Depressurization Dynamic Modeling and Effect on Flare

University of Calgary

PRISM: University of Calgary's Digital Repository

Graduate Studies The Vault: Electronic Theses and Dissertations

2016

Depressurization Dynamic Modeling and Effect on

Flare Flame Distortion

Shafaghat, Ali

Shafaghat, A. (2016). Depressurization Dynamic Modeling and Effect on Flare Flame Distortion

(Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/25558

http://hdl.handle.net/11023/2905

master thesis

University of Calgary graduate students retain copyright ownership and moral rights for their

thesis. You may use this material in any way that is permitted by the Copyright Act or through

licensing that has been assigned to the document. For uses that are not allowable under

copyright legislation or licensing, you are required to seek permission.

Downloaded from PRISM: https://prism.ucalgary.ca

UNIVERSITY OF CALGARY

Depressurization Dynamic Modeling and Effect on Flare Flame Distortion

by

Ali Shafaghat

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF ENGINEERING

GRADUATE PROGRAM IN CHEMICAL AND PETROLEUM ENGINEERING

CALGARY, ALBERTA

APRIL, 2016

© Ali Shafaghat 2016

ii

Abstract

The aim of equipment depressurization in an upset operation is to maintain the internal pressure

of the vessels and piping below the rupture pressure, as the material ultimate tensile strength

decreases with temperature tolerance beyond the acceptable limit. Depressurizing also causes to

decrease the extent and duration of leaks that may occur as a result of mechanical failure. In the

case of ignition and fire, a depressurization system can limit the fuel supply to the fire. In addition,

the main objective of the pressure relief facilities is to keep personnel safe as well as equipment

exposed to overpressure conditions that happen during process upsets. This thesis is intended to

examine the modeling of depressurization in different scenarios, evaluate flare flame distortion

and heat radiation as the most important consequences of this event, and consequently offer some

recommendations for the design of any gas plant that has potential for overpressure.

iii

Acknowledgements

First and foremost, I would like to declare deep appreciation to my supervisor professor Alex De

Visscher, for his support, value knowledge, and criticism during the course of my Master study

and research. His extensive knowledge, and his value book helped me from the first point to the

end of my research for developing and preparation of my thesis.

I am extremely thankful to my dearest wife, Samaneh Golpich, for her love, kindness and

motivation and encouragement in many respects through my studies. Besides, I would like to

express deep thankful to my parents and my brothers for their support and encouragement.

iv

Dedication

Dedicated to my gentle-hearted and beloved wife, Samaneh Golpich.

v

Table of Contents

Abstract ............................................................................................................................... ii Acknowledgements ............................................................................................................ iii Dedication .......................................................................................................................... iv Table of Contents .................................................................................................................v List of Tables .................................................................................................................... vii

List of Figures .................................................................................................................. viii List of Symbols and Abbreviations.................................................................................... xi 1 Chapter One: Introduction ........................................................................................17 2 Chapter Two: Literature Review ..............................................................................21

2.1 MAJOR SOURCE OF OVERPRESSURE AND RELIEF SCENARIOS ...............21

2.2 PRESSURE RELIEVING DEVICES.......................................................................22

2.2.1 Pressure relief valves .......................................................................................22 2.2.2 Rupture Disks...................................................................................................23

2.3 DEPRESSURIZATION SYSTEM ...........................................................................23

2.4 FLOW AND LEVEL CONTROLS ..........................................................................24 3 Chapter Three: Dynamic Modeling of Depressurization ..........................................27

3.1 MATERIAL AND ENERGY BALANCES .............................................................27

3.1.1 Modeling of High Pressurized Gas Discharges Across the Orifice .................29 3.1.2 Calculation of the vessel wall temperature ......................................................32

3.2 VALVE CORRELATIONS AND EQUATIONS USING FOR DYNAMIC

CALCULATION ......................................................................................................33 3.2.1 General valve equation ....................................................................................33

3.2.2 Supersonic valve equation ...............................................................................35 3.2.3 Subsonic valve equation ..................................................................................35

3.2.4 Masoneilan valve equation ..............................................................................36 3.2.5 Fisher / Universal gas sizing equation .............................................................37

3.3 CHARACTERIZATION OF DISCHARGES OF LIQUEFIED PRESSURIZED

GASES ......................................................................................................................37

3.3.1 Numerical Process to Determine Discharge Flow Type from the Vessel .......38 3.3.2 Modeling Discharge Flow of LPG Across the Vessel Holes ...........................47

3.4 PREDICTION OF DISCHARGE GAS FROM PIPELINES DUE TO RUPTURE 49

3.5 RELIEF SCENARIOS ..............................................................................................52 3.5.1 Fire case ...........................................................................................................52 3.5.2 Adiabatic case or cold depressurization ...........................................................54

vi

4 Chapter four: Flare Flame Distortion and Heat Radiation Modeling .......................56

4.1 PROCESS FLARES .................................................................................................56 4.1.1 Warm Flare System..........................................................................................56 4.1.2 Cold Flare System ............................................................................................56 4.1.3 Storage Tank Area Flare System .....................................................................57 4.1.4 Sour Gas Flare System .....................................................................................57

4.2 MODELING OF THE FLARE FLAME DISTORTION .........................................57 4.2.1 Calculation of Flare Diameter, Stack Height, and Flare Flame Distortion ......57

4.3 MODELING OF HEAT RADIATION FROM FLARE FLAME DURING

DEPRESSURIZATION ............................................................................................61 4.3.1 Determination of Jet Flare Flames at Flare Tip ...............................................65 4.3.2 Determination of the View Factors ..................................................................76

4.3.3 Mudan Model for Determination of View Factor ............................................77 4.3.4 Determining the view factors with consideration of the crosswind way .........78

5 Chapter Five: Depressurization Dynamic Calculation .............................................80

5.1 DEPRESSURIZATION DYNAMIC CALCULATION ..........................................80 5.1.1 Adiabatic Depressurization Study/Cold Depressurization ...............................81

5.1.2 Adiabatic case ..................................................................................................84

5.2 FIRE CASE DEPRESSURIZATION .......................................................................87

5.2.1 Adiabatic and fire case with different composition .........................................90 5.2.2 Adiabatic and fire case for liquid Methane ......................................................95

5.2.3 Dynamic calculation for determination of flare flame distortion and heat radiation

101

5.3 A CASE STUDY FOR PIPELINE .........................................................................108 6 Conclusion and Future Work ..................................................................................111

6.1 CONCLUSION .......................................................................................................111

6.2 FUTURE WORK ....................................................................................................114 7 References ...............................................................................................................115 Appendices .......................................................................................................................122

Appendix A: Determination of the Darcy Friction Factor fD ......................................122 Appendix B: Auxiliary Equation Buoyance flux parameter De Visscher Air Dispersion

modeling book ......................................................................................................124

Appendix C: Excess Data and Figures ........................................................................125 Appendix D: Fort McMurray Historical Wind Speed .................................................126 Appendix E: Mollier diagram ......................................................................................127

vii

List of Tables

Table 5-1 : Temperature data between years\ 1981 and 2010 in Fort McMurray, Alberta.81

Table 5-2 Assumption for adiabatic depressurization for methane gas .............................83

Table 5-3 Table 5-3: Assumptions for fire case depressurization for methane gas ...........86

Table 5-4: Assumption for adiabatic and fire case depressurization .................................89

Table 5-5: Depressurization in 15 min considering Fire API, CV 16.88 USGPM (60F, 1psi) and

Masoneilan valve ...............................................................................................................90

Table 5-6: Depressurization in 15 min considering Adiabatic, Cv 16.88 USGPM (60F, 1psi) and




Table 5-8: Assumptions for adiabatic and fire depressurization for liquid methane .........94

Table 5-9: Results for depressurization liquid methane at saturated pressure in 30 min Fire

API521 case by masoneilan valve .....................................................................................95

Table 5-10: results for depressurization, 100% opening by universal gas sizing/Fisher valve for

adiabatic case 30 min.. .......................................................................................................96

Table 5-11: Assumptions for flare flame distortion calculation ......................................100

Table 5-12: Flare tip exit velocity ....................................................................................103

Table 5-13: Results for flare flame length .......................................................................107

Table 5-14: Assumptions for Pipeline case study ............................................................107

Table C.1: Critical properties of some component (Reid et al., 1987) ............................124

Table D.1: Wind speed data represent the FortMcmurray ,Alberta .................................125

viii

List of Figures

Fig 2-1: Usual level control ...............................................................................................24

Fig 3-1: Discharge coefficient ...........................................................................................34

Fig 3-2: Schematic view of level blow up in a depressurizing vessel filled with liquefied

pressurized gas [Wilday, 1992] ..........................................................................................37

Fig 3-3: Tow phase flow pattern separately schematic ......................................................39

Figure 3-4: Flow regime transition criterion for upward two-phase flow in vertical tube 39

Fig 3-5: Adiabatic process [https://en.wikipedia.org/wiki/Adiabatic_process] .................54

Fix 4-1: Flare Stack And Flame Distortion Geometrical Factors[API521] .......................58

Fig 4-2: Absorption factors for water vapour ....................................................................63

Fig 4-3: Carbon-dioxide absorption factor ........................................................................64

Fig 4-4: quadrilateral flare flame shape (Chamberlain, 1987) ..........................................68

Fig 4-5: Geometrical factors for determination of lifted-off flare fames ...........................75

Fig 5-1: Depressing in 15 min adiabatic considering Masoneilan valve fully open ..........84

Fig 5-2: Depressing in 30 min adiabatic considering Masoneilan valve fully open ..........84

Fig 5-3: Depressurization in 15 min considering Fire API 521 and Masoneilan valve fully open

............................................................................................................................................87


............................................................................................................................................87

Fig5-5: Depressurization in 15 min considering Fire API, CV 16.8 USGPM (60F, 1psi) and


ix

Fig5-6: Depressurization in 15 min considering Adiabatic, CV 16.88 USGPM (60F, 1psi) and


Fig 5-8: Depressurization in 30 min considering Adiabatic, Cv 16.88 USGPM (60F, 1psi) and


Fig 5-9: Depressurization liquid methane at saturated pressure in 30 min Fire API521 case by

masoneilan valve ................................................................................................................95

Fig 5-10: Depressurization, 100% opening by universal gas sizing/Fisher valve for adiabatic case

30 min with CV equal to 21.48 USGPM (60F, 1psi).........................................................96

Fig 5-11: Depressurization 30 min adiabatic liquid methane by universal gas sizing/fisher valve

with 20% opening with CV 21.48 [USGPM (60F, 1psi ....................................................97


with 20% opening with CV 21.48 USGPM (60F, 1psi) ....................................................95

Fig 5-13: Depressurization 15 min adiabatic liquid CH4 by fisher valve with 30% opening and

CV21.48 [USGPM (60F, 1psi)]. ........................................................................................98

Fig 5-14: Mach number versus time in steady state (blue) and dynamic (red) calculation103

Fig 5-15: Flare exit velocity versus time. ........................................................................101

Fig 5-16: Heat radiation versus time at the time of depressurization by Chamberlin method.

..........................................................................................................................................102

Fig 5-17: Heat radiation versus time at the time of depressurization by API method. ... 103

Fig 5-18: Allowable design limit for flare system modeling and calculation [API 521] 104

Fig 5-19 Flare flame distortion from top view at normal condition, Chamberlain method105

Fig 5-20: Flare flame distortion from top view at normal condition API method ...........105

x

Fig 5-21: Flare flame distortion from top view at the time of depressurization Chamberlain

method..............................................................................................................................106

Fig 5-22: Flare flame distortion from top view at the time of depressurization by API method

..........................................................................................................................................106

Fig 5-23: Mach number versus distance in pipeline ........................................................108

Fig 5-24: Temperature versus distance in pipeline ..........................................................108

Fig 5-25: Pressure versus distance in pipeline .................................................................109

Fig A.1 Friction factor for flow in pipes by Moody chart ...............................................122

Table C.1: Critical properties of some component (Reid et al., 1987) .................................124

Fig C.2: Characteristics of control valve flow with piping losses ...................................124

Table D.1: Wind speed data represent the FortMcmurray ,Alberta .................................125

Fig E.1: Mollier diagram, an enthalpy–entropy versus pressure (GPSA 12 edition) ......126

xi

List of Symbols and Abbreviations

Symbol Definition

Ae Outlet cross sectional area [m2]

Af Jet cross section after vaporizing [m2]

Ah Hole cross sectional area [m2]

Ap Pipe cross sectional area [m2]

Ar Area ratio [unitless]

CAr Volume ratio [unitless]

Cd Discharge coefficient [unitless]

Cds Droplet size constant [unitless]

Cf Friction coefficient [unitless]

Cp Specific heat at constant pressure [J/kg⋅K]

Cv Specific heat at constant volume [J/(mol⋅K]

CV Valve capacity [USGPM(60F,1psi)]

CΦv Auxiliary variable [m]

dh Hole diameter [m]

dp Internal pipe diameter [m]

dv Vessel diameter [m]

D Diffusion coefficient [m2/s]

fD Darcy friction factor

lp Pipe length [m]

p Pressure ratio [unitless]

xii

pcr Ratio of critical pressure to atmospheric pressure[unitless]

Pc Critical pressure [pa]

qS,e Exit flow rate [kg/s]

qS,0 initial flow rate [kg/s]

QL Mass of liquid [kg]

Q0 Inventory mass [kg]

QV Vapour mass [kg]

QV,0 Initial vapour mass [kg]

tB Time constant [s]

tE Maximum time validity [s]

u Fluid velocity [m/s]

ua Wind speed [m/s]

ug Gas velocity [m/s]

ue Fluid velocity at exit [m/s]

uf Fluid velocity after flashing [m/s]

uj Fluid velocity after evaporation droplets [m/s]

us Speed of sound [m/s]

us,L Speed of sound in liquid [m/s]

us,V Speed of sound in vapour [m/s]

uVR Dimensionless superficial velocity [unitless]

U Internal energy of the gas [J/mol]

VL,E Volume of liquid after depressurization in the vessel [m3]

xiii

VL,0 Initial volume of liquid in the vessel [m3]

Vp Pipeline volume [m3]

ξ Liquid fraction in vessel [unitless]

ρ Density [kg/m3]

ρF Average density [kg/m3]

ρL Liquid density [kg/m3]

ρtp Two phase density [kg/m3]

ρV Vapour density [kg/m3]

ρe Density at exit [kg/m3]

ρf Density after flashing [kg/m3]

τcr sonic discharge time [unitless]

τs subsonic discharge time [unitless]

υa Air kinematic viscosity [m2/s]

υL Kinematic viscosity of liquid[m2/s]

υV kinematic viscosity of gas[m2/s]

Φm,f Final gas mass fraction [kg/kg]

Φv Void fraction [m3/m3]

Φv,av Median void fraction [m3/m3]

Chapter 3

L1 Lift off height of the flare flame [m]

L2 Flame length [m]

Lb0 Flame length, in low speed air [m]

xiv

Lf Quadrilateral length [m]

Mj Jet Mach number [unitless]

α Angle between flare tip and flame [°]

αc Absorption factor for CO2 [unitless]

αw Absorption factor for H2O [ [unitless]

xv

Abbreviations

I/O Input/output

ESD Emergency shutdown valve

PRV Pressure relief valve

PSHH Pressure switch high high

PA Pressure alarm

FC Failed to close

PT Pressure transmitter

Barg Bar gauge

HP High pressure

LP Low pressure

PFP Passive fire protective insulation

TERV Thermal expansion relief valves

DIERS Design Institute of Emergency Relief Systems

CV [USGPM(60F,1psi)] The flow coefficient of valve, which represent to gallons per

minute of water that can pass through the valve in 60° F and 1psi pressure drop through the

valve.

17

1 Chapter One: Introduction

Process upsets happen when the pressure, temperature, level, and flow controls are not maintained

within the operating limit. These controls can affect each other and a minor upset of one control

loop can cause a major process upset. Therefore these process variables must be kept within

acceptable operating limits. When process variables enter the action limit and there is no action

taken in a short time by the operators, operating malfunction takes place. Any malfunctions of

these parameters can impact on each other and the plant production quality, which can be noxious

for the plant economy and environment. Operating mistakes can activate interlocking systems and

mechanical safety devices. Interlocking and logical systems including programmable logic

controller [PLC], fieldbus control system [FCS], distributed control system [DCS], Emergency

Shutdown System [ESD] and mechanical safety devices protect the equipment, personnel and

environment. However activation of some of these devices will mostly lead to production losses.

The process upsets or operating mistakes can lead to decreasing equipment efficiency and product

quality, unnecessary shutdowns which leads to production losses by releasing them to the

atmosphere through flare systems and in some plants such as polyethylene may lead to

decomposition.

On the other side the most important consequences of depressurization event is to evaluate the

flare flame distortion. Flare flame distortion and heat radiation from flare flames at the event of

depressurization depends on wind velocity, flare tip velocity, flow rate, stack height, stack

diameter, gas composition and other meteorological and stack variables. Flame distortion, caused

by lateral wind acting on the gas jet leaving the flare stack, is an important aspect of heat radiation

because it leads to higher ground-level radiation from the flames. Besides, many factors have to

18

be taken into account, which are very important for evaluation of flame length, and flame

distortion, which include radiation exposure from gases burning, radiant heat fraction, flame length

and centre and flame careen. Following API alone is good for flare flame distortion and heat

radiation evaluation but for deressurization event without consideration of dynamic simulation,

depressurization event may face with event escalation. Therefore, for the depressurization

evaluation and fluid thermodynamic behavior, it is recommend doing dynamic simulation.

Consequently, dynamic calculations for determination of the depressurization procedure and the

evaluation of flare flame distortion and heat radiation have been carried out which gave some

important and accurate information to avoid event escalation. Since a depressurization event is the

most important factor for the safety of employees, equipment and plant operation, data taken by

dynamic calculation presented in this thesis offer a solution for determination of depressurization

procedures, depressurization consequences on equipment and flare flame, and how to avoid event

escalation.

All of the gas plants can become an unsafe by suddenly increasing pressure. Overpressure can take

place due to different reasons such as instrument failure, utility failure, and power loss. If pressure

rises suddenly, a depressurization system must take action in place to depressurize to a safe

operation. The pressure must be controlled through an appropriate valve, up to the time when it

reaches a safe range. The high pressure excess gas can be sent to a pressure vessel or directly to

the flare, and appropriate valves have to be considered for these vessels to prevent overpressure as

well. On oil wells, the major gas depressurization valves are installed for this purpose. When the

wells are not in operation, the pressure can rise. Consequently, a depressurization valve releases

the high pressure excess gas to the flare, in which the hydrocarbons must be burned before being

19

vented into the atmosphere due to environmentally hazardous consequences [4, 38] Dynamic

modeling for relief systems can lead to a substantial decrease in capital cost, while concurrently

improving plant safety. This thesis takes to account the importance of dynamic analysis to major

areas of each gas plant and description of how upset events can have an effect on flare flame

distortion, the shape of the flame in a crosswind. Additionally, since radiation of flare flame is an

important safety issue as it can cause equipment damage, injury and even death, modeling is

discussed for finding the amount of heat radiation. Moreover, the important parameters will be

assessed to determine how dynamic modeling can help designers and operators to control this

event appropriately in an acceptable time. Besides, precisely specifying relief loads and metal

temperatures and material selections can maintain safety of the plant and provide decision support

of capital disbursement. Detailed depressurization dynamic modeling and calculation is a key

factor of the safety evaluation of oil and gas plants and other high pressure equipment. Rapid

depressurization not just determines the load amount on the pressure relief system such as the flare

network. Rather most importantly, it can lead to considerable reduced temperatures of the vessel

walls, which can cause to breakable and high thermal stresses. Very little research has been done

for evaluating of the depressurization process. Haque et al. (1990) accomplished an analytical and

experimental research for fast depressurization during 100 seconds to evaluate the change of the

fluid and the inner wall temperatures during that time. Another research for pressure vessel

contains methane, conducted through an experimental study with method of slow depressurization

by Yadigaroglu-Wieland (1991), with consideration of four different situations. The

depressurization process takes 4-18 hours and the temperature and pressure data indicated

accordingly. Yadigaroglu-Wieland, numerically indicated the depressurization process and got

20

satisfactory results through the experimental data. Other studies have been carried out by, Botros

et al. (1978) (1989), for calculating time for gas pipeline depressurization, and by Failer and

Breslouer (1988), for modeling the depressurization and venting of a fire case containment

chamber, by Picard and Bishnoi (1989), for evaluating the effect of real fluid conditions throughout

the fast dense decompression, natural gas component, and by Kim (1986), to review the process

of storage tank depressurization. This thesis considered three major areas of gas plants with subject

to depressurization in the case of a process upset. Vessel and piping, pipeline in case of puncture

on the wall or total rupture for liquefied pressurized gas and high pressure gas has been modeled

and consequently flare flame distortion which leads to abnormal heat radiation in this case has

been modeled and simulated.

This thesis consists of five chapters. Chapter 2 is the literature review. It will introduce the

definitions of the technical terms used in this thesis, description of major sources of overpressure,

modeling of some possible cases, which cause depressurization, instructions for required relieving

rates according to specified situations, pressure relieving devices and relief scenarios. Chapter 3

explains a general & detailed description of flare flame distortion and relevant equations. Chapter

4 provides a detailed overview of depressurization dynamic modeling, methodology &

assumptions, experiment data, calculation results, equations description, and calculation

procedures will be discussed. Accordingly, Chapter 5 consists of the conclusions.

21

2 Chapter Two: Literature Review

2.1 MAJOR SOURCE OF OVERPRESSURE AND RELIEF SCENARIOS

Pressure vessels, towers, heat exchangers, compressors and other operating facilities and piping

should be sized to maintain the pressure of the system. Sizing of equipment should be based on

some important factors that are subject to the design pressure and design temperatures. In addition,

the consequences of process upsets which can happen at operating conditions, and effect of process

variables on each other in upset conditions that cause overpressure are other considerations.

Besides, some natural disasters such as earthquake also can be recognized as a source of

overpressure, as they may cause cracking or rupture of pipe/vessels, which has to be evaluated

based on safety integrity level of plant. At the design stage of any gas plant the minimum relief

load must be calculated to prevent the impact of overpressure in other equipment beyond the

maximum permissible pressure.

Different scenarios have to be considered for calculation of relief loads as well as designing safety

relieve valves and the analysis should be based on the contingencies outlined in [API 521]. One

example that cause to overpressure and process upsets is gas blowby. When the liquid level in a

two-phase separator falls down too low, gas blowby will occur. In this condition gas comes out

through the liquid outlet nozzle because of level control malfunction. This will lead to gas from

the high pressure separator going into the low pressure facilities downstream of the liquid level

control valve. Gas relieving loads have to be calculated by use of the control valve sizing data. The

gas blowby load will then be calculated from the gas valve sizing equation by use of the CV of the

relevant valve which is on the fully open situation. Although enough information is not available

22

at this point, engineering assumptions have to be taken into account which is very important. These

assumptions should be considered to minimize gas blowby relief load where possible.

2.2 Pressure relieving devices

Systems that are subject to internal pressure must be equipped with overpressure protection. A

safety device can be activated by inlet static pressure. They have to be configured to open in an

emergency or upset situation to protect equipment and plant against the system overpressure or

increase of equipment internal pressure beyond the specified design value. There are different

kinds of devices that can be utilized in a gas plant, including pressure relief valve, a non-reclosing

pressure relief device, and a vacuum relief valve [API 520].

2.2.1 Pressure relief valves

The safety relief valve is a kind of relief valve which can be utilized to control or bound the buildup

pressure in a vessel or system at the time of process upset which can occur because of instrument

or mechanical failure, or in case of fire. The pressure is alleviated by enabling the pressurized gas

or liquid to gush out from the system by a specific route. The safety relief valve has to be set to

open at a preordained pressure.

An excess fluid which can be liquid, gas or liquid–gas mixture is typically transferred through a

piping system named a flare header to an elevated gas flare where gases are typically burned and

the combusted gases are discharged to the environment [API 520].

23

2.2.2 Rupture Disks

These devices are non-reclosing pressure relief devices utilized to protect tanks/vessels which

have potential for overpressure during normal operation condition, as well as protect piping and

other pressurized equipment from excessive pressure and vacuum. Rupture disks are utilized in

single and multiple relief device installations. Besides, they can be used as redundant pressure

relief devices [API 520].

2.3 Depressurization System

The layout of specific valves, piping and instrumentation logical facilities in order to control rapid

reduction of pressure in pressurized equipment by releasing gases has to be taken into account at

the design stage of any gas plant. Monitored depressurization of the vessel can decrease stress in

the vessel walls.

The modeling of depressurization systems is intended to examine the specific parameters that have

to be taken into account to better control the process upset or fire case. All of these parameters are

important key factors for the depressurization model and consequently the model of flare flame

distortion and radiation of the flame that can have hazardous consequences on equipment and

environment at the event of a process upset. Because pressure build up is the key factor of

depressurization systems, many factors such as heat radiation, flare flame distortion at this event

has to be evaluated, since it directly depends on discharge gas flow rate and discharge time. Hence,

dynamic modeling can evaluate the most important variables that affect flare peak load, and as a

consequence flare flame distortion. Logic facilities that can be included a distribution control

systems (DCS), an interlocks, emergency shutdown systems (ESD) and programmable logic

24

controllers (PLC) should be considered to do an appropriate actions when they receive adequate

signals from pressure transmitters to shutoff the process line and open the bypass line to reroute

gas to Flare. Some logical systems can be installed as an fieldbus or non-fieldbus, which means an

action can be done automatically in the field or an action can be done by operator whether at the

control room or in the field.

2.4 Flow and Level Controls

Several methods exist to specify the flow rate of liquids and gases. All of these methods are based

on some specified flow detectors that have to be installed on specific locations. The most common

flow measurement methods used in gas plants are based on creating a pressure drop in a pipe. As

the flow in the pipe is transport through a reduced area, the pressure before the flow meter is higher

than afterwards or downstream. In the constrains, the velocity of the fluid increases, as the same

quantity of flow must pass before and in the constrain. By increasing the velocity a differential

pressure will be created through the flow meter as a result of the Bernoulli effect. Accordingly, by

measuring the pressure differential through the flow meter one can compute the flow rate. In fact,

due to increasing the differential pressure relatively to the square of the flow rate, so ΔP ∝ Q2 .

In other words, Q ∝ √𝛥𝑃 .

Where: Q = the volumetric flow rate [m3/s]

𝛥𝑝 = differential pressure

On the other hand, the term of Level is used for measuring the amount of liquid. In the vessel

containing liquid, the pressure is directly rely on the liquid height in the vessel named as

25

hydrostatic pressure. Figure 2-1 shows, by increasing the level in the vessel, the pressure affected

by the liquid will raise linearly in which the equation is as follows:

P = ρ.g.H Equation 2-1

Where: P = pressure [Pa]

H = height of liquid column [m]

ρ = liquid Density [kg/m3]

g = acceleration due to gravity [9.81 m/s2]

Finally, the liquid level in a closed vessel can be calculated by the pressure reading if density of

the liquid is constant.

Fig 2-1 Usual level control, basic instrumentation measuring devices and basic PID control

Technical Training Group, (2003)

So the formula would be as follows:

P high = P gas + ρ.g.H Equation 2-2

26

P low = P gas

ΔP = P high – P low = ρ.g.H Equation 2-3

27

3 Chapter Three: Dynamic Modeling of Depressurization

3.1 Material and Energy Balances

For gas phase energy balance in a vessel can be written as follows:

2.1

2

dU VsH q Qsoutdt [W] Equation 3-1

In addition, mass balance can be written as follows:

dmqs

dt [kg/s] Equation 3-2

We have:

1U m u [J] Equation 3-3

.H q hsout out Equation 3-4

If well mixed then:

.H q hsout [W] Equation 3-5

Hence, the energy balance becomes:

2( )

2

Vd m u sq h q Qs sdt

[W] Equation 3-6

The left –hand side can be expanded as:

dm duu m

dt dt Equation 3-7

Substitution of the mass flow rate qs leads to:

duu q ms

dt Equation 3-8

28

Hence, the energy balance becomes:

21(( ) ( ) ( )

2

du Vu q q h q Qs s s

dt m Equation 3-9

Which we have:

Q U A T [W] Equation 3-10

And

T = T Tout in [C ] Equation 3-11

Where:

IU = Internal energy in vessel [J]

U= heat transfer coefficient [W/ (m2.K)]

u= Internal energy per kg in vessel [J/kg]

h= enthalpy per kg [J/kg]

A= wall area [m2]

T = temperature difference between outside and tank [ C ]

m= mass in vessel

At any time, density is calculated as m

V. Then, ρ and U are used to calculate temperature (T) and

pressure (P) based on an equation of state. T and P are used to calculate h which can be shows as:

H= u+pv Equation 3-12

sq is calculated based on a valve equation (section 3.2).

Across the valve, assuming adiabatic conditions, we have:

29

22,

2 2

VV s outsidesh+ houtside

Equation 3-13

When the left term is known, we can solve for the first right term at P= 1 atm. Hence,

temperature of gas leaving the choke can be calculated.

Where:

m= mass in vessel [kg]

.H out = enthalpy in exit stream [J]

Vs= velocity of gas at outlet [m/s]

hout = enthalpy per kg leaving can be = h if well-mixed [J/kg]

3.1.1 Modeling of High Pressurized Gas Discharges Across the Orifice

The discharge flow of gases from holes and pipes, and the dynamic behaviour of an adiabatic

depressurization of a high-pressure gas in the vessel, will be described in this section. Due to any

leakage in a pressurized vessel, the left over liquids in the vessel will be quickly depressurized and

expanded which causes low temperature. Since vessels contain gas mixtures, in some cases low

volatile elements might condensate (Haque, 1990). Taking in to account the first law of

thermodynamics, and with consideration of expanding gas which delivers volumetric work, and

by implementing an equations for non-ideal gases, we can determine the reduction of pressure and

temperature throughout the discharge of the compressed gas (Haque et al. 1992).

For adiabatic flow, we can use the following equations to determine pressure [32-43, 63]:

30

2( 1) ( 1)0.5

RT (2 2)1 A 20P P 1 t0 2 V M 1

[bar] Equation 3-14

( 1)( 1)(2 2) 2RT 2 P0Q A

0 M 1 P0

[Kg/s] Equation 3-15

Where:

A= cross section area of the orifice [m2]

M= gas molecular weight [kg/Kmol]

R= universal gas constant [J/kg.mol.K]

T= gas absolute temperature [k]

Q= mass flow from the vessel [kg/s]

P= pressure in the vessel [bar]

V= vessel volume [m3]

=C pCv

gas specific heat ratio [unitless]

= gas density [kg/m3]

P0= vessel pressure [bar]

0 = initial gas density [kg/m3]

t= step time [s]

Considering isentropic depressurization for adiabatic case and equation 2-48 the energy balance

would be:

31

Hi =Hc+

2

2

s Equation 3-16

Hi = Hc+2

c

c s

P

Equation 3-17

Hi= enthalpy of gas in the vessel [J/kg]

Hc= enthalpy of gas passing the orifice [J/kg]

Pc= gas pressure passing the orifice [bar]

c = gas density passing the orifice [kg/m3]

Consequently, the mass flow can be calculated by:

PcQ C A cdc

[kg/s] Equation 3-18

Where:

Cd = discharge coefficient

The discharge coefficient can be calculated by two items, contraction and friction according to the

following formula:

Cd = Cf × Cc Equation 3-19

where

Cf = friction coefficient

Cc = contraction coefficient

When the fluid in the vessel is expanding from all directions, components will have such velocity

vertical to the axis of the expansion. The flowing fluid has to be made curved in the way parallel

to the hole axis. The fluid’s inertia leads to the smallest cross sectional area, without radial

32

acceleration, which is smaller than the area of the expansion. The recommended value for the

discharge coefficient orifice contraction, where friction is small is 0.95 0.99Cd . [Beek,

1974].

It should be noted that the discharge flow is critical or choked when:

( )1 1

( )2

Pd

Pu

Equation 3-20

Pd = initial gas pressure [bar]

Pu = upstream gas pressure [bar]

3.1.2 Calculation of the vessel wall temperature

The following equations for calculation of the vessel wall temperature can be used [S M

Richardson et al. 1991].

1 11 2 20 0 1 0

xn n nT F T F T qr rk

Equation 3-21

1 1 11 21 1

n n n nT F T F T Tr ri i i i

Equation 3-22

( 1 to n)i

1 11 2 211

xn n nT F T F T qr ri i i k

Equation 3-23

2

tFr

x

Equation 3-24

Where:

nT = temperature in any step time n [C]

33

n= step time

0q = heat flux from the medium in the vessel to the inner vessel wall [W/m2]

1q = heat flux from the medium in the vessel to the inner vessel wall [W/m2]

x = thickness of the vessel represent to each side of the vessel, inner and outer layer [mm]

Fr = Fourier number

k = thermal conductivity [W/(m.K)]

wall thermal diffusivity [mm2/s]

3.2 Valve correlations and equations using for dynamic calculation

Five types of valves are common for controlling depressurization and can be selected in a

calculation. Industrial approach allows users to choose any of these valves. This study is based on

two most common and major depressurization valves, known as Masoneilan and Fisher universal

gas sizing [37, 39].

3.2.1 General valve equation

This model can be used if the valve effective throat area is known at the beginning stage. The

model creates restricting assumptions regarding the features of the orifice. The valve equation is

as follows:

2Discharge Flow= C 43200 ( )1

CK G P Kup upterm C Equation 3-25

Where:

Gc = 1 in SI units [2kg.m / N.S ] and 32.17 in imperial units [

2lb.ft / lb . f S ]

34

Pup= upstream pressure

up = upstream density

C1 can be determined based on geometry of the valve, and at the time of sizing orifices, it will be

the same as the orifice coefficient discharge.

( 1)

2 2 ( 1)

( 1)Kterm

Equation 3-26

Where:

C p

Cv Equation 3-27

The model for this valve also can be shown as follows:

0.5Valve rate=C ( )Area K P Density Kuptermd Equation 3-28

C = Discharge coefficientd

Also Cd can be determined by Fig 3-1.

35

Fig 3-1: Discharge coefficient(C ) for square-edged circular orifices with corner taps.

[Tuve and Sprenkle, Instruments, 6,201(1933).]

d

3.2.2 Supersonic valve equation

When there is not enough information available regarding the valve, this model can be considered

for calculation. The valve equation is as follows:

Flow rate= C ( )Area P Densityupd Equation 3-29

3.2.3 Subsonic valve equation

Subsonic model can be considered just at the time when the flow over the valve is anticipated to

be entirely subsonic. In general this condition will exist if the pressure is lower than twice of the

backpressure valve at the upstream side. The related equation which has been used for modeling

of this kind of valve is as follow:

36

(P )( )Discharge Flow= C

1

P P Pup up upback back

Pup

Equation 3-30

Where:

Pup = upstream pressure

Pback

= back pressure

up = upstream density

3.2.4 Masoneilan valve equation

This model can be considered as a general depressurization valves model by the following

equation:

Flow rate= C ( )1

C C Y Pv up upf f Equation 3-31

3Y 0.148f y y Equation 3-32

cp1

3 p1.4

yK

T

Equation 3-33

Where :

K= gas specific heat ratio

pc = calculated pressure drop

pT = total pressure drop

37

where is expansion factory , Cf is critical flow factor and C1 can be determined based on geometry

of the valve. The expansion is ratio of flow coefficient for a gas to that for a liquid at the same

Reynolds number.

3.2.5 Fisher / Universal gas sizing equation

Fisher / universal gas sizing/Fisher is another type of valve with the following equation.

1

1

52059.64SCFH v

PQ C P

P GT

Equation 3-34

G = Specific Gravity

T= Temperature [˚C]

P1= inlet pressure [bar]

3.3 Characterization of Discharges of Liquefied Pressurized Gases

When liquefied pressurized gas is depressurized, it will lead to the creation of bubbles in the liquid.

Hence, expansion of the liquid at boiling point is a quite complex physical process. When a

liquefied pressurized gas exist in the vessel, a rapid depressurization leads to a flash of the liquid

inside the vessel, that means, because of the rapid depressurization, the liquid, vaporizes quickly

until the out coming vapour/mixture is cooled under the boiling point at the last pressure.

Consequently, raise of gas bubbles in the liquid phase will occur and if the expanded liquid

develops over the hole in the vessel, a two-phase flow will be obvious through the hole in the

vessel. The level blow up is shown in Figure 3-2 [9-10, 42, 51, 53-54, 63, 71]

38

Fig 3-2: Schematic view of level blow up in a depressurizing vessel filled with liquefied

pressurized gas [Wilday, 1992]

3.3.1 Numerical Process to Determine Discharge Flow Type from the Vessel

In this procedure, at the beginning the criteria regarding the type of fluid within the vessel and

raising up of liquid level model will be discussed. Then, the initial and end situation of the

numerical process will be introduced accordingly. Subsequently, the model in the form of a

numerical process will be discussed.

Any flow type depends on to its variables of the basic process. The numerical process should be

continued until an acceptable end situation is reached. An accurate analytical procedure for

determining of the flow type for two-phase flow, within a vertical vessel at the time of

depressurization has been investigated by the design institute of Emergency Relief Systems of

AIChE . [DIERS, 1986 and Melhem, 1993].

39

For calculation of discharge gas flow rate,s

q , equation 3-56 in section 3.3.2 are applicable to

determine the discharge flow rate. Then the median superficial velocity of vapour within the vessel

can be calculated by:

, ( )

qsuV m A

V L

[m/s] Equation 3-35

And bubble increase velocity can be calculated by:

( )41, 2

gL Vu C

Db iL

[m/s] Equation 3-36

Where as per Wallis the limit can be:

1.181

CD

bubbly flow

1.531

CD

churn flow

σ = surface tension [N/m]

Surface tension play an important role at the time of depressurization, at boiling point and also

viscosity is important that is an important factor for determination of flow type. The surface tension

by implementing Walden’s law Pe[ rry,1973] can be calculated as follow:

( )C L TV B L

[N/m] Equation 3-37

And

1

76.56 10C

[m] Equation 3-38

Where:

C Wlden’s law constant

40

bubbly slug churn wispy annular annular

Fig 3-3: Tow phase flow pattern separately schematic

(http://www-thd.mech.eng.osaka-u.ac.jp/mpe04002/page/research05.htm)

Fig 3-4: Flow regime transition criterion for upward two-phase flow in vertical tube

([http://hmf.enseeiht.fr/travaux/bei/beiep/content/g19/types-flow-pattern)

41

Where:

VsL = liquid superficial velocity

VsG = gas superficial velocity

In Figure, 3-3 and 3-4 the bubble flow area and the churn turbulent flow area are indicated. The

ratio of superficial vapour velocity, which is dimensionless, can be calculated by:

uVu

VR ub

[unitless] Equation 3-39

Where:

u =VR

superficial velocity [unitless]

u =b

bubble velocity [m/s]

u =V

median superficial velocity [m/s]

Then we need to calculate dimensionless superficial velocity for usual two-phase flow forms. It

should be noted that the dimensionless superficial velocity for bubbly flow has to be higher than

u VR,bf , and for churn flow it has to be higher than u VR,cf with appropriate formulas as follows:

2(1 )

, 3((1 ) (1 ))2

uVR bf

CV VD


u = VR,bf

bubbly flow minimum superficial velocity [unitless]

And

2

,cf (1 )2

VVR C

VD


42

=VR,cf

u churn flow minimum superficial velocity [unitless]

In which D2C = 1.2 for bubbly flow and D2C = 1.5 for churn flow.

Then we need to identify if two-phase flow is occurring in the vessel by the following rules:

,u uVR VR cf

two phase churn flow

,u uVR VR bf

two phase bubbly flow

,u uVR VR bf

, ,

u uVR VR cf

gas flow

After a rapid depressurization, a liquid flash inside the vessel will occur, and because of the

existence of vapour bubbles in the vessel, expansion of liquid will happen consequently. Therefore,

liquid level at the tank or vessel will decrease. Mayinger theory can be utilized for computation of

the void fraction in the liquid state in vessels. Additionally, the process can be utilized to calculate

the increasing of the liquid level due to discharge flow over the sidewall of the vessel, to determine

the state of the discharge flow. The void fraction at the time of depressurization can be computed

by the following process for the liquid phase (Belore 1986). Determination of the superficial

velocity at the beginning time is important factor that can be calculated according to the following

formula:

,0,0

,0

qs

uV A

LV

[m/s] Equation 3-42

And the vapour phase that hast to be released would be as follow:

43

1(1 ) ,1,

1 ,1

1 ,

d

n U CDg m etop top b iQ

Vtop m e LVm e gtop

Equation 3-43

For two-phase flow, the nature of the top discharge ,m e can be evaluated by the following

equations for churn and bubbly flow form respectively [1, 50, 53-54, 75]:

U1,

,1

2

CD Vb i LV Q Vg gd

m eVtop LV gtop

Equation 3-44

U1,

(1 )1

,

11

CD Vtopb i Ltop top V Q Vg gtopd

m eVtop LV gtop

Equation 3-45

Where:

top = void fraction after depressurization

U,b i

= increase of bubble velocity

VL

= liquid specific volume [m3/kg]

44

V g = gas specific volume [m3/kg]

Qd

= discharge flow rate [kg/s]

While is the top void fraction, in should be considered that the median void fraction ,V aV

within the vessel before the process upset and depressurization can be calculated by:

1,V aV

[m3/m3] Equation 3-46

= filling degree of vessel [m3/m3]

,V aV = average void fraction in the vessel [m3/m3]

The liquid kinematic viscosity proportion to the gas kinematic viscosity at boiling point should be

determined by utilizing Arrhenius’s correlations for liquid viscosity (Perry 1973) and Arnold’s

relations for gas viscosity (Perry 1973), which can be introduced by the following equation:

3637 ( 10 ) ( 1.47 )

27 36( )

u T Ti V BL

TV L

Equation 3-47

Where :

C =AA

constant 1 6 × kmolm

[ K]

By definition of assistant equation:

( ( ))C

V gL V

[m] Equation 3-48

45

When the pressure goes down, velocity goes up and this can be leads to shear stress impact to the

liquid droplets which can be sufficient large to entrain liquid droplets inside the vapor phase.

The void fraction after depressurization with consideration of viscous losses can be calculated by:

2,0 0.376 0.176 0.585 0.2560.73 ( ) ( ) ( ) ( )

( ) ( )

u CV V L Ltop g C d

V V L V V

[m3/m3]

Equation 3-49

Two-phase flow in a pipe has different flow forms. Due to the transfers of mass, momentum and

energy among the phases, identifying the flow regime is very important in the numerical modeling

of two-phase flow. Takes to account in mist flow regime, due to the gas velocity is too high and

there is too much small liquid droplets scattered in continuous gas phase that might be stripped

through the wall, this flow regime is not shown in Figures 3-3 and 3-4.

The liquid and bubbles, which expanded to a new volume, can be explained as:

,0L, 1

VL

VE

top

[m3] Equation 3-50

So, for a vertical cylindrical vessel we have:

AL

=Abase

[m2]

V = A ×hL L L [m3] Equation 3-51

For horizontal cylindrical vessel:

A =2 L (2 )L

r h hL L

[m2] Equation 3-52

46

12V =L cos (2 r h )

L

hLr r h h

L L Lr

[m3] Equation 3-53

For spherical vessel:

2 2( )A r r hL L

[m2] Equation 3-54

2 (3 )3

V h f r hL L L

[m3] Equation 3-55

Where:

A =L

liquid surface [m2]

Abase= vertical cylinder base [m2]

HL= heigh of liquid[m]

r = sphere radius [m]

Φv = void fraction [m3/m3]

CΦv= auxiliary variable [m]

qS = exit flow rate [kg/s]

AL = vessel liquid surface [m2]

dv = vessel diameter [m]

T = liquid/vapour temperature [k]

μi = molecular weight [kg/mol]

ρL = liquid density [kg/m3]

ρV = vapour density [kg/m3]

Lv[ΤΒ] = enthalpy/heat of vaporisation at boiling temperture[J/kg]

47

TB = boiling point [k]

F= function of pressure

UV,0 = superficial vapour velocity [m/s]

σ = surface tension [N/m]

g = 9.8 [m/s2]

υL = kinematic viscosity of liquid [m2/s]

υV = kinematic viscosity of vapour [m2/s]

L,EV = final liquid volume after expansion [m3]

L,0V = initial liquid volume [m3]

V =L

liquid specific volume [m3/kg]

3.3.2 Modeling Discharge Flow of LPG Across the Vessel Holes

When the medium is considered as a two-phase flow, the related formula for calculation of

volumetric flow rate can be as follows [1, 42, 50, 53-54, 63]:

2 VP PaQ AC ghLd

[m3/s] Equation 3-56

In which:

Pa= atmospheric pressure [pa]

Pv= initial gas pressure [pa]

liquid density [kg/m3]

Ah= hole area [m2]

48

Cd= discharge coefficient

g= 9.8 [m/s2]

hL= height of liquid [m]

Some recommended values of discharge coefficient as per Beek (1975) can be considered for

some types of orifices, which are sharp orifices, straight orifices, rounded orifices, and for a pipe

rupturewith value of 0.62, 0.82, 0.96, 1 respectively.

1

(1 )( )

F g g

v L

[kg/m3] Equation 3-57

Where g = mass fraction of gas in the two-phase flow [unitless]

F= median fluid density [kg/m3]

When the gas and liquid are not in equilibrium condition pressure decrement can be calculated as

follow (Abuaf et al., 1983):

8

1.5 8 0.81 2.2 10111.1 10

1L

TQ

depTcP P Ts a

gTc

[bar] Equation 3-58

In addition, mass flow rate across the orifice can be calculated by:

2 LQ C A P Pu xd [kg/s] Equation 3-59

Where:

Px= orifice pressure [bar]

Pu= upstream pressure [bar]

49

Pa= absolute pressure [Pa]

Ps= saturated vapour pressure

T = upstream orifice absolute liquid temperature [K]

TC = upstream orifice absolute liquid critical temperature [K]

Qdep

= depressurization rate [Pas]

g gas density [kg/m3]

L liquid density [kg/m3]

= liquid surface tension [N/m]

3.4 Prediction of Discharge Gas from Pipelines Due To Rupture

At the time of an unexpected rupture in the pipeline, a backpressure can start going up in opposite

way of the speed of sound. This means that, the impose of the backpressure will be on upstream

pressure. The Wilson model of the gas discharge flow over the pipelines can be used to predict the

mass flow rate that is depend on the initial conditions over a periodic of time. At the time of

pipeline, mass flow rate can be calculated by the following semi-experimental model introduced

by Wilson that shows as follow [10, 41, 47, 52-54, 61, 75]:

0

,0( )

2,0( ( ) )( )1

0 0( ) e e

,0 ,0

qs

q ts qst t t

BQ QtQ Bt q t qB Bs s

[kg/s] Equation 3-60

Where:

50

qS,0 = initial flow rate [kg/s]

Q0 = inventory mass [kg]

tB = time constant [s]

t = time after rupture [s]

The inventory Q0 in the pipeline can be computed as follows:

0 0Q A lp p [kg] Equation 3-61

Where pipe cross section area can be determined by:

2

4

d pAp

Equation 3-62

dp= pipe diameter

And the discharge flow rate at the beginning stage qS,0 will be computed by equation 2-41, with

consideration of Ap instead on Ah.

For total rupture in the pipeline the value of 1.0Cd can be considered as the worst case.

The gas sonic velocity s , with considering adiabatic expansion ( 0S ) can be calculated with

the following formula:

( )dp

s sd

[m/s] Equation 3-63

By consideration and implementing the equations of state, we have:

( )

d

dP P

[s2/m2] Equation 3-64

0z R T

sM

[m/s] Equation 3-65

51

Where =M molecular weight [kg/mol]

The Colebrook White equation for determination of Darcy friction factor, and estimated for high

Reynolds value, can be determined by the following formula: [detail in appendix A]

2

101/ ( 2 log( / (3.715 )f d pD Equation 3-66

The time constant tB is introduced with the following:

2 / 3 / ( / )t l f l dsB D Equation 3-67

Eventually, the mass flow rate can be calculated at any time t later on the pipeline rupture and by

implementing Wilson model introduced by the mentioned equations above. For ensuring the

applicability of the model, at the time of the backpressure moving upstream and arrives at the

opposite way of the pipeline the following correlation can be used to determine the final

depressurization time through the pipeline.

ltE

s

[S] Equation 3-68

The definition of symbols used in this section, which have not been described before:

pd = Pipe diameter [m]

lP = pipe length [m]

Q =0

inventory mass in pipeline [kg]

P0= initial pressure [Pa]

q =S,0

initial discharge flow [kg/s]

T0= initial temperature [k]

52

tE= max allowable time [s]

fD = darcy friction factor [unitless]

ε = wall roughness [m]

ζ = constant [unitless]

ρ =0

initial gas density [kg/m3]

ρ = gas density [kg/m3]

3.5 Relief Scenarios

There are different scenarios that need a depressurization to avoid escalation of the event. The

assumption typically made in each scenario are included as well.

3.5.1 Fire case

Basically, the production and processing equipment should be unintegrated into fire regions, by

means of fire walls, plated decks, or edge of the plant. Throughout a fire in one of the fire regions,

all facilities within that region are presumed to be fully exposed to the fire. It is presumed that

throughout a fire there is no feed flow to downstream or product from an affected system, and all

normal heat sources have stopped. Fire relief loads should be computed for pool fire and jet fire

events where relevant. Depressurization is assumed to be isenthalpic as a conservative estimate.

In practice, the depressurization will be between isenthalpic and isentropic (appendix F). Takes to

account the isenthalpic case leads to the largest required release flow rate, and is therefore the

worst case scenario.

53

3.5.1.1 Heat absorption to liquids through the vessel wall

When vessels containing vapor or/and liquid the total heat absorbed by the insulated vessel can

be calculated by the following equations according to API 521:

Q = C1FAws 0.82 Equation 3-69

Where: Q = total heat absorption to the wetted wall, [Btu/hr]

C1= constant [43 200 in SI units, [21 000 in USC units]];

F = environment factor

Aws= total wetted surface, [ft2]

The terms, Aws 0.82 is the area exposure element or ratio. This proportion determines the concept

that big vessels are less probably than small ones to be entirely exposed to an open fire.

3.5.1.2 Heat absorption from the surface of a vessel covered by water film

Water films can absorb a significant amount of radiation in equipment exposed to fire flame and

it can protect the metal surface. The credibility of water film in contact with the vessel wall relies

on many items. Cold weather, winds, water supply quality including PH, surface tension, and

vessel surface situations that can keep consistent water distribution [API 521].

3.5.1.3 Environmental factor for depressurizing and emptying facilities

Controlled depressurization of the vessel decreases inner pressure and possibility of rupture of the

vessel walls. For designing of depressurization systems some important factors has to be taken into

account to achieve an appropriate objective. The environmental factor, define as a correction

coefficient which is depends on vessel thickness, has an effect on total heat absorption through the

54

vessel wall and therefore leads to more liquid vaporization in the vessel and consequently higher

depressurization rate. Accordingly, the environmental factor has to be considered at the maximum

value of one with consideration of following factors according to API521 manual.

First, manual controls close to the vessel may not be accessible at the time of fire. Second, failure

status such as fails to close [FC] or fails to open [FO] of the depressurization valve should be

determined to prevent increasing of the fire duration and flare load at the time of an instrument air

failure, to prevent environmental hazardous consequences. Third, ahead of time initiation of

depressurization is suitable to minimize vessel stress to satisfactory values appropriate for the

vessel wall temperature which may result from a fire. Moreover, the last one, a safe location has

to be provided for releasing the excess gas from the system flaring. These factors can have an

effect on environmental factors and the worst case should be considered in these events. [API 521]

Q = C2·F·Aws0.82 Equation 3-70

where C2 is a constant [70 900 in SI units [34 500 in USC units]].

3.5.2 Adiabatic case or cold depressurization

It is often essential to depressurize, and this process can be slow or fast. Depressurization can lead

to a significant reduction of the temperatures for fluid inside the vessel as well as the vessel wall,

because of significant heat transfer to the fluid. This can be hazardous when the wall temperature

goes below the rupture stress temperature of the vessel. As a consequence, it is essential to know

conditions of the vessel during depressurization.

In an adiabatic process, there is no heat transfer between a system and its environment. The

adiabatic process follows the thermodynamics’ first law and energy is changed just as work. This

55

is the isentropic case, which is the worst case for cold depressurization, because it leads to the

lowest temperature (Appendix F).

Rapid chemical and physical process can be explained by the adiabatic process, which means there

is not sufficient time for energy as heat transfer from the system [3-6, 49].

Fig 3-5: Adiabatic process

(https://commons.wikimedia.org/wiki/File:Adiabatic.svg)

56

4 Chapter four: Flare Flame Distortion and Heat Radiation Modeling

4.1 Process Flares

The purpose of the flare system is to safely collect and to dispose all hazardous and flammable

fluids discharged from equipment and systems of the process plants to a safe place. For this reason

different types of flare systems should be considered at the time of designing of the gas plant. It is

not necessary to implement all equipment in all gas plants.

4.1.1 Warm Flare System

To dispose gases with depressurizing temperatures above 0° C, a warm flare collecting system can

be established. This warm flare system should pass the gases including gases with considerable

contents of water released from pressure safety devices to the flare tip.

4.1.2 Cold Flare System

Gases and liquids with depressurizing temperatures below 0°C have to be released through a cold

flare system. The cold flare system comprises of a collecting system for cold gases and another

system for liquids includes the cold blowdown drum and a system to heat the cold flare gases.

Condensing hydrocarbons should be collected in the cold blowdown drum. The gases are routing

through the blowdown drum and are passing to the flare line. Warm flare gases and warmed up

cold flare gases are passed in a common flare line and from there to the flare stack.

57

4.1.3 Storage Tank Area Flare System

The low-pressure storage tanks should be linked to the tank flare. The flare should be established

near the tank area. Gases discharged from pressure safety devices should be routed simultaneously

directly to the flare stack.

4.1.4 Sour Gas Flare System

For the sour gases coming from the treatment units, a separate collection system should be

established. The gases should be routed to the sour gas flare where the combustible components

of the sour gases are converted in the high temperature flame near the front of the burner.

4.2 Modeling of the Flare Flame Distortion

Modeling of distortion and geometrical shape of the flare flames factors are necessary to determine

the flame lift off and its angle concerning the object. Besides, this calculation can be used for

determination of the view factor. In addition, the flame geometry can be used to determine the

surface area of the flame.

4.2.1 Calculation of Flare Diameter, Stack Height, and Flare Flame Distortion

Two different methods have been introduced, API521 and Chamberlain (1987) models known as

Thornton model in the following sections.

When gas leaves the relief outlet piping, quick changes happen on velocity and density. Different

procedures for computing the required size of outlet piping have been formulated.

58

The API manual recommends the calculation of the outlet Mach number as follows:

0.5.53.23*10

2 2.2

q Z TmMaMP d

Equation 4-1

where

qm = gas mass flow rate, [kg/s]

Z = gas compressibility factor,

T = absolute temperature, [K]

P2= absolute pressure on the flare tip during flaring, [kPa]

M = relative molecular weight of gas.

Takes to account the flow can be sonic in some parts of the system and the critical pressure at the

exit condition will be calculated by considering 2

Ma = 1.0, as a sonic flow.

Takes to account having the Mach number and sonic velocity we can calculate flare tip exit

velocity which can be introduced as follow:

Flare tip exit velocity = Jet Mach Number × Sonic Velocity [m/s]

59

Fig 4-1: Flare Stack and Flame Distortion Geometrical Factors [API 521]

Another approach for calculation of Mach number can be introduced by equation 4-2, which

widely can be used for dispersion modeling at the time of depressurization. Dynamic calculation

can give us an accurate data to implement on this model to determine when and where system has

potential to violate the regulatory. Therefore, Mach number in other form can be defined as follows

and can be calculated in any pressure p [3-6, 12-17, 24-27, 32].

60

1

2

( 1) 1 ( 1) 11

1 ( )21 1

2 2

aM

p p

p pa a

p p

p pa a

Equation 4-2

Where:

Pa= ambient pressure

C p

Cv

And the effective area of the jet in related to the following Mach number can be calculated by:

(1 ) 1

2

pA

E paA

M a

[m2] Equation 4-3

Where:

AE = exit cross section area

The velocity at flare tip by API method can be calculated by the following formula [API 521,

2008]:

2 / 4

qU j

d [m/s] Equation 4-4

q= actual vapour volume flow rate [m3/s]

d= stack diameter [m]

Where q is volume flow rate of the gas and d is the flare stack diameter.

Finally, the maximum heat radiated can be calculated by the following equation [API 521].

61

2 4D kF

Q

Equation 4-5

Where:

F= heat fraction, radiated

Q = heat released [kw]

K= heat radiation (maximum allowable heat radiation from flare flame) [kw/m2]

τ= radiated heat fraction transmitted through the atmosphere

4.3 Modeling of Heat Radiation from Flare Flame during Depressurization

Fire heat transfer lead to a heat flux with the possibility of damage to objects located in its

surroundings. At the time of fire by hydrocarbons, the flame can be composed of high temperature

burning components with a radiation temperature at 800 to 1600 ˚K. By determination of the

temperature and radiation range of the flame, we can calculate the heat flux. Generally, combustion

energy in the flames can be exchanged by three fundamental methods of heat transfer known as

heat convection, heat radiation, and heat conduction. Stefan-Boltzmann theory of the heat transfer

rate caused by a flame-radiating surface can be introduced by the following equations [7-8, 11-18,

27-31, 51, 74-76]:

4 4( )SEP T Taf in which 0 < ε < 1

2[J/(m .s)] Equation 4-6

Where:

SEP = Surface Emissive Power, in [J/[m2⋅s]]

ε = emissivity factor

62

σ = constant of Stefan-Boltzmann, 85.6703 10 [J/[m2⋅S⋅T4]]

Tf = temperature of the radiator surface of the flame, in [K]

Ta = ambient temperature, in [K]

It should be noted, use of the Stefan- Boltzmann equation is restricted to computation of the

flames’ surface emissive power. Consequently, the well-known solid flame theory can be utilized,

that means, a portion of the burning heat is radiated by the observable flame surface area of the

flame.

The Surface Emissive Powers [SEPs] describes the heat flux as an emission from a two

dimensional surface as an approximation of a complex three-dimensional process [Crowley, 1991].

Theoretical Surface Emissive Powers [SEPs] can be calculated by the following combustion

energy per second and the equation can be introduced as follows:

theoreticaSEP

l

'Q

A Equation 4-7

Where:

A =Surface area of the flame, in [m2]

Q' = Combustion energy per second, in [J/s]

The calculation of Q' can be driven forward by the following formula:

' ' [J/s]Q m Hc Equation 4-8

Where:

m´= mass flow rate [kg/s]

ΔH = c heat of combustion [j/kg]

63

Maximum Surface Emissive Powers [SEPs] can be calculated from TheoreticalSEP and the fraction of

the heat radiated from the flare flame that will be generated, can be determined by:

SEP =F ×SEPmax s theoretical Equation 4-9

where

Fs = combustion fraction energy radiated from the flare flame

For fire case, equation 4-10 and 4-11 either can be used for computation of the combustion fraction

energy radiated from the flare flame.

0.32( )6

F C Ps sv Equation 4-10

in which:

C6 = 0.00325 [Pa]0.32

Psv = saturated vapour pressure before depressurization in [Pa]

The correction factor which can have an effect on surface emission power can be used to

determine SEP in large scale as follow:

0.21 exp 0.00323 0.14jF us Equation 4-11

For calculation of the outlet velocity of the expanding jet, u j we can follow the semi-empirical

model in Section 3.3.1.

The heat flux q at a specific distance from the fire that is considered with the receiver per unit

area can be computed as follows:

q SEP F aviewMax Equation 4-12

64

Where:

q = heat flux at a specific length, in [J/[m2⋅s]]

Fview = View factor

τa = Atmospheric transmissivity

For determination of atmospheric transmissivity, the following formula and figures can be utilized.

Fig 4-2: Water vapour absorption factor (Raj 1977)

Through this figure the absorption factor for water vapour αw for median flame temperature of Tf

at a distance x from the flame can be determined. Water partial vapour pressure Pw and relative

humidity [RH] can be computed by:

P RH Pw w [Pa] Equation 4-13

= P w saturated water vapour pressure [Pa]

65

Besides, for the calculating the absorption constant factor for carbon dioxide αc at distance x

from the flame surface for a median flame temperature of Tf [K] we can use Fig 4-3.

Fig 4-3: Carbon-dioxide absorption factor (Raj 1977)

Then atmospheric transmissivity can be determined by:

1 wa c Equation 4-14

If the amount of Pw × X is between 104 and 105 N/m then we can use the following formula:

1

0.082.02 ( )a

P xw

Equation 4-15

4.3.1 Determination of Jet Flare Flames at Flare Tip

A methodology that intends to model the consequence of flare flame geometries on the radiated

heat flux form the flare flame by calculation the radiation source is another procedure that can be

used to calculate the flame distortion and heat radiation. In fact, Chamberlain model (1987) has

been carried out by experimental and practical study while API more depend on practical for flare

66

flame study. Chamberlain model (1987) which was developed in several years of a research, well

known as Thornton-model, can determine the flame geometry and the radiation area of the flare

flame from the stacks and flare tip. This model has been confirmed by wind tunnel experiments

and practical evaluation in the field, for onshore plant and offshore plant. The principal theory

for the behaviour of the flare flame shape introduced by Becker et al(1981). Comparison

of experimental data taken in laboratory and data taken from a practical examination on the field

has illustrated that flare flames shape prediction can be determined with subject to a wider range

of ambient and flow conditions. The factors for the buoyancy force and the wind force needs

a usual flare flame length scale over the forces direction. The procedure to calculate the heat

flux at a specific distance of a jet flame can be done by determining some important factors. First,

determination of the outlet velocity of the expanding jet and dimension of the flame. Then, surface

emissive power [SEP], view factor and the last one is determination of the heat flux at a specific

distance. These steps individually will be described in this section. The outlet velocity of a flare

tip is a key factor for determination of the flare flame length, flare flame lift-off and the widths of

the flare flame throat. [18, 30-31, 43-47, 70-76].

For determination of the outlet velocity of the flare tip we have:

0.5( )Tj

u M Rj j Wg Equation 4-16

Where:

R = gas constant 8.314 [J/[mol⋅K]]

Tj = gas jet temperature [K]

Wg = gas molecular weight [kg/mol]

67

Mj = Mach number

= Specific heat ratio

In which:

Jet Mach number for choked flow can be calculated by:

1

( 1) 2

1

Pc

Pair

Mj

Equation 4-17

And for unchoked flow we have:

2T

1 m' j1 2( 1) 1

20.000036233 d0

1

Wg

M j

Equation 4-18

Where :

In addition for determination of jet momentum flux we have:

2 2

4

u dj j jG

[N] Equation 4-19

m´= mass flow rate [kg/s]

d0= hole diameter [m]

d j = jet diameter [m]

And PC = static pressure at the outlet can be calculated by:

2ln( ) ln( ) ln

1 1P Pc init

[Pa ] Equation 4-20

68

And the jet gas temperature at flare tip can be calculated by:

1ln( ) ln( ) ( ) ln( )

Patmospheric

T Tj initial P

initial

[k] Equation 4-21

Nevertheless, for high-pressure gas, it would be essential to compute specific heat ratio more

accurately:

Cp

CV

in which for ideal gas R

C CV P W g

[J/[kg⋅˚K]] Equation 4-22

The Thornton model introduces the following rough estimation of the mass fraction of flammable

substances in a stoichiometric mixture with air, W, for use in next section.

(15.816 0.0395)

WgW

Wg

Equation 4-23

4.3.1.1 Thornton Model for Determination of Flare Flame Geometry

Geometric factors of the flare flame is introduced by Fig 4-4. Calculation of these factors will be

discussed in this section [7-8, 11-18, 27-31, 53-54, 72-76].

69

Fig 4-4: quadrilateral flare flame shape used by Thornton model (Chamberlain,

1987, Institute of Chemical Engineering)

The five fundamental factor used to correlate the flare flame form are R , W , W , α and bL 1 2

.

Computation of the quadrilateral which represented to fare flame shape surface area with a median

width can be implemented as an alternative way as follows:

22 2 2 2 1( ) ( ) (

1 2 1 24 2 2

W WA W W W W R

L

[m2] Equation 4-24

A= quadrilateral surface area [m2]

70

W1 = width of quadrilateral base [m]

W2= throat tip width [m]

RL= throat length [m]

For quadrilateral geometry parameter determination equation 4-25 can be used.

2( ) ( )

1 2 1 2

2 2 2

W W W WA R

L

[m2] Equation 4-25

Where A = cylinder surface area [m2]

For calculation of the quadrilateral width at flare tip:

1 1(0.18 0.31) (1 0.47 )

2 (1.5 ) (25 )W L

b R Rww ee

[m] Equation 4-26

Where

W2 = width of quadrilateral at flare tip [m]

Lb= length of the flame from flare tip [m]

RW=wind speed ratio to the jet speed [unitless]

And for calculation of the quadrilateral base width we have:

'70 ( )1 1

(13.5 1.5) 1 11 6 15

C RwP R Dsair iW D es R Pwe j

[m] Equation 4-27

Where:

1' 1000 0.8(100 )

CRwe

Equation 4-28

Where wind speed to jet speed ratio can be determined by:

71

uwRW u

j

Equation 4-29

uw = wind velocity, [m/s]

uj = jet velocity, [m/s]

R =i

Richardson number

Moreover, the density ratio among jet and air can be calculated by:

( )

T Wj airair

T Wgj air

Equation 4-30

Where

W1= width of quadrilateral [m]

In addition, air density can be determined by:

P Wairatmosphericair R Tair

[Kg/m3] Equation 4-31

in which:

Pc= static pressure at the hole exit plane [Pa]

Wair = air molecular weight [kg/mol]

Rc = gas constant 8.314 [J/[mol⋅K]]

Tair = air temperature, [K]

We need to determine the Richardson number, which relies on the burning point diameter, which

can be utilized for the computation of the quadrilateral base width:

3( ) ( )4

air gR D Lsi G

Equation 4-32

72

For calculation of the length of quadrilateral, we can use:

1

2 2 2 2sin ( ) cos( )R L b bL b

Equation 4-33

Where RL = length of quadrilateral, [m]

We can calculate the flame lift-off by implementing equation 4-19 in the following correlation:

0.141b G air Equation 4-34

Where:

α = angle between hole and flame

200.185 0.015

RwK e

Equation 4-35

In tranquil air, α is equal to 0°, and b = 0.2 × L . Additionally, for weak flames pointing straightlyb

when wind speed is too low is equal to 180°.

bb = 0.015 × L .The Richardson number of the flame in tranquil air can be calculated by:

13

( ) 02 20

gR Li L b

D ub s j

Equation 4-36

If 0.05Rw , then the flame is jet dominated. The flame distortion angle can be calculated by:

80001( 90 ) (1 )

(25.6 )( )

0

RwjV R Rwe i L

b

[˚] Equation 4-37

in which:

jv = angle among the hole axis and the wind horizontal direction

Ri[Lb0] = Richardson number based on Lb0

73

L = b0

flame length in tranquil air [m]

And If Rw > 0.05, then the flame distortion progressively turns to dominated by wind forces

which can be described by the following formula:

12

(134 1726 0.026 )1=( 90 ) (1 )

(25.6 )( )

0

RwjV R Rwe i L

b

[˚] Equation 4-38

Following the modeling, diameter of combustion source can be determined by the following

formula, which corresponding the throat diameter of an illusory nozzle scheme.

12

4 'D

ms

uair j

[m] Equation 4-39

Where:

Ds = hole diameter, [m]

m' = flow rate, [kg/s]

ρair = air density [kg/m3]

uj = jet velocity [m/s]

If the size of the hole is specified, the mass flow rate at the outlet hole should be computed with

the models from Chapter 2 with respect to the computation of the gas discharge rate.

When we deal with choked flow, the actual hole diameter can be computed by:

WgPcj R Tc j

[Kg/m3] Equation 4-40

74

12

jD ds j

air

[m] Equation 4-41

in which:

Pc = static pressure at the hole outlet [Pa]

dj = diameter of the jet at the outlet hole [m]

ρj = gas jet density [kg/m3]

We can consider that the jet diameter is approximately equal to the diameter of the hole. In the

model, computation of the first excess factor Y by can be driven forward by performing iteration

with the following equation:

2.853 32 2 230.024 0.2 ( ) 032

g Ds Y Y YWu j

Equation 4-42

Where :

Y = dimensionless variable

W = stoichiometric mass fraction (refer to equation 4-23)

The parameter represent the scale among the wind momentum flux in vertical line and jet

momentum flux can be introduced by:

04

air L uairbG


Or it can be calculated as a linear by the following equation:

tan( )

0.178


75

In addition, to compute the jet flame length in tranquil air we can use the following formula:

0L Y Dsb

[m] Equation 4-45

0Lb

= flame length, in tranquil air [m]

And the length of the jet flame from the flare tip to the centre of the exit plane can be calculated

by:

0.51 6.07(( 0.49)) (1 ) ( 90 ))

0 3( 0.4 ) 10L L

b b jVuwe

[m] Equation 3-46

=uw wind velocity [m/s]

The parameters of transformation also determine when jv j :

2 2' ( sin ) ( cos )j jX b X b Equation 4-47

sin' 90 arctan( )cos

j

j

j

b

X b

Equation 3-48

with consideration of 90jv j jv

' 1 2

4

W Wx X

Equation 3-49

Where:

X= flare flame length distance to the object [m]

X' = length distance to the object from the centre of flare flame[m]

Θ' =angle among liftoff flame and plane the bottom centre of the flare flame and object. [°]

Θ =j

angle among hole axis in horizontal direction [°]

W2 = quadrilateral width tip, (refer to Fig 4-4) [m]

76

W1= quadrilateral base width (refer to Fig 4-4) [m]

Object

Fig 4-5: Geometrical factors for determination of lifted-off flare fames

Knowing the SEP and also by consideration of present correlations, and implementing equations

4-51 to 4-65 we can determine FS and FV and with equation 4-66 we can calculate maximum view

factor and apparently maximum heat flux from equation 4-12 where:

F =v view factor in vertical axis

1 2R=4

W W [m] and

' '

1, ,X X L R Equation 4-50

4.3.2 Determination of the View Factors

Three different radiator shapes can be considered for determination of the view factor. These

shapes can be included a vertical cylindrical radiator, a spherical radiator and a vertical flat

radiator. Nevertheless, the most important for elevated flame has been described in this section.

quadrilateral

77

4.3.3 Mudan Model for Determination of View Factor

Mudan in 1987 introduced a theory, which determines the geometrical view factor for horizontal

and vertical surface at a specified point, for cylinder and rectangular shape.

The vertical and horizontal axis view factors can be described by the Atallah (1990) model with

following equations[ 53-54, 72-76]:

2 2( 1) 2 (1 sin ) cos1 1

F tan tan ( )a b b a AD

E D EV AB B C

2 2sin sin1 1

tan ( ) tan ( )ab F F

FC FC

Equation 4-51

2 21 sin sin sin1 1 1

tan ( ) tan ( ) tan (ab F F

Fh D C FC FC

2 2( 1) 2( 1 sin ) 1

tana b b ab AD

AB B

Equation 4-52

Which:

( )LLL bf or

R R R Equation 4-53

Xb

R Equation 4-54

2 2( ( 1) 2 ( 1) sin )A a b a b Equation 4-55

2 2( ( 1) 2 ( 1) sin )B a b a b Equation 4-56

2 21 ( 1) cosC b Equation 4-57

78

1

1

bD

b

Equation 4-58

cos

sin

aE

b a

Equation 4-59

2( 1)F b Equation 4-60

Lf = the inclined flame distances.

L =b

flame length to exit centre of plane [m]

L =f

quadrilateral flame length [m[

L = average flame height [m]

The angle of incline θ is determined with regard to the vertical specified destination which is placed

across the wind direction from the origin point that can be considered positive amount and it can

be considered negative for specified destination situated upwind from the origin point.

4.3.4 Determining the view factors with consideration of the crosswind way

With consideration of the crosswind way which its direction is perpendicular to the incline angle

the calculation of view factors for an specified point can be calculated as follows: [20, 55, 75]

sin sinsin sin1 1 1 12 2 tan tan tan 2 tan ( )

ab abF F FF D

h I I I I

2 21 11 2 sin 2 sin

( ) tan tana b HD a HD a

G G G

Equation 4-61

79

2 21 2 sin2

sin cos2 ln

2 2 2 2 22( sin ) 1 2 sin

Fa b a

a bFV Fa b a b a

b

sin sincos 1 1

tan tan

ab ab

F F

I I I

2 2cos 1 2 sin 2 sin1 1tan tan2 2 2sin

ab a b HD a HD a

G G Gb a

1

2 2 2

2 costan

sin

abD

b a

Equation 4-62

Where:

2 2 2 2 2 2(( 1) 4 ( sin ))G a b b a Equation 4-63

2 2( 1)H a b Equation 4-64

2 2( sin )I b Equation 4-65

The maximum view factor is determined as follows:

2 2F ( )max F FV h

Equation 4-66

80

5 Chapter Five: Depressurization Dynamic Calculation

5.1 Depressurization Dynamic Calculation

Dynamic calculation has to be implemented at the basic engineering design stage to determine

temporary increasing pressure to compute necessary relief rates and other important variables. In

addition, by dynamic calculation we can understand what occurs at the time of relief. Dynamic

calculation should be carried out with respect to facilities such as distillation towers, compression

units, refrigeration systems with multiple loops, and tube ruptures of heat exchanger [API 521].

Also it is very important for evaluation of flare systems during depressurization. If dynamic

calculation is carried out for distillation tower relief arrangement design, it is required to check the

model to make sure it is conservative with regards to computation the total relief load and in some

cases assumptions have to be made. These assumptions should be examined with accurate analyses

to evaluate their effect on the tower relief load. For instance, many calculation runs need to be

carried out to find out the impact of different parameters on different trays on the relief load.

Besides, it is better to share this dynamic modeling with operating personnel since time to respond

to the situation and controlling depressurization can help plant and personnel for preventing of any

hazardous consequences. Generally, for depressurization calculation two major scenarios are keys

for the estimation of peak flow, relief time, temperature and other important variables. The first

scenario is cold depressurization or well known as the adiabatic case. It is intended to simulate the

actual gas depressurization of vessels and piping containing high pressure fluid. The second one

is the fire case that can be carried out to simulate emergency situations in a plant. The fire is

represented by a heat transfer to the vessel. This scenario is described by API 521. For both cases,

81

HYSYS software is used to evaluate the effect of different factors for controlling the conditions.

The depressurization item in HYSYS can be used to evaluate the required time as a function of

pressure and consequently help engineers to recognize material loses at this time. The model

consists of three different stages which are, physical explanation of the pressurized equipment,

thermodynamic conditions of the process, and discharge flow conditions during depressurization

across the valve.

5.1.1 Adiabatic Depressurization Study/Cold Depressurization

Adiabatic depressurization calculation will be evaluated with some assumption data. Since in this

case there is no injection of heat to the system, one important factor for adiabatic calculation is

ambient temperature. The minimum ambient temperature can be taken into account as a safe

margin assumption for the system initial temperature. This assumption is the best engineering

practice for small vessels without insulation. For large vessels, consideration of varying ambient

temperature with some conservatives and delays has to be taken into account for calculation[API

521]. The conservative amount relies on heat amount on the system and maximum heat transfer

rate. An accurate computation should be carried out to determine the minimum temperature in the

system throughout coldest time of the year. Extreme cold can lead to brittleness of construction

materials, and loss of tensile strength and hence to pipe rupture. Table 5-1 shows average minimum

temperature in Fort McMurray in Alberta which can be used to determine the minimum

temperature in worst case at the time of cold depressurization with consideration of other factors.

82

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Daily

Average

[°C]

-17.4 -13.3 -6.2 3.3 9.9 14.6 17.1 15.4 9.5 2.3 -8.6 -15.1

Extreme

Wind

Chill[°C]

-58 -60 -57 -46 -21 -6 0 -6 -16 -32 -50 -53

Daily

Maximum

[°C]

-12.2 -7.1 0.6 10 16.9 21.5 23.7 22.2 15.8 7.4 -4.3 -10.1

Daily

Minimum

[°C]

-22.5 -19.5 -12.9 -3.5 2.8 7.7 10.5 8.6 3.2 -2.8 -12.9 -20

Extreme

Minimum

[°C]

-50 -50.6 -44.4 -34.4 -17.3 -4.4 -3.3 -3.1 -15.6 -24.5 -37.8 -47.2

Table 5-1: Temperature data between years 1981 and 2010 in Fort McMurray, Alberta

Since the temperature goes down, the heat flux among the fluid and the vessel is the key important

factor. One example is to evaluate the depressurization of settle out pressure of compressor cycles

at the time of emergency shutdown. The depressurization model needs a factor to determine degree

of degradation for consideration. As a safe conservative, adiabatic depressurization has considered

as an isentropic depressurization while fire case considered as an isenthalpic depressurization.

However, depressurization calculation assumption for implementing this degree can be between

isenthalpic and isentropic process. As seen in to the Mollier diagram (Appendix F) the isentropic

process gives the lowest temperature for adiabatic case while the isenthalpic process gives the

highest peak flow rate for the fire case, which can be used at the design stage.

Some data has been calculated to evaluate different parameters that can effect on flare flame

distortion and heat radiation. Depressurization evaluation has been carried out by Hysys

depressurization utility v8.6 and some figures for flare flame developed by Microsoft Excel 2013.

83

A depressurization system has to be taken into account to decrease the vessel stress to a safe level

to avoid of vessel rupture and event escalation. According to API, which is based on experimental

studies, a pressure relief system must be capable to reduce the pressure by 50 % in 15 - 30 minutes.

In the calculation below, the valve capacities (CV), which are used for the restriction orifice size,

needs to reduce the pressure by 50% in 15 or 30 minutes as determined by trial and error and

comparing with few existence experimental data.

84

5.1.2 Adiabatic case

Assumption for the related figures are as follows:

Table 5-2 Assumptions for adiabatic depressurization for methane gas

Adiabatic Case

Vessel volume [m3] 64

Vessel thickness [mm] 130

Insulation thickness [mm] 200

Vessel length [m] 9

Vessel diameter [m] 3

Initial pressure [bar] 65

Ambient temperature [C˚] -33.7

Initial temperature [C˚] -27.7

Pipe length [m] 100

Methane [CH4] mole fraction 1

85

Fig 5-1: Depressing in 15 min adiabatic considering Masoneilan valve fully open

Fig 5-2: Depressing in 30 min adiabatic considering Masoneilan valve fully open

86

A depressurization evaluation has been simulated by Hysys, and Fig 5-1 reveals that with

consideration of reaching 50% of design pressure in 15 minutes, vapor at the outlet can reach a

minimum value of -91.62 ˚C in the range between 515 to 537 seconds. With a maximum allowable

time of 30 minutes, as per API concept, it will reach a minimum value of -87.92 ˚C in the range of

630.5 to 638.5 seconds while vessel wall temperature reaches -29.57 ˚C.

Fig 5-2 considering 30 minutes time for depressurization was obtained with a vapour valve

capacity, CV [USGPM(60F,1psi)] equal to 6.58. It shows that peak flow rate is 6115 kg/h, while

Fig 5-1 in 15 minutes is obtained with a vapour CV [USGPM(60F,1psi)] equal to 12.25, shows

the peak flow rate is 11382 kg/hr. These data are highly dependent to the final pressure setting

with consideration of the point where vessel can be ruptured. While the minimum vessel inner wall

temperature reaches to -29.57 ˚C we can evaluate and change the material of construction right

after vessel outlet nozzles both from top and bottom due to the effect of heat transfer. When

increasing time for depressurization by setting final pressure to 50 % of design pressure, since

there is more time for heat transfer, consequently final temperature will be lower in 15 minutes in

comparison with the 30 minutes case. However, in comparison to set Hysys to find a final pressure,

temperature would be lower due to lower final pressure cause to lower temperature. Consequently,

Since the most important factor at the time of depressurization is to avoid rupture of the vessel and

pipe, especially when historical data does not exist at the operation stage, it is recommend to

consider reduction of pressure to the 50% of design pressure in depressurization case at the

operation stage, while for new projects at the design stage for material selection, it is recommend

to consider Hysys to find a valve capacity (CV) in fire cases as the worst case for 15 and 30 minutes

87

time based on maximum material tensile strength, and then implement these values to find a final

pressure in adiabatic depressurization.

5.2 Fire case depressurization

Assumptions for calculation of this case are as follows:

Table 5-3: Assumptions for fire case depressurization for methane gas

API521 Fire Case




Vessel length [m] 9





Pipe length [m] 100

Methane [CH4] mole fraction 1

88



89

These figures in comparison to the adiabatic case (Fig 5-1 and 5-2), show that heat absorption

through the vessel wall from fire leads to higher flow rate discharge required from the vessel. In

addition, density in this case decreases during the depressurization time while in the adiabatic case

in time between 10-14 minutes we can see increasing density versus time. It happens because of

external heat input into the vessel wall.

90

5.2.1 Adiabatic and fire case with different composition

Assumptions for calculation of these cases are as follows:

Table 5-4: Assumptions for adiabatic and fire case depressurization

Adiabatic and Fire Case




Vessel length [m] 9





Pipe length [m] 100

Methane 0.9060

Ethane 0.0515

Propane 0.0013

i-Butane 0.0013

n-Butane 0.0021

Nitrogen 0.0360

Phase Gas

91

Fig 5-5: Depressurization in 15 min considering Fire API, CV 16.8 USGPM (60F, 1psi) and

Masoneilan valve

CV (USGPM) [60F,1psi] 16.8

Final gas Temp. ( C ) -83.4

Inventor Mass (Kg) 4907

Final Gas Mass (kg) 2458

Peak Flow (kg/hr) 1360

Table 5-5: Depressurization in 15 min considering Fire API, CV 16.88 USGPM (60F, 1psi) and

Masoneilan valve

92

These figures have been taken by setting Hysys, first fire API521 case, as the worst case scenario

for depressurization to reach to the 50% design pressure on 15 minutes and then based on given

CV, adiabatic case has been set to determine final pressure.

Fig 5-6: Depressurization in 15 min considering Adiabatic, CV 16.88 USGPM (60F, 1psi) and

Masoneilan valve


Final Gas Temp. at Valve Exit( C ) -86.6

Minimum Gas Temp. at Valve Exit( C ) -95.8

Final Inner Wall Temp. ( C ) -30.6

Minimum Liquid Temp. at Valve Exit( C ) -38.5

Inventor Mass (kg) 4907

Final Gas Mass(kg) 1823

Final Liquid Mass (kg) 25.6


Final Pressure (bar) 24

Table 5-6: Depressurization in 15 min considering Adiabatic, CV 16.88 USGPM (60F, 1psi) and

Masoneilan valve

Vessel wall temperature yellow is liquid and brown is gas

93

Fig 5-8: Depressurization in 30 min considering Adiabatic, CV 16.88 USGPM (60F, 1psi) and

Masoneilan valve




Final Inner Wall Temp. ( C ) -32.9

Inventor Mass (Kg) 4907

Final Gas Mass(Kg) 657

Final Liquid Mass (kg) 6


Final Pressure (bar) 9.64


Masoneilan valve

Vessel wall temperature yellow is liquid and brown is gas

94

Fig 5-6 and 5-8 revealed that the minimum vessel inner wall temperature reaches to -38.56 ˚C for

liquid section and -30.63 in gas section in 15 minutes and by increasing time to 30 minutes vessel

wall temperature for liquid and gas will reach to -48.89 ˚C and -32.9 ˚C respectively. The valve

outlet minimum temperature must be taken into account for material of construction downstream

of the depressurization valve. Two figures shows increasing depressurization time leads to

decreasing vessel metal wall. The study revealed that in some cases following this rule, which is

more realistic for emergency depressurization causes choke flow. Figure 5-6 shows right after

reaching 44% of design pressure that is the limit, based on criteria introduced in equation 3-20,

( )1 10 ( )

2

P

Pa

we will be faced with choke flow. Having the specific heat ratio and pressure

ratio, we can confirm this issue. Increasing time to 30 minutes for the adiabatic case presented by

Fig 5-8, revealed that the final pressure would reach to 9.6 bar, below the critical value for choke

flow with these conditions. Choke flow is hazardous because it can cause vibration on pipes

downstream of depressurization valve and consequently blowout of the flare header pipe. Hence,

determination of allowable time for depressurization must be determined by dynamic calculation

to avoid event escalation.

Takes to account due to in some cases if the final pressure cannot reach to the atmospheric pressure

in a certain time, which is more important for maintenance and plant shutdown, we need to increase

depressurization time by consideration of allowable material tensile strength at the operation stage

or at the design stage increase the downstream pipe size. Engineering cost estimation is

recommend to determine changing material of construction can be beneficial or changing

downstream pipe size.

95

5.2.2 Adiabatic and fire case for liquid Methane

Assumptions for this case would be as follows:

Table 5-8: Assumptions for adiabatic and fire depressurization for liquid methane

Adiabatic and Fire Case




Vessel length [m] 9





Pipe length [m] 100

Methane [mole fraction] 1

Mass density (kg/m3) 211.46

96

Fig 5-9: Depressurization liquid methane at saturated pressure in 30 min Fire API521 case by

masoneilan valve


Final Gas Temp. at Valve Exit( C ) 12.45



Table 5-9: Results for depressurization liquid methane at saturated pressure in 30 min Fire

API521 case by masoneilan valve

97

Fig 5-10: Depressurization, 100% opening by universal gas sizing/Fisher valve for adiabatic case

30 min with CV equal to 21.48 USGPM (60F, 1psi)





Final Pressure (bar) 25.86

Table 5-10: results for depressurization, 100% opening by universal gas sizing/Fisher valve for

adiabatic case 30 min.

98


with 20% opening with CV 21.48 [USGPM (60F, 1psi)


with 20% opening with CV 21.48 USGPM (60F, 1psi)

99

Fig 5-13: Depressurization 15 min adiabatic liquid CH4 by fisher valve with 30% opening and

CV21.48 [USGPM (60F, 1psi)].

Phases have flipped between the vapor and liquid slots in the vessel. Also, a spike or discontinuity

has happened in the dynamic calculation. This happens with supercritical fluid.[refer to Appendix

C]. A spike and discontinuously in pressure in Fig 5-9 reveals that between time 2 to 10 minutes

the system is faced with high pressure drop in a short period across the orifice and cause to

vibration in pipe. In addition, increase velocity/kinetic energy by significant decrease of

pressure/potential energy leads to increasing bubble formation exit from top that cause to valve

rupture.

In terms of characteristics of control valve flow, choosing a quick opening valve for supercritical

fluid cannot be a good procedure for depressurization because the time available to respond by

operators is low, around 4 minutes according to Figure 5-10 and 5-13. Consequently, choosing

equal percentage can be a good suggestion (Appendix C).

100

Choosing universal gas sizing/Fisher with setting the opening percentage to 20%, with calculated

CV by fire API 521 case equal to 21.48, in 15 minutes can be a good solution to control

depressurization event of liquid methane. It should be noted setting more than 20% leads to same

problem shown by Figures 5-10 and 5-13, where fluid will reach the critical point and Cv fail to

converge to a value. This means that due to sudden depressurization we may be faced with vacuum

conditions in vessel or pipe before the allowable time.

101

5.2.3 Dynamic calculation for determination of flare flame distortion and heat radiation

Flare flame distortion and heat radiation for depressurization case has been evaluated by API and

the Chamberlain method known as the Thornton model and figures developed by Microsoft Excel

2013. Assumptions are as follows:

Table 5-11: Assumptions for flare flame distortion calculation

Normal inventory 550

Total inventory volume [m3] 700

Tip diameter [mm] 600

Normal flow [kg/hr] 123300

Peak flow for depressurization [kg/h 156427


Ambient temperature [˚C] -37

Initial temperature [˚C] -27

Pipe length [m] 100

Methane [mole fraction] 0.969

Ethane [mole fraction] 0.03

Propane [mole fraction] 0.0001

Butane [mole fraction] 0.0001

Local wind speed [m/s][Refer to Appendix D] 15

Stack height [m] 57

102

Fig 5-14: Mach number versus time in steady state (blue) and dynamic (red) calculation

Fig 5-15: Flare exit velocity versus time

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950

Mac

h N

um

ber

Time (s)

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

200.00

220.00

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950

Fla

re e

xit

vel

oci

ty

Time (s)

103

Fig 5-14 shows consideration maximum Mach number equal to 0.45 and the steady state

calculation Mach number will violate the criteria, while dynamic results shows that during

depressurization the Mach number may violate the maximum Mach number for only around 1

minute, which is acceptable. Hence, because the process upset is not continually, engineering

judgment for determination of flare header size can help reducing cost of material for construction,

whereas by considering steady state calculation we would conclude that we need to increase flare

header size. In this figure, the blue line represents the steady state calculation and red line represent

to the dynamic results.

Fig 5-16: Heat radiation versus time at the time of depressurization by Chamberlin method

Having the calculation results based on every step time, and by implementing values we can

determine change of Mach number and heat released versus time. As the time to respond to control

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950

Hea

t R

adia

tion (

Kw

/m2)

Time (S)

104

the event is highly dependent to the historical data taken by calculation, implementing a dynamic

calculation and using data for evaluation of flare flame distortion is the way to meet the safety

regulations while steady state may increase cost of material and pipe size.

Fig 5-17: Heat radiation versus time at the time of depressurization by API method

Velocity at exit Sonic velocity Mach No. at exit

193.300 402.716 0.479

Table 5-12: Flare tip exit velocity

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

4.500

5.000

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950

Hea

t R

adia

tion

(K

w/m

2)

Time (s)

105

Fig 5-18: Allowable design limit for flare system modeling and calculation [API 521]

Refer to table 5-18, radiation upper than 4.73 needs an immediate action, which has to be watch

over for the design and calculation of the flare at the basic and detail engineering design.

106

40 m

85m

Ground

Fig 5-19: Flare flame distortion from top view at normal condition, Chamberlain method

Ground

Fig 5-20: Flare flame distortion from top view at normal condition API method

107

Ground

Fig 5-21: Flare flame distortion from top view at the time of depressurization Chamberlain

method

Ground

Fig 5-22: Flare flame distortion from top view at the time of depressurization by API method

43 m

95 m

43 m

108

Flame Length (m) Normal operation Depressurization

Chamberlin 40 43

API 85 95

Table 5-13: Results for flare flame lenght

5.3 A Case Study for Pipeline

Assumptions for the evaluation of a 7 km pipeline transferring methane gas where a puncture

occurs at a point close to the end of the pipe are shown in Table 4-12.

Input

Methane [mole fraction] 1

Temperature [˚C] -27

Pressure [bar] 65

Flow rate [kg/hr] 1,700,000

Pipeline length [m] 7000

Pipeline Diameter [in] 40

Elevation Change [m] 1

Pipe Schedule type 40

Table 5-14: Assumptions for Pipeline case study

109

Fig 5-23: Mach number versus distance in pipeline

Fig 5-24: Temperature versus distance in pipeline

110

Fig 5-25: Pressure versus distance in pipeline

The study assumes maximum inventory, and a puncture or hole close to the destination. The study

revealed that having the Mach number versus distance for any case can give us an important

information for upstream conditions at the time of depressurization. According to Fig 5-23, we can

determine when and where system can violate the criteria then we can install a valve or reroute the

gas to the flare to avoid increasing velocity and Mach number to minimize possible damage to the

pipe. This precaution can prevent escalation of the event.

111

6 Conclusion and Future Work

6.1 Conclusion

This thesis consists of three principal topics. Depressurization dynamic modeling of vessel and

piping, pipeline and consequently flare flame distortion and heat radiation evaluation. Dynamic

calculations for depressurization can play a role as a root term model to determine some important

data regards to the quantity of fluids discharge into the environment. As shown in Figures 5-9 to

5-13 depressurization by current industrial approach, considering 100% valve opening causes

problems downstream of the depressurization valve when supercritical fluid needs to be

depressurized. Data shows choosing fisher/universal gas sizing valve by setting in 20% opening

can handle depressurization in 15 minutes. Therefore, by considering an appropriate logical system

we can control this condition. According to data represented in Figures 5-6 and 5-8, set final

pressure as an unknown variable that should be determined by having the valve capacity,

increasing depressurization time leads to decreasing vessel metal wall, while Figures 5-1 and 5-2

shows increasing time by setting final pressure to the 50% of design pressure leads to higher

temperature. Therefore, at the design stage it is recommend to find a final pressure, by

implementing valve capacity (CV) taken by worst case scenario, instead of setting final pressure

to a fixed value to 50% of design pressure. Therefore, following this procedure leads to taking an

accurate data and choosing an appropriate material of construction that causes to avoid vessel and

pipe rupture and event escalation. In addition, it is recommend to takes to account a determination

of possible choke flow far after restriction orifice to consider adequate safety items to avoid event

escalation.

112

Dynamic results have been used for evaluation of flare flame distortion and heat radiation by two

principal models, API and Chamberlain known as a Thornton-model. The study by the

Chamberlain model shows that in normal operation flare flame length would be equal to 40 m

while with the API model the flame length is 85 m. At the time of depressurization, the flame

length by Chamberlain model would be equal to 43m while the API method equal to 95m. Besides,

maximum radiation predicted at the time of depressurization by Chamberlain model is equal to

5.15 kw/m2, while the API method predicted 3.984 kw/m2. Comparison of the two methods shows

difference around 52m in flare flame length at the time of depressurization. Using the Chamberlain

method shows that increasing jet velocity causes increasing length of the flame and consequently

increasing heat radiation. On the other side, data taken by using the API method shows that flame

stability highly depends on jet velocity that cause to stability and leads to lower heat radiation,

since it leads to increasing distance from center of the flame to the object as well as the height of

the flame, represented in Fig 4-1. While some regulatory limit the exit velocity, following the API

method shows increasing velocity even though Mach number met the criteria, leads to decreasing

radiation, so radiation limit in the engineering approach following API method has adverse with

any regulation which limit the flare tip exit velocity by considering depressurization case, since

decreasing jet velocity cause to increasing heat radiation by this method.

Taking into attention an extinguished flare flame and considering Fig 5-1 and Fig 5-2, gas density

change versus time also can reveal that increasing density between the time of 6 to 10 minutes for

a maximum 15 minutes and 10 to 14 minutes for a maximum 30 min for the adiabatic case has the

maximum amount. Therefore, with consideration of the equation 2.6 and 2.7 in Air Dispersion

Modeling: Foundations and Applications by De Visscher, the buoyancy flux parameter will have

113

a maximum value in this time range and consequently the plume rise has the maximum value at

this time range in terms of plume rise theory viewpoint. The plume rise can be evaluated

dynamically versus time for a detailed review based on air dispersion modeling concept. Three

dimensional numerical model for determination of flare flame distortion can present detailed

information in terms of the momentum flux area in the flare flame, and the velocity that anticipate

a flame geometrical shape which will let them be utilized to anticipate complicated three

dimensional flows. Finally, implementing dynamic calculation can give us accurate results that

can be more practical to evaluate pipe and vessel fluid behaviour at the time of depressurization

both for adiabatic and implementing fire API 521 equation.

114

6.2 Future work

Since different theories exist for the determination of flare flame distortion and heat radiation, a

good engineering judgment has to be based on historical and experimental data whether taken by

modern software or by equations and laboratory experiments in different situation. Rapid

depressurization is one of the most important factors that has to be taken into account with high

attention to all consequences and safeguards. A good engineering design can be carried out with

high attention to the safety to keep personnel and plant safe for operation. The current study

emphasises to consider many factors that effect on basic and detailed engineering design. Taking

to account in some conditions of depressurization can take more than the allowable time, in large

volume inventory, many other factors can be evaluated to determine environmental consequences

in terms of biological or air pollution by this event. Consequently, a future study can be focused

on dynamic calculation of air dispersion with special attention to determine the effect of steam

assisted and air assisted flare. Evaluation of depressurization by consideration of small step size

may give us huge paper reports that can be used for flare flame distortion and heat radiation, so a

new programming can be written associate with depressurization, flare flame distortion, heat

radiation and eventually dynamic calculation of air dispersion consequences.

115

7 References

1) A Survey of Thermodynamics, American Institute of Physics Press, New York, (1994).

2) American Flame Research Committee, International Symposium on Alternative Fuels and

Hazardous Wastes, Oklahoma. (1984).

3) API 520, Sizing, Selection, and Installation of Pressure-relieving (2008).

4) API standard 521, sixth edition, Pressure Relieving and Depressurization systems (2008).

5) ASME Section II, Part D, materials e Properties. (2007).

6) ASTM Data Series DS 11S1, an evaluation of the elevated temperature, tensile, and creep-

rupture (2011).

7) Bayer, D. W. and Pankhuast, R. C.: Pressure- Probe Methods for Determining Wind Speed

and Flow Direction, H.M. Stationery Office, London (1971).

8) Becker, H.A., Liang D. and Downey C.I., Effect of burner orientation and ambient airflow on

geometry of turbulent free diffusion flames. 18th Int. Symp. on Combust, (1981).

9) Beychok, Milton R. Fundamentals Of Stack Gas Dispersion, Flare Stack Plume Rise (2005).

10) Botros K. K.,. Jungowski W. M. and M. H. Weiss, Models and Methods of Simulating Gas

Pipeline Blowdown, Canadian J. Chem. Eng., 67, 529 (1989).

11) Botros P.E., Brzustowski T.A., 5An experimental and theoretical study of the turbulent

diffusion flame in cross-flow symposium Int. Symp. on Combustion, (1979).

12) Briggs, G.A.; Plume Rise and Buoyancy Effects; Atmos. Sci. Power Prod. (1984).

13) Brzustowski T.A, and Sommer E. C. Jr. Predicting Radiant Heating from Flares Proceedings—

Division of Refining, 53, API, Washington, DC, 865–893 (1973).

14) Brzustowski, T. A., Gollahalli, S. R., and Sullivan, H. F. Combust. Sc: Tech. (1975).

116

15) Brzustowski, T. A., Gollahalli, S. R., Gupta, M. P., Kaetein, M., Ano Sullivan, H. F.: Radiant

Heating from Flares, ASME Paper 75-HT-4 (1975).

16) Brzustowski, T. A., Kennedy L. A., Ed.Turbulent Combustion Prog. Astro. and Aero, (1978).

17) Brzustowski, T.A.; Flaring in the Energy Industry; Progress in Energy and Combustion

Science, (1976).

18) Chamberlain G.A., Developments in design methods for predicting thermal radiation from

flares, (1987).

19) Chemical Process Quantitative Risk Analysis - guidelines for Center for Chemical Process

Safety of the American Institute of Chemical Engineers, AIChE (1989).

20) Davis, B.C. and Bagster, D.F., The computation of view factors of fire models, L Loss Prev.

Process Ind. 2. 224-234 (1989).

21) De Visscher A. Air Dispersion Modeling: Foundations and Applications, J.Wiley & Sons

(2013).

22) Duggan J. J., Gilmour C. H., and Fisher P. F., Requirements for Relief of Overpressure in

Vessels Exposed to Fire, Transactions of the ASME, (1944).

23) Franco M., Cost-effectiveness of an ultrasonic flare-gas monitoring system (1991).

24) Gollahalli, S. R., Brzustowki, T. A., and Sullivan, H. F., Trans. CSME, 3:205 combustion and

flame 52:91-106 (1983).

25) Gore, J.P. and Jian, C.Q., Trajectories of horizontal buoyant free jet flames, ASME/ JSME

Thermal Engineering Proceedings, 127-138 (1981).

26) GPSA Engineering Data Book 12 edition [2004].

117

27) Guidelines for Engineering Design for Process Safety, Center for Chemical Process Safety,

(1993).

28) Guidelines for Pressure Relief and Effluent Handling Systems, Center for Chemical Process

Safety (1998).

29) General control device and work practice requirements 40 CFR 60.18.

30) H.M. Brightwell and A.J. Carsley A.D. Johnson, Model for predicting the thermal radiation

hazards from large-scale horizontally released natural gas jet fires, Shell Research Ltd.,

Thornton Research Centre, P.O. Box 1, Chester CHI 3SH (1997).

31) Hajek J. D. and Ludwig E. E., How to Design Safe Flare Stacks, Part 1, Petro/Chem Eng. Part

2, Petro/Chem Engineer, (1960).

32) Haque M. A., Richardson S. M. & Saville G. - Blowdown of pressure vessels - I computer

model.

33) Haque M. A., Richardson S.M. & Saville G. - Blowdown of pressure vessels - II Expe.

Validation.

34) Haque, S. Richardson, G. Saville and G. Chamberlain, Rapid Depressurizafion of pressure

vessel (1989).

35) Health and safety technical report for the Riley Ridge environmental, Michigan University

(1982).

36) Heller F. J., Safety Relief Valve Sizing: API Versus CGA Requirements Plus a New Concept

for Tank Cars, Proceedings—Refining Department, American Petroleum Institute,

Washington, D.C., 123–135. (1983)

37) Hysys v8.6 and HYSYS manuals 2005.

118

38) ISO 23251, Petroleum and natural gas industries—Pressure relieving and depressurization

systems (2007).

39) Duggan J. J., Gilmour C. H., and Fisher P. F., Requirements for Relief of Overpressure in

Vessels Exposed to Fire, Transactions of the ASME, 1–53 (1944).

40) Buettner J. K. J., Heat Transfer and Safe Exposure Time for Man in Extreme Thermal

Environment, Paper 57-SA-20, ASME, New York, (1957).

41) Xia J. L., Smith B. L., and Yadigaroglu G., Simplified model for depressurization of gas-filled

pressure vessels (1993).

42) Johnson, A.D., A model for predicting thermal radiation hazards from largescale LNG pool

fires, IChemE Symp. Series No. 130. Major Hazards - Onshore and Offshore, UMIST

Manchester, 507-524 (1992).

43) Johnson, C.R. and Wilson, D.J.; A Vortex Pair Model for Plume Downwash into Stack Wakes;

Atmospheric Environment Vol. 31, No. 1, 13-20 (1997).

44) Jones, W.P. and Lindstedt, R.P., Predictions of radiative heat transfer from a turbulent reacting

jet in a cross-wind, Combust. & Flame. 89. 45. (1992).

45) Joseph W. Nichols and Schmid P.J. The effect of a lifted flame on the stability of round fuel

jets Laboratoire d’Hydrodynamique, CNRS–E´ cole Polytechnique, 91128 Palaiseau, France.

(2014).

46) Kalghatgi, G.T.; the Visible Shape and Size of a Turbulent Hydrocarbon Jet Diffusion Flame

in a Cross Wind; Combustion and Flame, (1983).

47) Keller, M and Smith, Designing Flares for Enhanced Service Life, Presented at a Seminar

arranged by the Canadian Gas Producers Association June (1983).

119

48) Kim R. H. Storage Tank Blowdown Analysis, PVP, vol. 102, 141 (1986).

49) Lapple E., Isothermal and Adiabatic Flow of Compressible Fluids, Trans. Am. Inst. Chemi.

Eng. (1943).

50) Leung J. C., Overpressure During Emergency Relief Venting in Bubbly and Churn Turbulent

Flow, AIChE Journal, 33, (1987).

51) Ludwig Ernest E., Applied process design for chemical and petrochemical plants, (2014).

52) M.H. Weiss, K.K. Botros, W.M. Jungowski, Simple Method Predicts Gas Line Blowdown

Times Oil & Gas Journal, Dec. 12, 1988.

53) Loss prevention in process industries, volume 2, second edition, Lees F.P, (1996).

54) Mannan, S., Lees’ Loss Prevention in the Process Industries - Hazard Identification,

Assessment and Control 4th Edition (2012).

55) Mudan K.S., Geometric view facors for thermal radiation hazard assessment, fire safety

journal,12,pp.89-96 (1987).

56) Mudan, K.S. et al. (1984), gravity spreading and turbulent dispersion of pressurized releases

containing aerosol.

57) Noble R. K., Keller M. R., and Schwartz R. E., An Experimental Analysis of Flame Stability

of Open Air Diffusion Flames, American Flame Research Committee, International

Symposium on Alternative Fuels and Hazardous Wastes, (1984).

58) Overa, S.O., & Stange, E., & Salater, P., Determination of Temperatures and Flow Rates

during Depressurization and Fire, presented at the 72 Annual GPA Convention, (1993).

120

59) Overaa S. J., Stange E., and Salater P., Determination of temperatures and flare rates during

depressurization and fire, paper presented at 72nd annual Gas Processors Association (GPA)

Convention, San Antonio, Texas, (1993).

60) Parankar, S. V.: Numerical Prediction of Elliptic Flows, (course notes) U. of Waterloo (1974).

61) Picard D.J. and Bishnoi, P. R. the Importance of Real-Fluid Behaviour and Nouisenlxopic

Effects in Modeling Decompression Characteristics of Pipeline Fluids for Application in

Ductile Fracture Propagation Analysis, Canadian J. Chem. Eng., 66, 3 (1988).

62) R. E. and White, J. W. Flare Radiation Prediction: A Critical Review Schwarts, 30th Annual

Loss Prevention Symposium, Session 12, (1996).

63) Raimondi L., Rigorous Calculation of LPG Releases from Accidental Leaks (2012).

64) Raithby, G. D., TORRANCE, K. E.: Computers and Fluids (1974).

65) Reed R. D., Design and Operation of Flare Systems, Chemical Engineering Progress, (1968).

66) Richardson S., Saville G., Chamberlain G., Haque, Rapid depressurization of pressure vessels,

J. Loss Prev. Process Ind. Vol. 3 (1990).

67) Roache, D. J.: Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, N.M.

(1972).

68) Scenario-Based Training in the energy conversion sector Application in Nuon Power

Buggenum IGCC power plant Kotzampasis V., Eindhoven, (2008).

69) Schwartz R. E. and White J. W., Predict Radiation From Flares, Chemical Engineering

Progress (1997).

121

70) Schwartz R. E., Keller M., Environmental Factors versus Flare Application, Paper 13d,

presented at the 11th Loss Prevention Symposium, Houston, Texas, published by American

Institute of Chemical Engineers (1977).

71) Smith, S.H. and Mungal, M.G.; Mixing Structure and Scaling of the Jet in Crossflow; Journal

of Fluid Mechanics, 357, 83-122, (1998).

72) Sparrow, E.M. and Cess, R.D., Radiation Heat Transfer Brooks-Cole Publishing Co. (1966).

73) Turbulent Jet Flames in a Crossflow: Effects of Some Jet, Crossflow, and Pilot-Flame

Parameters on Emissions Bandaru R.V. and Turns S.R Propulsion Engineering Research

Center and Department of Mechanical Engineering, The Pennsylvania State University,

University Park, PA 16802, USA.(1974).

74) Turner, J. S. Buoyancy Effects in Fluids. Cambridge University Press. (1973).

75) Van den Bosch C.J.H., Weterings R.A.P.M., Methods for the calculation of physical effects,

GEVAARLIJKE STOFFEN, (2005).

76) Vessels, J. Loss Prey. Ind., 3, 4 (1990).

77) WILIAMS, F. A. Combustion Theory, Addison- Wesley, Reading (1965).

122

Appendices

Appendix A: Determination of the Darcy Friction Factor fD

The Darcy friction factor fD can be computed by the Colebrook-White law for the transition zone

as follow:

1 2.51102 log( )3.75 Redf fpD D

[unitless] ........................................ Equation 1

The Reynold’s number subject to the flow regime can be determined by:

Red p

u

[unitless] ................................................................................... Equation 2

where

fD = Darcy friction factor [unitless]

dp = pipe diameter [m]

ε = wall roughness [m]

Re = Reynolds number [unitless]

uf = fluid flow velocity [m/s]

ρf = fluid density [kg/m3]

η = dynamic viscosity [N⋅s/m2]

And the Darcy-Weisbach equation also determines the head loss in the pipe as follow:

2

2

f l upD fhLp g d p

[m] ................................................................................ Equation 3

Where

123

g = gravitational acceleration [m/s2]

ΔhLp = head loss [m]

lp = pipe length [m]

The Friction factor can also be determined by the Moody chart for flow in pipes (Figure A.1)

Fig A.1 Friction factor for flow in pipes by Moody chart [Perry's Chemical Engineers' Handbook

1984]

124

Appendix B: Auxiliary Equation Buoyance flux parameter De Visscher Air Dispersion

modeling book

2(1 )sF gr ws sb

[m4/S3] ............................................................................ Equation1

1 13 31.6F x

bhu

[m] .................................................................................. Equation 2

s = density of the gas at stack [kg/m3]

= density of the surrounding air [kg/m3]

rs = stack radius [m]

ws = stack gas velocity in vertical direction. [m/s]

x = distance downwind from the source [m]

u = wind speed [m/s ]

h = maximum plume height [m]

125

Appendix C: Excess Data and Figures

Table C.1: Critical properties of some component (Reid et al., 1987)

Characteristics of control valve flow

Fig C.2: Characteristics of control valve flow with piping

losses[http://www.flowserveperformance.com/performhelp/sizing_selection:valtek:flow_characteristics]

Solvent

Molecular weight Critical temperature Critical pressure Critical density

g/mol K MPa (bar) g/cm3

Methane (CH4) 16.04 190.4 4.60 (45.4) 0.162

Ethane (C2H6) 30.07 305.3 4.87 (48.1) 0.203

Propane (C3H8) 44.09 369.8 4.25 (41.9) 0.217

https://en.wikipedia.org/wiki/Kelvin

https://en.wikipedia.org/wiki/Pascal_%28unit%29

126

Appendix D: Fort McMurray Historical Wind Speed

Table D.1: Wind speed data represent the FortMcmurray ,Alberta

http://fortmcmurray.weatherstats.ca/metrics/wind_speed.html

http://fortmcmurray.weatherstats.ca/metrics/wind_speed.html

127

Appendix E: Mollier diagram

Fig E.1: Mollier diagram, an enthalpy–entropy versus pressure (GPSA 12 edition)

Documents

Depressurization Dynamic Modeling and Effect on Flare