling produce by an

earthquake. ................................................................................................................................................................. 42

Figure 34. Schematic of the load-resistance forces considered for tank overturning produce by an

earthquake. ................................................................................................................................................................. 43

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Figure 35. Representation of a fragility function with a lognormal cumulative distribution [61]. ................... 45

Figure 36. Methodology to calculate the damage probability of a storage tank integrating the uncertainty

within a purely probabilistic framework. .................................................................................................................. 46

Figure 37. Algorithm to calculate the probability of buckling damage in a tank impacted by a flood. .......... 48

Figure 38. The probability cumulative function and the corresponding Probit function Y vs hazard

intensity 𝐿𝑛(𝑉𝑖). .......................................................................................................................................................... 50

Figure 39. Location of the storage tank under study, Caribbean coast. ........................................................... 53

Figure 40. NaTanks first tab: Sizing of a storage tank based on API-650. ...................................................... 54

Figure 41. Heights and thicknesses for each course of the storage tank TK-201. ......................................... 55

Figure 42. Geometry of tank shell TK-201. ........................................................................................................... 55

Figure 43. NaTanks second tab: flood characterization based on the speed and height of the wave......... 56

Figure 44. NaTanks third tab: fragility curves for NaTech Events. .................................................................... 58

Figure 45. Probability of damage due to buckling of the TK-201 (O=0%) impacted by a wind load

represented by a Probit function. ............................................................................................................................. 60

Figure 46. Probability of damage due to debris impact of an empty TK-201 represented by a Probit

function. ....................................................................................................................................................................... 60

Figure 47. Flow of spilled gasoline due to TK-201 failure caused by flood. ..................................................... 60

Figure 48. Volume of spilled material vs. release time due to TK-201 failure caused by flood. ................... 60

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Tables: Table 1. Natural Hazard Classification Based on Intensity or Impact vector [6], [36], [37]. ........................... 23

Table 2. Types of damage produced by different natural events. ...................................................................... 29

Table 3. Fourier coefficients proposed by different authors. ............................................................................... 35

Table 4. Equivalent axisymmetric pressure at different wind velocities. ........................................................... 37

Table 5. Threshold values for damage for Johnson's damage number 𝐽′ [51]. ................................................ 39

Table 6. Constant values for fragment penetration reported in Lee’s textbook [52]. ...................................... 40

Table 7. Minimum plate thickness for different diameters [38]. .......................................................................... 41

Table 8. Stability criteria for the overturning of a storage tank [39]. .................................................................. 43

Table 9. Limit state Equation for different types of damage. ............................................................................... 44

Table 10. Parameters with random behavior for each natural event. ................................................................ 47

Table 11. Failure probabilities for different types of failure on storage tanks. .................................................. 49

Table 12. Storage tank configuration (TK-201) according to API-650............................................................... 53

Table 13. Fragility curves for tank damage due to different natural hazards. .................................................. 59

Table 14. Accidental scenario establish with event tree. ..................................................................................... 61

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List of Symbols and Abbreviations: Latin letters: 𝑎: Constants which depend on the target material

𝑎𝑖: Fourier coefficients

𝑎𝑡: Unitary dichotomous variable to represent the anchoring state 𝐴: Orifice area

𝐴𝑏𝑜𝑙𝑡: Anchor bolt area

𝐴𝑝: Debris area

𝐴𝑡: Surface area of the tank

𝛬𝑡: Anchoring force 𝑏: Constants which depend on the target material

𝐶𝐴: Corrosion allowance

𝐶𝐵: Blockage coefficient

𝐶𝑑: Drag coefficient for wind 𝐶𝐷: Depth coefficient

𝐶𝑂: Orientation coefficient

𝐶𝑜: Release coefficient 𝐶𝑝: Pressure coefficient

𝐷: Nominal tank diameter 𝑑𝑝: Debris diameter

𝐸: Elasticity module

𝐸𝑐: Kinetic energy

𝜀𝑢: Ultimate strain of the tank

𝐹𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦: Buoyancy force

𝐹𝑑𝑟𝑎𝑔: Drag force

𝐹𝑔𝑟𝑎𝑣𝑖𝑡𝑦: Gravity force

𝐹𝑖: Impact force

𝐹𝑓𝑐𝑟: Critical floating force

𝐹𝑠𝑐𝑟: Critical sliding force

𝐹𝑓𝑙: Floatation force

𝐹𝑟: Resistance force 𝐹𝑠𝑙𝑑: Sliding force

𝑓: Natural hazard frequency

𝑓𝑎𝑠: Frequency of final accidental scenario 𝑓𝑢: Ultimate strength of the Tank

𝑓𝑦: Bolts minimum yield strength

𝑔: Gravity 𝐺: Design specific gravity of the liquid to be stored

𝐺𝑠: Gust factor

ℎ1: Height of the bottom shell course

ℎ𝐿0: Orifice height

ℎ𝑝: Penetration depth

ɦ: Maximum design liquid level

𝐻: Tank height 𝐼: Importance factor

𝐽: Johnson’s number

𝐽′: Modified Johnson’s number 𝐾𝑑: Wind directionality factor

𝑘𝐿: Constant for large fragment

𝑘𝑆: Constant for small fragment

𝑘𝑤: Wind direction factor 𝐾𝑧: Velocity pressure exposure coefficient

𝐾𝑧𝑡: Topographic factor

𝑘1 𝑎𝑛𝑑 𝑘2: Probit constants

𝑘𝑑: Hydrodynamic coefficient of water 𝑀: Debris mass

𝑛: Parameter to minimize critical pressure

𝑁: Number of iterations 𝑝: Wind load or wind pressure

�̂�: Probit percentage

𝑃𝑐𝑟: Critical pressure

𝑝𝑑: Damage probability 𝑝𝑓: Failure probability

𝑃𝑓: Pressure generated by the stored fluid

𝑃𝑟: Tank resistance pressure

𝑃𝑤: External load applied by flood

𝑃𝑤𝑑 : Maximum dynamic pressure generated by a flood 𝑃𝑤𝑠: Maximum static pressure generated by a flood

𝑄𝑚: Release flow of stored material

𝑞𝑒𝑞: Wind equivalent axisymmetric pressure

𝑞𝑧: Velocity pressure

𝑟: Nominal tank radius 𝑟𝑝: Debris radius

𝑟𝑟: Roof radius 𝑅𝑒: Reynolds number

𝑆: Flood wave height

𝑆𝑑: Allowable stress for tile design condition 𝑇: Release time

𝑇𝑒: Total time of release

𝑡: Course shell thickness

𝑡𝑖: Impact time 𝑡𝑟𝑐: Cone roof thickness

𝑡𝑟𝑑: Dome roof thickness

𝑈: Debris velocity 𝑈0: Impact velocity

𝑉: Wind or flood speed

𝑉𝑖: Natural hazard intensity 𝑉𝐿: Volume of material released

𝑣𝑝: Debris velocity for wind

𝑊𝑙𝑖𝑞𝑢𝑖𝑑 : Stored liquid weight

𝑊𝑡𝑎𝑛𝑘: Tank Weight 𝑌: Probit points Greek letters

𝛼: Impact angle 𝜌𝑓: Stored fluid density

𝜌𝑝: Debris density

𝜌𝑤: Water density

𝜌𝑊: Wind density 𝜎𝐷: Dynamic yield stress of the Tank

Ф: Tank filling level

𝜃: Longitude measured from windward

𝜏: Parameter for load combinations 𝜈: Poisson's coefficient

𝜇𝑠: Coefficient of soil-tank friction

𝜇𝑊: Wind viscosity

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Abbreviation Hazmat: Hazardous materials NaTech: Natural Hazard Triggering Technological Accidents LOC: Loss of containment JRC: Join Research Center ARIA: Analyze, Recherche et Information sur les Accidents FACTS: Failure and Accidents Technical Information System MHIDAS: Major Hazard Incident Data Service MARS: Major Accident Reporting System ICHEME: Institution of Chemical Engineers

NRC: National response center API: American petroleum institute CE: Critical event or initiation event SCE: secondary critical events FE: final events or major events ASCE: American Society of Civil Engineers LSE: Limit state Equation NTA: NaTech Tank Analyzer SGC: Servicio Geológico Colombiano IDEAM: Instituto de Hidrología, Meteorología y Estudios Ambientales CCPS: Center for Chemical Process Safety

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1. Introduction Any chemical industry, petrochemical, textile, etc., is not exempt from a major accident due to the unwanted release of energy and hazardous materials. These accidents may be due to operational failures, such as the incident in a pesticide factory owned by the Union Caribe company in Bhopal-India, where maintenance errors and working procedures resulted in an undesired release of methyl-isocyanate which spread throughout the city causing serious health problems and even death to thousands of people, and therefore large economic losses to both the company and the nation [1]. On the other hand, accidents can be caused by external sources such as a natural event: floods, earthquakes or hurricanes. A good example is Hurricane Floyd, which affected the oil industry on the east coast of the United States and Canada, because the spillage of thousands of gallons of oil, gasoline and chemicals causing a great environmental impact and incalculable economic losses [2]. Natural hazards have the characteristic of covering very large areas, affecting entire cities in their path, constituted by coastal zones, a great variety of industries and areas of high urban density. All these are factors, together with climatic conditions and subsoil composition, can aggravate or mitigate the consequences of a natural hazard. This type of events that are of natural origin, occur from an abnormal variability in the climate of planet Earth. Relevant changes in the climatic conditions of the planet use to appear within large periods of time (millions of years), but in the last century they have been presented in relatively short time intervals (decades). This climatic variability can be evidenced in the increase of the atmospheric temperature, causing an increase in frequency and severity of the natural event, which brings consequences on the ecosystems of the planet [3], [4]. In recent years, the concern of the chemical and petrochemical industry has increased worldwide because of the great potential of an extreme natural event, such as flooding, earthquake, forest fire, storm, hurricane, landslides and cyclones, of damaging industrial installations and hazardous material (hazmat) storage areas. These kind of incidents cause the unplanned release of hazmat into the atmosphere, resulting in accidents with serious impacts on people’s health, property and the environment [5]. These types of accidents are known as NaTech events (technological accident triggered by a natural event) [6]. Different studies have found that the natural events that have been registered as the cause of most of the industrial accident are earthquakes and floods, followed by landslides, hurricanes and electric shocks, and finally droughts [2]. In addition, it has been found that hazardous material losses during NaTech events can be transformed into fires, explosions or dispersion of toxic substances. In recent decades, the occurrence of natural disasters has been increasing. In 2004, a study was conducted in which it was found that different natural phenomena have been increasing over time. This study was conducted throughout the United States between the years 1980 and 1989, which yielded the following results: 228 earthquakes, 26 hurricanes, 16 floods, 15 thunderstorms, 13 blizzards and 7 storms [7]. Additionally, 1022 flood events were presented worldwide in the decade of the 90s, while in the last decade, the occurrence of this type of natural events has increased by 74% [8]. An historical analysis conducted by Campedel showed that the industrial equipment’s most affected by natural hazards are storage tanks and pipelines. Additionally, the substances involved in most NaTech events are crude oil, diesel and gasoline; substances that, at the time of loss of containment (LOC), have the capacity to cause explosions, fires and toxic dispersions [9]. Therefore, considering the great threat presented by natural hazards on industrial facilities, especially in equipment that holds the capacity to house large quantities of hazmat such as storage tanks, this study proposes a methodology for the fragility and vulnerability assessment of NaTech events, due to the impact of earthquakes, floods and extreme winds on vertical storage tanks. The proposed methodology, in Section 3, presents a sequential procedure that integrates design information from the process equipment and the solicitation of the natural hazard. Considering that risk is the combination between hazard, vulnerability and exposure, it is necessary to classify the hazard in order to determine an initial risk criterion. In this study, the natural hazards are classified according to its impact vector, this classification is presented in section 3.1. Likewise, given the great variety of different types of storage tanks, in Section 3.2, a parameterization of the tanks from their components and mechanical properties is proposed. Through event trees, Section

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3.3., possible accidental scenarios are defined, determined by a literature review on industrial accidents triggered by natural hazards in the last 70 years. Subsequently, by means of damage models developed by different authors, in Section 3.4., the resistance forces of the tank and the solicitation forces of the natural hazard are estimated. Given the variability of some parameters of the used models due to their natural behavior, through a probabilistic approach represented by fragility curves, the uncertainty generated by this behavior is treated for each of the parameters. In Section 3.5., the probabilistic procedure used to estimate the probability of damage of a storage tank is presented, which integrates the uncertainty of the natural behavior of the parameters. Through the transformation of the fragility curves, Probit models are presented and proposed for the estimation of the damage probability from the intensity of the natural hazard and the geometrical characteristics of the tank. Finally, given the serious consequences that NaTech events can produce, the loss of containment calculation (LOC) of hazardous material is also estimated in Section 3.5., in order to establish guidelines for future emergency plans. Additionally, the methodology was incorporated into a computational tool presented in Section 4, which performs the fragility assessment on any structural configuration of a storage tank and 3 different natural hazards. The integration of each one of the presented steps: the parameterization of a tank, the hazard classification, the definition of the accidental scenario, the calculation of damage and failure probability integrating the uncertainty of the parameters used and the estimation of the LOC, allows to estimate the frequency of occurrence of a NaTech event with great precision, where the results represent a significantly approximation to reality. It is important to highlight that the proposed methodology can be used for both new and existing tanks, allowing the prediction of possible industrial accidents caused by natural hazards.

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2. Past NaTech Events Due to the increase in the occurrence of NaTech events in recent years, different authors have developed studies, analysis and management of risk associated with this type of events. For example, in 2008 the French Ministry of Sustainable Development carried out a study assessing the distribution of natural phenomena along the European continent and which in turn caused serious human, social and economic losses. The results of this study are presented in Figure 1, different types of natural phenomena affect in different proportions the countries of this continent [10].

Figure 1. Natural disasters in Europe between 1975 and 2008 [10].

Storms and floods are the natural phenomenon that most affects the majority of European countries (like Austria, Belgium, Denmark, France, Germany, Ireland, the Netherlands and England). The increase in these natural events is not only due to the type or amount of surface that each country has, but to other factors such as exposure to coastal zones, changes in climatic conditions, subsoil composition and urban density (especially near to industrial areas). All these factors may aggravate or mitigate in some way the consequences of the natural event. As a result of the large number and increase in time of natural events around the world, entities such as the JRC (Join Research Center) have begun studies to understand better the impact of natural hazards on chemical industries because of its potential to cause serious accidents [11]. As an example, the JRC developed a RAPID'N tool to map and analyze NaTech risks, which contributes to the identification of areas prone to NaTech events, to analyze and visualize their risks, and support the decision making of authorities before and after the event [12]. There are other sources from where information on NaTech events is collected; some of the main European databases are ARIA (Analyze, Recherche et Information sur les Accidents), FACTS (Failure and Accidents Technical Information System), MHIDAS (the Major Hazard Incident Data Service), MARS (Major Accident Reporting System) and ICHEME (Institution of Chemical

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Engineers). On the other hand, the most used database in the American continent is the NRC (National Response Center). In Figure 2, the distribution of the records identified among the aforementioned databases is presented [9].

Figure 2. Distribution of the NaTech accident events identified in the analysis of the available chemical accident databases: (a) flood events (272

records, 1960-2007), (b) seismic events (78 records, 1930-2007) [9].

From the historical analysis presented in Figure 2, the industrial equipment mainly involved in each type of accident were identified. In the case of floods it was found that the most susceptible equipment to be damaged by the impact of a wave front were the storage tanks (atmospheric and pressurized) and pipelines. Likewise, the same procedure was carried out for seismic events, taking the 78 records, in which it was again found that the most susceptible equipment to be damaged were the pipelines and storage tanks. Figure 3 shows the equipment affected by each of these natural events. Finally, the substances normally involved in NaTech accidents are oil, diesel and gasoline, as can be seen in Figure 4. These substances have the ability to cause explosions, fires or toxic dispersions.

Figure 3. a) Industrial Equipment mainly involved in accidents triggered by flood events. b) Industrial Equipment mainly involved in accidents

triggered by seismic events) [9].

For natural events that involve extreme winds, such as tornadoes, hurricanes and storms, many authors agree that the most affected units are storage tanks [13]. However, in order for these types of natural events to affect or damage a storage tank, the equipment must be empty or partially full (0% to 10% fill level) [14], [15]. Thus, the most relevant final consequence of the NaTech event will be the damage or loss of the process equipment and not the loss of containment of hazmats itself [16]. From Figure 4, the main substances that will be analyzed in the present work are liquid phase fuels, mainly crude oil and gasoline, however, the proposed methodology serves as a basis for the treatment of another type of hazardous substances.

ICHEME; 13; 5%

ALTRO; 6; 2%

ARIA; 72; 26%

FACTS; 14; 5%

NRC; 154; 57%

MHIDAS; 13; 5%

ICHEME; 11; 14%

ALTRO; 14; 18%

ARIA; 0; 0%

FACTS; 1; 1%

NRC; 44; 56%

MHIDAS; 9; 11%

Cylindrical Vessels

5%

Compressors and Pumps

4%

Pipelines17%

Storage Tanks74%

Cylindrical Vessels1%

Pipelines65%

Storage Tanks34%

a) b)

a) b)

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Figure 4. Substances commonly involved in NaTech accidents [9].

Figure 5 shows some of the most relevant NaTech events recently, Figure 5a correspond to a flood caused by Hurricane Katrina. Figure 5b shows the consequences by the impact of a wind load caused by Hurricane Katrina. Figure 5c present a fire caused by the impact of a lightning on a storage tank. And Figure 5d present severe damage in spherical storage tanks caused by Tohoku earthquake in 2011.

a)

b)

c)

d)

Figure 5. Storage tanks impacted by different natural hazards. a) Flood. b) Wind load. c) Lightning d) Earthquake [6].

162

11

8

5

5

5

3

3

1

0 50 100 150 200

Hydrocarbons

Fertilizar

Aromatics

Ammonia

Oxides

Cyanide

Acetylene

Explosives

Detergent

Number of events reported.

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The previous figures shows the serious human, environmental and infrastructure consequences of a NaTech event. Only one or two tanks are shown in each figure, but there is a possibility that a complete tank farm will be affected, aggravating the consequences and increasing the probability of a domino effect. Therefore the importance to understand the risk associated to major industrial accident for this type of events. According to the United Nations Office for Disaster Risk Reduction (UNISDR) [17], the risk of suffering a catastrophic loss varies significantly depending on 3 main factors, a hazardous object or event, vulnerability and exposure, as shown in Figure 6.

Figure 6. Factors that aggravate or mitigate risk in a NaTech event.

The hazard is commonly associated with a process or phenomenon that can cause fatal consequences including human death, and socioeconomic or environmental losses. As mentioned by Burton I. Et Al [18], a natural hazard has an element of human and structural participation. A physical event is an event with no affectation either to people or the infrastructure, therefore it is known as natural phenomena but not as a natural hazard. Natural phenomena that occur in large populated or industrial areas are hazardous events, capable of causing a great number of fatalities or incalculable damages to the property, and thus resulting in a natural disaster. Therefore, for process safety, in areas where there is no presence of people or industrial facilities, the natural phenomena do not constitute hazards and consequently will not cause a disaster. This type of events of natural origin do not only have the ability to destroy any structure in its path, but they are also characterized by covering large areas affecting multiple targets at the same time. Vulnerability is associated with physical, socioeconomic or environmental factors that increase the susceptibility of people or facilities to the consequences of hazards. From the NaTech event, the loss of containment of dangerous material will be the determining factor to estimate the consequences of the event. Finally, the exposure measures the number of people or assets located in the area of affectation, for our particular case, the storage tanks. Taking into account the great threat presented by natural events on industrial facilities, different authors have developed knowledge for the analysis and management of the risks associated with NaTech events. The study of NaTech events and their risks can be done through two approaches. The a posteriori analysis, which consists of identifying information that allows to characterize the event from the analysis of historical data or reports of past events. On the other hand, an a priori analysis consists of identify possible accidental scenarios and analyze the risks they present [19]. Based on the above, a bibliographic review of different works developed around the risk analysis of NaTech events was carried out. Figure 9 presents a timeline with models developed for the estimation of damage of a storage tank by different natural hazards (left side) and the methodologies for risk estimation associated with NaTech events (right side). The methodologies presented use damage models for risk assessment.

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Figure 7. State of the art for the a priori analysis of NaTech events [19]–[27].

Based on the damage models presented in Figure 7, and complementing the information with models of international standards, the fragility and vulnerability assessment for a vertical storage tank will be carried out. The tanks work at atmospheric conditions and are designed to store liquids. Next section will present the proposed methodology to perform a fragility and vulnerability assessment of a storage tank.

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3. Methodology for fragility and vulnerability assessment of storage tanks associated with NaTech events generated by different natural phenomena.

Figure 8 presents the proposed methodology for the assessment of fragility and vulnerability in storage tanks associated with technological accidents caused by a natural hazard. The methodology uses both qualitative and quantitative information about the tank and natural hazard.

Figure 8. Methodology for fragility and vulnerability assessment of the storage tanks associated with NaTech events generated by different

natural hazards.

Each of the steps presented in Figure 8, are composed of procedures, models and tools, which in conjunction with information that must be fed, establishing the necessary elements to develop each of the stages that make up the proposed methodology. All together allows to perform the fragility and vulnerability assessment:

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Natural hazard.

Storage tank

Possible accidental scenarios.

Tank structural resistance (resistance pressure, resistance force).

Hazard intensity (solicitation).

Damage and failure probability.

LOC.

3.1. Natural Hazards There are various potentially hazardous natural phenomena. The geophysical events, such as earthquake, tsunamis and volcanic activity. Meteorological events such as tropical cyclone, extratropical storms, convective storm and hurricanes. Hydrological events such as floods and mass movements. Climatological events such as extreme temperature, drought and forest fires. One of the major concerns of the industry sector worldwide is the increase in the frequency of high intensity natural events. As can be seen in Figure 9 [28], the natural phenomena that most frequently affect the planet are those of hydrological and meteorological origin. From this, the natural hazards considered for the study of NaTech events in storage tanks are floods in the case of hydrological events, hurricanes in meteorological events and earthquakes in geophysical events.

Figure 9. Relevant natural loss events worldwide (1980-2017) [28].

In addition, the increase in frequency of natural events, the economic losses associated with the damage caused by the phenomenon also increase. Not only because the world suffers more natural hazards, but because their intensity also increases over time, having the ability to affect structures with greater resistance. Figure 10 [28], shows an estimate of total annual economic losses worldwide due to the effect of all natural hazards as a whole. The estimated value of the economic losses takes into account the costs associated with damages and reparation of private and public property (including industrial sector), assistance and reparation to victims, emergency response, remediation to the environment, among other costs. The costs annually are significantly high, so it is necessary to analyze the vulnerability and risk in NaTech events since the damage in industrial facilities can aggravate the consequences in surroundings.

22

Figure 10. Overall and insured losses worldwide in US$ (1980-2017) [28].

The starting point of the proposed methodology is to define the natural hazard (step 1, Figure 8) that will affect our assets at risk, once defined, it is important to identify the reference conditions of the hazard. Each natural hazard is characterized according to its frequency and severity. Antononi et al. [26], presents an

expression to calculate the frequency of a natural hazard in terms of the return period 𝑡𝑟, which measures in years the likelihood of occurrence of a natural event of a certain intensity. The frequency 𝑓 (1/𝑦𝑒𝑎𝑟) of a natural hazard can be estimated as follows:

𝑓 =1

𝑡𝑟 (1)

The values for the return period are usually reported in the literature, however, the reported values are defined for specific regions or areas of the world by different government agencies. For instance, the responsible government agencies in Colombia for collecting and reporting information related to seismic events is the Colombian Geological System (SGC). The management of scientific information on hydrological and meteorological events is carried out by the Institute of Hydrology, Meteorology and Environmental Studies (IDEAM). Since values for the entire planet are not available, different studies propose models for their estimation. As for floods they use hydrological models [29], [30], for earthquakes they use the ground motion [31], [32], and the wind loads in terms of their speed [33], [34]. The natural hazards that are considered for the development of this work are floods, extreme winds and earthquakes. Floods are caused mostly by storms or heavy rainfall, and are essentially distinguished by two types: coastal flooding and river flooding. Both are characterized by having an impact wave that has the potential to cause damage to objects with the passing of the wave front. Additionally, by hydrostatic/dynamic forces and lifting effects, floods have the ability to drag objects, which can cause significant damage with direct impacts [35]. Table 2 shows the classification of a flood used in the present work. Extreme winds are present in natural phenomena such as hurricanes or storms. They are usually generated over warm ocean water at low latitudes and are particularly dangerous because of their destructive potential. The presence of a hurricane is considered to have wind speeds equal to or greater than 120km/h (74mph). The damage to an industrial facility results from the direct impact of the wind as well as from wind borne objects. For wind classification, the Saffir/Simpson hurricane scale was used, which is shown in Table 1.

23

Table 1. Natural Hazard Classification Based on Intensity or Impact vector [6], [36], [37].

FLOODS

Wave Front Hazard Classification Water

Depth (m) Water

Speed (m/s)

Low Velocity Very low ≤0.5 ≤0.2

Low >0.5-1 >0.2-0.5

Medium Velocity

Moderate >1-1.5 >0.5-1.0

High Velocity High >1.5 >1.0

EXTREME WINDS

Wind Load

Hurricane Category

Hazard Classification

Wind Speed (km/h)

Storm Surge (m)

Low load 1 Very low 119-153 1.2-1.5

Medium load 2 Low 154.4-177 1.8-2.4

High load 3

Moderate 178.5-209 2.7-3.6

4 210-249 3.9-5.4

Very High load 5 High >250 >5.4

EARTHQUAKES

Seismic Intensity

Hazard Classification PGA (%g) With Probability of

Exceedance Equal to 10% PGA (%g) of the Elastic Response

Spectrum at period T=0

Low Acceleration

Very low <0.05 0.05

Low 0.05-0.15 0.15

Medium Acceleration

Moderate >0.15-0.25 0.25

High Acceleration

High >0.25 0.35

Earthquakes are caused by the sudden release of slowly accumulated strain energy along a fault in the earth's crust. Earthquakes occur most commonly at the collision zone between tectonic plates. They represent a particularly severe threat due to the irregular time intervals between events, lack of adequate forecasting, and the hazards associated with ground shaking due to its direct hazard to any structure located near the earthquake's center. Industrial structural failure could take many human lives in densely populated areas caused by a loss of containment of hazmats [20]. Table 1 shows the classification of an earthquake based on the PGA.

3.2. Vertical Storage Tank Characterization As mentioned in section 2, one of the findings by Michela Campebel [9], is that the equipment mainly affected by natural events are storage tanks (step 2, Figure 8). Normally the consequences produced by an accident in this type of equipment are quite significant due to the large amount of hazmat stored. From this, the fragility and vulnerability analysis will be carried out on vertical atmospheric tanks that work near to atmospheric conditions. To characterize and parameterize this type of equipment, the standard API-620 and API-650 were taken as reference [38], [39]. This standards establishes minimum requirements for each of a storage tanks components and functionalities for the petrochemical industry. Among its requirements, stablishes criteria for design, construct, inspection and maintenance of vertical storage tanks that work at atmospheric conditions. In Figure 11, the main components of a vertical storage tank are presented based on API-650/620.

24

Figure 11. Configuration of a storage tank based on API-620/650 standards.

There is no clear way to classifying storage tanks based upon a single criterion. In order to perform a complete sizing of the tank, the equipment will be classified according to three (3) main components: the shell of the tank, the type of roof and the type of base.

3.2.1. Storage Tank Shell Atmospheric storage tanks are the most common type of tanks in the chemical and petrochemical industry, these tanks are usually operated at an internal pressure slightly above the atmospheric pressure, no more than 0.5psig [40]. To parameterize the type of shell that will contain the stored fluid, the following characteristics are needed: shell material, number and type of connections, diameter, height and thickness of the tank. The type of material of the shell is one of the main parameters that allow us to establish the resistance of the tank, each material has its own "yield strength" and "tensile strength". To establish the thickness of the tank, API-650 proposes the following expressions in terms of the height and diameter of the tank [39]:

For the first course:

𝑡1 = (1.06 −0.0696𝐷

ɦ√ɦ𝐺

𝑆𝑑)(4.9ɦ𝐷𝐺

𝑆𝑑) + 𝐶𝐴 (2)

Where 𝑡1 is the bottom-course thicknesses in mm, ɦ the design liquid level in is 𝑚, 𝐷 is the nominal tank diameter in 𝑚, 𝐺 is the design specific gravity of the liquid to be stored, 𝐶𝐴 is the corrosion allowance in 𝑚

and 𝑆𝑑 is the allowable stress for the design condition in 𝑀𝑃𝑎.

For the second course:

𝑡2 =

{

𝑡1 → 𝑖𝑓

ℎ1(𝑟𝑡1)

0.5< 1.375

𝑡2𝑎 → 𝑖𝑓ℎ1

(𝑟𝑡1)0.5> 2.625

𝑡2𝑎 + (𝑡1 − 𝑡2𝑎) [2.1 −ℎ1

1.25(𝑟𝑡1)0.5] → 𝑖𝑓 1.375 ≥

ℎ1(𝑟𝑡1)

0.5≤ 2.625

(3)

Where ℎ1 is the height of the bottom shell course (𝑚𝑚), 𝑟 is the nominal tank radius (𝑚𝑚), 𝑡2𝑎 is the corroded thickness of the second shell course (𝑚𝑚).

25

For upper courses:

𝑡𝑖 =4.9𝐷 (ɦ −

𝑥1000

)𝐺

𝑆𝑑+ 𝐶𝐴 (4)

Where 𝑥 is the distance of the variable design point from the bottom of the course (𝑚). Equations 2 to 4 allows to characterize the shell of the tank, from geometrical characteristics and the type of tanks material. Below are the conditions of characterization of the roof of a storage tank.

3.2.2. Storage Tank Roof A storage tank can be constituted with two roofs, a fixed roof and/or a floating roof. As shown in Figure 12, the tanks can be opened at the top or closed by a fixed roof:

Figure 12. Basic configuration of a storage tank. a) open-top tank, b) Cone-roof tank, c) Dome-roof tank.

In the case of cone-roof tanks: cylindrical shells with a vertical axis of symmetry. The bottom is usually flat, and the top is made in the form of a shallow cone. Cone-roof tanks typically have roof rafters and support columns except in very small-diameter tanks (Figure 15b) [40]. According to API-650, the angle of inclination

𝜃 of the roof should be between 9.5o and 37o (slope 2:12 to 9:12).

𝑡𝑟𝑐 =𝐷

4.8 sin(𝜃)√𝜏

2.2+ 𝐶𝐴 (5)

Where 𝜏 is a parameter for load combinations. Equation 5 estimate the nominal thickness for the cone roof. In the case of dome-roof tanks: They are similar to tanks with a cone roof, but their shape is similar to an umbrella. These are usually of a size no larger than 20 meters in diameter. Unlike tanks with conical roof, these can be self-supporting structures (Figure 15c). According to API-650, the radius of the dome should be between 0.8𝐷 and 1.2𝐷.

𝑡𝑟𝑑 =𝑅𝑟2.4

√𝜏

2.2+ 𝐶𝐴 (6)

Where 𝜏 is a parameter for load combinations and 𝑅𝑟 is the roof radius (𝑚), Equation 6 estimate the nominal thickness for the dome roof.

26

Figure 13. Types of floating roof in a storage tank: a) External floating roof, b) Internal floating roof.

All the floating roofs are inside the storage tanks, they are a cover floating on the surface of the stored liquid. This cover is a disk-shaped structure that has sufficient buoyancy to ensure that the roof will float from specific conditions. Tanks with floating roof and without fixed roof, are known as external floating roof (Figure 13a), on the other hand, tanks with floating roof and fixed roof, are internal floating roof (Figure 13b).

3.2.3. Storage Tank Base Storage tanks have an additional resistance factor in their base. A tank can be anchored or unanchored to the ground, to avoid displacement of the equipment in case of suffering an external lateral load. Additionally, it can be built on a concrete ring whose function is to prevent the tank from sinking in the land where it was built.

Figure 14. Tank anchor detail.

Figure 14 presents a detailed schematic of the anchorage of a storage tank. The information required for the present study is the number of tank anchor bolts, their diameter and type of material. From the natural hazard characterization performed in section 3.1 and the structural configuration of the storage tank in section 3.2, possible accidental scenarios that may occur during the impact of the hazard on the process equipment are studied. Following are the accidental scenarios considered for the present study.

3.3. Definition of Possible Accidental Scenarios To define the possible final accidental scenarios (step 3, Figure 8), which can be triggered by floods, earthquakes or extreme winds on a vertical storage tank, the event tree method is used. ARAMIS [41] proposes a guide to develop event trees, which is adapted to NaTech events caused by the mentioned natural phenomena. The objective of the events tree is to identify the possible consequences of a critical

27

event or event (CE), which usually represents the failure of a component or an external failure. Later, the sequence of events or security functions that follow the initiating event is defined and must be overcome to obtain a certain result. These types of events are called secondary critical events (SCE), while the events at the end of each branch are known as final events or major events (FE) [42]. Final events are defined as the significant effects produced by secondary events capable of affecting people, structures and the environment. Figure 15 shows a representation of an event tree and its elements.

Figure 15. Structure of the event tree [42].

Once the event tree has been defined, the selected critical event (CE) is the impact of a flood, earthquake or wind load on a storage tank. The parameters that will allow to characterize the impact of a flood are the speed and height of the wave. That said, three (3) types of wave fronts have been established which are shown in Table 2. The parameter that characterizes the intensity of a seism or earthquake is the ground acceleration. Three (3) types of seismic intensity have been established which are shown in Table 2. Finally, the parameter that characterizes a wind load is the wind speed. Four (4) types of wind load have been established which are shown in Table 2. Regarding the secondary critical events (SCE), their selection depends on the consequences that the impact of oa natural hazard brings on a vertical storage tank. Some authors [9], [43], presents a historical data analysis where she identified different types of structural damage that storage tanks can suffer during a natural phenomenon. Based on these analyzes, three (3) types of secondary critical events were identified: damage modes, failure modes due to damage, and release modes (LOC). Considering damage modes, a storage tank can be damaged by: shell buckling, displacement or sliding, floatation, overturning and impact by debris. It should be noted that not all damage modes apply to all natural hazards. As a consequence of damage, five (5) different failure modes can be presented, which are: collapse of the structure, total failure of the connection, partial failure of the connection, failure of the roof of the tank and rupture of the shell. Figure 16 shows a generic event tree to identify the consequences of a NaTech event in storage tanks.

28

Figure 16. Event tree for the sequence of events due to the impact of a natural events on vertical storage tanks.

Once one of the possible failure modes happens, the loss of containment of hazardous material occurs. For this secondary critical event, three (3) release modes were established, which will be part of the spill volume estimation phase and depend on the typology of failure.

Figure 17. Event tree to identify the events sequence of a storage tank impacted by a wind load depending on the wind speed.

The release modes will be presented in detail in Section 3.5.1.3. Figure 17, shows the event tree for the identification of consequences or final accidental scenarios (FE) associated with the impact a wind load, which involve the elements presented above. The detailed event trees for each of the natural hazards considered in the present study are found in the annexes. Floods event tree annexes Figure 49 and earthquake event tree annexes Figure 50.

Mode 2

Impact by Debris Shell rupture

Floatation Failure of the tank's roof

Mode 3

Collapse of the structure

Rigid Sliding Total connection failure

Hazard Intensity Overturning Partial connection failure

Buckling

Natural Hazard Damage Mode Failure Mode Release Mode

Without Affectation

Mode 1

Impact by Debris Partial connection failureMode 2

Shell ruptureMode 2/3

Failure of the tank's roofMode 3

Collapse of the structureMode 1

Total connection failureMode 2

Overturning




Mode 2


Partial connection failure

Failure of the tank's roof

Without Affectation

Mode 1

Mode 2

Mode 2

Mode 2/3

Mode 3Wind Speed

Partial connection failure

Shell rupture

Buckling

Collapse of the structure

Total connection failure

29

3.4. Structural and Natural Hazard Analysis. As mentioned in Section 3.1, a natural hazard has the ability to inflict damage on a storage tank based on its solicitation. Figure 18 presents a simple outline of the scenario to be evaluated. An extreme natural event has the ability to generate an external load or solicitation (either by pressure or movement) of such magnitude that, when impacting any type of structure, the solicitation could exceed the resistance force to which it was designed, generating some type of structural damage.

Among the most common damages caused by a natural hazard on a tank are the shell buckling, the sliding or floating of the tank, damage to tank foundation, overturning, impact by debris, detachment of pipes and damage to bottom plate by buckling due to uplifting. In the present work the possible damages caused by the impact of a flood, earthquake and wind load will be analyzed (step 4, Figure 8). Table 2 summarizes the types of damage to evaluate for each of the natural events mentioned.

Table 2. Types of damage produced by different natural events.

Natural Event Type of Damage Solicitation* Storage Tanks Resistance

Earthquake Buckling Acting effort (𝜎𝜃) Critical effort (𝜎𝑟)

Overturning Stability factor (𝐽) -

Flood

Buckling Water pressure (𝑃𝑤) Resistance Pressure (𝑃𝑟)

Floatation Floatation force (𝐹𝑓) Critical floatation force (𝐹𝑓𝑐𝑟)

Rigid Sliding Sliding force (𝐹𝑠𝑙𝑑) Critical sliding force (𝐹𝑠𝑐𝑟)

Debris Impact Impact force (𝐹𝑖) Resistance force (𝐹𝑟)

Wind

Buckling Wind Pressure (𝑞𝑒𝑞) Resistance Pressure (𝑃𝑟)

Debris Impact Depth penetration (𝐷𝑝)

Impact force (𝐹𝑖) Thickness (𝑡)

Resistance force (𝐹𝑟)

Once defined the possible types of damage that will be evaluated for each one of the natural events, it should be quantified which will be the load exerted for each type of damage. Below the mathematical models proposed by different authors to determine the possibility of different types of damage are presented.

3.4.1. Storage Tank Damage by Floods Hazard Models presented below allow to estimate the damage for a storage tank caused by the impact of a flood. Figure 19 shows the different types of damage that a storage tank may suffer when is hit by a flood.

Figure 19. Types of damage to a storage tank impacted by a flood [6].

Figure 18. Damage due to natural danger.

30

The types of damage that will be taken into account in the present work are buckling of the shell due to the external pressure of the water, the flotation of the equipment, the sliding of the equipment and the collision or impact of objects floating in the water.

3.4.1.1. Shell Buckling The shell Buckling of a tank is commonly caused by external forces like wind pressure and water pressure, this last one exerted by a flood. However, Cozzani et [25], has pointed out that buckling as a potential damage caused by floods with the capacity to lead the shell collapse. Landucci et al. [21], developed a balance with the pressures that act on the shell of the vertical storage tank, to be impacted by a flood that has a certain speed and height, Figure 20. The resistance pressure of the tank corresponds to the pressure of the stored liquid and the material resistance pressure of the shell. While the pressure of the flood corresponds to the dynamic and static water pressure.

Figure 20. Schematic of the load-resistance forces considered for shell buckling.

The pressure of the flood 𝑃𝑤 (𝑃𝑎), is the sum of the maximum static pressure 𝑃𝑤𝑠 (𝑃𝑎) and the maximum dynamic pressure 𝑃𝑤𝑑 ( 𝑃𝑎):

𝑃𝑤 = 𝑃𝑤𝑠 + 𝑃𝑤𝑑 (7)

The dynamic and static pressure, 𝑃𝑤𝑠 and 𝑃𝑤𝑑 can be estimate as follows:

𝑃𝑤𝑠 = 𝜌𝑤𝑔𝑆 (8)

𝑃𝑤𝑑 =1

2𝜌𝑤𝑘𝑑𝑉

2 (9)

Where 𝜌𝑤 is the water flood density (𝑘𝑔/𝑚3), 𝑔 the gravitational constant, 𝑆 is the flood height (𝑚), 𝑘𝑑 the

water hydrodynamic coefficient and 𝑉 is the flood velocity (𝑚/𝑠).

On the other hand, the pressures that exert resistance over external loads 𝑃𝑟 (𝑃𝑎), are the pressure of the stored fluid (𝑃𝑓), and the material resistance pressure of the tank 𝑃𝑐𝑟 (𝑃𝑎) [44]. The latter can be calculated

from the mechanical properties of the tank material.

𝑃𝑟 = 𝑃𝑓 + 𝑃𝑐𝑟 (10)

𝑃𝑓 = 𝜌𝑓𝑔ℎ = 𝜌𝑓𝑔𝐻Ф (11)

31

𝑃𝑐𝑟 =2𝐸𝑡

𝐷

(

1

(𝑛2 − 1) (1 + (2𝑛𝐻𝜋𝐷

)2

)

+𝑡2

3𝐷2(1 − 𝜈2)(𝑛2 − 1 +

2𝑛2 − 1 − 𝜈

1 + (2𝑛𝐻𝜋𝐷

))

)

(12)

Where 𝐸 is the elasticity module (𝑃𝑎), 𝑡 the shell thickness (𝑚), H the tanks height (𝑚), D the tanks diameter (𝑚), 𝑛 is a parameter to minimize critical pressure and 𝜈 the poisson's coefficient.

𝐷𝑎𝑚𝑎𝑔𝑒 = {𝑖𝑓 𝑃𝑤 − 𝑃𝑟 > 0 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑏𝑢𝑐𝑘𝑙𝑖𝑛𝑔

𝑖𝑓 𝑃𝑤 − 𝑃𝑟 ≤ 0 𝑤𝑜𝑛′𝑡 𝑏𝑒 𝑏𝑢𝑐𝑘𝑙𝑖𝑛𝑔

(13)

With Equations 7 and 10, it is possible to establish a relationship between the loads that act over the tank at the time of being impacted by a flood. To determine if the equipment will suffer damage by buckling or deformation of its shell, the damage criteria is represented by Equation 13, where if the water pressure exceeds the tank resistance pressure, the buckling will occur.

3.4.1.2. Floatation The displacement of a storage tank due to its flotation is one of the most common and frequent types of damage that occur in floods. In the literature, displacements of up to 30 meters have been reported, with final consequences such as pipelines detachment or major structural damage [45]. To develop a mathematical expression that represents the critical flotation force action on a storage tank, a

balance of forces will be made over the equipment, as shown in Figure 21. The weight of the tank 𝑊𝑡𝑎𝑛𝑘 (𝑁) and the weight of the liquid stored 𝑊𝑙𝑖𝑞𝑢𝑖𝑑 (𝑁) represents the resistance forces of the equipment and the

anchoring force of the equipment 𝛬𝑡 (𝑁) according to standards API-650 represents an additional force due to anchorage to the ground. The latter has a value of 0 when the tank is not anchored.

Figure 21. Schematic of the load-resistance forces considered for tank floatation.

The critical floatation force 𝐹𝑓𝑐𝑟 (𝑁) of the storage tank can be calculated as follows [35]:

𝐹𝑓𝑐𝑟 = 𝑊𝑡𝑎𝑛𝑘 +𝑊𝑙𝑖𝑞𝑢𝑖𝑑 + 𝛬𝑡 (14)

Where 𝛬𝑡 = 𝑎𝑡𝑓𝑦 ∑𝐴𝑏𝑜𝑙𝑡, this parameter will depend if the tank has an anchoring system (e.g., bolts and

concrete foundations). 𝑎𝑡 is a unitary dichotomous variable to represent the anchoring state, 𝑓𝑦 the bolts

minimum yield strength (𝑃𝑎) and 𝐴𝑏𝑜𝑙𝑡 the area for a bolt (𝑚2). On the other hand, the floating force 𝐹𝑓𝑙𝑜𝑎𝑡 (𝑁) can be calculated as follows [46]:

𝐹𝑓 = (𝜋𝐷2

4)𝑃𝑤𝑠 = (

𝜋𝐷2

4)𝜌𝑤𝑔𝑆 (15)

32

Where 𝜌𝑤 is the water flood density (𝑘𝑔/𝑚3), 𝑔 the gravitational constant, 𝑆 is the flood height in (𝑚) and 𝐷

is the tanks diameter (𝑚).

𝐷𝑎𝑚𝑎𝑔𝑒 = {𝑖𝑓 𝐹𝑓 − 𝐹𝑓𝑐𝑟 > 0 𝑤𝑖𝑙𝑙 𝑓𝑙𝑜𝑎𝑡

𝑖𝑓 𝐹𝑓 − 𝐹𝑓𝑐𝑟 ≤ 0 𝑤𝑜𝑛′𝑡 𝑓𝑙𝑜𝑎𝑡

(16)

With Equation 14 and 15, it is possible to establish a relationship between the floatation force acting on the tank at the moment of being hit by a flood and thus be able to determine if the equipment will suffer damage by floating. The damage criteria is represented by Equation 16.

3.4.1.3. Rigid Sliding Cozzani et al. [43], states that the hydrodynamic pressure of a flood has the potential to cause a rigid sliding of a storage tank. Sliding can occur in both large tanks and small tanks, when this type of damage occurs, the consequences could be greater than the shell buckling due to the detachment of connected pipelines. To develop a relationship between the hazard and de equipment, the storage tank (with its components), the stored liquid and the force exerted by the flood must be taken into account. A balance of forces is made, where the weight of the tank 𝑊𝑡𝑎𝑛𝑘 (𝑁), the weight of the stored liquid 𝑊𝑙𝑖𝑞𝑢𝑖𝑑 (𝑁) and the anchoring force

𝛬𝑡 (𝑁) are the resistance force of the equipment, and the static and dynamic forces of the water are the total sliding force, Figure 22.

Figure 22. Schematic of the load-resistance forces considered for rigid sliding.

The critical resistance force 𝐹𝑠𝑐𝑟 (𝑁) of the storage tank can be calculated as follows:

𝐹𝑠𝑐𝑟 = 𝜇𝑠(𝑊𝑡𝑎𝑛𝑘 +𝑊𝑙𝑖𝑞𝑢𝑖𝑑 − 𝐹𝑓) +𝛬𝑡2

(17)

Where 𝜇𝑠 is the friction coefficient between ground and the storage tank. The sliding force 𝐹𝑠𝑙𝑑 (𝑁) produced by the flood can be calculated as follows [35]:

𝐹𝑠𝑙𝑑 = 𝑃𝑤𝑑(𝐷𝑆) = (1

2𝐾𝑑𝜌𝑤𝑉

2) (𝐷𝑆) (18)

Where 𝜌𝑤 is the water flood density (𝑘𝑔/𝑚3), 𝑆 is the flood height (𝑚), 𝑘𝑑 the water hydrodynamic coefficient

and 𝑉 is the flood velocity (𝑚/𝑠).

𝐷𝑎𝑚𝑎𝑔𝑒 = {𝑖𝑓 𝐹𝑠𝑙𝑑 − 𝐹𝑠𝑐𝑟 > 0 𝑤𝑖𝑙𝑙 𝑠𝑙𝑖𝑑𝑒

𝑖𝑓 𝐹𝑠𝑙𝑑 − 𝐹𝑠𝑐𝑟 ≤ 0 𝑤𝑜𝑛′𝑡 𝑠𝑙𝑖𝑑𝑒 (19)

33

With Equation 17 and 18, is possible to stablish a relationship to determine if the tank could suffer damage by sliding caused by a flood. Equation 19 present de damage criteria for rigid sliding.

3.4.1.4. Impact of Debris A flood has the ability to drag objects as it progresses. These objects or debris have the potential to affect the integrity of a storage tank on impact with it, Figure 23. Predicting the magnitude of the impact force and the point of action is very challenging and subject to several uncertain parameters [35].

Figure 23. Schematic of the load-resistance forces considered for rigid sliding.

Haehnel et al. [47], Proposed a way to calculate the impact force from an impulse-momentum approach:

𝐹𝑖 =𝑀𝑈

𝑡𝑖 (20)

Where 𝑀 is the debris mass (𝑘𝑔), 𝑡𝑖 is the impact duration, which is the measurement from the moment of impact until the moment in which the maximum value of force is reached. ASCE-7 (2006) has adopted a value of 0.03 seconds [48]. Usually the debris velocity 𝑈 (𝑚/𝑠) is assumed equal to the water speed 𝑉. Because large debris does not always go at flood speed, ASCE-7 suggests a modification to the impact force 𝐹𝑖 (𝑁):

𝐹𝑖 =𝑀𝑈𝐶𝑂𝐶𝐷𝐶𝐵

𝑡𝑖 (21)

Where 𝐶𝐷 is the depth coefficient to account for the debris’ velocity reduction due to possible dragging along

the bottom and 𝐶𝐵 is the blockage coefficient to account for the debris’ velocity reduction due to prior collisions with other obstacles.

{

𝑖𝑓 𝑆 ≤ 0.3𝑚 → 𝐶𝐷 = 0.0

𝑖𝑓 0.3 < 𝑆 ≤ 1.5𝑚 → 𝐶𝐷 = 0.833(𝑆 − 0.3)

𝑖𝑓 𝑆 > 1.5𝑚 → 𝐶𝐷 = 1.0

{

𝑖𝑓 𝑊 ≤ 1.5𝑚 → 𝐶𝐵 = 0.0

𝑖𝑓 1.5 < 𝑊 ≤ 9𝑚 → 𝐶𝐵 = 0.133(𝑊 − 0.3)

𝑖𝑓 𝑊 > 9𝑚 → 𝐶𝐵 = 1.0

Finally, Haehnel et al. [47], Suggested an expression to calculate the impact force of woody debris:

𝐹𝑖 = 1550𝑈√𝑀 (22)

34

To evaluate the damage from the impact of a debris, Equation 21 will be used to calculate the impact force. This Equation takes into account both the physical properties of the rubble and the characteristics of the flood. The impact force will be compare with the resistance force 𝐹𝑟 (N) of the tank, represented by the following Equation:

𝐹𝑟 = 𝑃𝑟𝐴𝑝 (23)

Where 𝑃𝑟 is the resistance pressure of the tank calculated with Equation 10, and 𝐴𝑝 is the deris area (𝑚2).

𝐷𝑎𝑚𝑎𝑔𝑒 = {𝑖𝑓 𝐹𝑖 − 𝐹𝑟 > 0 𝑑𝑎𝑚𝑎𝑔𝑒𝑖𝑓 𝐹𝑖 − 𝐹𝑟 ≤ 0 𝑛𝑜 𝑑𝑎𝑚𝑎𝑔𝑒

(24)

With Equation 21 and 23, is possible to establish a relationship to determine if the tank could suffer damage by debris impact drag by the flood. Equation 24 present de damage criteria for debris impact, where if the impact force exceeds the resistance force strength of the tank, it is assumed that the debris will break the tank shell.

3.4.2. Storage Tank Damage by Extreme Winds The models presented below allow to estimate the damage for a storage tank caused by extreme winds. Figure 24 shows the different types of damage that a storage tank can suffer when exposed to high wind speeds.

Figure 24. Types of damage to a storage tank exposed to high wind speeds.

Vertical storage tanks with cylindrical shape are equipment with the capacity to store large quantities of different materials, such as crude, fuel and chemicals. They are welded and have a structure with very thin walls with long diameters and heights. The types of damage that will be analyzed in the present work will be the buckling of the walls due to the external pressure exerted by the wind and the damage of the tanks shell due to impact of projectiles dragged by the wind. In the case of damages due to buckling of the shell, this type of damage usually occurs when they are empty or partially full [14], [15]. This is why, in most cases, the final result is a great loss of financial and human resources and not so much in the amount of hazmat that can be spilled [16].

3.4.2.1. Shell Buckling Following the same procedure that was carried out for the case of buckling of tanks shell by flood, a pressure balance is presented over the storage tank, Figure 25. Where the resistance pressure of the tank is represented by the Equation 10 and the load over the tank will be represented by the external pressure produced by the wind.

35

Figure 25. Schematic of the load-resistance forces considered for shell buckling produce by wind.

According to international standards, such as the American Petroleum Institute (API-650), American Society of Civil Engineers (ASCE-7) and European Standard (EN 1991-1-4 and EN1993-1-6) the model for the calculation of wind pressure is based on the type of exposure of the affected structure. The wind pressure can be determined from the following expression [39], [48], [49]:

The velocity pressure 𝑞𝑧, evaluated at height z shall be calculated by Equation 26:

𝑞𝑧 = 0.00256𝐾𝑧𝐾𝑧𝑡𝐾𝑑𝑉2𝐼𝐺𝑠 [

𝑙𝑏

𝑓𝑡2] (25)

𝑞𝑧 = 0.613𝐾𝑧𝐾𝑧𝑡𝐾𝑑𝑉2𝐼𝐺𝑠 [

𝑁

𝑚2= 𝑃𝑎] (26)

Where 𝐾𝑧 is the velocity pressure exposure coefficient (1.04 for exposure C at a height of 12m), 𝐾𝑧𝑡 is the topographic factor (1.0 for all structures except those on isolated hills or escarpments), 𝐾𝑑 is the wind

directionality factor (0.95 for round tanks), 𝑉 is the wind speed (𝑚/𝑠), 𝐼 is an importance factor (1.0 for category II structures) and 𝐺 is the gust factor (0.85 for exposure C). The wind load or wind pressure 𝑝 (𝑃𝑎) action on the structure surfaces over a storage tank can be defines as Equation 27 [14], [15]:

𝑝 = 𝐶𝑝𝑞𝑧 (27)

Where 𝐶𝑝, is the wind pressure coefficient. For cylindrical tanks, they usually vary both in circumference and

in height. Y.Zhao et al [15], establish that the variation in height is not as pronounced compared to the variation in the circumference, that been said, the variation of the pressure coefficients are assumed constant along the height and only depend on the longitude, Figure 26. To estimate de the wind pressure coefficients, several authors and design codes have proposed an expression (Equation 28) based on Fourier series decomposition, Table 3 show the representative Fourier coefficients proposed by some authors [15]:

𝐶𝑝(𝜃) =∑𝑎𝑖𝑐𝑜 𝑠(𝑖𝜃)

𝑚

𝑖=0

(28)

Where 𝜃 is the longitude measured from windward, and 𝑎𝑖 is the Fourier Coefficient.

Table 3. Fourier coefficients proposed by different authors.

Parameter Author

Greiner Rish ACI-334 EN 1993-4-1

𝒂𝟎 -0.65 -0.387 -0.2636 −0.54 + 0.16(𝐷/𝐻)

𝒂𝟏 0.37 0.338 0.3419 0.28 + 0.04(𝐷/𝐻)

𝒂𝟐 0.84 0.533 0.5418 1.04 + 0.20(𝐷/𝐻)

𝒂𝟑 0.54 0.471 0.3872 0.36 + 0.05(𝐷/𝐻)

36

𝒂𝟒 -0.03 0.166 0.0525 −0.14 + 0.05(𝐷/𝐻)

𝒂𝟓 -0.07 -0.066 -0.0771

𝒂𝟔 -0.055 -0.0039

𝒂𝟕 0.0341

Figure 26. External wind pressure coefficients along the circumference of cylinders.

It should be noted that the Fourier coefficients mentioned above are related only for tanks with closed-top and therefore the internal pressure of the wind is not included. For tanks with an open-top, a uniform negative wind pressure coefficient should be included to take into account the internal suction.

𝐶𝑝 = {−0.8 → 𝐻/𝐷 ≥ 2−0.5 → 𝐻/𝐷 ≤ 1

The non-uniform distribution of pressure 𝑝 resulting from external wind loading on cylindrical tanks may, for the purpose of shell buckling design, be substituted by an equivalent uniform external pressure 𝑞𝑒𝑞 (𝑃𝑎) as

shown in Figure 27 [49], estimated through Equation 29:

Figure 27. a) Wind pressure distribution around shell circumference, b) equivalent axisymmetric pressure distribution around shell circumference

[49].

𝑞𝑒𝑞 = 𝑘𝑤𝑝𝑚𝑎𝑥 (29)

Where 𝑝𝑚𝑎𝑥 is the maximum non-uniform pressure (𝑃𝑎).

a) b)

37

𝑘𝑤 = 0.46(1 + 0.1√(𝐶𝜃𝑟)/(𝜔𝑡)) (30)

Where 𝐶𝜃 is an external buckling factor for medium-length cylinders, 𝜔 is a relative length parameter for

shell, 𝑟 the radius of the tank (𝑚) and 𝑡 the thickness of the tank (𝑚). Figure 28 shows the non-uniform profile of wind pressure for different wind velocities. The direction of the wind is taken at the 0° angle. In addition, the uniform external equivalent pressure is shown in Table 4:

Figure 28. Wind pressure distribution around shell circumference at

different velocities.

Table 4. Equivalent axisymmetric pressure at different wind velocities.

Wind Speed (𝒎𝒑𝒉) 𝒒𝒆𝒒 (𝑷𝒂)

75 0.7135

125 1.9820

175 3.8846

225 6.4215

𝐷𝑎𝑚𝑎𝑔𝑒 = {𝑖𝑓 𝑞𝑒𝑞 − 𝑃𝑟 > 0 𝐵𝑢𝑐𝑘𝑙𝑖𝑛𝑔

𝑖𝑓 𝑞𝑒𝑞 − 𝑃𝑟 ≤ 0 𝑁𝑜 𝐵𝑢𝑐𝑘𝑙𝑖𝑛𝑔 (31)

With the model presented, it is possible to establish a relationship between the load acting on the tank (Equation 29) at the time of being affected by extreme winds and the resistance pressure of the tank (Equation 10), to determine if the equipment will suffer damage by buckling or deformation of its shell (Equation 31).

3.4.2.2. Overturning International entities have collected information about storage tanks affected by an extreme wind source, one of the most recent cases is Hurricane Katrina, which produced winds up to 280 km/h, and had the potential to overturn a tank locate onshore . According to some studies, this type of damage is the least likely to manifest, and when it occurs the tank must be completely empty and without anchoring. However, the API-650 standard establishes various stability criteria for a specific wind load. In the present work, the damage caused by overturning will be evaluated for storage tanks without anchorage to the ground. In section 5.11 of the API-650 standard, stability criteria are established for tanks without anchoring, Figure 29.

38

Figure 29. Schematic of load-resistance forces considered the overturning by a wind load.

However, in section 5.12 of the standard the criteria for anchored tanks are presented. The stability criteria for overturning by an external wind load on a non-anchored tank are represented by Equation 32-33:

0.6𝑀𝑤 +𝑀𝑃𝑖 <𝑀𝐷𝐿

1.5+𝑀𝐷𝐿𝑅 → 𝐹𝑜1 < 𝐹𝑟1 (32)

𝑀𝑤 + 𝐹𝑝(𝑀𝑃𝑖) <(𝑀𝐷𝐿 +𝑀𝐹)

2+𝑀𝐷𝐿𝑅 → 𝐹𝑜2 < 𝐹𝑟2 (33)

Where 𝐹𝑝 is a pressure combination factor, 𝑀𝑃𝑖 moment about the shell-to-bottom joint from design internal

pressure, 𝑀𝑤 overturning moment about the shell-to-bottom joint from horizontal plus vertical wind pressure,

𝑀𝐷𝐿 moment about the shell-to-bottom joint from the nominal weight of the shell and roof structural supported by the shell that is not attached to roof plate, 𝑀𝐹 moment about the shell-to-bottom joint from

liquid weight and 𝑀𝐷𝐿𝑅 moment about the shell-to-bottom joint from the nominal weight of the roof plate plus any attached structural.

𝐷𝑎𝑚𝑎𝑔𝑒 = {𝑖𝑓 𝐹𝑜1 − 𝐹𝑟1 > 0 𝑎𝑛𝑑 𝐹𝑜2 − 𝐹𝑟2 > 0 𝑂𝑣𝑒𝑟𝑡𝑢𝑟𝑛𝑖𝑓𝐹𝑜1 − 𝐹𝑟1 ≤ 0 𝑜𝑟 𝐹𝑜2 − 𝐹𝑟2 ≤ 0 𝑁𝑜 𝑂𝑣𝑒𝑟𝑡𝑢𝑟𝑛

(34)

Through Equation 32-33, it’s possible to establish a relationship between the overturning forces 𝐹𝑜𝑖 produced by the wind on the tank at the time of being affected by extreme winds and the resistance force

of the tank 𝐹𝑟𝑖, to determine if the equipment will suffer damage by overturning, Equation 34.

3.4.2.3. Impact of Debris Hurricanes or tornados have great potential for destruction, particularly these natural hazards have a long time of action. By destroying a structure, the waste produced by the destruction turn into debris or flying projectiles with the potential to impact other structures and cause considerable damage [50]. The area covered by dangerous winds is significantly wide, which allows multiple structures to be vulnerable to the impact of several debris, expanding the domino effect on other structures. Like a flood, extreme winds has the capacity of drag objects as it progresses. This objects represent a hazard to the integrity of a storage tank. An object dragged by the wind can carry enough force to cause damage to the elements of a storage tank. The model to calculate the force of impact of an object driven by the wind is made from a balance of forces on the debris, which varies according to the debris characteristics and wind conditions.

39

Figure 30. Schematic of the load-resistance forces considered for impact of debris drag by the wind.

As can be seen in Figure 30, the object dragged by the wind has a force that depends on the wind speed which will be related to the resistance force of the tank to assess possible damage. Salzano and Basco [51], propose a different methodology to evaluate vulnerability of a storage tank based on the severity of the impact, determined by Johnson's number 𝐽′ and the depth of penetration ℎ𝑝 by the impact. This methodology

relates details and information of the process equipment, the impact object and the impact speed 𝑈0. In impact dynamics, Johnson’s number is adopted for evaluating the severity of the impact on a continuum loaded impulsively and impinged by the initial velocity pulse and can be estimated with Equation 35.

𝐽′ =𝑈02

𝜎𝐷𝑡

𝑀

𝑟𝑝2 (35)

Where 𝑈0 is the impact speed (𝑚/𝑠) also take as the wind speed, 𝑀 debris mass (𝑘g), 𝜎𝐷 dynamic yield

stress (𝑃𝑎), 𝑡 course shell thickness of the tank and 𝑟𝑝 debris radius. Table 5 shows the range values of

Johnson’s number with the corresponding regimes. In order to evaluate the damage produced by the impact of an object in a storage tank, Johnson's number has been modified in [52] as:

Table 5. Threshold values for damage for Johnson's damage number 𝐽′ [51].

𝑱 Regime Probability of Damage

1x10−3 Quasi-static elastic 0

1x10−2 Moderate plastic behavior 0.1

1x10+1 Extensive plastic deformation 0.5

On the other hand, Lin [53], proposed a methodology to perform a risk assessment for urban structures impacted by flying objects dragged by the wind. In the present work, the methodology proposed by Lin will be applied to a vertical storage tank. The determining factor for estimating whether an object can buckle or

penetrate a storage tank will be the impact force 𝐹𝑜𝑏 (𝑁), which can be calculated from the physical properties of the object and the impact velocity, Equation 36.

𝐹𝑜𝑏 =1

2𝜌𝑊𝑈0

2𝐴𝑝𝐶𝐹 (36)

Where 𝜌𝑊 is the wind density (𝑘𝑔/𝑚3), 𝐴𝑝 debris area (𝑚2), 𝐶𝐹 is an aerodynamic force coefficient.

Equation 36 applies to those debris not attached to the ground, so that when the aerodynamic force of the debris exceeds the gravitational force (𝐹𝑖 > 𝑀𝑔), the object can be moved and lifted by the wind. Equation

37 allows to determine the speed at which a debris starts its flight. Since 𝑀𝑔 = 𝐴𝑝ℎ𝜌𝑝𝑔.

𝑈02 =

2ℎ𝜌𝑝𝑔𝐼

𝜌𝑊𝐶𝐹 (37)

40

Where ℎ is a debris characteristic dimension (𝑚), 𝜌𝑝 is the density of the debris material (𝑘𝑔/𝑚3) and 𝐼 is

a fixed strength integrity parameter, calculated as the ratio between the wind force required to overcome the friction force, divided by debris weight. Finally, once the tank has been damage by the impact of a debris, a possible and useful way to validate Johnson's damage number is by calculating the penetration depth ℎ𝑝 (𝑚) of an object from its impact

parameters. It should be noted that for industrial accidents, the penetration depth by a projectile or debris is an important factor of reference to evaluate a loss of containment of an industrial equipment. If ℎ𝑝 exceeds

the thickness 𝑡 of the affected equipment, the unwanted release of the stored hazmat will occur. A simplified approach to estimating ℎ𝑝 is reported in Lee's textbook in terms of minimum thickness [52].

ℎ𝑝,𝑠𝑚𝑎𝑙𝑙 = 𝑘𝑆𝑀

𝑎𝑈0𝑏 𝑀 ≤ 1𝑘𝑔 (38)

ℎ𝑝,𝑙𝑎𝑟𝑔𝑒 = 𝑘𝐿𝑀

𝐴𝑝𝑙𝑜𝑔10(1 + 5x10

−5𝑈02) 𝑀 > 1𝑘𝑔 (39)

Where 𝑘𝑆 and 𝑘𝐿 are constants for small and large debris respectively. As can be seen in 38 and 39, the model for calculating ℎ𝑝 don’t take into account the characteristics of the affected process equipment. Table

6 presents the parameters for Equation 38 and 39.

Table 6. Constant values for fragment penetration reported in Lee’s textbook [52].

Target Material 𝒌𝑺 𝒌𝑳 a b

Concrete 1.8x10−5 1x10−3 0.4 1.5

Steel 6.0x10−5 5x10−5 0.3 1

Brickwork 2.3x10−5 2.5x10−3 0.4 1.5

Mébarki et al [54], proposed a more robust model for the calculation of the penetration depth ℎ𝑝 (𝑚) of a

projectile. The model takes into account both the characteristics of the impact material and the properties of the target material, Equation 40 and 41.

Penetration depth for the case 𝛼 ≠ 0:

ℎ𝑝 =

(−𝑑𝑝 ∙ cos(𝛼) +√(𝑑𝑝 ∙ cos(𝛼))

2+4𝜋∙ tan (𝛼) ∙ (

𝐸𝑐𝑓𝑢 ∙ 𝜀𝑢

)

23)

2 ∙ tan (𝛼)

(40)

Penetration depth for the case 𝛼 = 0:

ℎ𝑝 = (𝐸𝑐

𝑓𝑢 ∙ 𝜀𝑢)

23∙

1

𝜋 ∙ 𝑑𝑝 (41)

Where the kinetic energy is defined as 𝐸𝑐 =𝑀∙𝑈0

2

2 (𝑘𝑔 ∗ 𝑚2/𝑠2), 𝑑𝑝 is the debris diameter (𝑚), 𝑓𝑢 and 𝜀𝑢 are

the ultimate strength and ultimate strain of the target´s constitutive material (𝑃𝑎), respectively. Figure 31 shows the penetration scheme of a rod projectile, where 𝑒𝑡 = 𝑡 is the target’s thickness and 𝑙𝑝 = ℎ is the

length of the fragment.

41

Figure 31. Impact of a projectile (fragment) on a target (a plate) [54].

The debris and objects dragged by the wind have irregular geometries, therefore, instead of considering real fragments, it is assumed that the projectiles have spherical shapes or rods. In the case of rods of projectiles it is necessary to calculate the equivalent diameter in function of their length 𝑙𝑝 and area 𝐴𝑝. The

equivalent diameter is calculated by the following expression:

𝑑𝑝 =

(√(𝜋 ∙ 𝑙𝑝)2+ 2 ∙ 𝜋 ∙ 𝐴𝐷 − 𝜋 ∙ 𝑙𝑝)

𝜋

(42)

The standard API-620, establishes minimum thicknesses according to the diameter of the tank. This value

(Table 8) will be assumed as the critical thickness (𝑒𝑐𝑟) for the shell of the storage tank.

Table 7. Minimum plate thickness for different diameters [38].

Tank Diameter (m) Minimum Thicknesses (mm)

≤15.2 4.8

>7.6 – 18.3 6.4

>18.3 – 30.5 8

>30.5 9.6

𝐷𝑎𝑚𝑎𝑔𝑒 = {𝑖𝑓 𝐹𝑜𝑏 − 𝐹𝑟 > 0 𝑑𝑎𝑚𝑎𝑔𝑒𝑖𝑓 𝐹𝑜𝑏 − 𝐹𝑟 ≤ 0 𝑛𝑜 𝑑𝑎𝑚𝑎𝑔𝑒

(43)

With Equation 23 and 36, is possible to establish a relationship to determine if the tank could suffer damage by debris impact drag by the wind. Equation 43 present de damage criteria for debris impact.

3.4.3. Storage Tank Damage by Earthquakes An earthquake has the capacity to affect all types of industrial facilities [55], [56]. From the threat imposed by an earthquake on all structures that are subject to seismic movements, the calculation of the probability of damage and the risk estimation against these events is significantly important for the chemical industry [24]. The model presented in the present section allows to compute the response of a storage tank when subjected to seismic events (ground accelerations). In particular, models for the analysis of shell buckling due to compressive shell stresses and tank overturning will be presented, Figure 32.

42

Figure 32. Types of damage to a storage tank exposed to an earthquake.

3.4.3.1. Buckling

In order to estimate the resistance and demands in terms of shell compression stress, which causes shell buckling (Figure 33), the methodology presented in API-650 was complemented with shell resistance

calculations 44 by Licai Yang et al. [57]. The compressive stress acting 𝜎𝑐 on the shell for a given peak ground acceleration (PGA) is calculated according to Equations present in section E.6.2.2 of API-650 (Compression stresses for Self-anchored and Mechanically Anchored tanks).

Figure 33. Schematic of the load-resistance forces considered for shell buckling produce by an earthquake.

Shell Compression in Self-Anchored Tanks,

𝜎𝑐 = (𝑤𝑡(1 + 0.4𝐴𝑣) +1.273𝑀𝑟𝑤

𝐷2)

1

1000𝑡𝑠 𝐽 < 0.785 (44)

𝜎𝑐 = (𝑤𝑡(1 + 0.4𝐴𝑣) + 𝑤𝑎0.607 − 0.18667[𝐽]2.3

− 𝑤𝑎)1

1000𝑡𝑠 𝐽 > 0.785 (45)

Shell Compression in Mechanically-Anchored Tanks,

𝜎𝑐 = (𝑤𝑡(1 + 0.4𝐴𝑣) +1.273𝑀𝑟𝑤

𝐷2)

1

1000𝑡𝑠 (46)

Where 𝑀𝑟𝑤 is the overturning moment (𝑁𝑚), 𝑤𝑡 tank and roof weight acting at base of shell (𝑁/𝑚), 𝐴𝑣 vertical earthquake acceleration coefficient (%𝑔), 𝐽 anchorage ratio, 𝑡𝑠 thickness of bottom shell course less

corrosion allowance (𝑚𝑚). Once the compression stress acting on the shell is calculated, it is compared to the resistant compressive stress for a cylindrical large storage tank, 𝜎𝑟 [57]:

𝜎𝑟 = 0.413𝑀𝑃

𝐸𝑡

𝐷 (47)

𝑀𝑃 = 0.979√𝐸𝑡𝐸

(48)

43

Where 𝑀𝑃 is a plasticity correction coefficient, 𝐸 is the elasticity modulus, 𝑡 shell thickness, 𝐸𝑡 is the tangent modulus of steel, and 𝐷 is the tank’s diameter.

𝐷𝑎𝑚𝑎𝑔𝑒 = {𝑖𝑓 𝜎𝑐 − 𝜎𝑟 > 0 𝐵𝑢𝑐𝑘𝑙𝑖𝑛𝑔

𝑖𝑓 𝜎𝑐 − 𝜎𝑟 ≤ 0 𝑁𝑜 𝐵𝑢𝑐𝑘𝑙𝑖𝑛𝑔 (49)

With the model presented, it is possible to establish a relationship between the loads acting on the tank produced by an earthquake and the resistance force of the tank. Equation 49 determine if the equipment will suffer damage by buckling or deformation of its shell.

3.4.3.2. Overturning

In order to evaluate the storage tank stability, the stability factor or anchored ratio 𝐽 present in the API-650 was used. This factor depends on the moment generated by the impulsive and convective masses of the structure, and it was modified so that the anchorage bolts were taken into account when calculating the overturning moment, Figure 34. In general, the overturning moment 𝑀𝑟𝑤 for a storage tank is:

Figure 34. Schematic of the load-resistance forces considered for tank overturning produce by an earthquake.

𝑀𝑟𝑤 = 𝑊𝑖𝑋𝑖 +𝑊𝑐𝑋𝑐 −𝑀𝑎𝑛 (50)

Where 𝑊𝑖 and 𝑊𝑐 are the calculated weights for impulsive and convective modes (𝑁), and 𝑋𝑖 and 𝑋𝑐 are the

effective heights for each of the mentioned modes (𝑚). In order to calculate the moment resisted by the anchor bolts (if present), it was assumed they were uniformly distributed along the tank’s perimeter, and

that they worked on purely axial stress. Then, the resisting moment of the anchorage system 𝑀𝑎𝑛 (𝑁𝑚) is calculated around the perpendicular axis to the seismic acceleration direction, as:

𝑀𝑎𝑛 = ∑ 𝐴𝑏𝑜𝑙𝑡𝑓𝑦𝑑𝑖

𝑁𝑏𝑜𝑙𝑡𝑠

𝑖=1

(51)

Where 𝑁𝑏𝑜𝑙𝑡𝑠 is the number of present bolts, 𝐴𝑏𝑜𝑙𝑡 is the bolt area, 𝑓𝑦 is the bolt’s yield stress (assuming

metallic behavior), and 𝑑𝑖 is the distance to the axis perpendicular to the seismic acceleration direction (around the center of the tank). Once the acting moment is calculated, stability factor 𝐽 is computed with Equation 52 from API-650:

𝐽 =𝑀𝑟𝑤

𝐷2(𝑤𝑡(1 − 0.4𝐴𝑣) + 𝑤𝑎 − 0.4𝑤𝑖𝑛𝑡) (52)

Table 8. Stability criteria for the overturning of a storage tank [39].

Anchorage

Ratio 𝑱 Criteria

𝐽 ≤ 0.785 No calculated uplift under the design seismic overturning moment. The tank is self-anchored.

0.785 < 𝐽 < 1.54 Tank is uplifting, but the tank is stable for the design load providing the shell compression requirements are satisfied. Tank is self-anchored.

𝐽 > 1.54 Tank is not stable and cannot be self-anchored for the design load. Modify the annular ring if 𝐿 <0.035𝐷 is not controlling or add mechanical anchorage.

44

In this case, the compliance function is as given in API-650 presented in Table 8. The damage criterion is in function of the stability ratio. If 𝐽 exceeds the value established by the norm, it will be assumed that the tank has suffered damage by overturning.

3.4.4. Definition of Limit State Equations (LSE) The limit state Equations allows to determine if a system is exposed to an acceptable or unacceptable region. These Equations make a basic comparison between the resistance of the system (𝑅) under study

against a solicitation or external load (𝑆) [58]. Starting from this, to determine the probability of damage of a storage tank, it is necessary to establish a relationship to define if the tank will resist an external load or solicitation, product of the impact of a natural hazard. In the reliability and risk analysis the calculation of the probability of damage of a system is a fundamental factor to make future decisions.

The basic reliability problem proposed in the present work, makes a comparison between the resistance 𝑅 of a tank against a solicitation 𝑆 to which our system is subject. The following expression describes the moment at which a tank can be damaged by an external load:

𝑅 − 𝑆 ≤ 0 (53)

According with the last, the limit state Equation 𝑔(𝑅, 𝑆) will be represented by Equation 54 [59]:

𝑔(𝑅, 𝑆) = 𝑅 − 𝑆 ≤ 0 (54)

Since the hazards considered are from natural origin, the parameters used in the mathematical models present a random variability or uncertainty associated with the natural behavior of the hazards. This uncertainty is necessary to treat in order to obtain a probability of damage more accurate to reality. The following expression defines the probability of different types of damage for a storage tank:

𝑝𝑑 = 𝑝(𝑔(𝑅, 𝑆) ≤ 0) (55)

Considering the systems of interest for this work, the external load generated by the natural hazard is defined as the solicitation and the resistance forces of the tank as the resistance of the system. Table 9 presents each of the LSEs for each of the types of damage considered. Table 9. Limit state Equation for different types of damage.

Natural Hazard

Damage Mode Tanks

Resistance Solicitation LSE

Flood

Buckling 𝑃𝑟 𝑃𝑤 𝑔(𝑃𝑟 , 𝑃𝑤) = 𝑃𝑟 − 𝑃𝑤

Floatation 𝐹𝑓𝑐𝑟 𝐹𝑓 𝑔(𝐹𝑓𝑐𝑟 , 𝐹𝑓) = 𝐹𝑓𝑐𝑟 − 𝐹𝑓

Rigid Sliding 𝐹𝑠𝑐𝑟 𝐹𝑠𝑙𝑑 𝑔(𝐹𝑠𝑐𝑟 , 𝐹𝑠𝑙𝑑) = 𝐹𝑠𝑐𝑟 − 𝐹𝑠𝑙𝑑

Debris Impact 𝐹𝑟 𝐹𝑜𝑏 𝑔(𝐹𝑟 , 𝐹𝑖) = 𝐹𝑟 − 𝐹𝑜𝑏

Wind

Buckling 𝑃𝑟 𝑞𝑒𝑞 𝑔(𝑃𝑟 , 𝑞𝑒𝑞) = 𝑃𝑟 − 𝑞𝑒𝑞

Debris Impact 𝑡 𝐹𝑟

ℎ𝑝

𝐹𝑖

𝑔(𝑡, ℎ𝑝) = 𝑡 − ℎ𝑝

𝑔(𝐹𝑟 , 𝐹𝑖) = 𝐹𝑟 − 𝐹𝑖

Earthquake Buckling 𝜎𝑟 𝜎𝑐 𝑔(𝜎𝑟 , 𝜎𝜃) = 𝜎𝑟 − 𝜎𝑐

Overturning 𝑗 = 1.54 𝐽 𝑔(𝐽) = 1.54 − 𝐽

Each of the LSEs defined for the different damage modes will be evaluated within the probabilistic approach through Equation 55. Evaluating if a solicitation generated by the natural hazard is sufficiently strong to produce a damage to the tank. Below is the construction of the fragility curves from the damage probability.

45

3.5. Storage Tanks Fragility Analysis in NaTech Events. A common definition of fragility is "the quality of being easily broken or damaged". Kennedy et al. [60], was one of the first to introduce the concept of fragility in the engineering field, based on fragility functions for structures affected by earthquakes. Their fragility functions were defined as a probabilistic relationship between the frequency of damage of a structural component (in nuclear plants) and the peak ground acceleration of an earthquake. From this, a fragility function (Figure 35), can be defined as a mathematical function that expresses the probability that some unwanted event occurs (such as the damage of a process equipment or its elements) based on some measure of environmental excitation (solicitation or natural hazard intensity) [61].

Figure 35. Representation of a fragility function with a lognormal cumulative distribution [61].

To estimate the probability of damage of a storage tank by the impact of the natural hazards considered, a tool was designed and programmed together with the civil engineers Santiago, from the department of civil engineering at the Universidad de los Andes. The computational tool, called NaTech Tank Analyzer (NaTanks), was design using the mathematical software MATLAB R2016a. NaTanks allows to perform a fragility assessment for a single storage tanks associated with NaTech events. NaTanks is based on the methodology presented in Figure 8, in which with a characterization of the storage tank and the natural hazard, is possible to perform a probabilistic approach to obtain the fragility curve of the equipment associated with the NaTech event. The tool developed for the fragility assessment is presented in section 4 with the case study.

3.5.1. Fragility Curves To derive the fragility curves of a storage tank impacted by a natural hazard (step 5, Figure 8), NaTanks perform Monte Carlo simulations in order to deal with the uncertainty associated with the parameters of the models with natural random behavior. The fragility curves are a function of the damage probability, Figure 36 presents a diagram summarizing the general methodology to estimate the damage probability, based on an iterative process which seeks to treat the uncertainty of the parameters considered. Generally, the term probability is used in situations or affirmations to determine how close they are to reality, that is, that probability is a way of expressing the likelihood or change of occurrence of a reality. Applying this concept, the probability that a storage tank may suffer some type of damage due to the impact of a natural hazard will be estimated.

46

Figure 36. Methodology to calculate the damage probability of a storage tank integrating the uncertainty within a purely probabilistic framework.

Following the process presented in Figure 36, once the process equipment and the natural hazard have been established, the parameters of the models that present variability must be set. As mentioned above, several authors’ state that for each damage models develop, they estimated punctual values for parameters with uncertainty given their nature. Based on this, Table 10 presents the selected parameters with random behavior for each of the natural hazards, in addition to the statistical parameters for analysis. The parameters variability was complemented from historical data from different parts of the world, in addition to others suggested by different authors. Once the random parameters have been defined, the values of the other parameters that make up the models must be specified for each of the natural hazard. As presented in section 3.4., damage models are specified according to the impact vector (Tables 1), the geometry of the tank, the mechanical properties of the tank, the filling level and the density of the stored fluid. For parameters variability, the tool allows to select which values of the models will have uncertainty and assign the type of probability distribution for each parameter. The types of distribution included in the tool are: normal, uniform, lognormal, exponential, Weibull and gamma. For each of the parameters associated with natural hazards, the intensity scales established in section 3.1 were taken as reference.

47

Table 10. Parameters with random behavior for each natural event.

Parameter Unit Type of

distribution Mean (µ)

Coefficient of

variation (𝒄𝒐𝒗)

Flood

𝑘𝑑 - Normal Uniform

Lognormal Exponential

Weibull Gamma

1.8 1.8%

𝜌𝑤 𝑘𝑔/𝑚3 1100 9.1%

𝜌𝑓 𝑘𝑔/𝑚3 Density of the stored at 1atm and 25oC 9.1%

Wind Load

𝜌𝑊 𝑘𝑔/𝑚3 Normal Uniform


Weibull Gamma

Air density of the affected area 9.6%

𝜌𝑝 𝑘𝑔/𝑚3 Debris density 10.2%

𝜌𝑓 𝑘𝑔/𝑚3 Density of the stored at 1atm and 25oC 9.1%

𝐾𝑧 - 1.26 11.9%

𝐾𝑧𝑡 - 1.0 5%

𝐾𝑑 - 0.95 8.2%

Earthquake

𝜌𝑓 𝑘𝑔/𝑚3 Normal Uniform


Weibull Gamma

Density of the stored fluid at 1atm and 25oC 5%

𝐹𝑦 𝑃𝑎 Ultimate strength of the tank 5%

With the parameters and variables of both the natural hazard and storage tank defined, it’s possible perform a basic reliability problem to evaluate if the solicitation exceeds the resistance of the equipment. The following Equation set the calculation of the damage probability of a storage tank impacted by a natural hazard.

𝑝𝑑 =1

𝑁𝑠𝑖𝑚∑ 𝑔(𝑖)

𝑁𝑠𝑖𝑚

𝑖=1

=𝑁𝑑𝑁𝑠𝑖𝑚

(56)

𝑔(𝑖) = {1 𝑖𝑓 𝐿𝑆𝐸 ≤ 00 𝑖𝑓 𝐿𝑆𝐸 > 0

(57)

Where 𝑁𝑠𝑖𝑚 is the number of simulation or iterations of the Monte Carlo algorithm and 𝑁𝑑 is the number of iterations in which the damage criteria is met, Equation 57. The algorithm to calculate the damage probability is used independently for each of the types of damage proposed in Table 9. For example, the most common damage caused by the impact of a flood on a tank is the shell buckling. Figure 37 presents a pseudocode designed to calculate the probability of buckling damage. The pseudocode is based on multiple Monte Carlo simulations, as presented in the methodology of Figure 37.

48

% Definition of values that describes flood buckling model. % Tank: 𝐷, 𝐻, 𝑡, Ф, 𝐸, ; % Define parameters values of to estimate the tank resistance. % Hazard 𝑉 = speed value ; % Define the flood speed to estimate the solicitation.

𝑆 = linspace(Initial Height, Final Height, Height Variation) ; % Define the flood heights (vector) to estimate the solicitation. % Parameters with uncertainty 𝑁 = # ; % Number of iterations 𝑘𝑑 = Type of distribution (mean, standard deviation,[1,N]) ; % Generates random values for the hydrodynamic coefficient of water

𝜌𝑤 = Type of distribution (mean, standard deviation,[1,N]) ; % Generates random values for floodwater density.

𝜌𝑓 = Type of distribution (mean, standard deviation,[1,N]) ; % Generates random values for the store fluid

density. % Calculation of tank resistance pressure for i=:N 𝑃𝑓 = 𝜌𝑓(𝑖)𝑔𝐻Ф ; % Estimate the fluid pressure.

𝑃𝑐𝑟 =2𝐸𝑡

𝐷(

1

(𝑛2−1)(1+(2𝑛𝐻

𝜋𝐷)2)+

𝑡2

3𝐷2(1−𝜈2)(𝑛2 − 1 +

2𝑛2−1−𝜈

1+(2𝑛𝐻

𝜋𝐷))) ; % Estimate the resistance pressure of tanks

material

𝑃𝑟 = 𝑃𝑓 + 𝑃𝑐𝑟

end % Calculation of flood pressure. for i= length(𝑆)

for j=:𝑁 𝑃𝑤𝑠(𝑖) = 𝜌𝑤𝑔𝑆(𝑖) ; % Flood static pressure

𝑃𝑤𝑑(𝑗) = (1

2) 𝜌𝑤(𝑗)𝑘𝑑𝑉

2 ; % Flood dynamic Pressure

𝑃𝑤(𝑖, 𝑗) = 𝑃𝑤𝑠(𝑖) + 𝑃𝑤𝑑(𝑗) ; % Flood pressure end

end % Calculation of the damage probability for i= length(𝑆)

for j=:𝑁 𝑁𝑑(𝑖, 𝑗) = 𝑃𝑟 (𝑗) <= 𝑃𝑤1(𝑖, 𝑗) ; % Damage criteria (1 or 0). end

end 𝑝𝑑 = 𝑠𝑢𝑚(𝑁𝑑/𝑁) ; % Damage probability

Figure 37. Algorithm to calculate the probability of buckling damage in a tank impacted by a flood.

The algorithm presented in Figure 37 was applied in MATLAB -2016a mathematics software. Forming the basis of programming for the NaTanks tool design. Finally, if there is a probability of tank damage, it is important to know which of the possible failures are likely to occur in one of the tank's components. In the following section, the failure probability is established by the impact of a natural hazard.

3.5.1.1. Failure Probability The failure probability is associated with the way in which loss of containment is carried out. That is, the failure of some component of the tank will define the type of hole through which the stored fluid will leak. For example, the total collapse of a tank will have a material discharge with a type 1 release mode, which represents an instantaneous release of the entire content. In the event trees for each natural hazard, the release modes are defined for each of the failure modes. Additionally, in section 3.5.1.3., the dynamics for each of the release modes are defined.

49

At this point it is important to establish the difference between damage and failure. Damage is related to an affectation or malformation suffered by the tank, however, even if there is a probability that the tank could be damaged, it doesn’t mean that the material stored loss its containment. While the failure is associated with a crack or opening caused by a defect in the tank, by which the stored material will be release. From this, a dependence is established between the damage probability and the failure probability, where the damage of the equipment must first be given for its subsequent failure. To determine the failure probability of a component of the storage tank after the tank has suffered a damage, a historical data analysis was made from several databases (ARIA, FACTS, MHIDAS, MARS, ICHEME, NRC) that collect information related to industrial accidents caused by different natural hazards, complemented by studies conducted for NaTech events [19]. Table 11 summarizes the values obtained for each of the types of failure associated with the intensity classification of the natural hazard.

Table 11. Failure probabilities for different types of failure on storage tanks.

Failure Probabilities

Failure Mode Low Load Medium Load High Load

F W E F W E F W E

Collapse of the structure 0.20 0.00 0.00 0.20 0.08 0.10 0.10 0.10 0.13

Total connection failure 0.40 0.00 0.00 0.50 0.11 0.10 0.20 0.13 0.12

Partial connections failure 0.40 0.00 0.80 0.30 0.23 0.60 0.10 0.17 0.36

Shell rupture 0.00 0.00 0.00 0.00 0.32 0.10 0.40 0.40 0.27

Failure of the tanks roof 0.00 1.00 0.20 0.00 0.26 0.10 0.20 0.20 0.12

Where W is wind, F is flood and E is earthquake.

Particularly a floods have the place of impact from the base of the tank to the level of height of the flood wave, which is why at low and medium intensity there is no probability of failure in the elevated elements of the tank such as the upper shell courses or the roof. For winds, it is totally the opposite, since the thickness of the tank decreases in height, it is more likely that the upper elements of the tank will be affected by a wind load. Finally, earthquakes have the potential to cause failures in any tank element at medium and higher loads, depending on the level of tank filling.

3.5.1.2. Probit Functions to Estimate Damage Probability of a Storage Tank Due to the Impact of a Natural Hazard.

In this section, we present the calculation of the damage probability as a Probit function. As mentioned in the previous section, the behavior of the cumulative probability functions has a certain similarity to dose-response curves. In Crowl textbook [62], the Probit functions are used to estimate the probability to affect a living being or a structure (buildings or houses) by the exposure to a given dose. Among its most common uses, is the calculation of the probability of personal injury from fire, explosion or toxic dispersion. The present work will work Probit functions to estimate the damage probability of a tank affected by the impact of a natural hazard. This method consists in relating the affectation probability (damage) and the Probit points (Equation 58), yielding as a result, a linear function that allows to estimate the Probit points according to the dose (intensity of the event).

�̂� = 0.5 (1 +𝑌 − 5

|𝑌 − 5|) 𝑒𝑟𝑓 (

|𝑌 − 5|

√2) (58)

50

Figure 38. The probability cumulative function and the corresponding Probit function Y vs hazard intensity 𝐿𝑛(𝑉𝑖).

Due to the similarity between cumulative probability curves and dose-response curves. It can establish the vector of impact or intensity of the natural hazard as the dose, and the response, how probable to cause the tank to suffer some kind of physical damage due to the impact of the natural hazard. For the application

of the Probit model, Crowl textbook [62] proposes a logarithmic function which relates the Probit points (𝑌) with the intensity (𝑉𝑖) of each of the natural hazards, Equation 59.

𝑌 = 𝑘1 + 𝑘2 𝐿𝑛(𝑉𝑖) (59)

Where 𝑘1 and 𝑘2 are the constants of the model, and depend on the geometry of the tank and the type of

natural hazard and 𝑉𝑖 is the intensity parameter for each natural hazard, wind speed for wind loads, height and speed for floods and PGA for earthquakes. Figure 38 present a Probit function (blue line) for a tank impacted by a natural hazard. As mentioned above, a storage tank is designed to withstand high wind loads. This behavior will be evidenced in the study case, where a storage tank is only affected if it is empty or partially empty (less than 10% of the filling level). From this, a general probit function is proposed to calculate the probability of damage in a storage tank impacted by a wind dose. The function applies to tanks with a level close to 0%

and 10% and for substances stored with a density between 750 𝑘𝑔/𝑚3 and 1100 𝑘𝑔/𝑚3.

𝑌 = 𝑘1 + 𝑘2 𝐿𝑛(𝑉) (60)

To estimate the constants of Equation 60 multiple simulations of different tank configurations were performed, and through the method of least squares the following expressions are proposed to calculate the constants of the model according to the geometrical characteristics of the tank.

Probit constant for a completely empty tank:

𝑘1 = −143075,25𝑥2 + 3964,9𝑥 − 100,8 (61)

𝑘2 = 19043,4𝑥2 − 423,2𝑥 − 16,65 (62)

Probit constants for a tank with a 10% fill level.

𝑘1 = 714608,5𝑥

2 − 10999,8𝑥 − 63,996 (63)

51

𝑘2 = −72026𝑥2 + 1149,61𝑥 + 13,523 (64)

𝑥 = 𝐻𝑡/𝐷 (65)

Similarly, Nicolas Villalba [19] applied the Probit model in storage tanks impacted by flooding, proposed a logarithmic function to estimate the probability of damage by shell buckling of the tank, where the impact vector is defined by the flood speed (𝑉) and the flood height (𝑆). The model proposed by Villalba (Equation 66) is designed for any structural configuration of the tank and different levels of filling, however, it only applies to tanks that store fuels.

𝑌 = 𝑘1 + 𝑘2 𝐿𝑛(𝑉) + 𝑘3 𝐿𝑛(𝑆) (66)

Finally, Giovanni Fabbrocino et al. [63] performed a quantitative risk analysis associated with seismic events that affect storage facilities. Their proposed methodology uses the Probit method to estimate the probability of failure due to the collapse of a storage tank. Fabbrocino proposes a Probit model based on the 𝑃𝐺𝐴 of an earthquake, applicable for anchored and not anchored storage tanks.

𝑌 = 𝑘1 + 𝑘2 𝐿𝑛(𝑃𝐺𝐴) (67)

During the development of the Probit functions, as well as for the fragility curves, the treatment of uncertainty associated to the parameters of the models, are used to calculate the different damage probabilities. This process is carried out to consider the natural behavior of those parameters. The above will improve the results of the risk calculation in NaTech events in storage facilities.

3.5.1.3. Vulnerability Analysis for a Tank Impacted by a Natural Hazard In seismic engineering, vulnerability is defined as the degree of loss of an element or group of elements, under risk resulting from an earthquake of a given magnitude or intensity [58]. Some important aspects to perform a vulnerability assessment of as process equipment are (step 6, Figure 8): 1) the evaluation criteria, which refer to the strength and form of the equipment, so that the process equipment has the capacity to maintain its integrity and functioning. 2) The type of loss, such as reduction in the capacity to provide a service, number of injured, lost stored material, repair costs, among others. 3) Scenarios of losses, these tend to be the most probable or frequent final events, or the one that entails maximum social or economic consequences. Vulnerability is commonly measure as the percentage or degree of loss of a system based on an event. It is important to state that vulnerability is not fragility, vulnerability measures loss, while fragility measures probability. So the vulnerability functions refer to damage functions, loss functions and vulnerability curves [61]. The type of loss that will be evaluated in the present work is the loss of containment of the stored material. A loss of containment can generate different scenarios such as explosions, fires or toxic dispersions. Which can cause serious consequences in the surroundings (people, structures, and environment). Each of these scenarios have different effects, a fire can produce high heat radiation, an explosion can generate an overpressure in the atmosphere and a dispersion can generate toxicity levels highly harmful to living beings. For the estimation of the loss of containment in methodologies for risk analysis in NaTech events, conventional models are commonly used. This work focuses on the loss of containment of hazmats in liquid state. Considering the above, the volume of spilled material will be the parameter that will allow the assessment of the aforementioned scenarios in the future. To estimate the amount of material released after the system has been damaged, it is necessary to establish the different modes of material release. Some guidelines and international standards have established

52

release modes for different types of process equipment [64]–[66]. Based on these studies, the release modes for atmospheric storage tanks are: • Release Mode 1: Instantaneous release of entire contents. • Release Mode 2: Release of entire contents in 10 min in a continuous and constant stream. • Release Mode 3: Continuous release from a hole with an effective diameter of 10 mm. The detailed event trees in annexes presents the release modes for each of the types of failure in the different natural hazards. Once the release modes have been identified, they should be related to the types of failure caused by a damage of a storage tank. The event tree (Figure 19), we present the different types of failure considered for the types of damage established, it should be noted that not all modes of release are related to the types of failure, the release mode will allow to estimate the volume of spilled material stored. Once the release modes are established, source models or release models are used, which describe the material release process. Crowl [62] and the National Institute of Public Healt and the Environment [66] propose different methods to calculate the material released. For release mode 1, no model is developed since it is an instantaneous total discharge. For release mode 2, is necessary to establish what type of failure causes the LOC, that is, it can be failure due to total rupture of the connections or rupture of tanks shell. The release by both failures can be modeled as a flow through an orifice, the difference lies in its discharge coefficient. In the total rupture of the connections the diameter of the pipe or connection is known, while the rupture of the shell of the tank or a partial failure of the connections has an indefinite orifice geometry. The release mode 3, can also be modeled as a leak through a hole, because the model is flexible with the size of the orifice. To model the flow of a liquid through a hole in a tank 𝑄𝑚 (𝑘𝑔/𝑠), we start from the principle of conservation

of mass and a mechanical energy balance. Where ℎ𝐿0 represents the height at which the release hole is

located. To calculate the leakage flow at any time, Equation 68 is used [62]:

𝑄𝑚 = 𝜌𝑓𝐶𝑜𝐴√2 (𝑔𝑐𝑃𝑔

𝜌+ 𝑔ℎ𝐿

0) −𝜌𝑓𝑔𝐶𝑜

2𝐴2

𝐴𝑡𝑇 (68)

Where 𝜌𝑓 is the stored fluid density (𝑘𝑔/𝑚3), 𝐶𝑜 is the release coefficient, 𝐴 is the orifice area, 𝑔𝑐 is the

gravitational constant (𝑚∗𝑘𝑔𝑚

𝑘𝑔𝑓∗𝑠2), 𝑃𝑔 is the gauge pressure (𝑃𝑎), 𝑔 acceleration due to gravity (𝑚/𝑠2), ℎ𝐿

0 is the liquid

height above the leak (𝑚), 𝐴𝑡 is the surface area of the tank (𝑚2) and 𝑇 is the release time (𝑠). The decrease of liquid stored over time is determined by the following Equation:

ℎ𝐿 = ℎ𝐿0 −

𝐶𝑜𝐴

𝐴𝑡√2(

𝑔𝑐𝑃𝑔

𝜌𝑓+ 𝑔ℎ𝐿

0𝑇) +𝑔

2(𝐶𝑜𝐴

𝐴𝑡𝑇)

2

(69)

The Equation 70 determine the emptying time of the tank up to the level of discharge orifice 𝑇𝑒 (𝑠).

𝑇𝑒 =1

𝐶𝑜𝑔(𝐴𝑡𝐴) [√2 (

𝑔𝑐𝑃𝑔

𝜌+ 𝑔ℎ𝐿

0) − √2𝑔𝑐𝑃𝑔

𝜌] (70)

Finally, to estimate the total volume release 𝑉𝐿 (𝑚3), the following Equation is used:

𝑉𝐿 = ∫ 𝑄𝑚𝑑𝑡𝑇𝑒

0

(71)

53

Equations 68-71 estimate the volume of unplanned spilled hazardous material. These Equations represent a good approximation to calculate the volume leaking through a hole in a storage tank. The volume of spilled material is important since the estimation of the consequences will depend on this value. Among the most common consequences is the environmental contamination by liquid dispersion or toxic cloud, fire of flammable material or explosions. According with the last, the greater the amount of spilled volume, greater the consequence associated with the NaTech event.

3.5.1.4. Frequency of Final Accidental Scenario As can be seen in the event tree, a NaTech event is limited by the occurrence of a series of situations that lead to the loss of containment of a Hazmat. The calculation of the probability of the final accidental scenario 𝑝𝑎𝑠 is determined by the combination of secondary events of the tree branches, Equation 72.

𝑝𝑎𝑠 = 𝑝𝑑 ∗ 𝑝𝑓 (72)

Based on this, the frequency of the final accidental scenario 𝑓𝑎𝑠 (1/𝑦𝑒𝑎𝑟) will be the multiplication of the frequency of the initiating event 𝑓 by the probability of the accidental scenario 𝑝𝑎𝑠, as shown in Figure 13.

𝑓𝑎𝑠 = 𝑓 ∗ 𝑝𝑎𝑠 (73)

The Center for Chemical Process Safety (CCPS) defined the risk for industrial accidents, as the measure of economic, human or environmental losses, in terms of the probability of occurrence or frequency of the incident and the magnitude of the losses or injuries. From this, the calculation of the frequency of the final accidental scenario is fundamental given that it is an input parameter for the risk calculation. The frequency must be related to the consequences, which are a function of the volume of hazmat spilled.

4. Case Study The proposed methodology for fragility assessment was applied to a vertical storage tank (Figure 39) of a petrochemical industry located on the Caribbean coast. The tank works at atmospheric conditions. Table 13 shows the configuration of tank TK-201, also in Figure 40 the parameters are present within the NaTanks tool.

Table 12. Storage tank configuration (TK-201) according to API-650.

Parameter Unit Value

Diameter m 60.69

Height* m 12.192

Steel Grade - 275

Thickness mm 7.94-25.4

Stored fluid - Gasoline

Filling degree (%) 50

Typo of Roof - Dome

Roof Thickness mm 7.94

Dome Radius m 30.345

Bottom plate thickness mm 14

Anchorage - None

Floating Roof - None

* Based on the height of each shell course of the tank.

Figure 39. Location of the storage tank under study, Caribbean

coast.

54

4.1. Storage Tank TK-201 Characterization Figure 40 shows the interface of the NaTanks tool, which is basically composed of 3 tabs. In the first tab is required to define the input parameters for the characterization of a storage tank. As mentioned above, the sizing of a tank is based on the API-650 standard, from this, the sizing of a tank will be based on the 3 main components, the shell, the roof and its base. The necessary characteristics of the shell of the tank are obligatory, it is required to specify the geometric dimensions of the tank. The parameters regarding the roof and the base are optional, given that a tank may or may not have a roof (fixed or floating) and its base may or may not be anchored (including the concrete ring). Below is the required information:

Shell: Diameter, height (based on tank course levels), thickness (for each ring) and material.

Roof: Type of roof (roof or conical), roof thickness, support for fixed roof, floating roof, type of floating roof seal.

Base: Anchor to the ground, number of anchor bolts and their diameter, thickness of the bottom plate and concrete ring.

Figure 40. NaTanks first tab: Sizing of a storage tank based on API-650.

55

It is important to note that the height of the tank is based on the height of each one of the courses that make up the storage tank. In total the tank has 5 courses, with heights and thicknesses defined for each one, Figure 41 specified the parameters for each course of the storage tank. This information is entered by clicking on the "Specify Shell Courses" button of the NaTanks tool. The NaTanks tool is designed to perform the fragility assessment to a single storage tank. Since a natural hazard tends to cover large areas, this tool gives a first approach to estimate if a storage tank could be damage, and to infer whether a tank near the one studied could also be damaged. The information fed in the first tab of the NaTanks tool allows to estimate the resistance forces of the storage tank, given that each of its components adds a factor of resistance or stability to the structure, in addition to the operating conditions, where the level Filling plays an important role for the tank when is impacted by the natural hazard.

Figure 41. Heights and thicknesses for each course of the storage tank TK-201.

Through the “Plot Tank Geometry” button it is possible to draw the order and dimension of the tanks shell. Presents the distribution of shell courses and shows the diameter/height ratio. Figure 42 shows a preview of the TK-201 entered in NaTanks.

Figure 42. Geometry of tank shell TK-201.

56

La herramienta NaTanks es flexible en cuanto al tanque para analizar, dado que su configuración se realiza en base a características mecánicas y geométricas, NaTanks permite establecer tanto tanques nuevos como existentes. Con base a esto, se pueden tomar decisiones respecto al diseño del equipo antes de su construcción dado que ha sido evaluada su resistencia frente al impacto de un peligro natural.

4.2. Wind Hazard Characterization The characterization of the natural hazards considered in the present work were presented in section 3.1. The intensity of a flood is defined by the height and speed of the wave. An earthquake is classified according to the PGA and a wind load is defined by the wind speed at a set height. The second tab of the NaTanks tool performs the characterization of each of these natural hazards, as shown in Figure 43. This section of the tool allows to calculate the load generated by each natural hazard on the storage tank. Figure 43 presents the characterization for a flood with wave speed of 9 𝑘𝑚/ℎ and wave height of 3 𝑚, which has a high risk classification.

Figure 43. NaTanks second tab: flood characterization based on the speed and height of the wave.

57

In the annexes, the wind load generated by Hurricane Katrina, which reached a category 5 on Saffir/Simpson scale, is presented (annexes, Figure 51). Additionally, an earthquake of magnitude 9, equivalent to the earthquake that shook the Tohoku coast in 2011, which reached a PGA of 99 % 𝑔 (annexes, Figure 52).

4.3. TK-201 Fragility Curves Figure 44 present the fragility curves for TK-201 (50% filling level) impacted by flood solicitations. The results shows, as the flood becomes deeper, the probability of buckling damage increases. It is expected that if the speed of the flood decreases, the probability profile moves to the right and therefore the probability of damage decreases, because the pressure exerted by the flood will be proportional to the speed of the flood. When the speed decreases, the depth of the flood must increase to replace the gradient of pressure delivered by the speed. Unlike a wind load, shell buckling by flood is more likely to occur in the lower part of the tank, since this part is the one in contact with the floodwater. Possibly causing the rupture of the shell or the pipes connections and therefore the loss of containment. Figure 44 shows the tab of the NaTanks tool where the fragility curves are obtained for a certain type of damage associated with a storage tank impacted by a selected natural hazard. As you can see, the tool allows to define the type of damage to evaluate, the hazard intensity and the number of iterations for the Monte Carlo simulation. The curves correspond to tank TK-201, defined in Table 12. Once Monte Carlo simulations finished, the damage probabilities for a given structural configuration of a tank (TK-201) and different hazard intensities are obtained. With these results it is possible to obtain the fragility curve whose behavior can be observed in Figure 44. It is important to note that the fragility analysis is made for a storage tank and a single natural hazard. The tool does not perform multi-hazard analysis, that is, several natural events at the same time. Additionally, Table 13 shows the fragility curve by buckling damage and rigid sliding for TK-201 at different fill levels. It is observed how increasing the filling level of less likely to suffer buckling damage, given that the stored liquid adds an additional resistance factor to the tank, and therefore a greater intensity of the hazard is required to affect it. Significantly important result to make decisions about the operating conditions for a tank located in a flood prone area. For rigid sliding case, as the impact vector of the flood increases, the curve moves to the left, from this it’s possible to conclude that filling the tank to a higher level, the tank will be less prone to suffer the damage. These results are consistent with the system since it is expected that as the impact of the flood increases, the tank is more likely to be damaged.

58

Figure 44. NaTanks third tab: fragility curves for NaTech Events.

To understand the threat posed by each of the natural hazards on the configuration of the tank TK-201 established above, the fragility curves of the tank impacted by the three natural hazards were derived. The type of damage to be evaluated is the same for all cases, buckling of the walls of the tank.

59

Table 13. Fragility curves for tank damage due to different natural hazards.

The flood speed is 2.5 m/s (9 km/h).

The filling level of the tank is 20 %.

Table 13 shows the fragility curves for buckling damage by extreme winds, as the wind speed increases the probability of damage by shell buckling increases as well, this is because when the wind speed increases, the pressure or load on the storage tank also increases. Additionally, it can be observed how the filling level of the tank significantly influences in the probability of damage. When the tank is completely empty, less wind speed will be needed to produce the damage. As for the flood case, by filling the tank at a level of 10%, this stored liquid gives the tank additional resistance thanks to his weight, causing the need of greater wind speeds to produce buckling of the tank’s shell. Additionally, the fragility curves for buckling damage of the TK-201 impacted by an earthquake are presented. As the peak ground acceleration increases, the probability for the tank to suffer shell buckling (elephant foot) damage increases. As can be seen, the filling level has a direct impact on the probability of damage (like in floods and wind loads), as the tank is more full, the pressure exerted by the fluid on the shell will increase and the excited mass increases significantly, causing greater shear forces and overturning moments to be exerted on the tank’s structure. That said, it is more likely that the shell buckling damage occurs in the lower part of the tank, forming the elephant foot, due to the exerted compression stress accumulating in the first shell course of the tank.

60

The results presented above agree with cases reported in literature. In a study conducted by Godoy [45], presented the different damages caused by the passage of Hurricane Katrina and Rita over several storage areas, where the natural hazard conditions were similar to those evaluated in the present case study. In the

study performed by Godoy, the tanks presented damage by floods with heights of up to 5 𝑚 and speeds of up to 8 𝑚/𝑠. In the case of winds, the tanks presented damage for wind speeds higher than 160 𝑘𝑚/ℎ. Additionally, Godoy identifies two important factors that significantly influence equipment damage, the filling level and tank anchoring. The fuller the tank is, the greater the stability against an external load, and the anchoring of the tank will give greater resistance to being moved by the load of both wind and flood forces.

Figure 45. Probability of damage due to buckling of the TK-201

(O=0%) impacted by a wind load represented by a Probit function.

Figure 46. Probability of damage due to debris impact of an empty

TK-201 represented by a Probit function.

Figures 45 show the probability of buckling damage due to a wind load over tank TK-201 established above (Equivalent to the fragility curves presented in Table 13), the different curves presented are for the tank loaded with 4 different filling levels. Figure 46 shows the probability of damage by the impact of debris drag by the wind over the tank, the Probit points are a function of the number of Johnson which depends on both the impact speed and the mass of the debris. Finally Figure 47 and 48 shows the possible amount of hazmat spilled due to shell rupture failure.

Figure 47. Flow of spilled gasoline due to TK-201 failure caused by

flood.

Figure 48. Volume of spilled material vs. release time due to TK-

201 failure caused by flood.

61

Considering the study case carried out in the NaTanks tool, the following is the calculation of the frequency of the final accidental scenario corresponding to the impact of a flood of 2.3 𝑚 high and velocity of 3 𝑚/𝑠 on the TK-201 with a filling level of 50 %.

Table 14. Accidental scenario establish with event tree.

Risk Information Unit Value

Asset at risk - TK-201 ()

Stored Fluid - Gasoline

Flood height 𝑚 2.3

Flood Speed 𝑚/𝑠 3

Return period 𝑦𝑒𝑎𝑟 500

Damage mode - Shell Buckling

Damage probability % 53.2

Failure mode - Shell Rupture

Failure Probability % 40

Frequency of final accidental scenario 𝟏/𝒚𝒆𝒂𝒓 𝟒. 𝟐𝟓𝟔 ∗ 𝟏𝟎−𝟒

Spilled volume 𝒎𝟑 13228

The calculation of the final accidental scenario (Table 14) takes into account the uncertainty associated with the input parameters of the natural hazard models for the calculation of the damage probability, so that the natural behavior of these parameters is taken into account. These results will improve the risk analysis associated with NaTech events caused by different natural hazards, given that the values found are input to quantitative risk methods. NaTech events are industrial accidents whose probability of occurrence is significantly low. However, when these types of events materialize, they have great consequences both for the nearby population, the environment and the company's infrastructure due to the loss of containment of the stored material. Based on this, it is very important to understand the risks presented by this type of events in order to better support decision-making when exist the possibility that an industrial facility suffers the load of an extreme natural event. Considering that risk analyzes are commonly carried out for mechanical failures or human errors, now with the proposed methodology it is possible to include events of natural origin in the classic risk analyzes for industry.

62

Conclusions The focus of this work is to analyze the undesired events that can occur if a vertical storage tank could be damage during an extreme natural event. To evaluate the fragility or damage probability in a vertical storage tank impacted by a natural hazard, a systematic methodology was proposed which integrates both qualitative and quantitative information, related to the NaTech scenario evaluated. It allows a researcher to perform a preliminary fragility and vulnerability assessment associated with NaTech events integrating both the parameterization of a storage tank based on the API-650 and API6-620 standards and the solicitation of different natural hazards according to damage models or international standards, this integration allows an easy application in the industrial sector. The proposed methodology consider the variability or uncertainty of parameters associated with the process equipment and natural hazard. Additionally, the probability of damage is associated to the possible accidental scenario, determined using event trees, which present a series of situations that materialize in sequence to cause the loss of containment of the liquid stored in the tank. The event tree was implemented for each of the natural hazards considered, where different types of damage that each hazard can cause were identified. The integration of all the information used in the methodology for the fragility assessment allows to obtain results more accurate to reality, considering both the information of the equipment at risk and the hazard behavior. To estimate the damage probability of a storage tank due to the impact of a natural hazard, a simple computer tool called "NaTech Tank Analyzer (NaTanks)" was designed, which follows the proposed methodology for fragility analysis. This tool allows to integrate both the storage tank parameterization and the natural hazard characterization. Additionally, create fragility curves and Probit curves from synthetic data obtained from the uncertainty treatment associated with the input parameters to each of the models considered. The treatment of the uncertainty was carried out through Monte Carlo simulations, which allow the calculation of the damage probability in any structural configuration of the tank (new or existing) against the intensity or impact vector of the natural hazard. The tool is designed in such a way that the user can define the number of simulations he wants to perform, where by increasing his value will obtain results closer to reality and the curves will be finer. Through the fragility curves, its transformation to Probit functions was carried out, in such a way, Probit models are propose for storage tanks impacted by floods, extreme winds and earthquakes, which allows to estimate the damage probability from the geometric characteristics of the tank and the hazards solicitation. The case study implemented in NaTanks tool, aims to represent the conditions of real infrastructure of a storage tank, results coming from each of the studied hazards (wind loads, hydraulic loads, and seismic forces) were computed and validated. The results regarding the validation of the models show that the physical characteristics and the operation level of the tank, significantly influence the stability of the equipment when impacted by the natural hazard, behavior reflected in the fragility curves obtained. Furthermore, the proposed loss methodology was used to estimate the expected losses due to the applicable damages in the tank’s structure. Finally, this lead to the computation of risks and expected consequences for the input hazards, which is of great value in order to feed risk mitigation frameworks present by different studies. The proposed methodology integrates the design parameters of storage tanks under API-650 and API-620 standard, and the natural hazard solicitation base on validated models, in order to calculate the probability of damage, estimates the probability of failure and estimate the volume of loss of containment as a consequence of natural hazard flows, such as floods, extreme winds and earthquakes.

63

Acknowledgement Mainly to God for allowing me to do my postgraduate studies. Many people have contributed to the process and conclusion of this work. I thank my family, my mother Martha, my father Jesus and my brothers Julian and Daniel for their unconditional support from start to finish in my engineering graduate, to my co-workers for their immense help at different times. I also have a special thanks to the people who worked directly in the development of this study in NaTech events, my thesis director Felipe Muñoz for his constant guidance and advice in two years of work. Engineer Santiago Zuluaga and Professor Mauricio Sanchez for the great effort in the construction of the NaTanks computer tool. And finally, but not least, Professor Ernesto Salzano and Jean-Paul Pinelli for their invaluable knowledge and shared advice to successfully finish this work. To all infinite thanks.

64

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Annexes

Figure 49. Event tree to identify the events sequence of a storage tank impacted by a flood depending on the water speed and depth.




Water Depth



Floatation Partial connection failureMode 2


Impact by Debris Partial connection failureMode 2





Water Speed



Rigid Sliding Partial connection failureMode 2

Buckling Partial connection failureMode 2



Without Affectation



68

Figure 50. Event tree to identify the events sequence of a storage tank impacted by an earthquake depending on the peak ground acceleration.


(Elephant Foot)


Overturning Partial connection failureMode 2



PGA

Buckling Partial connection failureMode 2



Without Affectation



69

Figure 51. NaTanks second tab: wind load characterization based on the wind speed.

70

Figure 52. NaTanks second tab: earthquake characterization based on the peak ground acceleration (PGA).

Documents

Fragility Assessment Methodology of Storage Tanks in