Contents. LWN edition:

Transcription

1 Contents 7. Introdution General Sizing Proedure Seletion of the Sizing Standard Engineering Support List of Symbols Properties of Gases Critial and Subritial Gas Flow Liquid Properties and Visous Flow Phase Change and Two-Phase Flows Examples Calulation of the Compressibility Fator of a Gas Critial and Subritial Gas Flow Sizing Formulas - Summary Sizing aording to ASME Code Set. VIII and API RP 5 and API Premise on ASME Setion VIII and API RP List of Symbols/Nomenlature Aording to API RP Gases and Vapors - Critial Flow Gases and Vapors - Subritial Flow Steam Liquids Two-Phase Flows aording to API RP 5, 7th Edition,, Appendix D Saturated Liquid and Saturated Vapor, Liquid Flashes Highly Subooled Liquid, Non-Condensable Gas/Condensable Vapors, Non-Flashing7.4- Liquid (Frozen Flow) Subooled Liquid enters the Valve and Flashes, No Vapor or Gas at the Inlet Fire Case and Hydrauli (Thermal) Expansion a. to API 5 and ISO List of Symbols/Nomenlature Hydrauli Expansion (Thermal Expansion) External Fire - Wetted Vessels External Fire - unwetted vessels Consideration of Aumulated Pressure in Fire and Non-Fire Contingenies Lift Restrition aording to Code Case Examples Gases and Vapors - Critial Flow () Gases and Vapors - Critial Flow () Gases and Vapors - Subritial Flow Steam Liquids Two-Phase Flow - Saturated Liquid and its Saturated Vapor Two-Phase Flow - Highly Subooled Liquid and a Gas Two-Phase Flow - Subooled Liquid Hydrauli (Thermal) Expansion a. to API External Fire a. to API 5 - Unwetted Walls External Fire a. to API 5 - Wetted Walls Sizing aording to ISO Introdution List of Symbols/Nomenlature Saturated or Superheated Steam - Critial Flow Wet Steam Gaseous Media - Critial Flow ourring at lower dryness fration Gaseous Media - Subritial Flow Liquids Disharge Coeffiient of Valves with Restrited Lift Disharge Coeffiient of Valves at High Bak Pressures Examples Gases - Critial Flow Gases - Subritial Flow Dry Steam Wet Steam Superheated Steam LWN 754. edition:.3. 7-

2 Liquid - Visous Flow Determination of a Required Lift Restrition Determination of the Disharge Coeffiient for Higher Bak Pressures Sizing aording to AD -Merkblatt A List of Symbols / Nomenlature Gases and Vapors Steam Non-Boiling Liquids Disharge Coeffiient of Valves with Restrited Lift Disharge Coeffiient of Valves at High Bak Pressures Summary AD - Merkblatt A Examples Gas - Critial Flow Gas - Subritial Flow Saturated Steam Non-Boiling Liquid Sizing Standards Applying to Cryogeni Appliations Sizing a. to ISO List of Symbols/Nomenlature Example Sizing a. to EN List of Symbols /Nomenlature Guidelines for Speifi Appliations Shell Boilers and Tube Boilers Pressure Side of a Pump Control Valve Failure Pressure Reduing Valve Heat Exhanger Pressurized Hot Water (T > C) Indiative Values for Physial Quantities (k, Z, µ, ν) Undersizing (not less than 3%) Pressure Loss Considerations Conversion Between US and Metri Units Length Area Mass Temperature Density Mass flow Volume Flow Operating Conditions Volume Flow Standard Conditions Pressure Dynami and Kinemati Visosity Energy Speifi Energy Speifi Heat Physial Property Databases Physial Properties of Gases Physial Properties of Liquids Additional Literature Soures LWN 754. edition:.3. 7-

3 7. Introdution Nowadays sizing of safety valves is generally performed with the help of sizing software like VALVESTAR, whih make the sizing and seletion proess fast and relatively easy. The purpose of this hapter of ENGINEERING is to: provide an overview about the most important sizing standards and the formulas whih are used within sizing software based on LESER s long experiene provide helpful advie how to deal with speifi appliations or sizing problems explain some of the physial bakground, whih is helpful to understand speifi problems. This hapter is limited to the sizing of safety valves. The alulation of pressure loss in the inlet line bak pressure reation fore noise emission an be found in hapter 6 Installation and Plant Design LWN 754. edition:

4 7.. General Sizing Proedure A safety valve must be sized to vent the required amount of fluid so that the pressure within the proteted equipment does not exeed the maximum allowable aumulated pressure (MAAP). The fluid an be steam, a gas or vapor, a liquid or a two-phase mixture, e. g. oil and gas or an evaporating liquid. The general sizing proedure foresees: The determination of the required mass flow The alulation of the minimum orifie area using the seleted sizing standard The seletion of a larger orifie area from the LESER atalog Safety valves must be sized and seleted by those who have a omplete knowledge of the safety requirements of the pressurized unit to be proteted. These requirements omprehend at least but not exlusively the Knowledge of the fluid state during venting (gaseous, liquid, frozen or flashing two-phase) Relieving pressure and temperature Mass or volume flow rate Bak pressure Fluid properties at the relieving temperature For liquids: density, visosity For gases, vapors: isentropi oeffiient, ompressibility fator, molar mass, density For two-phase flows: those of the liquid and gas phase. Furthermore, for flashing flows, saturation enthalpies and speifi volumes. If some data are missing, it is general rule to onsider those ourring in the worst possible ase senario, whih onsiders the simultaneous ourrene of all possible auses of overpressure. One the required data are olleted, there are three alternative ways to determine the orret size of the safety valve: Using VALVESTAR ( ) VALVESTAR is LESER s sizing software and it delivers diretly both the orifie size and the omplete doumentation for the safety valve aording to the hosen sizing standard. Sizing formulas They permit the user to size the valve by himself. This presumes that the user is familiar with the sizing proedures and the formulas. It is one aim of this hapter of ENGINEERING to guide the users and to familiarize with the sizing proedures. Capaity harts They are tabulated apaities for steam, air and water in funtion of the relieving pressure, whih are available in our atalogues for eah valve type and orifie area. The user an immediately selet the orifie area whih meets or exeeds the required mass flow rate. Capaity harts were a ommon sizing tool, when no sizing software like VALVESTAR was available In US tehnial literature, this quantity is often referred to as ratio of speifi heats LWN 754. edition:

5 7.. Seletion of the Sizing Standard The information ontained in hapter 7 Sizing is based on following edition of odes and standards: Code / Standard Edition ASME Setion VIII 8 ASME Setion I 8 API RP 5 API 5 7 ISO 46-4 TRD TRD AD Merkblatt -A 6 Table 7..-: Sizing standard edition This hapter of ENGINEERING overs the sizing proedures and their appliation with several examples aording to the most ommon standards. The standards whih are desribed here for the sizing of gas and vapor, steam and liquid flows are ASME Setion I & VIII and API RP 5, inl. two-phase flow sizing from Appendix D, fire ase and thermal expansion of entrapped liquids from API 5 ISO 46- AD Merkblatt -A (6) as well as TRD 4 and TRD 7 If the ustomer does not give any indiation, aording to whih standard the sizing should be done, LESER adopts: Sizing standard seleted by LESER Customer based in Setion in this hapter ISO 46 Europe, inl. Russia and former CIS States Setion 5 AD -A Setion 6 ASME Setion VIII US or in an other ountry/region whih usually adopts Setion 4 Amerian standards, like North Ameria, Middle East or Far East Asian ountries. API RP 5 only if expliitly requested by ustomer Setion 4 Table 7..-: Seletion of sizing standard LWN 754. edition:

6 7. Engineering Support In this setion the norms are based on following edition: ASME Setion VIII (8) and API RP 5 (), ISO 46- (4), ISO 46-7 (4) The setion Engineering Support is a quik and onise guide to the physis involved in the sizing of safety valves. It explains the most important physial properties used in sizing formulas. 7.. List of Symbols Symbol Desription Units [SI] Speifi heat at onstant pressure [J/(kg K)] p v Speifi heat at onstant volume [J/(kg K)] G Speifi gravity [--] h Speifi enthalpy [J/kg] h Speifi enthalpy (gas) [J/kg] G h Speifi enthalpy (liquid) [J/kg] L h Speifi enthalpy (two-phase mixture) [J/kg] mix h GL Δ Latent heat of evaporation [J/kg] M Moleular weight [kg/kmol] k Isentropi oeffiient [--] p Pressure [bar] p b Bak pressure [bar] p Critial Pressure [bar] p Redued Pressure [--] r p Relieving Pressure [bar] R Gas onstant divided by the moleular weight [J/(kg K)] T Temperature [K] T Critial temperature [K] T r Redued temperature [--] v Speifi volume [m³/kg] Z Compressibility fator [--] x Gas mass portion in two-phase stream (quality) [--] ρ Density [kg/m³] μ Dynami visosity [Pa s] Table 7..-: List of symbols LWN 754. edition:

7 7.. Properties of Gases Vapors and gases are gaseous media: a vapor is in a state of equilibrium with the liquid phase, like steam and water, while a gas is in a thermodynami state, where no liquid or solid an form at that temperature, suh as oxygen at typial ambient temperatures. It means that a vapor an ondense or evaporate respetively by inreasing or dereasing the pressure, while a gas an not. The gas formulas in the sizing standards are based on the equation of state in equation p v = Z R T (Eq. 7..-) The density ρ is the inverse of the speifi volume and identifies the mass of a medium ontained in a volume. The speifi gravity G of a gas is the ratio of the density of the gas to that of air at the standard referene ondition, see Eq ρ G = G (Eq. 7..-) ρ air If the gas is pure (= no mixture of different gases), is at the same temperature and pressure of air and an be treated like an ideal gas (Z=), the speifi gravity G is the ratio of the moleular weights, see Eq The moleular weight is the mass of one mole of a ompound. A mole of any substane onsists of an Avogadro's number (6.4 3 ) of atoms or moleules. M G G = ( G Tair M air T = ; p G = pair ; Z G = Z air = ) (Eq ) The ompressibility fator Z is determined from Fig in funtion of the redued temperature and the redued pressure, whih are defined in Eq and as the ratio between the atual (absolute) pressure or temperature and the ones at the ritial point. T r = T T (Eq ) and p r = p p (Eq ) Figure 7..-: Compressibility fator Z in DIN EN ISO 46-7, Page 6 LWN 754. edition:

8 The isentropi exponent or ratio of speifi heats k is the ratio between the speifi heat at onstant pressure Cp and the one at onstant volume Cv, Eq k = p v (Eq ) The sizing proedures require the knowledge of the isentropi exponent at the relieving ondition. Sine both speifi heats are funtion of temperature and pressure, the isentropi oeffiient at the relieving ondition may differ signifiantly from the tabulated values at atm and 5 C in ISO 46-7 or 4.5 psi and 6 F in API RP 5. For instane, air at bar and C has an isentropi oeffiient of.6 ompared to.4 at atmospheri pressure. In general, at atmospheri pressure the isentropi oeffiient is expeted to derease with the temperature. The value of the ompressibility and that of the isentropi oeffiient may not be predited a priori by a simple rule of thumb method. Dediated ommerial software for pure gases and gas mixtures, like NIST Standard Referene Database or GERG-4 and AGA8 for natural gas omponents may ontain a detailed database for a speifi appliation. LWN 754. edition:

9 7..3 Critial and Subritial Gas Flow The distintion between ritial and subritial gas flows is present in all sizing standards and it generates two distinguished sizing formulas. In both ases the mass flow of gas in a safety valve is equal to that of an ideal nozzle multiplied by the disharge oeffiient. On an engineering perspetive, the gas flow in a nozzle is assumed to be adiabati, that is without heat exhange with the ambiene, and energy losses are usually negleted. Under these assumptions the relationship between the pressure and the speifi volume follows Eq p v k = onst (Eq ) If the bak pressure p b is below the ritial value p, the mass flow in the nozzle is alled ritial and it depends only on the relieving ondition, otherwise it is alled subritial and it is a funtion of the ratio of the bak pressure p b and the relieving pressure. Critial gas flow Subritial gas flow pb p p > b p The ritial pressure ratio in the nozzle depends only from the isentropi oeffiient following Eq In the alulation of the ritial pressure ratio both the relieving and the bak pressure are absolute pressures. p p k k = k + (Eq ) Table lists the ritial pressure ratios for some gases at C and atmospheri pressure (soure: ISO 46-7, 4). Gas K p /p Air.4.58 Ethylene Methane Nitrogen.4.58 Ammonia Table7..3-: Critial pressure ratios for seleted gases at C and atmospheri pressure LWN 754. edition:

10 7..4 Liquid Properties and Visous Flow The density ρ of liquids hanges with temperature but it is almost unhanged with pressure, unless the pressure is in the order of hundreds of bar. The speifi gravity G replaes liquid density in the sizing proedure of API RP 5. It is defined as the ratio of the density of the liquid to that of water at the same temperature. Therefore, substanes with a speifi gravity greater than are denser than water and those with a speifi gravity of less than are less dense than water. The dynami visosity μ is a measure of the resistane of a fluid to flow when it is deformed under stress. Visous liquids need larger pressure differenes to move the same mass flow than invisid liquids. When sizing a safety valve, larger valves are neessary the more visous the liquid is. The effet of the liquid visosity in sizing a safety valve is aounted in the visosity orretion fator Kv, whih is expressed in funtion of the Reynolds number Re at the orifie area. The Reynolds number Re, see Eq , is the ratio of the inertial to the visous fore at the orifie area. Re Q 4 μ π A = m (Eq ) orifie The sizing standards onsider the required mass flow rate in the definition of the Reynolds number, even if it is less than the atual disharged mass flow. VALVESTAR optimizes the sizing proedure so that it determines the safety valve for the atual disharged mass flow at the relieving onditions. In Fig and the visosity orretion fator in funtion of the Reynolds number is shown as it is respetively in ISO 46- and in API RP 5. Figure 7..4-: Visosity orretion fator in DIN EN ISO 46-7, Page 9 LWN 754. edition:

11 Figure 7..4-: Visosity orretion fator in API RP 5, Page 54 Question: Is there a threshold in visosity so that the proper safety valve an be seleted without the alulation of the visosity orretion fator? Answer: There is no general rule to define a threshold, sine the Reynolds number depends not only on the visosity of the liquid but also on the mass flow and on the orifie area. Question: What should be done if the Reynolds number is below 34? Answer: This ourrene is not yet regulated within the normative standards and there are some few publiations in the sientifi literature on the topi. In some ases it may be suffiient to heat up the liquid in order to redue the visosity and inrease the Reynolds number. In other ases performing flow tests with the visous medium and a preliminary seleted safety valve maybe the only option. LWN 754. edition:

12 7..5 Phase Change and Two-Phase Flows Depressurization of vessels partially filled with liquids may result in two-phase flows at the inlet of the safety valve. This paragraph presents a short introdution on the topi of phase hange and twophase flows and is helpful to understand the sizing algorithms presented e.g. by API RP 5 (see setion 7.4.7). For any ombination of temperature and pressure a substane is present in one, two or even three states of agglomeration in equilibrium. Usually this information is reported in a phase diagram, where temperature and pressure are the oordinates and the result is the existing phase(s), see Fig for water. The triple point is individuated by that ombination of temperature and pressure, where all three phases (solid, liquid, vapor) oexist in equilibrium. The ritial point individuates the highest pressure and temperature where the gas and the liquid phase oexist. At any pressure between the triple point and the ritial point there is a unique saturation temperature, when the liquid evaporates or the vapor ondenses. A liquid at a temperature below that of saturation is said to be subooled or sub-saturated, while a vapor, whose temperature is above that of saturation is superheated..6 bar 9 Critial point 8 atm 7 C Pressure Solid (ie) Liquid (water) 3.6 bar Triple point Gas (water vapour). C Temperature C 374 C Figure 7..5-: Phase diagram for water Along the saturation urve the fluid is a two-phase mixture of liquid and vapor. From it is however unlear how muh of eah phase is effetively present in the mixture. Therefore a seond diagram, alled saturation diagram, is neessary reporting the speifi enthalpy of the vapor and the liquid at any saturation temperature or pressure, see Fig for water and steam. LWN 754. edition:

13 Critial Point Lines of onstant pressure D Temperature Two phase region (Wet steam) A B X C Figure 7..5-: Saturation diagram for water and steam. Enthalpy The diagram is made up of three setors: the sub-ooled liquid region is on the left side, the region of superheated steam on the right and the two-phase region lies in the middle below the belt given by the saturation urves of vapor and liquid. It shall be assumed that steam in a pressurized vessel at onstant pressure is ooled from the initial state of superheated steam (Point D) to that of sub-ooled water (Point A). The first ooling redues the temperature of steam until it reahes saturation. Any further ooling does not lead to a derease in temperature but to ondensation of some vapor: in any Point X the medium is present as a twophase mixtures. The ondensation goes on until the ondition of saturated steam (Point C) is reahed. Any further ooling of the now fully ondensed water leads to a temperature redution. The differene between the enthalpy of the saturated liquid and that of the vapor is alled latent heat of evaporation, Eq Δ h = h h (Eq ) GL G L LWN 754. edition:

14 Fig shows that the latent heat of evaporation diminishes with the inrease in the saturation pressure until it disappears at the ritial point. From the knowledge of the enthalpy of the mixture and those of vapor and liquid the perental weight of steam in the mixture or quality an be alulated on the base of Eq x h h mix L = (Eq ) G h h L Graphially, the quality x is the ratio of the segment between Point B und Point X to that of the segment between Point B und Point C of Fig The saturation diagram is not representative to estimate the quality of a two-phase mixture, whih is vented in a safety valve in a very short time. The fast depressurization in the safety valve an ause some evaporation of the liquid, whih is usually referred to as flashing. If the liquid is very subooled or the medium is a two-phase mixture of a liquid with a non-ondensable gas, it is more possible that no phase hange ours at all and that the quality of the mixture, here meaning the perental weight of the gas in the mixture, remains onstant during the flow. This type of two-phase flows is alled frozen. LWN 754. edition:

15 7..6 Examples Calulation of the Compressibility Fator of a Gas Example What is the ompressibility fator of ethylene (C H 4 ) at the relieving ondition of 55 C (38.5 K) and 6 bar a? Solution. The first step is to find the ritial temperature and pressure of ethylene. From Table they are respetively 8.85 K and 5.57 bar. The redued temperature and pressure at the relieving ondition are then T 38.5 K p 6 bar a T = = =.6 p = = =. r T 8.85 K p 5.57 bar a r implying a ompressibility fator of around.7 aording to Fig Critial and Subritial Gas Flow Example A buffer reservoir filled with air at 6 bar ( k =. 4 ) vents to the ambiene. Determine if the flow is ritial or not. Solution. The ritial pressure ratio Eq is equal to p p k.4 k.4 = k + =.4 + =.58 The bak pressure to relief pressure ratio for this valve is equal to p b p.35 bar = 6 bar =.69 whih is below the ritial pressure ratio and therefore the flow is ritial. LWN 754. edition:

16 7.3 Sizing Formulas - Summary The following overview is a short summary of the main sizing formulas overed in the following setions. The information ontained in this setion is based on following editions of odes and standards: ASME Setion VIII (8) and API RP 5 (), ISO 46- (4), AD Merkblatt -A (6). Medium Unit ASME VIII / API RP 5 ISO 46- AD Merkblatt A Gases and Vaporsritial flow US SI W A = C K K K P b d T Z M A = Q p C K dr T Z M m qm A =. 79 ψ α p w T Z M Gases and Vaporssubritial flow - US A = 735 W F K K d T Z M P P P A = Q p C K b K dr T Z M m 7.9 W A = ZT SI F KdK M P( P P) Steam US A 5.5 W = m A = PK bkkd K N K SH.883 C Kdr p Q v x qm A = α p w SI A = 9.5 W K PKdKbKKN SH Liquids US A orr = 38 Q K K K K d v w G P P A =.6 A =. 6 m Qm v α w ρ( p pa ) K dr Kv p pb q.78 Q G A = SI KdKwKKv P P Referene Setion 7.4 Setion 7.5 Setion 7.6 Table 7.3-: Summary sizing formulas LWN 754. edition:

17 General symbols: A : Flow area, orifie area G : Speifi gravity (proess) Q : Volume flow (proess) W/Q m : Mass flow (proess) Z/T : Relieving temperature (proess) v : Speifi volume (proess) Z : Compressibility fator (proess) Symbols in ASME VIII / API RP 5: F : Coeffiient of subritial flow see Eq K b : Capaity orretion fator due to bak pressure (gas, vapors, steam) see Fig K = (safety valve without rupture disk) and.9 (safety valve with rupture disk) K d : Disharge oeffiient (LESER atalog) K N : Corretion fator for Napier equation see Eq and Eq K SH : Superheat steam orretion fator see Table K v : Corretion fator due to visosity see Eq K w : Corretion fator due to the bak pressure (liquids) see Fig P : Relieving pressure (proess) P : Bak pressure (proess) C : Coeffiient The oeffiient C is determined as follows. In USC units: C = 5 k k + k ( ) ( k + ) ( ) In SI units: C =.3948 k k + k ( ) ( k + ) ( ) Symbols in ISO 46-: C : Funtion of the isentropi oeffiient see Eq C = k k + ( k + ) ( k ) K b : Theoretial apaity orretion fator for subritial flow see Eq K dr : Certified derated oeffiient of disharge (LESER atalog) K v : Visosity orretion fator see Fig p : Relieving pressure (proess) : Bak pressure (proess) p b Symbols in AD Merkblatt A: p : Relieving pressure (proess) p b : Bak pressure (proess) α w : Certified disharge oeffiient (LESER atalog) ψ : Outflow funtion (gas flows) see Table x : Pressure medium oeffiient (gas flows) or vapour void fration (two-phase flows), see Eq LWN 754. edition:

18 7.4 Sizing aording to ASME Code Set. VIII and API RP 5 and API 5 The information ontained in this setion is based on following editions of odes and standards: ASME Setion VIII (8), API RP 5 (), API 5 (7), API 56 (), API Standard (998), API Standard 5 (), ISO 35(7), pren 45- () 7.4. Premise on ASME Setion VIII and API RP 5 The ASME Code is a pressure vessel ode that overs the ertifiation of safety valves for the flows of saturated steam, water, air and natural gas (Setion VIII UG-3). API RP 5 is a reommended pratie to standardize the pre-seletion of safety valves for gases, vapors, liquids and two-phase flow servie already in the design phase of the plant. API RP 5 uses the same basi formulas as the ASME Code but extends them with orretion fators, e.g. for bak pressure and visosity, to make them appliable to many pratial appliations. Both the ASME Code and API RP 5 apply for relieving pressures above 5 psig. In API RP 5 the pre-seletion of a safety valve requires the determination of an effetive relief area and an effetive oeffiient of disharge, whih are nominal values and therefore independent from the seletion of either the design or the manufaturer. The effetive relief areas are those listed in API 56 in inreasing order from letter D to T. One the safety valve orifie is seleted it must be proven that the ertified apaity meets or exeeds that of the preliminary sizing. For this alulation the engineer must use the atual disharge oeffiient and the atual disharge area from the manufaturer s atalog. In many pratial ases it is enough to verify that the produt of the atual area and the atual disharge oeffiient exeeds that of the effetive area and the effetive disharge oeffiient, as shown in Eq Atual orifie areas and disharge oeffiient of LESER safety valves are doumented in the ASME NB-8 (Red Book) 3. K atual A K A (Eq ) atual d effetive effetive LESER failitates the seletion of the safety valves by introduing LEO (LESER Effetive Orifie). By using LEO the engineer an selet the final size of the safety valve after the preliminary sizing by hoosing a valve with a LEO larger than the effetive orifie. LEO = A K K (Eq ) atual atual d effetive 3 ASME National Board Pressure Relief Devie Certifiations NB-8, Edition: Feb. 9 LWN 754. edition:

19 The atual disharge oeffiients must be ertified by ASME. The appliation of API RP 5 formulas with the ASME ertified atual disharge oeffiient and the atual relief areas from the manufaturers atalog is ommonly alled Sizing a. to ASME Setion VIII. ASME VIII and API RP 5 are interonneted with eah other and it is therefore ommon pratie to present them together as a unique sizing proedure. All formulas are ited here in US units. In VALVESTAR a similar struture is present: The option Sizing a. to ASME VIII is a one-step sizing proedure onsidering the sizing formulas in API RP 5 with their orretion fators and using the atual disharge areas and atual disharge oeffiients. The option Sizing a. to API RP 5 onsiders the two-step sizing proedure disussed before. In both ases the same safety valve will be seleted. Table lists the effetive and the atual disharge oeffiients as well as the effetive and atual disharge areas for LESER API Series Type 56. Medium API RP 5 ASME Code Set. VIII LESER API Series 56 Kd effetive [-] K atual [-] Gas, vapors, steam (Orifie D).8 (Orifie E-T) Liquid (Orifie D).579 (Orifie E-T) Two-phase flows.85 No ertifiation proedure Orifie letter API RP 5 Effetive disharge area ASME VIII Atual disharge area LESER API Series 56 [in ] [mm ] [in ] [mm ] D E F G H J K L M N P Q R T Table 7.4.-: Effetive and atual disharge oeffiients and disharge areas for LESER API Series Type 56 LWN 754. edition:

20 7.4. List of Symbols/Nomenlature Aording to API RP 5 Symbol Desription Units [US] A Required disharge area of the safety valve in C Coeffiient determined from an expression of the ratio of speifi heats of the gas or vapor at relieving onditions lb lbmol R lb hr F Coeffiient of subritial flow -- G Speifi gravity of the gas at standard onditions referred to air at standard onditions or Speifi gravity of the liquid at flowing temperature -- referred to water at standard onditions k Ratio of the speifi heats -- Capaity orretion fator due to bak pressure (gas, vapors, K b steam). -- Applies to balaned bellows valves only K Combination orretion fator for safety valves installed with a rupture disk upstream of the valve -- K d Disharge oeffiient -- K N Corretion fator for Napier equation -- K SH Superheat steam orretion fator -- K v Corretion fator due to visosity -- K Corretion fator due to the bak pressure (liquids). w Applies to balaned bellows valves only -- M Moleular weight of the gas or vapor at inlet relieving lb lbmol onditions P Relieving pressure psi P Bak pressure psi Q Flow rate gpm T Relieving temperature R U Visosity of the liquid at the flowing temperature SSU sfm at 4.7 psia V Required flow through the devie and 6 F W Required flow lb/hr Compressibility fator for the deviation of the atual gas Z -- from a perfet gas, evaluated at relieving onditions μ Absolute visosity of the liquid at the flowing temperature P Table 7.4.-: List of symbols The relieving pressure P is defined in Eq as the sum of the set pressure, the overpressure and the atmospheri value. P = P + ΔP + P set overpressure atm (Eq ) f The orretion fator for the bak pressure, K b, is obtainable from LESER s atalog. Pilot and onventional valves in ritial flows do not neessitate suh a orretion. The ombination orretion fator K in the preliminary sizing must be taken equal to.9 if a rupture disk is inserted upstream of the valve. Otherwise K =.. LWN 754. edition:

21 7.4.3 Gases and Vapors - Critial Flow W T Z A = (Eq ) C K K K P M b d V TZM A = (Eq ) 6.3 CK K K P b d The orretion fator due to the bak pressure V TZG A = (Eq ).75 CK K K P b d Kb for the preliminary sizing is given in Fig Figure : Bak pressure orretion fator for gases and vapors Kb from API RP 5, Page Coeffiient C ,,4,6,8,,4,6,8 3 3, 3,4 3,6 3,8 4 4, 4,4 4,6 4,8 5 Isentropi Exponent k [-] Figure : Coeffiient C in funtion of the speifi heat ratio from API RP 5, Page 44. LWN 754. edition:

22 In alternative to Fig the oeffiient C an be alulated from Eq k + k C = 5 k Unit: k + lb lb lb m mol f hr R (Eq ) LWN 754. edition:

23 7.4.4 Gases and Vapors - Subritial Flow W T Z A = (Eq ) 735 F K K M P P P d V ZTM A = (Eq ) 4645 F K K P d ( P P ) or equivalently V ZTG A = (Eq ) 864 F K K P d ( P P ) A = 735 W F K K d P T Z M r with P P r = (Eq ) where F is alulated from Eq or obtained from Fig k k k r k F = r (Eq ) k r,9 F,8,7 k = ,6,4,5,6,7,8,9, Bak pressure to relieving pressure ratio [psi / psi ] Figure : Coeffiient F in funtion of the ratio of absolute bak pressure on absolute relieving pressure for various speifi heat ratios. LWN 754. edition:

24 7.4.5 Steam W A = (Eq ) 5.5 PK K K K K b d N SH The orretion fator for Napier equation The Superheat steam orretion fator Table 9 on Page 5 of API RP 5. K N is expressed by Eq and P K N = if P > 5 psia (Eq ).9 P 6 K N = if P 5 psia (Eq ) KSH an be taken from Table , whih is extrated from Set Temperature [ F] pressure [psig] Table : Corretion fators K for superheat steam a. to API RP 5 SH LWN 754. edition:

25 7.4.6 Liquids Q G A = (Eq ) 38 K K K K P P d v w The orretion fator due to the bak pressure K w for the preliminary sizing an be read from Fig The orretion fator due to visosity Kv an be either alulated from Eq K v = (Eq ) Re Re by using the definition of the Reynolds number in Eq Q G Re = 8 or μ A Q Re = 7 (Eq ) U A or graphially estimated from Fig When a safety valve is to be sized for visous liquids, it should first be sized as the fluid were in visid ( K v = ) to obtain a preliminary minimum disharge area using Eq The next larger effetive orifie area is then seleted from Table to alulate the Reynolds number in Eq , whih is used to determine the visosity orretion fator in Eq This orretion fator K v is introdued bak into Eq to orret the preliminary disharge area. If the orreted area exeeds the hosen standard orifie, this proedure should be repeated using the next larger standard orifie area from Table Figure : Bak pressure orretion fator for liquids K w from API RP 5, Page 38 LWN 754. edition:

26 7.4.7 Two-Phase Flows aording to API RP 5, 7th Edition,, Appendix D In API RP 5 on page 69 there is a short prefae intended for people approahing two-phase flow alulation routines. The reader is invited to read it arefully before using this sizing proedure. The most relevant points are that. This sizing proedure is just one of the several tehniques urrently in use.. This sizing proedure has not been yet validated by tests. 3. There is no reognized proedure for the ertifiation of safety valves in two-phase flows. Two-phase flows our in a variety of senarios, where either a liquid vaporizes within the safety valve, or a two-phase mixture enters the safety valve or a vapor ondenses in the safety valve a superritial fluid enters the safety valve and ondenses In all ases a two-phase mixture is likely to be disharged from the safety valve. The omplete list of the two-phase flow senarios for safety valves is presented in Table Saturated liquid and saturated vapor enter the valve and the liquid flashes. No non-ondensable gas is present (flashing flow). Superritial fluid ondensing in the safety valve. Highly subooled liquid and either non-ondensable gas, ondensable vapors or both enter the valve but the liquid does not flash (frozen flow). Subooled liquid enters the valve and flashes. No vapor or gas is present at the inlet. Generi two-phase flow with a subooled or saturated liquid and non-ondensable gas with or without ondensable vapor. Table : Two-phase flow senarios See setion See setion See setion (not present in this hapter) The sizing proedure of API RP 5 Appendix D is based on the Omega method of Leung 4. This sizing method uses the so-alled Omega-parameter, whih is a measure of the ompressibility of the two-phase mixture. The required steps of this method are: Calulation of the Omega-Parameter Determination if the flow is ritial or subritial Calulation of the mass flux, whih is the mass flow per unit area Calulation of the required orifie area of the safety valve among those in API RP 56 4 Leung, J.C. On the appliation of the method of Landau and Lifshitz to soni veloities in homogeneous twophase mixtures, J. Fluids Engineering, 996, 8,, LWN 754. edition:

27 Some additional nomenlature, whih is neessary for two-phase flows, is given in Table Symbol Desription Units [US] C Speifi heat at onstant pressure of the liquid at the safety valve inlet Btu/(lb R) p G Mass flux lb/(s ft²) Latent heat of vaporization at the safety valve inlet. For multiomponent systems, it represents the differene between the vapor and the liquid Btu/lb speifi enthalpies at the safety valve inlet h vl h vls Latent heat of vaporization at P s. For multi-omponent systems it is the differene between the vapor and liquid speifi enthalpies at P s Btu/lb P Pressure at safety valve inlet psi P Downstream bak pressure psi a P Critial pressure psi P r Relative pressure [--] Saturation pressure (single-omponent flows) or bubble point pressure P s (multi-omponent flows) at the relieving temperature T psi Q Volumetri flow rate gal/min T Temperature at safety valve inlet R T Relative temperature [--] r v Speifi volume of the vapor at safety valve inlet ft³/lb v v Speifi volume of the two-phase mixture at safety valve inlet ft³/lb Speifi volume of the vapor, gas or ombined vapor and gas at the safety valve inlet ft³/lb Differene between the vapor and the liquid speifi volumes at the safety valve inlet ft³/lb v vls Differene between the vapor and the liquid speifi volumes at P s ft³/lb v Speifi volume evaluated at 9% of the safety valve inlet pressure 9 (= relieving pressure), assuming isentropi flashing ft³/lb x Vapor (or gas or ombined vapor and gas) mass fration (quality) at safety valve inlet [--] η Ratio between ambient pressure and relieving pressure [--] v vg v vl a η Ratio between ritial pressure and relieving pressure [--] η Ratio between saturation pressure at relieving temperature and relieving s [--] pressure ρ Density of the liquid at the inlet of the safety valve lb/ft³ l ρ 9 Density evaluated at 9% of the saturation pressure (single-omponent flows) or bubble point pressure (multi-omponent flows) Ps at T. The lb/ft³ flash alulation should be arried out isentropially. ω Omega Parameter [--] ω Omega Parameter for subooled liquid flows at safety valve inlet [--] s Table : List of symbols for two-phase flows LWN 754. edition:

28 Saturated Liquid and Saturated Vapor, Liquid Flashes The definitions of the Omega-Parameter in Eq , and an be employed for multi-omponent systems, whose nominal boiling range, that is the differene in the atmospheri boiling points of the heaviest and the lightest omponents, is less than 5 F. For single-omponent systems with relative temperature T r. 9 (see Eq ) and pressure (see Eq ) p r. 5, either Eq or Eq an be used. x v v v vl 85 p vl ω = (Eq ) P v h vl C T P v v h vl xv C = T P v v p vl ω (Eq ) vk v hvl For multi-omponent systems, whose nominal boiling range is greater than 5 F or for singleomponent systems lose to the thermodynami ritial point or superritial fluids in ondensing two-phase flows Eq must be used. v 9 ω = 9 (Eq ) v The two-phase flow is ritial if the ritial pressure is larger than the bak pressure P > b < P b P P the two-phase flow is ritial the two-phase flow is subritial The ritial pressure ratio, η = P P, is the iterative solution of Eq ( ω ω )( η ) + ω ln( η ) + ω ( η ) = + η (Eq ) The mass flux is defined in Eq for ritial flow and in Eq for subritial flow G = 68.9 P v G 68.9 P = η ritial flow (Eq ) ω v [ ω ln( Pa P ) + ( ω )( Pa P )] ω( P P ) + a subritial flow (Eq ) Finally, the required area of the safety valve an be omputed from Eq W A =.4 (Eq ) K K K G b d For a preliminary sizing to alulate the effetive orifie area the disharge oeffiient assumed equal to.85 and the orretion fator for bak pressure is that in Fig Kd an be LWN 754. edition:

29 Highly Subooled Liquid, Non-Condensable Gas/Condensable Vapors, Non-Flashing Liquid (Frozen Flow). Same sizing proedure as in Setion but with the Omega Parameter in Eq xv vg ω = (Eq ) vk Subooled Liquid enters the Valve and Flashes, No Vapor or Gas at the Inlet For subooled liquid flows the Omega-Parameter is generally referred with ω s. For multi-omponent systems with nominal boiling range less than 5 F ω s an be alulated either from Eq or from Eq For single omponent systems with a relative temperature and pressure within the limits T. 9 and. 5 ω is given by Eq r p r s v vls ω =.85 s ρl C pt Ps (Eq ) hvls For multi-omponent systems, whose nominal boiling range is greater than 5 F or for singleomponent systems lose to the thermodynami ritial point ω is given by Eq ρ l ω = 9 s (Eq ) ρ9 When a liquid enters the safety valve in a subooled state, it is neessary to determine where indiatively it saturates and the extension of the subooling region on the base of the following table: s ωs P s > P + ω ωs P s < P + ω s s low subooling region (flashing ours before the valve throat) high subooling region (flashing ours at the valve throat) The ondition for the existene of ritial and subritial flow are: in the low subooling region in the high subooling region Critial flow Subritial flow P > Pa P < Pa P s > Pa P s < Pa The mass flux in ase of low and high subooling is: Low subooling region High subooling region.5 { ( ηs ) + [ ωsη s ln( ηs η ) ( ωs )( ηs η) ] } P ρ ω ( η η ) + G= 68.9 l with s s. 5 [ ( P )] G = 96.3 ρ l P with η = η Crit. flow η = η a P = P s P = P a Subrit. flow Crit. Flow Subrit. flow LWN 754. edition:

30 The required area of the pressure relief valve is alulated from Eq Q ρl A =.38 (Eq ) K K K G b d The orretion fator for bak pressure for balaned bellow valves is K w in Fig The disharge oeffiient K d for a preliminary sizing is equal to.65 for subooled liquids at the safety valve inlet or.85 for saturated liquids. LWN 754. edition:

31 7.4.8 Fire Case and Hydrauli (Thermal) Expansion a. to API 5 and ISO 35 This standard deals with the planning of safety requirements for pressure-relieving and depressurizing systems. It analyses the major auses for overpressure and gives some indiative values for the determination of the individual relieving rates in a variety of pratial ases. It is fully introdued in the new standard 5 ISO 35. Formulas in both standards are idential, exept for the units. For the appliation of API 5 formulas the user must use the US units, whih are reported on the third olumn of Table , while for the formulas in ISO 35 the SI units, defined of the fourth olumn of the same table. This setion of ENGINEERING shows the equations for the sizing in ase of Hydrauli Expansion (API 5 Par. 5.4, ISO 35 Par. 5.4) External Fire Case (API 5 Par. 5.5, ISO 35 Par 5.5) Hydrauli expansion or Thermal expansion is the inrease in the liquid volume due to an inrement in temperature. Typially it ours for liquids, whih are trapped in vessels, pipes, heat exhangers and exposed to heat, for instane from eletrial oils, ambient heat, fire, et. In the external fire ase sizing API 5 distinguishes between wetted and unwetted vessels aording to the following definitions and presents for eah of them a sizing proedure. A wetted vessel ontains a liquid in equilibrium with its vapor or a gas. Wetted vessels ontain temperated systems. In onsequene of the heat transfer from the external fire a partial evaporation of the liquid ours. In the alulation of the portion of vessel exposed to fire only that portion in ontat with the liquid within a distane of 5 feet (in ISO m) above the fire soure must be onsidered for sizing, see Table If the exposure to fire leads to vapor generation from thermal raking, alternate sizing methods may be appropriate. An unwetted vessel is a vessel, whih is either thermally insulated on the internal walls or filled with gases, vapors or a superritial fluid. Unwetted vessels ontain gassy systems. Vessels with separated liquid and vapor under normal onditions whih beome single-phase at relieving onditions belong here as well. However, vessels, whose walls beome thermally insulated due to the deposition of oke or material from the ontained fluids, are still onsidered wetted for fire sizing ase however additional protetion is required. In omparison to wetted vessels the thermal flow from the walls to the interior is low in unwetted vessels due to the large thermal resistane. In ase of prolonged exposure of the outside surfae to the fire soure the temperature within the walls may be so high to ause thermal rupture of the vessel. Figure: : Hydrauli (thermal) expansion and fire ase 5 ISO 35 Petroleum and natural gas industries Pressure relieving and depressuring systems, 7 LWN 754. edition:

32 List of Symbols/Nomenlature Symbol Desription Units [US] Units [SI] A Effetive disharge area of the valve [in²] * A ' Exposed surfae area of the vessel [ft²] * A Total wetted surfae [ft²] [m²] ws Cubial expansion oeffiient of the liquid at the expeted temperature [/ F] [/ C] Speifi heat apaity of the trapped liquid [Btu/(lb F)] [J/(kg K)] F Environment fator d Relative density referred to water at 6 F (5.6 C) α v h Latent heat of vaporization [Btu/lb] [J/kg] vl K D Coeffiient of disharge φ Total heat transfer rate [Btu/hr] [W] M Moleular mass of the gas [lb/lb mol ] [kg/k mol ] P Upstream relieving absolute pressure [psi] * Q Total absorbed (input) heat to the wetted surfae [Btu/hr] [W] q Volume flow rate at the flowing temperature [gpm] [m³/s] q m Relief load / mass flow rate [lb/hr] * T Gas temperature at upstream relieving pressure [ R] * T Reommended max. vessel wall temperature [ R] * w Table List of symbols for sizing a. to API 5 * The sizing formulas in ISO 35 are idential to those in API 5, whih are expressed in US Units. Conversion fators to speified SI units have been not yet provided. The appliation of the formula using US units is therefore reommended. LWN 754. edition:

33 Hydrauli Expansion (Thermal Expansion) The mass flow rate for the sizing of the safety valve for a liquid vessel exposed to a heat soure an be approximated by Eq (Eq ) for the ase that the trapped liquid does not evaporate. However, the mass flow rates are usually so small that a safety valve sized NPS ¾ x NPS (DN x DN 5) should be suffiient a. to API 5 Par αv φ q = 5 d αv φ q = d (API 5) (Eq ) (ISO 35) (Eq ) The ubial expansion oeffiient of the liquid should be obtained from the proess data; however, for water and hydroarbon liquids at 6 F (5.6 C) some referene values are given in Table However, more preise values should be obtained from proess design data. Gravity of liquid ( API) α v [/ F] α v [/ C] and lighter.9.6 Water..8 Table Value of ubial expansion oeffiient for hydroarbon liquids at 6 F in API 5 If the liquid is supposed to flash or form solids during the flow in the safety valve, the sizing proedure for two-phase flows in API RP 5 is reommended. LWN 754. edition:

34 External Fire - Wetted Vessels Class of vessels Portion of liquid inventory Remarks Liquid-full, e.g. treaters All up to the height of 5 ft (7.6 m) Surge or knokout Normal operating level up to the height of drums, proess 5 ft (7.6 m) vessels Frationating olumns Working storage Normal level in bottom plus liquid hold-up from all trays dumped to the normal level in the olumn bottom; total wetted surfae up to the height of 5 ft (7.6 m) Max. inventory level up to 5 ft (7.6 m), normally exluding the portions of the wetted area in ontat with the foundations or the ground Spheres and spheroids Table Portions of wetted surfaes to be onsidered Up to the height of 5 ft or up to the max. horizontal diameter, whihever is greater Level in reboiler is to be inluded if the reboiler is an integral part of the olumn For storage and proess tanks, see API Standard 6 or pren 45-7 The amount of heat absorbed from a non-insulated vessel filled with a liquid depends at least on The type of fuel feeding the fire The degree of envelopment of the vessel with fire, whih is a funtion of its size and shape The immediateness of firefighting measures and the possibility of drainage of flammable materials from the vessel The total heat absorption Q for the wetted surfae an be estimated by Eq in ase of adequate drainage and prompt firefighting measures and by Eq in ase of absent adequate drainage and/or firefighting measures. US units SI units Drainage and firefighting measures.8 Q= FA ws.8 Q=43 FA ws (Eq ) Absent drainage and/or firefighting measures.8 Q=345 FA ws.8 Q=79 FA ws (Eq ) Adequate drainage of flammable fuels might be implemented with a strategi use of sewers and trenhes as well as of the natural slope of the land. The values of the environment fator F for some types of installations are olleted in Table In ase the onditions for Eq and are not present, either higher values of the environment fator are assigned on the base of engineering judgment or some protetion measures against fire exposure must be introdued to the plant. For water appliation failities on bare vessels and depressurizing or emptying failities insulation should withstand dislodgement by fire hose streams. Some example drainage riteria are given in API Standard API Standard Venting atmospheri and low pressure storage tanks : nonrefrigerated and refrigerated, pren 45-: Speifiation for the design and manufature of site built, vertial, ylindrial, flat-bottomed, above ground, welded, metalli tanks for the storage of liquids at ambient temperature and above Part : Steel tanks,. 8 API Standard 5 Design and onstrution of liquefied petroleum gas installations (LPG), LWN 754. edition:

35 Type of Equipment F Bare vessel. Insulated vessel, with insulation ondutane values for fire exposure onditions 4 [Btu/(hr ft² F)].7 [W/ (m² K)] Water-appliation failities, on bare vessel. Depressurizing and emptying failities. Earth-overed storage.3 Below-grade storage. Table Values of the environment fator F for various types of installations Heat absorption equations in Eq and are for proess vessels and pressurized storage of liquefied gases. For other storage, whether on pressure vessels or vessels and tanks with a design pressure of 5 psig or less the reommended heat absorption rates in ase of external fire exposure an be extrated from API Standard. The wetted areas for pressurized vessels of different forms in respet of Table are olleted in Table Some examples are desribed also graphially in Fig The symbols are onform to those in VALVESTAR. Class of vessels Sphere Horizontal ylindrial vessel with flat ends Portion of liquid inventory and remarks A = π D F A wet eff D D β D L + D sin β F β π D L D + F π D π D + F 4 wet = eff wet = eff Horizontal ylindrial vessel with spherial ends A ( ) Vertial ylinder with flat ends Partially filled ( F < L ) Totally filled ( F = L ) Vertial ylinder with spherial ends A A wet = eff D π D + F = π D F wet = eff Table Calulation of the total wetted surfae for some vessels. A wet eff LWN 754. edition:

36 Figure : Possible positions of wetted vessels, partially filled with liquids The angle β in Table is defined in Eq Feff ( F D) β = os (Eq ) and the height is the effetive liquid level up to a max. distane of 5 feet away from the flame soure, Eq (Eq ) F eff F eff = min( 5 ft; F) H (API 5) (Eq ) = min( 7.6 m; F) H (ISO 35) (Eq ) The mass flow rate to the safety valve is determined by Eq , onsidering that all absorbed heat vaporizes the liquid W = Q (Eq ) / hvl LWN 754. edition:

37 External Fire - unwetted vessels If the vessel is filled with a gas, a vapor or a superritial medium, Eq may be used to find the safety valve disharge area F' A' A = (Eq ) P F may be determined from Eq if the alulated value is less than., then a reommended minimum value equal to. must be taken. When the available information is not enough to use Eq , then the environment fator an be assumed equal to.45. The reommended maximum vessel wall temperature T w for the usual arbon steel plate materials is F (593 C). For plates made of alloys the wall temperature must be hanged to a more adequate reommended max. value. The onstant C is given from Eq F'.46 C K d ( T T ).5 w =. 656 T (Eq ) The relieving temperature T is determined from Eq in funtion of the normal operating temperature and pressure, respetively T n and p n, and of the relieving pressure P = (Eq ) T T n Pn For plates made of alloys the gas mass flow rate an be alulated from Eq W P A' ( T T ).5 w =.46 M. 56 T (Eq ) The derivation of the formulas for unwetted vessels is based on the physial properties of air and ideal gas laws. Furthermore, they assume that the vessel is non-insulated and without its own mass, that the vessel wall temperature will not reah rupture under stress and that the fluid temperature does not hange. All these assumptions should be heked if they are appropriate for the partiular situation. LWN 754. edition:

38 Consideration of Aumulated Pressure in Fire and Non-Fire Contingenies The requirements on the aumulated pressure in API RP 5, se. 3.5., page 39-4 propose different treatments for the ases of fire and non-fire ontingenies. In non-fire ontingenies the aumulated pressure shall be limited to % of the maximum allowable working pressure (MAWP) in vessels that are proteted by only one safety valve. If the MAWP lies between 5 and 3 psig, the allowable aumulation is fixed to 3 psi. In vessels whih are proteted by more valves in non-fire ontingenies, the aumulated pressure shall be limited to 6% of the maximum allowable working pressure (MAWP) or to 4 psi, if the MAWP lies between 5 and 3 psig. Typially the first safety valve is set at % of the MAWP and it is smaller than all other ones so to minimize the produt loss. The additional valve is larger and it is sized in order to ensure the protetion against the maximum required mass flow. In fire ontingenies the aumulated pressure shall be below % (= % above %) of the maximum allowable working pressure (MAWP), independently if the vessels are proteted by one or more safety valves. Safety valves sized for the fire ase may be also used in non-fire situations, provided that they satisfy the onstrain on the aumulated pressure of % (one valve) and 6% (= % above 5%) (more valves) respetively. Following the strategy of Table , whih is extrated from the table on Page 39 in API RP 5, a safe sizing with a minimum produt loss is possible. The supplemental valves are installed in ase of an additional hazard, like fire ase or other soures of external heat. Supplemental valves are in addition to devies for non-fire ontingeny. Single valve installation Multiple valve installation Contingeny Max. set pressure [%] Max. aumulated pressure [%] Max. set pressure [%] Max. aumulated pressure [%] Non-fire ontingeny First valve 6 Additional valves Fire ontingeny First valve Additional valves Supplemental valve - - Table Set pressure and aumulated pressure limits for safety valves LWN 754. edition:

39 7.4.9 Lift Restrition aording to Code Case Code Case of the ASME Boiler and Pressure Vessel Code provides the guidelines for restriting the lift of a safety valve to ahieve a redued relieving apaity. Safety valves of NPS ¾ or larger an be lift restrited to not less than 3% of the full rated lift, nor less than.8 inh /. mm. A lift restrition aording Code Case requires a ertifiation by an ASME designated organization, whih LESER urrently does not have. As LESER API safety valves have double ertifiation by ASME VIII and PED / ISO 46, LESER an supply API 56 series with a lift restrition aording to PED / ISO 46. In this ase the API valve will not arry an UV-stamp. For details please refer to setion and LWN 754. edition:

40 7.4. Examples Gases and Vapors - Critial Flow () Example It is required to size a onventional valve without rupture dis for a vessel filled with ethylene (C H 4 ) at the relieving temperature of 55 C (59.7 R) and a set pressure of 55 bar g (797.7 psig). The mass flow rate and the bak pressure are respetively 4 kg/h (959 lb m /hr) and bar g (45 psig). The safety valve shall be from the LESER API Series 56. Solution. The relieving pressure is alulated from Eq and it values P = P + P + P = psig psig+ 4.7 psi 89. psi set overpressure atm = From the Example the alulated ompressibility fator Z is.7. The isentropi exponent k and the moleular weight M are given from the ustomer as.9 and 8.3 lb/lb mol respetively. The bak pressure oeffiient an be alulated from Fig , by expressing the set pressure and the bak pressure in psig p barg 45 psig b = = =.8 p 55barg psig s and it results that no orretion for the bak pressure is neessary ( K =. ). The value of the oeffiient C is obtained from Eq C= 5 k k+ k+ k = = 336. The ritial pressure ratio an be alulated from Eq k.9 k.9 p = = =.5664 P k+.9+ ritial flow The absolute pressure ratio for this sizing problem is p b 45psig+ 4.7psi = =.78 P 89.psi lb lb whih is muh lower than the ritial pressure ratio and therefore the flow is ritial. The minimum required effetive disharge area an be alulated from Eq with K =. 975 W A= CK K K b d P TZ 959 = M lb f mol hr b R in² =.in² 8.3 From Table 7..- the disharge area of the effetive orifie E ( A =.96 in² >. in² ) exeeds the minimum requirement. It must be now proven that the atual disharge area of the E orifie ( K d =.8 ; A=.39in² ) meets or exeeds the minimum required atual relief area. W A= CK K K b d P TZ 959 = M in² =.49 in² 8.3 The disharge area of the atual Orifie E is larger than that the required minimum relief area and therefore it suffies the sizing. From the Seletion Chart on Page / of the Catalog LESER Series API the required flange ratings are 6 for the inlet and 5 for the outlet. The safety valve size would be then LESER Type 56 E (56.7). d LWN 754. edition:

41 7.4.. Gases and Vapors - Critial Flow () Example A safety valve is required for a vessel ontaining natural gas (= methane, M = 6.4 lb / ) venting to the ambiene. The required mass flow is 6 lb/hr. The relieving lb mol temperature is 65 R and the design pressure (= set pressure) of the vessel is 8 psig. Solution. The relieving pressure for an overpressure of % values P = P + P + P = 8 psig+ 8 psig+ 4.7 psi. psi set overpressure atm = 7 The ritial temperature and pressure of methane are extrated from Table 7 on Page 43 of API RP 5. They are 673 psi and -6 F ( = 343 R). The relative temperature and pressure are therefore T 65 R P.7 psi T = = =.895 p = = =. R T 343 R p 673 psi 5 R The ompressibility fator Z from Fig for the alulated relative temperature and pressure is about.98 (NIST WebBook :.993). The isentropi exponent k from the NIST Chemistry WebBook is almost.86. The bak pressure oeffiient an be extrated from Fig in terms of ratio between the set pressure and the bak pressure, both in psig p 4.7 psig b = =.837 p 8 psig s and here as well no orretion for the bak pressure is neessary ( K =. ). The value of the oeffiient C is obtained from Eq C= 5 k k+ k+ k = = The ritial pressure ratio an be alulated from Eq p P ritial flow k.86 k.86 = k+ =.86+ =.548 lb lb The absolute pressure ratio is muh lower than the ritial pressure ratio and therefore the flow is ritial. The minimum required effetive disharge area from Eq is W TZ A= = in² = 4.4in² CK K K P M b d From Table the effetive disharge area of the orifie N exeeds the minimum requirement. It remains to prove that the atual disharge area of the N orifie ( K d =.8 ; A= 5.3 in² ) lb f b mol hr R exeeds the minimum requirement. W TZ A= = in² = 5.6in² OK CK K K P M b d and therefore the atual orifie N will be seleted. From the Seletion Chart on Page / of the LESER Catalog API Series the required flange levels are 5 for both the inlet and the outlet and therefore the safety valve LESER Type 56 4N6 (56.59) suits the requirements. LWN 754. edition:

42 Gases and Vapors - Subritial Flow Example Same ase as Example but with a set pressure of psig ( =37.7 psi), bak pressure psig (4.7 psi) and Z =. Solution. The ritial pressure ratio is again that of the Example k.86 k.86 p = = =.548 P k+.86+ ritial flow However, this time the ratio of the absolute bak pressure on the relieving pressure, whih is P 4.7 psi r = = =.655 P 37.7 psi is larger than the ritial pressure ratio and therefore the flow is subritial. The parameter F from Eq is equal to k /.86 k k r.86 / F = r =.655 =.779 k r The minimum required effetive disharge area from Eq is W TZ 6 65 A= = =.73in² 735FK KdP M r The effetive disharge area is then an R orifie. It must now be verified that the atual disharge area of a R orifie of LESER Type 56 ( K =. 8; A= 9.48in² ) is large enough, whih is when it d exeeds the minimum atual required area of W TZ 6 65 A= = = 4.8in² OK 735FK KdP M r The final hoie of the safety valve is therefore LESER Type 56 6R8 (56.665) Steam Example A safety valve must be sized for a large vessel ontaining saturated steam ( K = ) at a set pressure of 6 psig (% aumulation). The expeted mass flow rate is of SH 54 lb/hr. Solution: A onventional safety valve ( K = ) without additional rupture disk ( K = ) is hosen. b The relieving pressure is P = Pset + Poverpressure+ Patm = 6 psig+ 6 psig+ 4.7 psi= psi The orretion fator for Napier equation K N is alulated from Eq P K N = = =.5.9 P The minimum required effetive disharge area is alulated from Eq W 54 A= = =.79 in² 5.5 PK bkkdknksh whih is exeeded by seleting an orifie K. The orifie K of LESER Type 56 ( K =. 8 ; A=.5in² ) is seleted for the atual disharge d area sine it exeeds the minimum requirement of W 54 A= = =.8in² 5.5 PK bkkdknksh The required flanges are 9 (inlet) and 5 (outlet) aording to Page /4 of LESER Catalog for the API Series and therefore the safety valve to be purhased is LESER Type 56 3K6 (56.53). LWN 754. edition:

43 Liquids Example A safety valve must be sized for a flow rate of 5 l/s (79.5 gpm) of glyerin ( G =. 6 ; µ = 4 P ). The set pressure is bar-g (45 psig) with % aumulation and atmospheri bakpressure. Solution The relieving pressure is P = Pset + Poverpressure+ Patm = 45 psig+ 4.5 psig+ 4.7 psi= 74. psi The proedure in API RP 5 foresees a preliminary relief area for invisid servie by using Eq assuming K =. The minimum preliminary effetive disharge area is A = 38 K Q v G 79.5 = prel KdKw P P =.85in² whih would lead to an F orifie ( A=.37 in² ) as effetive disharge area for the invisid fluid. Now the visosity of the fluid has to be onsidered. The assumption of the API RP 5 is that the effetive relief area for the invisid flow may also suit the sizing of the visous flow. Therefore the user must alulate the Reynolds number on the base of Eq on that orifie area. QG Re = 8 = 8 = µ A 4.37 and on the base of this Reynolds number the visosity orretion fator from Eq K v = Re Re = = The orreted (effetive minimum) disharge area for the visous liquid is then Q G A = =.343in² orr 38 K K KK P P = d v w Sine the effetive minimum orreted disharge area exeeds the foreseen orifie, the above proedure for visous flows must be repeated with the larger orifie G ( A=.53in² ). For sake of brevity the Reynolds number, visosity orretion fator and orreted minimum disharge area are given here below Re= 79.6 K =. 87 A orr =.353in² v Sine the orreted minimum disharge area is smaller than the G orifie, the seleted orifie size is suffiient. A quik verifiation that the atual G orifie of LESER Type 44 ( K =. 579 ; A=.66 in² ) suffies is given as following. d A prel =.3in² Re= K =. 794 A orr =.43in² The required valve, inl. the flanges, is LESER Type 56 ½G3 (56.45). v LWN 754. edition:

44 Two-Phase Flow - Saturated Liquid and its Saturated Vapor Example A safety valve must be sized for a two-phase flow of saturated water at bar g (45 psig). The mass flow rate to be delivered is 5 kg/h (75 6 lb/hr). Solution. The relieving pressure is P = Pset + Poverpressure+ Patm = 45 psig+ 4.5 psig+ 4.7 psi= 74. psi The saturation temperature ( T sat = 83 R ) is the temperature at the inlet of the safety valve. At that temperature the physial properties for saturated water and steam are Metri units US units v.63 m³/kg.64 ft³/lb v v.386 m³/kg.84 ft³/lb l h kj/kg vl p Btu/lb C 4.44 KJ/(kg K).66 Btu/(lb R) The Omega Parameter for the ase of saturated liquid at inlet ( x ) is alulated from Eq = P v C ptp vl vvl = +.85 xv v ω = v hvl v hvl ω =4.39 The ritial pressure ratio is the solution of Eq , alulated by means of an iterative trial and error proedure. For ω > a good approximation 9 is given by the following expliit solution 3 = lnω.46 ln ω +.4 ln ω =. η ( ) ( ) 877 Whih leads to the (fluid dynamial) ritial pressure ratio of P = 74.psi.877= 5. 84psi The flow is ritial, sine G= 68.9 η P ωv P > Pa and therefore the mass flux is given by Eq = = lb s ft² The minimum required effetive orifie area is alulated from Eq W 756 A=.4 =.4 = 8.47 in² K K K G b d whih leads to the seletion of an orifie 6Q8 ( A=.5 in² ) (56.657). 9 J.C. Leung Venting of runaway reations with gas generation, AIChE J., 99, 38, 5, LWN 754. edition:

45 Two-Phase Flow - Highly Subooled Liquid and a Gas. Example A safety valve must be sized for a mixture of air and water ( x =. ) at bar g (45 psig) and 5 C ( R) for the mass flow rate of 5 kg/h (75 6 lb/hr). Solution. The relieving pressure is again 74. psi. The required fluid properties at the relieving onditions (74. psi ; R) are Metri units US units v.698 m³/kg.84 ft³/lb v v.9 m³/kg.665 ft³/lb l v kj/kg Btu/lb k.4.4 The speifi volume of the mixture is given as v = xv + x v = ( ).63 ft lb v l = ³ The Omega Parameter is alulated from Eq ω = xv vg vk..84 = = The iterative solution of Eq with this value of the Omega-parameter gives a ritial pressure ratio of η =. 5464, whih orresponds to a ritial pressure of P = psi The flow is again ritial and the mass flow rate an be alulated again from Eq P 74. lb G= 68.9 η = = ωv s ft² The minimum required effetive orifie area is alulated from Eq W 756 A=.4 =.4 = 7.46 in² K K K G b d whih leads again to the seletion of an orifie 6Q8 ( A=.5 in² ) (56.657). LWN 754. edition:

46 Two-Phase Flow - Subooled Liquid Example It is required to size a safety valve for a heating oil at a set pressure of bar g (74. psig) and 4 C (.7 R) with a flow rate of.5 m³/h (55.3 gpm). The bak pressure is bar. Solution. The relieving pressure is P = Pset + Poverpressure+ Patm = 74. psig+ 7.4 psig+ 4.7 psi= 6. psi The saturation pressure at 4 C, P s, is.89 kpa (58 psi) and therefore the medium enters the safety valve subooled ( P >Ps ). The (thermodynami) ritial point is 5 C (39.7 R) and 33. bar (48 psi). The physial properties of the mixture at saturated onditions and the liquid properties at inlet ondition for the alulation of the Omega-parameter are given in the table here below. Metri units US units v.388 m³/kg.388 ft³/lb vls h 6. kj/kg 88.7 Btu/lb vls ρ 687 kg/m³ lb/ft³ l C 65 J/(kg K).633 Btu/(lb R) p The value of the Omega Parameter is alulated by means of Eq , sine T r =.87<. 9 and P =.43<. 5. r = v vls.388 ω.85 s = ρlcptps = hvls 88.7 Determination of the extension of the subooling region ωs 7.8 P = 6. =. 5 psi high subooling region!!! + ω s This highly subooled flow is ritial sine.5 [ ( P P) ] = ( 6. 58) 7.8 P s > Pa and therefore the ritial mass flux is.5 [ ] lb ( ft s) G= 96.3ρl s = 88 The minimum required effetive area of the safety valve from Eq is Q ρl A=.38 =.38 =.668in² K K K G b d whih is satisfied by hoosing the orifie F( A=.37 in² ) (56.3) as the minimum effetive area. LWN 754. edition:

47 Hydrauli (Thermal) Expansion a. to API 5 Example The vessel ontaining the heating oil of the previous example is exposed to sun light. Calulate the mass flow rate that would our in ase of thermal radiation and size the safety valve for the same relieving and bak pressure, assuming a maximum heat transfer rate of 55. kj/hr (58.4 BTU/hr). Solution: The speifi gravity of the heating oil at relieving onditions is G = = The gravity of the liquid in API for oils is alulated on the base of the well known formula API = 3.5= 3.5= 74.8 G.6876 whih orresponds to a value of the ubial expansion oeffiient B of approx..7. The mass flow rate to be released aording to Eq is B H Q gpm = = =. 87 gpm (.56 kg/hr) 5G C The minimum effetive safety valve flow area an be alulated as shown in the previous example. However, for suh a small flow rate the smallest safety valve, orifie D (56.), is by far enough External Fire a. to API 5 - Unwetted Walls Example A arbon steel vessel ( T w =56 R ) is filled with air at a set pressure of psig. The exposed surfae area A is 5 ft². The normal temperature and pressure are 5 F (584.7 R) and 8 psig (94.7 psi). Solution:The relieving pressure aording to Paragraph is P = P + P + P = psig+ psig+ 4.7 psi 35. set overpressure atm = 7 psi On the base of Eq the relieving temperature is P 35.7psi T = Tn = R = R P 94.7psi n The speifi heat ratio at relieving onditions aording to the NIST WebBook Database is almost k.4 ( k =. 39 ). With this isentropi oeffiient the value of the parameter C is alulated with Eq k+.4+ k.4 lbmlbmol R C= 5 k = 5.4 = k+.4+ lbfhr The parameter F is determined from Eq '.46 ( T ).46 ( ) w T F = = =. C K d T Finally, the minimum effetive relief area for the safety valve a. to Eq is F' A'.9 5 A = = =.4 in² P 35.7 whih is satisfied by an effetive orifie G3 (56.45). LWN 754. edition:

48 7.4.. External Fire a. to API 5 - Wetted Walls Example A vertial vessel with spherial ends at a set pressure of psig ontains benzene at F (559.7 R). The vessel has a diameter of 5 ft, a length of 4 ft and an elevation of 5 ft. The maximum fluid level is ft. Assume that the fire-fighting measures intervene promptly in the eventuality of fire and that adequate drainage is present. Solution The amplitude of the wetted walls, heated by the flames, must be estimated to alulate the input thermal flow to the liquid. The free surfae of benzene is 3 ft over the ground. Assuming that the fire level is at the ground, the height of the wetted walls, heated by the flames, is a. to Eq equal to F eff = min( 3 ; 5) 5= ft. And the size of the wetted area from Table is A = π D F = π 5 ft 47.3 ft wet eff = The thermal heat flow is alulated from Eq , assuming the worst ase of bare vessel (with F= from Table ).8.8 Q FA = 47.3 Btu/hr = Btu/hr = wet The relieving pressure P in the vessel is equal to 56.7 psi (= *.+4.7 psi). From NIST WebBook Database the latent heat of vaporization of benzene at 56 psi ( T vap = T = R ) is about 4.9 Btu/lb m. The disharged mass flow of vapor is alulated from Eq W Q / h = / Btu/lb m. = vl The parameter C at relieving onditions is alulated from Eq with the speifi heat ratio at relieving onditions of k. 3 taken from the NIST WebBook Database. C= 5 k k+ k+ k = = 34.3 The required effetive flow area is given by Eq for ritial vapor flow assuming ideal gas behavior. W TZ A= = =.8in² CK K K P M b d For this requirement the orifie 3J4 (56.6) would be large enough. lb m lb lb f mol hr R LWN 754. edition:

49 7.5 Sizing aording to ISO 46- The information ontained in this setion is based on following editions of odes and standards: ISO 46- (4), ISO 46-7 (4), ISO 35 (7) Introdution ISO 46- is a Standard for the sizing and the ertifiation of safety valves. The flow area, whih is extrated from LESER s atalog, must be in exess of the minimum required flow area, whih is alulated with the formulae in Paragraph 5. to 5.6 of this Chapter. In omparison to API RP 5 there are no predefined effetive orifies to selet in a preliminary sizing proedure and the sizing for fire ase and thermal expansion is desribed in the separate norm ISO 35, whih is based on the API 5 (7). ISO 46- is appliable to safety valves with a flow diameter of at least 6 mm and at set pressures equal or above. bar gauge. The sizing formulas in this setion are solved expliitly in terms of the required flow area A, whih permit the immediate seletion of an atual flow area from LESER atalog. The sizing formulas in ISO 46- are idential to those presented here exept that they are written in terms of the mass flow rate Q m List of Symbols/Nomenlature Symbol Desription Units [SI] A Flow area of the safety valve [mm²] C Funtion of the isentropi oeffiient -- K Theoretial apaity orretion fator for subritial flow -- b K Certified derated oeffiient of disharge -- dr K Visosity orretion fator -- v k Isentropi oeffiient (see Par. 3.) -- M Molar mass [kg/k mol ] p Relieving pressure [bar] p Bak pressure [bar] b Q Mass flow rate [kg/hr] m T Relieving temperature [K] μ Dynami visosity [Pa s] v Speifi volume at atual relieving pressure and temperature [m 3 /kg] x Dryness fration of wet steam at the safety valve inlet at atual -- relieving pressure and temperature Z Compressibility fator at atual relieving pressure and temperature (see Par. 3.) -- Table 7.5.-: List of symbols for sizing aording to ISO 46- The relieving pressure p is defined in Eq as the sum of the set pressure, the overpressure and the atmospheri pressure. In Eq the overpressure is generally % of the set pressure also for safety valves, whih are fully open at set pressure plus an overpressure below %. p = pset + Δ pover + pamb (Eq ) ISO 35 Petroleum, petrohemial and natural gas industries pressure-relieving and depressurising systems, 7 LWN 754. edition:

50 7.5.3 Saturated or Superheated Steam - Critial Flow with Qm ν A = (Eq ).883 C K p dr ( k + ) ( k ) C = k (Eq ) k + Values for the isentropi oeffiient k at ambient temperature and pressure of many ommon pure gases, whih are ited in ISO Wet Steam x Qm ν A = (Eq ).883 C K p dr The formula applies only to homogeneous wet steam with a minimum dryness fration of 9 %. The dryness fration of 9% is an indiative value to distinguish between a wet steam flow and a more omplex two phase flow Gaseous Media - Critial Flow ourring at lower dryness fration. Qm ZT A = (Eq ) p C K M Gaseous Media - Subritial Flow dr with Liquids Qm ZT A = (Eq ) p C K K M b dr k ( k + ) k k p b pb k p p K b = (Eq ) ( k + ) ( k ) k k + A =.6 Qm K K dr v p v p b (Eq ) The visosity orretion fator K v in funtion of the Reynolds number Re follows Fig The Reynolds number is defined as Q m 4 Re = (Eq ) 3.6 μ π A Two phase flow is not yet overed by ISO 46, however F Dis ISO 46-part overing two phase flow will be published soon. ISO 46-7 Safety devies for protetion against exessive pressure Part 7: ommon data, 4. LWN 754. edition:

51 7.5.8 Disharge Coeffiient of Valves with Restrited Lift A restrited lift allows the user to limit the disharged flow apaity from the safety valve to a value equal or loser to the required apaity. The restrition of the valve lift makes sense, when: Gas or Two-phase flows the safety valve is oversized AND the inlet pressure loss is larger than 3% ( possibility of valve hattering) or the built-up bak pressure is too large due to exessive flow. Liquid flows the inlet pressure loss is larger than 3% ( possibility of valve hattering) or the built-up bak pressure is too large due to exessive flow. Thermal expansion alone is not a reason. In any ase, oversizing alone is not the reason to install a lift restrition and there is no rule of thumb determination of an indiative perentage of allowable oversizing. It rather depends on the installation onditions of the safety valve, for instane on the inlet and outlet line onfiguration. A lift restrition should be installed to redue problems with exessive inlet pressure loss or built-up bak pressure aused by the exessive flow in an oversized safety valve. The lift restrition limits the flow of the safety valve to the required one and therefore redues the pressure loss at the inlet and the built-up bak pressure at the outlet. ISO 46- Par allows the manufaturer to restrit the lift to a value larger than either 3 % of the unrestrited lift or mm, whihever is greater. However, in ase the optimal lift is less than 3 % but more than mm, onsult the following setion for AD- Merkblatt A. The appliation of the AD- Merkblatt A is in ompliane with PED requirements. For safety valves with a restrited lift the manufaturers are required to generate a urve showing the hange of the disharge oeffiient with the lift, like that in Fig for LESER Type 44/44. VdTÜV guidane requires that this urve must be obtained with a ratio of the absolute bak pressure on the relieving pressure, p a /p, above the ritial pressure ratio. An example how to alulate the restrited lift is proposed at the end of this hapter. In VALVESTAR the user an selet the option of restrited lift with just a mouse lik and the software sizes the safety valve with the minimum lift required to deliver the required mass flow. VdTÜV-Merkblatt Siherheitsventil, Rihtlinie für die Baumusterprüfung von Siherheitsventilen im Geltungsbereih der Rihtlinie 97/3/EG (Drükgeräte-Rihtlinie),6 LWN 754. edition:

52 Figure Disharge oeffiient K dr for gases in funtion of the lift h over flow diameter d o for LESER Type 44 LWN 754. edition:

53 7.5.9 Disharge Coeffiient of Valves at High Bak Pressures ISO 46- Setion also onsiders the possibility that the disharge oeffiient for gases and vapors in subritial flows is less than that in ritial onditions. Conretely, if the ratio of the absolute bak pressure P a to the relieving pressure P exeeds the value of.5, the oeffiient of disharge an depend upon this ratio. The manufaturer is required to ertify the flow apaity of the valve for ratios of the absolute bak pressure on the relieving pressure between.5 and the maximum pressure ratio. This urve may be extended to over the tests with pressure ratios less than.5, if neessary. VdTÜV states expliitly that this urve must be obtained with a onstant lift ratio, h / d. Fig represents suh an example of a bak pressure dependene for the safety valve LESER Type 44. From its internal databases VALVESTAR selets the disharge oeffiients of the safety valve whih our for the given ratio of absolute bak pressure to relieving pressure. Figure Disharge oeffiient K dr for gases in funtion of the ratio of the absolute bak pressure P a on the relieving P pressure for LESER Type 44 LWN 754. edition:

54 7.5. Examples Gases - Critial Flow Example A safety valve for ethylene (C H 4 ) at the relieving temperature of 55 C (38.5 K) and a set pressure of 55 bar g for a relieving mass flow rate of 4 kg/h and bak pressure of bar g is required. For the type assume LESER Type 459 with a K equal to.8. Solution. The relieving pressure values P = Pset + ΔPoverpressure + Patm = 55 bar bar + atm = 6. 5 bar From the Example the ompressibility fator Z is.7, the isentropi exponent k and the moleular weight M are respetively.9 and 8.3 kg/k mol. The flow funtion C is alulated from Eq C = k k + k + k = =.553 The ritial bak pressure is alulated from Fig and it is equal to k ( k ).9 (.9 ) p = p = 6.5 bar = k and the flow is ritial sine the bak pressure of. bar is lower than the ritial pressure. Therefore the oeffiient K b is in this ase not neessary. The required neessary relief area omes from Eq Q Z T m A = = mm = 95.4 mm p C K M dr whih is satisfied by the valve with a relief area of 33 mm² (diameter: 3 mm) (4593.5). bar dr Gases - Subritial Flow Example Same as Example but with a bak pressure of 35 bar g (36. bar). Solution. The flow in the safety valve is in this ase subritial and therefore the orretion fator must be alulated a. to Eq k ( k + ) k.9 (.9+ ).9 k p b pb k p p K = = b =.999 ( k + ) ( k ) (.9+ ) (.9 ) k.9 k The minimum required relief area, alulated from Eq is Q Z T m A = = mm = 7. mm pc K dr K b M whih is satisfied again by the LESER Type 459 with a relief area of 33 mm² (4593.5). Note: Observe that the derated disharge oeffiient is less than that of the previous example due to the higher bak pressure ratio. See Example for a detailed example. LWN 754. edition:

55 Dry Steam Example A safety valve must be sized for (saturated) steam in a large vessel at a set pressure of.4 bar gauge for a mass flow rate of 698 kg/hr, assuming % overpressure. Solution. The relieving pressure is P = Pset + ΔPoverpressure + Patm =.4 bar +.4 bar +. bar =. 45 bar The speifi volume and the isentropi exponent of saturated steam at relieving onditions a. to IAPWS IF 97 tables 3 is equal to.3885 m³/kg and.966, whih is in good agreement with the value, obtained by interpolating the data from ISO With this isentropi oeffiient the required parameter C from Eq is C = k k + k + k = =.3636 In view of the high pressure and apaity requirements, a safety valve LESER Type 458 is seleted. At first we size using the derated disharge oeffiient of.84, whih suits for most of the sizes of this safety valve type. With that value of the disharge oeffiient the required flow area from Eq is Qm v A = = mm = 98 mm.883 C K dr p Consequently, a relief area of 964 mm² (DN 8/) (458.64) would suffie. However, the derated disharge oeffiient for that size is.83; nevertheless, introduing of the true value of the disharge oeffiient the valve size is onfirmed. Qm v A = = mm = 34 mm.883 C K p dr Note. The isentropi oeffiient of steam at the relieving onditions is different in ISO 46-7 and IAPWS Database Wet Steam Example Same problem as in Example but assuming a wet fration of 3 % Solution Wet Steam. The fration of dry steam on the wet steam is equal to 97 % or.97. For wet steam a smaller minimum flow area is required than that if the steam were dry. From Eq it is equal to Qm x v A = = mm = 94.3 mm.883 C K p dr The relief area of the safety valve is nevertheless again equal to 964 mm² (458.64). 3 W. Wagner, H. Kretzshmar Ed., International steam tables: Properties of water and steam based on the industrial formulation IAPWS-IF97, Springer, Berlin, 8 LWN 754. edition:

56 Superheated Steam Example Same problem as in Example but assuming superheated steam at a set pressure of.4 bar and 4 C Solution Superheated Steam. Also in ase of superheated heat values of the isentropi oeffiient and of the speifi volume at relieving onditions are needed. From IAPWS tables they are respetively.79 for the isentropi oeffiient and.4 m³/kg for the speifi volume and they are lose to the values from the interpolation of data in ISO On their behalf the parameter C from Eq is equal to k k.79 C = k = =.69 k Assuming the derated disharge oeffiient of.84, the required area using Eq must exeed Qm v A = = mm = mm.883 C K dr p whih suggests that again a relief area of 964 mm² is enough (458.64). Indeed, onsidering the orresponding derated disharge oeffiient for that valve size, whih is.83, the minimum required area is equal to Qm v A = = mm = 47. mm.883 C K p dr Liquid - Visous Flow Example A safety valve must be sized for a flow rate of 5 l/s of glyerin (density :6 kg/m³ and visosity: 4 mpa s) at a set pressure is bar-g and atmospheri bakpressure with % aumulation. Solution The (mass) flow apaity must be expressed with the units of ISO Q m = 5l / s 6kg / m 36s / hr = 68kg / hr For this high disharge appliation LESER Type 44 an be seleted. The relieving pressure is P = Pset + ΔPoverpressure + Patm = bar + bar +. bar =. bar The required minimum flow area is alulated with a two-step proedure. At first the relief area is alulated as the liquid were invisid. Aording to Eq this preliminary minimum flow area is Qm v A = = mm = 65.9 mm.6 K dr p pb Then the next larger relief area A ' must be seleted from the manufaturer s atalog, whih equals in this ase 46 mm² ( DN 5/4 ) and is assumed as the preliminary flow area. The ratio of the alulated A to A' gives the minimum value of the visosity orretion fator that the real fator is required to exeed. In this ase the minimum visosity orretion fator is K v min = A A' = =.639 Using the seleted relief area the Reynolds number is alulated from Eq Q Re = m = = μ π A' π 46 On behalf of this Reynolds number the visosity orretion fator from Fig is about.79. Sine this visosity orretion fator oeffiient exeeds the minimum required value, the safety valve LESER Type 44 DN 5/4 (44.438) is the final flow area a. to ISO 46. In ase it were not, the next larger A ' must be extrated from the manufaturer s atalog and the previously illustrated proedure routines until the minimum visosity orretion fator is exeed. LWN 754. edition:

57 Determination of a Required Lift Restrition Example Whih lift restrition would be neessary in Example to minimize the flow from the safety valve in exess of the required one? Solution. As a result from Example a flow area of 33 mm² (d = 3 mm) is hosen. However, from the proess data the atual disharged mass flow a. to Eq is muh larger than the required one and exatly it is M 8.3 kg Q = p C A K m real dr = = ZT h In order to have a disharged mass flow loser to the required one, the disk lift must be redued. The ratio between the redued and the full lift derated disharge oeffiient is given by the ratio of the required to the effetively disharged mass flow Kdr red Qm required Qm required 4 = Kdr red = Kdr full =.8 =. 58 K Q Q dr full m effetive m effetive whih orresponds to the lift ratio h/d of.74 or.3 mm, a. to Fig. on Page 5/ of the LESER Catalog Compat Performane, reported here below. LWN 754. edition:

58 Determination of the Disharge Coeffiient for Higher Bak Pressures Example Find the disharge oeffiient for the ratio of bak pressure on the relieving pressure in Example Solution. In Example the bak pressure is 35 bar gauge (36. bar) and the relieving pressure 6.5 bar, whih orresponds to a p a /p ratio p a 36. = =.5854 p 6.5 A. to Fig. 8 on Page 5/ of the LESER Catalog Compat Performane, reported here below, it orresponds to the derated disharge oeffiient of.7. LWN 754. edition:

59 7.6 Sizing aording to AD -Merkblatt A The information ontained in this setion is based on AD -Merkblatt A edition 6. AD Merkblätter are guidelines satisfying the requirements for the onstrution of pressurized vessels ontained in the PED diretives. Among all other information, AD A ontains indiations for the installation and the sizing of safety valves and may be used alternatively to ISO 46. Sizing a. to AD A is applied by LESER upon expliit request from ustomers. The minimal flow ross setion of the safety valve must exeed the minimum one, whih results from the following formulas. AD A presribes a minimal flow diameter of at least 6 mm for the general ase or mm for pressure vessels with greasy or powdery media or for media, whih are inlined to oalese. The minimum values of the derated disharge oeffiient that the safety valves are required to have are:.5 for full-lift valves, exept for those with a lift restrition.8 (Gas/Vapor).5 (Liquid) respetively for normal and proportional safety valves 7.6. List of Symbols / Nomenlature Symbol Desription Units [SI] A Minimal ross setion of flow [mm²] Isentropi exponent (see isentropi oeffiient in ISO 46) k (see Par. 3.) -- M Molar mass [kg/k mol ] p Dynami bak pressure behind the valve [bar] a p Pressure of the medium at saturation temperature [bar] s p Absolute pressure in the pressure hamber [bar] q Mass flow to be disharged [kg/h] m T Temperature of the medium in the proteted system [K] v Speifi volume of the medium in the pressure hamber [m³/kg] Y Outflow funtion (two-phase flows) -- Pressure medium oeffiient (gas flows) [h mm² bar/kg] x Vapour void fration (two-phase flows) -- Z Compressibility fator of the medium in the pressure hamber (see Par. 3.) -- α w Certified disharge oeffiient -- ψ Outflow funtion (gas flows) -- ρ Density Kg/m³ Table 7.6.-: List of symbols for sizing aording to AD A The relieving pressure p is defined in Eq as the sum of the set pressure, the overpressure and the atmospheri value. For the overpressure in Eq generally % of the set pressure is used, also for safety valves that are fully open at set pressure plus an overpressure below %, e.g. for full lift safety valves with 5% overpressure.. p = p + Δ p + p set over amb (Eq ) LWN 754. edition:

60 LWN 754. edition: Gases and Vapors M Z T p q A w m 79. α ψ = (Eq ) with the outflow funtion defined in Table Subritial flow + > k k a k p p k k a k a p p p p k k + = ψ Critial flow + k k a k p p + + = k k k k ψ Tab Outflow funtion for ritial and subritial gas flows Steam p q x A w m α = (Eq ) The pressure medium oeffiient x is defined in Eq ψ v p x.6 = (Eq ) The values of the speifi volume and the isentropi exponent for the alulation of ψ are extrated from State Variables of Water and Steam, Springer, Berlin, 969. AD A does not state, if more atual versions of this database, like the IAPWS tables, shall be onsulted. In replaement of Eq the pressure medium oeffiient for ritial flows an be taken from Fig For subritial flows as well as for set pressures below bar this graph an not be used and the pressure medium oeffiient must be alulated. Fig Pressure medium oeffiient for steam in funtion of the response pressure (set pressure)

61 7.6.4 Non-Boiling Liquids A =. 6 α w ρ q m ( p p ) a (Eq ) Non-boiling liquids do not hange phase when flowing in the safety valve. AD A gives no referene to a visosity orretion fator for visous liquids. Nevertheless, VALVESTAR follows the sizing proedure in ISO 46- for the determination of the visosity orretion fator Disharge Coeffiient of Valves with Restrited Lift The disharge oeffiient for safety valves with a lift restrition or in ase of high bak pressures are ertified a. to VdTÜV Merkblatt Siherheitsventile (see setion and 7.5.9). The lift must be at least mm without a perentage limitation as in ISO 46-. For all other details see Disharge Coeffiient of Valves at High Bak Pressures Qualitatively idential to Setion Summary AD - Merkblatt A The AD Code an be applied to satisfy the basi safety requirements of the Pressure Equipment Diretive (PED). That means, sizing a safety valve a. to AD A is in ompliane with the PED requirements. The sizing formulas in the standard AD A are for gases, vapors, liquids not requiring visosity orretion fators are idential to those in ISO 46-. A lift restrition below 3 % of the maximum lift is allowed as long as it is more than mm. LWN 754. edition:

62 7.6.8 Examples Gas - Critial Flow Example A safety valve is sized for a mass flow rate of 4 kg/h ethylene (C H 4 ) at the relieving temperature of 55 C and a set pressure of 55 bar g and bak pressure of bar g. The safety valve is the LESER Type 459 with α equal to.8. Solution. The relieving pressure values P = Pset + ΔPoverpressure + Patm = 55 bar bar + atm = 6. 5 bar w From Example the ompressibility fator Z is.7. The isentropi oeffiient k and the moleular weight M are given from the ustomer as.9 and 8.3 kg/k mol and the flow is ritial. The flow funtion ψ is alulated from the first line of Table ψ = k k + k + k = =.457 The required neessary flow area is alulated from Eq q T Z m A =.79 =.79 = 95.4 mm² ψ α p M w The flow area of 33 mm² (d = 3 mm) (4593.5), as already seen using ISO 46-, will be large enough to release the given mass flow rate. LWN 754. edition:

63 Gas - Subritial Flow Example Same as Example but with a bak pressure of 35 bar g (36. bar). The disharge oeffiient omes from Example and is equal to.7. Solution. From Example we know that the flow in the safety valve is in this ase subritial and therefore the outflow funtion must be taken from the first line of Table ψ = k k p p a k p p a k + k = =.4568 The minimum required flow area aording to Eq is q T Z m A =.79 =.79 = 7. mm² ψ α p M w whih is satisfied again by the LESER Type 459 with a relief area of 33 mm² (d = 3 mm) (4593.5) Saturated Steam Example A safety valve must be sized for saturated steam at a set pressure of.4 bar g with a mass flow of 698 kg/hr, assuming % overpressure. In view of the high pressure and apaity requirements, a safety valve LESER Type 458 with a disharge oeffiient of.83 is seleted. Solution. The relieving pressure is P = Pset + ΔPoverpressure + Patm =.4 bar +.4 bar +. bar =. 45 bar The speifi volume and the isentropi exponent of saturated steam at.45 bar are taken from IAPWS tables equal to.3885 m³/kg and.966. The outflow funtion ψ from Table equals ψ = k k + k + k = =.433 The pressure medium oeffiient is alulated from Eq as pv h mm² bar x =.6 =.6 =.98 ψ.433 kg The required flow area is finally alulated from Eq x qm A = = = 33.7 mm² α p w The required relief area would be 964 mm² (d = 4 mm) DN 8/ ( LWN 754. edition:

64 Non-Boiling Liquid Example A safety valve Type 44 must be sized for a flow rate of 5 l/s of water (density :998 kg/m³ ) and a set pressure is bar g with atmospheri bak pressure and % aumulation. Solution The required mass apaity is q m = 5 l s *998kg m³*36 s h *.m³ l = 7964kg / h The relieving pressure is P = Pset + ΔPoverpressure + Patm = bar + bar +. bar =. bar The required flow area aording to Eq is equal to qm 7964 A =.6 =.6 = 6. 5mm α ρ p p w ( ) ( ) a The required relief area is 54 mm², whih orresposnds to the size DN /3 (44.437) LWN 754. edition:

65 7.7 Sizing Standards Applying to Cryogeni Appliations In this setion the norms are based on following edition: ASME Setion VIII (8), EN 336 (), ISO 46- (4), ISO 3-3 (6), pren 693 (996) ASME Setion VIII, ISO 46- and AD Merkblatt A apply to the general sizing ourrene of a gas, vapor or liquid in a pressurized unit. However, in the speifi ase of pressurized vessels for LNG, LPG or similar, where high pressures and very low temperatures our, speial standards have been developed to estimate the mass flow rate to the safety devies. The standards presented in this setion are useful to alulate the mass flow rate to the safety valve used in the protetion of these vessels Sizing a. to ISO 3-3 This standard applies to vauum-insulated and non-vauum insulated ryogeni vessels under different onditions of intatness of the insulation system (outer jaket + insulating material). The outer jaket temperature is ambient temperature and the inner vessel is at the temperature of the ontained medium. It applies also for vessels with a totally lost insulation system and fire engulfment List of Symbols/Nomenlature Symbols Desription Units [SI] L Latent heat of vaporization of the ryogeni liquid at relieving onditions kj/kg L Speifi heat input, defined as h v at the relieving pressure p v and kj/kg temperature whih maximizes h v v v p v G Speifi volume of saturated vapor at relieving pressure m³/kg v L Speifi volume of saturated liquid at relieving pressure m³/kg W Quantity of heat per unit time W Table : List of symbols for sizing aording to ISO 3-3 p For the determination of the minimum mass flow requirements follow Table whih relates it to the ratio p /p of the relieving pressure p to the (thermodynamial) ritial pressure p (see set..3) p /p [-] less than.4 between.4 and more than or equal to 3.6 Q m [kg/h] 3.6 W L vg v L W v L G 3.6 W ' L Table Criteria to selet the mass flow rate into the safety valve. for standard The required heat input should be provided as input data, following the alulation sheme in the norm. The minimum required flow area is determined a. to ISO 46-. The sum of the relieving apaities of all the safety valves must be equal or exeed the minimum required mass flow Q m. from Table LWN 754. edition:

66 7.7.. Example Example Determine the mass flow rate to the safety valve for a vessel of liquid hydrogen at a relieving pressure of.8 bar. Consider an heat input of 5 W. Solution. The ritial point of hydrogen is 3 bar and 33. K and the relieving pressure is les than 4 % of the thermodynami ritial pressure. The latent heat L at that relieving pressure a. to NIST is kj/kg. The mass flow rate of hydrogen vapor to the safety valve is = 3.6W L = = 9.4 kg/h Q m LWN 754. edition:

67 7.7. Sizing a. to EN 336 The standard EN desribes alulation proedures to estimate the required mass flow rates of refrigerants in the gaseous phase List of Symbols /Nomenlature Symbol Desription Units [SI] ϕ Density of heat flow rate [kw/m²] η Volumetri effiieny estimated at sution pressure and disharge [--] v pressure equivalent to the safety valve setting ρ Vapor density at refrigerant saturation pressure/dew point at C [kg/m³] A Flow area of the safety valve [mm²] A Calulated flow area [mm²] A External surfae area of the vessel [m²] surf h Heat of vaporization alulated at. times the set pressure of the [kj/kg] vap safety valve K dr Derated oeffiient of disharge [--] n Rotational frequeny [min - ] Q Rate of heat prodution, internal heat soure [kw] h Q Calulated mass flow rate [kg/h] m Q Minimum required apaity of refrigerant of the safety valve [kg/h] md V Theoretial displaement [m³] Table 7.-: List of symbols for sizing aording to EN 336 If heat, whih is either internally generated or transmitted from an external soure, warms up the tank, overpressure may arise from a partial evaporation of the liquid. The minimum required vapor disharge apaity of the safety valve is determined by either Eq if the heat soure is external or Eq if internal. ϕ Asurf Qmd = 36 (external heat soures) (7.7.-) hvap If no better value is known, the density of heat flow rate φ an be assumed as kw/m². Qh Qmd = 36 (internal heat soures) (7.7.-) h vap The minimum disharge area of the safety valve in ase of overpressure in the vessel aused by ompressor inflow is determined using Eq Q md = 6 V n ρ η (ompressors) (7.7.-3) v The standard pren valve. overs the ase of ompressors running against a losed disharge 4 EN 336 Refrigerating systems and heat pumps Pressure relief devies and their assoiated piping Method for alulation,. 5 pr EN693 Refrigerating systems and heat pumps Safety and environmental requirements Refrigerant ompressors, 996. LWN 754. edition:

68 The minimum flow area of the safety valve is alulated from the minimum required mass flow rate determined from Eq to Eq using Eq To determine C and K b, see Paragraph and A Q C K = md (7.7.-4) dr K b v p The minimum produt of area oeffiient of disharge A K dr in ase of thermal expansion of trapped liquids shall be at least. mm² per liter of trapped volume. LWN 754. edition:

69 7.8 Guidelines for Speifi Appliations In this setion the norms are based on following edition: ASME Setion VIII (8), API RP 5 (), API 5 (7), ISO 46- (4), ISO 46-7 (4), ISO 35(7) In this hapter the user is given some quik but reliable guidane to determine the mass flow rate to the safety valve for some pratial ases of overpressure, whih are not expressively disussed in the above ited standards Shell Boilers and Tube Boilers There are two types of boilers, namely tube boilers and shell boilers. In tube boilers water is arried in tubes exposed to ombustion gases, while in shell boilers the hot gases flow in tubes immersed in a water bath. Both types of boilers an be either used for steam or hot water generators. Fig Marine type tube boiler for steam generation: steam generator (feedwater drum, steam drum, downomer tube) and superheater (Soure : Wikipedia Images) A. to EN 95-6 () every steam generator as well as all isolable heated vessels in a tube boiler steam generator, see Fig , inl. reheaters and eonomizers, must be proteted by at least one pressure relieving devie. The minimum diameter of the flow area of the safety valves must be 5 mm (EN 95-, Par 5..). The position of the safety valve for the protetion of the vessels in a tube boiler steam generator is given in Table Water-tube boilers and auxiliary installations Part : Requirements for safeguards against exessive pressure,. LWN 754. edition:

70 Tube boiler steam generator Steam generator (feedwater and steam drum) Non-isolable superheater no ontrol valve is present between superheater and steam generator Isolable superheater a ontrol valve is plaed between superheater and steam generator Position of safety valve in EN 95- () For a generator with no superheater the safety valves or the main valve of CSPRS 7 valves must be plaed on the steam side (EN 95-, Par. 5..3). The umulative ertified apaity of the safety valves installed on the steam generator must be at least equal to the max. steam generation (EN 95-, Par. 5..). A safety valve at the superheater outlet must prevent the release apaity to exeed the allowable wall temperature. Diret-loaded and supplementary loaded safety valves on the steam generator must disharge at least 75 % of the required release apaity. CSPRS valves instead at least 5 %: however, the CSPRS on the superheater an disharge the whole apaity provided that it is monitoring the pressure of the steam drum as well (EN 95-, Par. 5..5). These superheaters must be proteted with safety valves or the main valves of the CSPRS at the outlet of a superheater, whih must be sized for at least % of the required release apaity. The main valve of the CSPRS on the steam generator must disharge the whole allowable steam generation (EN 95-, Par. 5..6). Table 7.8.-: Position of the safety valve for the protetion of the vessels in a tube boiler steam generator Every reheater must be equipped with a safety valve as well. The release apaity of the safety valve or of the main valve of the CSPRS must orrespond to the max. design steam mass flow through the reheater (EN 95-, Par. 5..7). In EN 95-8 () every tube boiler hot water generator must be proteted by at least one pressure relieving devie. The umulative ertified mass flow of several safety valves must be at least equal to the generated mass flow rate of steam (EN 95-, Par. 5..), whih is alulated using Eq assuming that no heat is lost q = 36 Q / (7.8.-) with m L vap q m Steam mass flow rate [kg/h] Q Heat flow to the saturated water [kw] L vap Latent heat of evaporation [kj/kg] The minimum diameter of the flow area of the safety valves must be 5 mm (EN 95-, Par 5..). The safety valves must be plaed on or in proximity of the highest point of the feed line or on the feed line as lose to the boiler as possible (EN 95-, Par. 5..3). The safety valves must be sized for saturated steam flows at relieving onditions even for boilers where the valve is under water pressure (EN 95-, Par 5..5). 7 CSPRS : Controlled Safety Pressure Relief Systems 8 Water-tube boilers and auxiliary installations Part : Requirements for safeguards against exessive pressure,. LWN 754. edition:

71 Figure Shell boiler ; Soure: RISE, Murdoh University, Perth (AUS) In shell boilers the ontrol of the liquid and steam filling levels in the boiler should guarantee that the pressure in the shell boiler does not exeed the set value. In EN () every vessel in the shell boiler must be proteted by a safety valve, whih should be able to disharge the allowable steam mass flow. (EN 953-8, Par 4..) The minimum seat diameter of the safety valve must be 5 mm (EN 953-8, Par. 4..5). The position of the safety valve for the protetion of the vessels in a shell boiler is given in Table General shell boiler Position of safety valve in EN () Isolable eonomizer The min. relieving apaity of the safety valve must be determined on the base of the heat inflow to the eonomizer using Eq (EN 953-8, Par. 4..4). Non-isolable superheater no ontrol valve is present between superheater and steam generator Isolable superheater a ontrol valve is plaed between superheater and steam generator The release apaity of the superheater may be added to that of the steam generator in order to determine the min. relieving flow rate of the safety valves (EN 953-8, Par 4..). The superheater must have a safety valve at the outlet, whose release apaity must be at least 5 % of the whole apaity of the boiler (EN 953-8, Par 4..). This ondition may fall, when the max. expeted wall temperature does not exeed the sizing temperature (EN 953-8, Par 4..) The superheater must have an additional safety valve at the outlet, whose release apaity must be at least 5 % of the whole apaity of the boiler (EN 953-8, Par 4..). Table 7.8.-: Position of the safety valve for the protetion of the vessels in a shell boiler as well as the partiular requirements for steam generators and hot water generators For steam generator shell boilers the ertified steam apaity of the safety valves must exeed the allowable steam prodution. The alulation of the steam apaity of the safety valve for the steam onditions, for whih no ertified steam apaity is available, must omply with ISO 46- and it must exeed the allowable steam prodution (EN 953-8, Par 4..). In hot water generator shell boilers, the safety valve must be sized under the assumption of saturated steam flows at relieving onditions. In alternative (EN 953-8, Par 4..) the safety valves for oil- or gas-fired hot water generators may be sized for the maximum possible volumetri 9 Shell boilers Part 8: Requirements for safeguard against exessive pressure,. LWN 754. edition: