Safety Relief Valves Sizing Link: https://processpocket.streamlit.app/Safety%20Valves%20Sizing This tool was developed for process engineers to quickly estimate the outcome of the safety relief valve sizing equations on site. As a part of a larger project to develop what is similar to Carl Branan’s book “process engineers Pocket Handbook” these tools would allow a process engineer to quickly calculate/estimate equipment efficiencies or sizing using standardized calculations The aim here is to take little-known data from the field (flow, pressures, temperatures, compositions..etc.) and use it as input for a rough estimation without having to return to the office to use commercial software or calculations Excel sheets to validate or to calculate. Additionally, these tools may also serve as a gathered data validation tool. Nomenclature Tn T a π H Re ρ D L W Q Q h L1 C U Kd KSH Kv Kc Temperature (oK) Temperature at relieving conditions (oK) Temperature of insulation outer surface (1177 oK) Latent heat of vaporization (kcal/kg) Enthalpy (kcal/kg) Reynold’s number Density (kg/m3) Diameter (m) Length (m) W Required relieving capacity (kg/hr) Required relieving capacity (Nm3 /min or L/min for liquids) Relief Load (kW or kcal/hr) Depth of wetted portion (m) NLL in vessel/column (m) Coefficient determined from an expression of the ratio of specific heats of the gas or vapor Heat transfer coefficient (kcal/(m2.h°C)) The effective coefficient of discharge superheated correction factor (steam) Viscosity correction factor (liquid) Combination correction factor P P1/s/c/back t M µ k αv Cp Aw A/Acalc Ae G Z F F2 L2 v Kb KN Kw Pressure (kPa) Relief/Set/critical/back pressures (kPa) Thickness of insulation (m) Molecular weight M.wt Viscosity (cP) Gas specific heat ratio cubical expansion coefficient (1/°K) Heat Capacity (Kg/Kcal.hr. oC) Wetted area (m2) Minimum required effective discharge area (mm2) Effective area (mm2) Specific gravity Compressibility factor Environmental factor Coefficient for subcritical gas flow sizing equation Elevation above grade (m) Velocity (m/s) Capacity correction factor due to backpressure Correction factor for Napier equation (steam) Backpressure correction factor (liquid) Input Required Table 1: Note 1: Input required depending on the case 1. Calculating Relieving/Set Pressure 2. Relief Loads Estimation (Cont.) Case (non-fire/fire) - Closed Outlet (Heat Exchangers) MAWP kg/cm².g Hot side inlet temperature o Design Pressure (if Set pressure doesn’t equal MAWP) Disc Installation Type (If multiple device installation is chosen) 2. Relief Loads Estimation kg/cm².g Normal Cold Side rate Kg/hr One/additional/ Normal Cold Side composition Supplemental Normal Cold Side conditions (T&P) External Fire (Vaporization) C %vol o C/ kg/cm².a Inadvertent Control Valve opening normal stream composition %vol Control valve size inch normal stream conditions (T&P) o C/ kg/cm².a Control Valve opening % Aw calculations (If the stream is liquid, it appears) Type of Equipment m2 %vol Geometry inputs m Control valve inlet and outlet stream composition Control valve inlet and outlet normal stream conditions (T&P) Thermal Expansion Heat Absorbed kW Relieved stream composition %vol External Fire (Gas expansion) Relieved stream conditions (T&P) o Same input + Max. Heat load Kcal/hr vessel maximum wall temperature o C Closed Outlet (Vessel) o C/ kg/cm².a C/ kg/cm².a 3. Gas or Vapor/ Steam Mass flow rate Kg/hr Vessel Feed rate Kg/hr inlet/outlet stream composition %vol feed composition and %vol Inlet (relieved) stream conditions (T&P) o C/ kg/cm².a feed stream conditions (T&P) o C/ kg/cm².a Outlet (relief header) stream conditions (T&P) o C/ kg/cm².a Feed vapor mass fraction (if not calculated) 0-1 range Kb, kd, kc input (optional) - Closed Outlet (Vessel with reboiler) 3. Liquid Same + Same + Kw, kd, kc input (optional) - Output Obtained 1. Calculating Relieving/Set Pressure 3. Liquid Max. accumulated pressure kg/cm².g Max. Flow Capacity Kg/hr Relief device set pressure kg/cm².g Kg/m3/cP Allowable overpressure Overpressure Relieving pressure 2. Relief Loads Estimation Calculated Relief Load Calculated Relieving flow rate 3. Gas or Vapor/ Steam Flow Max. Flow Capacity Physical properties used in calculations: average cp/cv, µ, M.wt, Z Kb,kd,kc + (kSH, kN) for steam Minimum area Selected Area Orifice Designation Permissible inlet/outlet nozzles Table of Calculations Specifications sheet kg/cm² % kg/cm².a Physical properties used in calculations: Density/ µ Kw,kd,kc Minimum area Selected Area Orifice Designation Permissible inlet/outlet nozzles Table of Calculations Specifications sheet kW Kg/hr cm2/in2 cm2/in2 inches - Critical/Subcritical Kg/hr -/cP/-/cm2/in2 cm2/in2 inches - 1. Introduction Sizing pressure relief valves (PSV) requires a vivid understanding of the process where the safety valves are installed, the sizing equations, and the numerous relevant standards. In this document, we’ll be exploring the hand calculations required to preliminary size different safety valves. First, we’ll explore how to estimate the relieving and set pressures according to standards. Secondly, we’ll explore the basic safety orifices sizing equations (for gases, steam, or liquids) and learn how to estimate the required coefficients. Finally, we’ll take a glance at how to estimate the required relief loads for different processes and contingencies as an introduction to this complex matter. However, the back pressure calculations were not discussed in this document. The backpressure used in safety calculations is the sum of superimposed backpressure and built-up back pressure. The superimposed backpressure is the static pressure and the relief header before the valve opening, while the built-up back pressure is the pressure increase due to the valve opening building up extra pressure to overcome the outlet friction losses. The estimation of the built-up back pressure could be discussed later in the context of flare systems calculations. This document did not discuss the various safety valve types' working mechanisms, the rupture disc types and sizing procedures, or guidelines for sizing the inlet/outlet piping of PSV. However, you may find the mentioned topics in references and recommended reads. 2. Set/relief Pressure Calculations Table 2.1: Relief Pressure estimation table (percentages are applied to MAWP’s gauge pressures) [1] Contingency Installation Single-Valve Installations Set Pressure Max. Accumulated (%) pressure (%) Multiple-Valve Installations Set Pressure Max. Accumulated (%) pressure (%) Non-fire only First valve 100 110 [1] 100 116 [2] Fire only Additional valve(s) First valve --100 --121 105 100 116 [2] 121 Additional valve(s) ----105 121 Supplemental valve ----110 121 Note : All values are percentages of the maximum allowable working pressure. (1) 10% or 3 psi (0.21 kglcm2), whichever is greater. (2) 16% or 4 psi (0.28 kg/cm2), whichever is greater. (3) A supplemental valve installation provides relieving capacity for an additional hazard created by exposure to fire or other unexpected sources of external heat. Supplemental valves are used only in addition to valves sized for operating (non-fire) contingencies. [3] (4) In the case of ASME-application liquid service valves (that is, for protection of a liquid-full vessel), maximum accumulated pressure is limited to 110% of the maximum allowable working pressure for operating contingencies. In the case of non-ASME-application liquid service valves (for protection of piping without vessels included), 25 % overpressure is generally specified. [3] (5) The minimum pressure differentials between the set pressure of the valve and the operation pressure of the vessel are recommended as follows: Table 2.2: minimum differential pressure limitations [3] Set Pressure Ps Ps ≤ 70 psi (4.9 kg/cm2) Ps ≤ 1000 psi (70 kg/cm2) Ps > 1000 psi (70 kg/cm2) Minimum recommended Pressure differential 5 psi (0.35 kg/cm2) 10% of Ps 7% of Ps Figure 2.1: Pressure Level Relationships for Pressure-relief Valves [1] 3. Safety Relief Valves Sizing Gases Steam Subcritical Flow π΄= π΄= π΄= Acalc πΉ2 πΎπ πΎπ √π1 (π1 − π2 ) 258 ∗ π ∗ √ππΊπ πΉ2 πΎπ πΎπ √π1 (π1 − π2 ) π΄= π ∗ √ππ πΆπΎπ π1 πΎπ πΎπ √π 2.676 ∗ π ∗ √πππ πΆπΎπ π1 πΎπ πΎπ 14.41 ∗ π ∗ √ππΊπ π΄= πΆπΎπ π1 πΎπ πΎπ π΄= π1 ∗π ππ π ππΆπ 2 π⁄(π−1) ] =[ π1 π+1 π= πΆ = 0.03948√π [ πΉ2 = √[ Wmax[3] Critical Flow 17.9 ∗ π ∗ √ππ πΉ2 πΎπ πΎπ √ππ1 (π1 − π2 ) 47.95 ∗ π ∗ √πππ Liquids π΄= 190.5 ∗ π π1 πΎπ πΎπ β πΎπ πΎπ πΎπ π΄= 11.78π√πΊ πΎπ πΎπ€ πΎπ£ πΎπ √π1 − π2 2 π+1/π−1 ] π+1 π 1 − π (π−1)/π ] π 2/π [ ] π−1 1−π ππππ ∗ π΄π π΄ππππ A: mm2 W: kg/h Units Q: Nm3/min P1,P2: kPa T: Kelvin W (kg/h ) = 0.044 * M.wt * Q (Nm3/hr) Q (Nm3/min) = Q (Nm3/hr)/60 Conversion Q (L/min) = Q (m3/hr) *16.67 Notes P (kPa) = P (kg/cm2) * 98.0665 A (cm2) = A (mm2)*0.01 A (in2) = A (cm2) * 0.155 ππππ ∗ π΄π π΄ππππ A: mm2 W: kg/h P1,P2: kPa T: Kelvin ππππ ∗ π΄π π΄ππππ A: mm2 Q: L/min P1,P2: kPag T: Kelvin Table 3.1: Table of single-phase relief valve sizing equations [1] NOTE 1: The Napier coefficient KN must be considered when P1 ≥ 106.5 kg/cm2a. NOTE 2: for gas equations Kd = effective coefficient of discharge. For preliminary sizing, use the following values: = 0.975 when a pressure relief valve is installed with or without a rupture disk in combination. = 0.62 when a pressure relief valve is not installed and sizing is for rapture disk Wrated = maximum rated flow rate through the valve 3.1 Gas PSV Sizing[1] 1. Estimate if flow is critical or sub-critical from the following equation ππ = π1 ∗ [ 2 π+1 ] π/π+1 , where Pc is the critical pressure, P1 is the upstream pressure (relieving), both in absolute units k is the specific heats ratio for any ideal gas 2. Based on the flow condition, you can proceed with one of the following equations: Sub-critical Flow Pc < Pback π΄= π΄= Critical Flow Pc > Pback 17.9 ∗ π ∗ √ππ πΉ2 πΎπ πΎπ √ππ1 (π1 − π2 ) 47.95 ∗ π ∗ √πππ π΄= πΉ2 πΎπ πΎπ √π1 (π1 − π2 ) 258 ∗ π ∗ √ππΊπ πΉ2 πΎπ πΎπ √π1 (π1 − π2 ) π ∗ √ππ π΄= πΆπΎπ π1 πΎπ πΎπ √π 2.676 ∗ π ∗ √πππ π΄= πΆπΎπ π1 πΎπ πΎπ 14.41 ∗ π ∗ √ππΊπ π΄= πΆπΎπ π1 πΎπ πΎπ Table 3.2: Gas PSV sizing equations Where, πΆ = 0.03948√π [ 2 π+1 ] π+1/π−1 , refer to Figure 3.7 πΉ2 = πππππππππππ‘ ππ π π’πππππ‘ππππ ππππ€ = √[ π ] π 2/π [ π−1 1−π (π−1)/π 1−π ], refer to Figure 3.6 r: ratio of backpressure to upstream relieving pressure P2/P1 Balanced Pressure Relief Valves Balanced pressure relief valves should be sized using critical-flow equations. The back pressure correction factor in this application accounts for subcritical flow velocities and the tendency for the disc to drop below full lift (the use of subcritical flow equations is appropriate only where full lift is maintained). For this application, the back pressure correction factor, Kb, should be obtained from the manufacturer. Figure 3.1: Kb for balanced bellows relief valves (Gas) [1] [1] 3.2 Steam PSV Sizing Pressure relief devices in steam service that operate at critical low conditions may be sized using: π΄= 190.5∗π π1 πΎπ πΎπ β πΎπ πΎπ πΎπ , where Kb: The capacity correction factor is due to backpressure. Applied for balanced bellows valves only. Refer to Figure 1 For conventional valves, use a value for Kb equals 1.0. KN: correction factor for Napier equation = (0.1906 * P1- 1000)/(0.2292 *P1 - 1061) where P1 in kPa and 10339 kPa < P1 ≤ 22057 kPa KSH: Correction factor for superheated steam. For saturated steam use KSH =1.0 3.3 Liquid PSV Sizing [1] Pressure relief devices for liquid services may be sized using: π΄= 11.78 ∗ π ∗ √πΊ πΎπ πΎπ€ πΎπ£ πΎπ πΎπ √π1 − π2 Kd: effective coefficient of discharge that should be obtained from the valve manufacturer. For preliminary sizing estimation, a discharge coefficient of 0.65 can be used. Kw: correction factor for back pressure. If the backpressure is atmospheric, Kw =1.0. Balanced-bellow valves in backpressure service will require the correction factor obtained from Figure 2 Conventional valves require no special correction. Kv: correction factor for viscosity as determined from the following equation: ππ£ = (0.9935 + 2.878 342.75 −1 π π π π 0.5 + 1.5 ) 170 or ππ£ = ( π π −0.5 + 1) When a pressure relief valve is sized for viscous liquid service, it should first be sized as if it were for non-viscous type application (i.e., Kv = 1.0) so that a preliminary required discharge area, A, can be obtained from the previous equation. From API standard orifice sizes (Table 3.3 may be used for preliminary estimation), the next larger orifice size should be used in determining the Reynolds number, Re, the following equation: π π = π∗(18800∗πΊ) π√π΄ , µ: Liquid viscosity is cP Q: flow rate in L/min G: specific Gravity A: selected area mm2 After Reynold’s number, Re, is determined, the factor Kv is obtained, and Kv is then applied in the liquid sizing equation to correct the preliminary required discharge area. If the corrected area exceeds the chosen standard orifice area, the above calculations should be repeated using the next larger standard orifice size. Figure 3.2: Kw for kb for relief valves due to back pressure (liquid) [1] Table 3.3: Conventional and balanced-bellows valve selection table (API RP 526 and GPSA Section 3) [3] Figure 3.3: Kv for relief valves due to viscosity (liquid) [1] Figure 3.5: KSH for steam at T&P[3] Figure 3.4: Kb for conventional/pilot operated relief valves (Gas) [1] Figure 3.6: F2 Values for Gas PSV Sizing (subcritical Flow) Figure 3.7: C Values for Gas PSV Sizing (Critical Flow) 3.4 Calculating Equation Coefficients 1. Gas or Vapors Kb Capacity correction factor Kb = a + b(Pb /(Pset+POP)) 3 (abs. pressures) (Conventional and pilot operated) [6] γ Range % a b 1.1 66-90 1.3026 -1.137*10-6 1.3 63-90 1.294 -1.1703*10-6 1.5 56-90 1.203 -1.143*10-6 1.7 51-90 1.148 -1.109*10-6 Kb =1/( a + b(PB/Ps)3) (gauge pressures) (Balanced bellows) [6] Overpressure Range a b 10 30-50 0.8707 4.724*10-6 20 30-50 0.976 8.36*10-7 1. The curves above represent a compromise of the values [1] recommended several relief valve manufacturers and Figure 3.6: C for by Critical flow gas Sizing equation used when the make of the valve or the critical flow pressure point for the vapor or gas is unknown. The curves are for set pressures of 50 psig and above. They are limited to back pressure below critical flow pressure for a given set pressure. For set pressure below 50 psig or subcritical flow, the manufacturer must be consulted for values of Kb. [1] 2. For 21% overpressure, Kb equals 1.0 up to PB/PS = 50%.[1] 3. For pilot-operated PRVs, the valve lift is not affected by backpressure. For compressible fluids at critical flow conditions, a backpressure correction factor of 1.0 should be used for pilot-operated PRVs.[1] Alternatively, kb can be estimated for conventional and pilot-operated Relief valves using Figure 3.4 (Subcritical flow) [1] Kd Effective coefficient of discharge for PSV 0.975 when a PRV is installed with or without a rupture disk in combination; 0.62 when a PRV is not installed and sizing is for a rupture disk Kc combination correction factor 1.0 when a rupture disk is not installed. Figure 3.7: F2 for Subcritical gas equation [1] 0.9 when a rupture disk is installed with a pressure relief valve and the combination does not have a published value. 2. Steam KN Correction factor for Napier equation = 1.0 where P1≤ 106.5 kg/cm2a or 1339 kPa = (0.1906 * P1- 1000)/(0.2292 *P1 - 1061) where P1 in kPa and 10339 kPa (106.5 kg/cm2a) < P1 ≤ 22057 kPa (226.1 kg/cm2A) KSH Superheat steam correction factor For saturated steam at any pressure, KSH = 1.0 KSH can be obtained from figure 3.5 or KSH tables published in ref [1] P.86-90. 3. Liquid Kw Correction factor due to back pressure If the back pressure is atmospheric, Kw = 1.0. for conventional and pilot-operated PSVs, kw =1. Otherwise. Use Figure 3.2. Kw = 1.1165-0.01*(PB/Ps) for (PB/Ps) > 17 [6] Kv viscosity correction factor 2.878 342.75 −1 ππ£ = (0.9935 + 0.5 + ) π π π π1.5 170 −0.5 ππ£ = (1 + ) π π Or use Figure 3.3 1.Use the next larger orifice area to calculate Re 2.Correct calculated A without Kv by dividing it with new Kv Kd Effective coefficient of discharge for PSV 0.65, when a PRV is installed with or without a rupture disk in combination; 0.62, when a PRV is not installed, and sizing is for a rupture disk Notes on PSV sizing PSV sizing could be an iterative procedure or a two-step process After estimating the relieving capacity, you may want to check its impact on the relief header's total back pressure. The increased back pressure due to the calculated relieved capacity could impact your calculated/initially estimated Kb, resulting in another iteration/step to calculate the corrected relieved capacity. Refer to section 5.3.4.2 on ref [1] Inlet piping inlet piping pressure losses due to friction should not be higher than 3% of set pressure and calculated using the maximum rated capacity of the pressure relief device [1][3]. Exceptions were mentioned in recommended reads[II] When two or more pressure relief devices are placed on one connection, the inlet piping internal cross-sectional area shall be at least equal to the combined inlet areas of the pressure relief devices connected to it Selection Criteria of PSV 1. Conventional PSVs 2. The sum of the maximum variable superimposed back pressure plus the built-up back pressure is less than 10% of the set pressure. 3. Fouling or corrosive conditions are not expected. 2. Bellows Type PSVs 1. The sum of the variable superimposed back pressure plus built-up back pressure exceeds 10% of set pressure. 2. Fouling or corrosive conditions are expected and protection cannot be afforded by using alternative materials or devices. Backpressure Limitations on Bellows Type PSVs Total backpressure shall not reduce differential pressure across the PSV to a value limiting PSV relieving capacity to less than design capacity. This corresponds to a total backpressure of approximately 50% of set pressure for gas services. 3. 1. 2. 3. Pilot Operated PSVs Pilot-operated PSVs are recommended when maximum set point accuracy is required Pilot-operated PSVs shall generally be limited to clean gas service. Tanks designed to API STD 650, which may also require pressure relief devices, may be protected by pilotoperated relief valves. Pilot-operated relief valves shall protect tanks designed to API STD 620. More on the advantages and disadvantages of different PSV types can be found at recommended reads [II] [III] 4. Examining possible cases (Contingencies) Estimating the required relief loads could be a grueling task that requires extensive heat and mass balance calculations at relief conditions. It could be best to use simulation tools for this one. However, this section aims to familiarize readers with the basis and variables needed for different scenarios. Moreover, manual calculations could be an alternative option where minimum data are available for simulation in some cases. All causes of overpressure, or contingencies, must be evaluated for each PSV installation in terms of the pressures generated and the rates at which fluids must be relieved. Causes of overpressure in process equipment can range from a single event to a complex combination of events. The basis for calculating a valve size follows calculations of valid contingencies. The contingency that requires the largest effective area dictates the size of the PSV. More on “guidelines on estimating relief loads for different contingencies” can be found on recommended reads [V][I][III] Table 4.1: Guidelines on estimating relief loads for different contingencies [2] Item No. Condition 1 Closed outlets on vessels Pressure Relief Device (Liquid Relief) Maximum liquid pumpin rate Pressure Relief Device (Vapor Relief)* Total incoming steam and vapor plus that generated therein at relieving conditions Total vapor to condenser at relieving conditions Total incoming steam and vapor plus that generated therein at relieving conditions less vapor condensed by side-stream reflux Difference between vapor entering and leaving section at relieving conditions None, normally Same effect in towers as found for Item 2; in other vessels, same effect as found for Item 1 For towers, usually not predictable 2 Cooling water failure to condenser 3 Top-tower reflux failure — — 4 Side-stream reflux failure — 5 Lean oil failure to absorber 6 Accumulation of noncondensables — — 7 Entrance of highly volatile material: Water in hot oil or Light hydrocarbons in hot oil 8 Overfilling storage or surge vessel — Maximum liquid Pump-in rate — 9 Failure of automatic controls 10 Abnormal heat or vapor input — — 11 Split exchanger tube — 12 Internal Explosions — 13 Chemical reaction — 14 Hydraulic expansion 1. Cold fluid shut in 2. Line outside process area 3. Shut in 15 Exterior fire 16 Power failure (steam, electric, or other) Use Liquid expansion equation (table 4.7) Must be analyzed on a case-by-case basis Estimated maximum vapor generation including non-condensables from overheating Steam or vapor entering from twice the crosssectional area of one tube; also same effects found in Item 7 for exchangers Not controlled by conventional relief devices but by avoidance of circumstances Estimated vapor generation from both normal and uncontrolled conditions — — — Estimate by external fire equations (table 4.2) Study the installation to determine the effect of power failure; size relief valve for the worst condition that can occur 1. Fractionators — 2. Reactors — 3. Air-cooled exchangers — 4. Surge vessels Maximum liquid inlet rate All pumps could be down, with the result that reflux and cooling water would fail Consider failure of agitation or stirring, quench or retarding steam; size valves for vapor generation from a runaway reaction Fans would fail; size valves for the difference between normal and emergency duty — * Considerations may be given to the suppression of vapor production as the result of the device’s relieving pressure being above operating pressure, assuming constant heat input. (Procedures for sizing pressure relief devices are presented in Section 4 of API-RP-520.) After the specifications are determined, the next activity is to calculate a preliminary effective discharge area. Figure 4.1 shows the inputs used to determine the basis for calculating the size of a PSV. Figure 4.1: Sizing input flowchart [2] Relief Loads Estimation for individual contingencies External Fire Overpressure due to vaporization [4] External Fire Overpressure due to Gas Expansion [4] π βπ» W: relieving load kg/hr β³H: Enthalpy difference between normal and relieving conditions Kcal/kg Q: total heat absorbed kcal/hr NOTE: assuming to inlet or outlet flow π = ππ . πΉ. π΄0.82 Q: total heat absorbed kcal/hr F: Environmental factor A: wetted surface m2 qo: 37130, if drainage isn’t provided qo: 61000 Bare Vessel F=1 Insulated Vessel π ∗ (π − π) πΉ= πΆ. π‘ k: thermal conductivity of insulation ( W/m-K) at average of 904 oC and relieving temperature. Tf: temperature of vessel contents at relieving condition ( oC) a: temperature of insulation outer surface (904 oC) C: constant that equals 66570 t: thickness of insulation (m) Type of equipment Factor F Factor F API RP521 NFPA 30 Bare Vessel 1.0 1.0 When the vessels that contain no liquid, such as gas holders, are exposed to the fire contingency, overpressure will occur due to the gas expansion. The following equation can obtain the relieving loads for this case: π = Water application facilities on bare vessel Water application facilities on insulated vessel Depressurizing and emptying facilities Underground storage Earth covered storage above grade 1.0 0.3 1.0 0.15 1.0 - 0.0 0.03 0.3 - Table 4.2: Relief loads guidelines for External Fire π΄ (ππ€ − π1 )1.25 π = 0.1406√ππ1 ( ) π11.1506 W: relieving load lb/hr M: molecular weight P1: relieving pressure psia A: exposed surface area ft2 Tω: Vessel max. wall temperature, 593 for CS (oR) T1: relieving temperature (oR) T ∗P T1 = n 1⁄P n Pn: normal operating pressure (psia) Tn: normal operating temperature (oR) Closed Outlet Drums / flashing drum with reboiler [4] The vapor rate in the feed gas is treated as the relief valve's relieving rate. The relief rate is determined by estimating the emergency reboiler heat duty. See Vaporizer notes on table 4.5 Reboiler Duty (steam) Columns [4] When all outlets from the equipment are blocked, the relieving load should be at least as great as the capacity of the sources of pressure. If all outlets are not blocked, the capacity of the unblocked outlets may properly be considered (1) Valve block of reflux line 1 ′ [(βπΉ′ − βπΏ )ππΉ′ − (βπ· − βπΏ )ππ·′ − (βπ΅′ − βπΏ )ππ΅′ π + βππ ′ − βππΆ′ ] λ /hL: latent heat of vaporization/Liquid enthalpy at the top section of the tower (2 or 3 stages below the top tray) h’F: feed stream enthalpy (relieving) W’F: Feed stream flow rate (relieving) h’D/ W’D: Top distillate enthalpy and flow rate (relieving) h’B/ W’B: Bottom product enthalpy and flow rate (relieving) β³Q’R: Reboiler duty (relieving) β³Q’C: Condenser duty (relieving) π= π‘2′ − π‘1′ π ′ − π‘1′ ln( ′ ) π − π‘2′ βπ′ π βπ′ = ( )( ππππ )βπ (kcal/hr) βπ′ = βπ βπ′ ππ· π= (kg/hr) π Reboiler Duty (Oil) (2) Valve block of fractionation column overhead vapor product 1 [(βπΉ′ − βπΏ )ππΉ′ − (βπ΅′ − βπΏ )ππ΅′ + βππ ′ ] π Steam stripping is used: 1 ππ»πΆ = [(βπΉ′ − βπΏ )ππΉ′ − (βπ ′ − βπ ′′ )ππ ′ π − (βπ΅′ − βπΏ )ππ΅′ ] π = ππ»πΆ + ππ ′ WHC: hydrocarbon relieved W’s: steam relieved h’s: steam inlet enthalpy (relieving) h’’s: steam relieving enthalpy estimate relieved steam based on a full open steam control valve and pressure difference between the steam header and relieving pressure π= (π1 ′ − π‘2′ ) − (π2 ′ − π‘1′ ) π ′ − π‘2′ ln( 1 ′ ) π2 − π‘1′ βπ′ π βπ′ = ( )( ππππ )βπ (kcal/hr) βπ′ = ′ βπ = ( π= βπ ππ· π1 −π2′ π1 −π2 βπ′ π )βπ (kcal/hr) (kg/hr) Table 4.3: Relief loads guidelines for Drums and Columns Discharge line of rotary machinery Centrifugal pumps[4] Centrifugal compressors[4] An overpressure problem does not occur on the discharge line of a centrifugal pump because the centrifugal pump discharge system normally has a design pressure equal to or higher than the pump shut-off pressure. However, when the design pressure is set lower than the pump shut-off pressure, an overpressure problem will occur, and the flow rate at the head, equivalent to the set pressure of the PSV minus the maximum suction pressure, should be read from the pump performance curve for the relieving load. The relieving load should be determined based on the pump’s maximum speed when the steam turbine driver is provided. If the design pressure for the compressor discharge system is higher than the pressure of surge point at maximum speed, overpressure does not occur. If the design pressure is lower than that, overpressure protection should be considered. In this case, the relieving load should be the flow rate (FD) at the head equivalent to the design pressure (PD) at maximum speed or should be the anti-surge flow (FS) at maximum speed, whichever is greater. That value is usually obtained from such compressor performance curve as shown below: Reciprocating pumps[4] The relieving load shall be equal to the pump’s rated capacity. The calculation procedure is as follows. 1. Assume the discharge pressure is 1.1 times the design pressure. Based on the calculated discharge pressure, estimate the suction pressure of the compressor assuming the compressor is running on the surge control line. In case of variable speed compressor, whole range of the operating speed to be investigated. 2. Calculate weight flow through the compressor and required power of the compressor based on the suction and discharge pressures calculated in Step 1. 3. Check the calculated weight flow if it is available from upstream side of the compressor. 4. Check the required power if it is available from the driver. Relieving load is the maximum weight flow rate calculated in Step 2 considering the limitation of available flow rate and power checked in Step 3 and 4. In case the calculated suction pressure is equal to or higher than the design pressure of the suction side in Step 1, re-calculate the suction pressure assuming that the compressor is still running on the surge control line while the 1.1 times of the design pressure is replaced with the design pressure of discharge side. Reciprocating compressors[4] The relieving load should be equal to the compressor’s rated capacity. Table 4.5: Relief loads guidelines for Rotary Machinery Heat Exchangers Vaporization in Hex [4] If the vapor pressure of the cold medium at the inlet temperature of hot side is more than 1.3 times the design pressure of the cold side, overpressure protection due to vaporization is needed. If it is assumed that the outlet of the cold side is blocked off, and the hot medium continues to flow, the relieving load on the cold side should be determined as follows : π (π1 − π‘ππ ) . π (π1 − π‘ππ£ ) π‘1 + π‘2 π‘ππ£ = 2 W : relieving load (kg/hr) Q : normal heat exchanger duty (kcal/hr) λ : latent heat of vaporization at tbp (kcal/kg) T1: hot side inlet temperature (oC) Tbp: cold side inlet temperature (oC) tav: average cold side temperature (normal operation) (oC) t1/t2: cold side inlet/outlet temperature (oC) π = Vaporizer [4] When the outlet of the cold side is blocked off, and the hot medium continues to flow, overpressure will occur, and the relieving load should be calculated based on the vaporizer heat duty at the relieving condition obtained by the procedure shown in Table 4.3 Steam Vaporizer (1) Inlet and outlet temperatures of process fluid to/from reboiler at relieving pressure will increase, because the boiling temperature of process fluid increases, when the operating pressure reaches the relieving pressure. (2) When heating steam is supplied under steam flow control, the saturated temperature of steam at the pressure of supply header should be applied to ΔT calculation, because the flow control valve tend to open to maintain the steam flow at a constant. If the other control system is applied to the steam supply, the normal operating temperature of steam may be used. (3) Ucalc (calculated overall heat transfer coefficient ) should be used for recalculation. Hot Oil Vaporizer When the hot oil supply stops due to failures such as a hot oil pump stop, overpressure does not occur because of no heat input to the reboiler. If the hot oil supply continues, the heat duty should be calculated based on the temperature profile under the relieving conditions. (1) Inlet and outlet temperatures of process fluid to/from the reboiler will increase because the boiling temperature of process fluid increases when the operating pressure reaches the relieving pressure. (2) The flow rate of hot oil is maintained the same as in normal operation. (3) UCALC (calculated overall heat transfer coefficient) should be used for recalculation. Based on the above conditions, assume the outlet temperature of hot oil (T2’) and obtain the reboiler duty (ΔQ’) by trial and error calculation using the following equations : Table 4.6: Relief loads guidelines for Heat Exchangers Liquid Thermal Expansion [4] Solar Radiation [4] A 3/4-inch × 1-inch nominal pipe size (NPS) relief valve is commonly used, even though it will be oversized, since relieving load for thermal expansion will usually be small. If there is reason to believe that this size is not adequate, the relieving load should be obtained according to the following equation πΌπ π= πΆ ∗ π. πΊ ∗ πΆπ V: volumetric flow rate at flowing temperature (m3lhr) πΌ:cubical expansion coefficient (1/°K) Q: total heat transfer rate. ( kW) specific gravity, water = 1.0 (-) Cp specific heat of the fluid C: factor (1000) π = ππ ππ΄ Q: heat absorbed by solar radiation (kcal/hr) qs : heat flux by solar radiation (kcal/hr.m2) Τ : emissivity A: projected heat transfer area (m2) solar radiation When the solar radiation data is not available, the noon values in the following table can be applied to obtain the maximum heat absorbed from solar radiation. Maximum Expected Solar Radiation of Various North Latitudes Latitude (kcal/h.m2) (kW/m2) 24-hr N30° 353 0.41 average Noon value N40° N45° N30° 353 353 990 0.41 0.41 1.15 N35° N40° N45° Gravity of Oil [Deg API] 3 – 34.9 35 – 50.9 51 – 63.9 64 – 78.9 79 – 88.9 89 – 93.9 94 and lighter Temperature °C 15.6 20 30 40 50 αv 1/°C or 1/K (1/°F) 0.00072 (0.0004) 0.00090 (0.0005) 0.00108 (0.0006) 0.00126 (0.0007) 0.00144 (0.0008) 0.00153 (0.00085) 0.00162 (0.0009) αv 1/°C or 1/K (water) 0.00018 0.00021 0.00030 0.00040 0.00047 976 1.14 950 1.1 922 1.07 Above table presents typical highest values of monthly average solar radiation on a horizontal surface throughout the year, based on analysis of Weather Bureau records for a number of stations through the United States. Refer to Section 12 Table 12-5 of Perry’s Chemical Engineer’’ Handbook 7th Edition. typical value of emissivity Material Emissivity, ε 0.1 Clean and polished metal 0.3 Metals, general 0.8 Rusty metal 0.95 Painted surface For horizontal piping or vessels, vertical projected area on ground is used. For vertical piping or vessels, horizontal projected area may be used as conservative side. Table 4.7: Relief loads guidelines for Liquid Thermal Expansion and Solar radiation Inadvertent Control Valve Opening Flashing Liquid [4] (a) Calculate ΔP of the control valve at the relieving condition (b) Breakthrough flow rate should be calculated on a liquid phase basis by using the selected CV value, since LPG is in liquid phase at the inlet of the control valve. (c) Calculate the flashed vapor flow rate (VF) by the flash calculation at the relieving pressure. (d) If the vapor space is enough to accommodate the let down liquid for the operator’s response time, the relieving load (VR) = VF – VN ( VN = vapor flow rate at normal operation). (e) If the vapor space is not enough, consider the relieving of vapor-liquid mixture. (f) In this case, pay attention to an occurrence of slug flow in two phase lines. Gas Breakthrough [4] (a) Calculate ΔP of the control valve at the relieving condition. (b) Gas breakthrough flow rate (VB) should be calculated by using the selected CV value. (c) Relieving load (VR) = VB – VN , ( VN = vapor flow rate at normal operation). (d) In this case, pay attention to an occurrence of slug flow in two phase lines. Liquid [Note 1] [7] β³π ππΏ = 0.86 ∗ πΆπ£ . √ πΊ QL in m3 /hr β³P in kg/cm2 G: Specific gravity (-) Steam [7] ππ = 394.155 ∗ πΆπ£ . √ β³ π. π2 π Estimation of control valve Cv[Note 2][7] π£πππ£π πΆπ£ 1 Single-seated π (πππβππ ) = ( )2 valves 9 π (πππβππ ) = ( π£πππ£π πΆπ£ 1 )2 12 Double-seated valves π£πππ£π πΆπ£ 1 )2 20 Butterfly valve sizes Qs in kg/hr β³P and P2 in kg/cm2 T in oK Gas [Note 1][7] ππΊ = 386.67 ∗ πΆπ£ √ β³ π. π2 π2 . πΊ. π 3 Qs in Nm /hr β³P and P2 in kg/cm2 T in oK G is the molecular weight divided by 29 π (πππβππ ) = ( Table 4.8: Relief loads guidelines for Inadvertent open control valve NOTE 1: Assuming a subcritical and turbulent flow NOTE 2: Shortcut mentioned in ref [8] were used in the tool (Cv =10*d2), d in inches Wetted Area Calculations [5] To determine vaporization rate, the surface area wetted by a vessel's internal liquid and is up to 7.6 m (25 feet) above grade, denoted as "fire elevation", needs to be considered. The term "grade" usually refers to ground level, but may be at any level at which a sizable fire could be sustained. Semi-Ellipsoidal/Elliptical Heads Or Torispherical/Dished Heads z D Vessels Cylindrical part Vertical h π΄π€ π·2 β (( − 0.5) π΅ + 1 8 π· β 4π ( − 0.5) + π΅ 1 π· + ln( )) 4π 2 − √3 = π L D 2 β √ π΅ = 1 + 12 ( − 0.5) π· For 2:1 Elliptical head ε = 0.866, elsewise: Aw = 2πD*L Horizontal π = √1 − D z: inside dish depth h L π΄π€ = πΏπ· cos −1 (1 − (2β/π·)) Heads Hemispherical Heads D h π΄π€ = πβ π· 2 4π§ 2 π·2 π : Eccentricity of elliptical heads Shortcut Calculations for various wetted Areas [4] Figure 4.2: Heat exchanger U tube side Aw Figure 4.3: Fixed Heat exchanger tube side Aw Figure 4.4: Kettle reboiler Aw Figure 4.5: Floating head Hex. Aw Figure 4.6: Heat exchanger U shell-side Aw Figure 4.7: Fixed heat exchanger Shell-side Aw Figure 4.8: Spherical Tank Aw Figure 4.9: Vertical vessel fixed head Aw Figure 4.10: Vertical Vessel Elliptical Head Aw Figure 4.11: Horizontal Vessel Aw Figure 4.12: Trayed Column Aw Examples API RP 520 Example No. 1 Input Mass flow Molecular weight Relieving Temperature Design pressure of equipment Units Kg/hr o K kPa / kg/cm2 API RP 520 Part I 24270 51 348 517 Tool 24271 51 (Using composition) 74.85 oC 5.272 Backpressure Overpressure kPa / kg/cm2 % 101.325 10 1.033 10 (Calculated) 670 0.9 392 1.11 1 1 0.975 36.98 / 5.73 41.16 / 6.38 P 0.98 1.05 1 1 0.975 39.5 / 6.12 41.16 / 6.38 P Output Relieving pressure kPa / kg/cm2 Z Critical Pressure kPa / kg/cm2 Cp/Cv Kb Kc kd Acalculated cm2/ in2 Aselected cm2/ in2 Orifice Designation 1. Estimating Relief Pressure and constants Relief pressure for one relief valve, no rupture disc, and non-fire case will equal 1.1 the equipment design pressure Pr = 1.1 * 517 = 670 kPa (6.8321 kg/cm2) Kb = 1 as backpressure is atmospheric Kc = 1, as there’s no rupture disc installed Kd = 0.975 1. Checking whether the flow is critical ππΆπ = π1 ∗ [ 1.11⁄(1.11−1) 2 π⁄(π−1) 2 ] ] = 670 ∗ [ = 670 ∗ 0.5825 = 390.33 π+1 1.11 + 1 The PRV sizing is based on the critical flow equation since the backpressure (0 kPag) is less than the critical flow pressure (291 kPag). 2. Calculating Orifice Area πΆ = 0.03948√π [ 2 π+1 ] (π+1)/(π−1) =0.03948*√1.11 [ 2 ] (1.11+1)/(1.11−1) 1.11+1 0.02489 Using The C graph provided earlier (Figure 2.7), C = 0.0249 for Cp/Cv of 1.11 = 0.03948 ∗ 0.63045 = π΄= π ∗ √ππ πΆπΎπ π1 πΎπ πΎπ √π = 24270 348 ∗ 0.9 √ = 3698 ππ2 0.0249 ∗ 0.975 ∗ 1 ∗ 1 ∗ 670 51 See API 526 for the selection of the proper orifice size. API 526 provides standard effective orifice areas in terms of letter designations. For this example, a “P” size orifice should be selected since it has an effective orifice area of 6.38 in.2 (4116 mm2) Step 1: Calculate Relief Pressure Step 2: Input mass flow rate and composition Step 3: Input relief/back conditions (T&P) Step 4: Download your calculations table! API RP 520 Example No. 4 Input Mass flow Relieving Temperature Design pressure of equipment Units Kg/hr C kPag / kg/cm2g API RP 520 Part I 69615 427 11032 Tool 69615 427 112.5 Backpressure Overpressure kPag / kg/cm2g % 101.325 10 1.033 10 12236 (124.77) 1 1 0.975 1.01 0.855 12.87 / 1.995 18.41 / 2.853 L 124.77 1 1 0.975 1.01 0.862 12.75 / 1.97 18.41 / 2.853 L Output Relieving pressure kPa / kg/cm2 Kb Kc kd KN KSH Acalculated cm2/ in2 Aselected cm2/ in2 Orifice Designation 1. Estimating Relief Pressure and constants Relief pressure for one relief valve, no rupture disc, and non-fire case will equal 1.1 the equipment design pressure Pr = 1.1 * 11032 + 101.325 = 12236.5 kPa (124.77 kg/cm2) Kb = 1 for conventional valve discharging to atmosphere Kc = 1, as there’s no rupture disc installed Kd = 0.975 KSH : 0.855 from tables KN : P1 (124.77 kg/cm2.a) is > 106.5 kg/cm2.a KN = (0.1906 *1774.7 - 1000)/(0.2292 *1774.7- 1061) = 1.01 2. Calculating Orifice Area π΄= 190.5 ∗ π 190.5 ∗ 69615 = = 1287 ππ2 (12.87 ππ2 ) π1 πΎπ πΎπ β πΎπ πΎπ πΎπ 12236.5 ∗ 0.975 ∗ 0.855 ∗ 1.01 ∗ 1 ∗ 1 See API 526 for the selection of the proper orifice size. API 526 provides standard effective orifice areas in terms of letter designations. For this example, a “L” size orifice should be selected since it has an effective orifice area of 2.853 in.2 (1841 mm2) Step 1: Calculate Relief Pressure Step 2: Input mass flow rate and composition Step 3: Input relief/back conditions (T&P) Step 4: Download your calculations table! API RP 520 Example No. 5 Input Mass flow Specific Gravity Viscosity Units L/min Saybolt / cP Design pressure of equipment kPag / kg/cm2g Backpressure kPag / kg/cm2g Overpressure % Output Relieving pressure kPag / kg/cm2 Kc Kd Kw Kv Acalculated cm2/ in2 Aselected cm2/ in2 Orifice Designation 1. Estimating Relief Pressure and constants API RP 520 Part I 6814 0.9 2000 / 388.5 Tool 368010 (kg/hr) 0.9 388.5 1724 345 10 17.58 3.52 (4.55 abs) 10 1896 (19.33 kg/cm2.g) 1.0 0.65 1 1 (initially) / 0.982 31.22 / 4.84 41.16 / 6.38 P 20.37 (19.337 gauge) 1 0.65 0.97 0.99 30.71 / 4.83 41.16 / 6.38 P Relief pressure for one relief valve, no rupture disc, and non-fire case will equal 1.1 the equipment design pressure Pr = 1.1 * 1724 = 1896.4 kPa (kg/cm2) Kw = 1 as backpressure is atmospheric Kc = 1 as there’s no rupture disc installed Kd= 0.975 Kv: initially assumed 1 2. Calculating Orifice Area π΄= 11.78π√πΊ πΎπ πΎπ€ πΎπ£ πΎπ √π1 − π2 = 11.78 ∗ 6814 0.9 √ = 3066 ππ2 (30.66 ππ2 ) 0.975 ∗ 1 ∗ 1 ∗ 1 1896 − 345 See API 526 for the selection of the proper orifice size. API 526 provides standard effective orifice areas in terms of letter designations. For this example, a “P” size orifice should be selected since it has an effective orifice area of 6.38 in.2 (4116 mm2) 3. Check Kv and recalculate Acalculated π π = π ∗ (18800 ∗ πΊ) π√π΄ = 6814*18800*0.9 388.5√4116 −0.5 170 ππ£ = ( + 1) = 0.982 π π π΄= π΄π πΎπ£ = 3066 0.982 = 3122 ππ2 = 4625 Step 1: Calculate Relief Pressure Step 2: Input mass flow rate and composition Step 3: Input relief/back conditions (T&P) Step 4: Download your calculations table! Fire Case Example: Benzene in a Horizontal Vessel Input Units Reference [1] Units Converted Benzene 78.11 37.78 + 273.15 [Note] 1379 Atmospheric 21 Bare Vessel Horizontal + spherical heads 4.572 9.144 3.734 4.572 Tool kPa / kg/cm2 kCal/kg m2 Kg/hr kPa / kg/cm2 - 1769.88 95.62(input) 83.7 14665 1 (input) 18.04 kg/cm2.g (1769.7 kPa) 146 [Note 1] 121 13020.15 0.81 Critical 1.12 (input) 1 1 0.975 Critical 0.97 1 1 0.975 cm2/ in2 cm2/ in2 6.787 / 1.052 in2 8.303 / 1.287 in2 J (nozzles 2”/3”) 8.20495 / 1.27177 in2 8.303 / 1.287 in2 J (nozzles 2”/3”) Fluid Molecular weight Relieving Temperature Design pressure of equipment Backpressure Overpressure Vessel Geometry data K kPag / kg/cm2.g kPa / kg/cm2 % Diameter T-T Length Level (Normal liquid level) Height above grade m m m m Output Relieving pressure ΔH Wetted Area (Aw) Mass flow Z Critical Pressure Flow condition Cp/Cv Kb Kc kd C Acalculated Aselected Orifice Designation Notes: Benzene 78.11 250 + 273.15 [Note 2] 14.06 kg/cm2.g (1379 kPa) Atmospheric 21 Bare Vessel Horizontal + Cylindrical heads 4.572 9.144 3.734 4.572 1. Heat of vaporization is higher in the tool as a result of adding the heat required to bring the fluid from the subcooled phase to saturation temperature 2. A temperature of 250 was assumed to obtain benzene at the vapor phase; assuming relived and vaporized benzene at 37.78 C & 18 kg/cm2 is illogical. This, however, will increase Acalculaed. 3. Estimate Vessel wetted area Level of the wetted area = 7.6 – 4.57 = 3.03 m ratio of level = 3.03/4.57 = 0.663 Total Area of the horizontal vessel (spherical heads) = (L+D)*πD = (9.1 + 4.57)*π*4.57 = 196.26 m2 9.1 m Fraction of area (from Figure 4.11) = 0.6 Wetted area = Area fraction * total surface area = 0.6*196.26 = 117.75 m2 4.57 m 7.6 – 4.57 Wetted Area 4.57 m 3.73+4.57 m 7.6 m 2β π΄π€ (πΆπ¦πππππππππ ππππ‘) = πΏπ· cos −1 (1 − ( )) π· 3.03 )) = 587 ∗ cos −1 (−0.326) = 79.14 π2 4.57 π΄π€ (2 βππππ ) = πβπ· = 3.14 ∗ 3.03 ∗ 4.057 = 38.6 π2 π΄π€ π‘ππ‘ππ = 79.147 + 38.6 = 117.74 π2 4. Estimate Relief Load = 9.1 ∗ 4.57 πππ −1 (1 − (2 ∗ Q = qoFA0.82 F = 1 for Bare vessel qo = 37130 (adequate drainage is provided) Q = 37130*1*117.750.82 = 1853159.92 kCal/hr π= π 1853159.92 = = 12693 ππ/βπ βπ» 146 3. Estimating Relief Pressure and constants Relief pressure for one relief valve, no rupture disc, and fire case will equal 1.21 the equipment design pressure Pr = 1.21 * 1379 + 101.325 = 1770 kPa (18.05 kg/cm2) Kb = 1 as backpressure is atmospheric Kc = 1, as there’s no rupture disc installed Kd = 0.975 4. Checking whether the flow is critical 1.12⁄(1.12−1) 2 π⁄(π−1) 2 ] ] ππΆπ = π1 ∗ [ = 1770 ∗ [ = 1770 ∗ 0.5805 = 1027.5 πππ π+1 1.12 + 1 The PRV sizing is based on the critical flow equation since the backpressure (0 kPag) is less than the critical flow pressure (1027 kPag). 5. Calculating Orifice Area πΆ = 0.03948√π [ 2 π+1 ] (π+1)/(π−1) =0.03948*√1.12 [ 2 ] (1.12+1)/(1.12−1) 1.12+1 = 0.03948 ∗ 0.4 = 0.0249 Using The C graph provided earlier (Figure 2.7), C = 0.025 for Cp/Cv of 1.12 π΄= π ∗ √ππ πΆπΎπ π1 πΎπ πΎπ √π = 24270 348 ∗ 1 √ = 621 ππ2 0.025 ∗ 0.975 ∗ 1 ∗ 1 ∗ 1770 78.11 See API 526 for the selection of the proper orifice size. API 526 provides standard effective orifice areas in terms of letter designations. For this example, a “J” size orifice should be selected since it has an effective orifice area of 1.287 in.2 (830 mm2) Step 1: Calculate Relief Pressure Step 2: Select estimate relief loads and choose “External Fire due to vaporization” Step 3: input relieved stream composition and conditions Step 4: Input wetted Area required inputs Step 5: check your results and calculations’ matrix Step 6: go to “3. Gas or vapor” and use Calculated Relief Load Step 7: Input mass flow rate and composition Step 8: Download your calculations table! Note: 250 oC was used to obtain the vapor phase Definitions Maximum operating pressure is the expected maximum pressure during operation of the system upstream of the pressure relief valve. Maximum allowable working pressure (MAWP) is the maximum gauge pressure permissible at the top of a completed vessel in its operating position for a designated temperature. The pressure is based on calculations for each element in a vessel using nominal thickness, exclusive of additional metal thickness allowed for corrosion and loading other than pressure. The maximum allowable working pressure is the basis for the pressure setting of the pressure relief devices that protect the vessel. Design gauge pressure refers to at least the most severe conditions of coincident temperature and pressure expected during operation. This pressure may be used in place of the maximum allowable working pressure in all cases where the MAWP has not been established. The design pressure is equal to or less than the MAWP. Accumulation is the pressure increase over the maximum allowable working pressure of the vessel during discharge through the pressure relief device, expressed in pressure units or as a percent. Maximum allowable accumulations are established by applicable codes for operating and fire contingencies. Overpressure is the pressure increase over the set pressure of the pressure relief device, expressed in pressure units or as a percent. It is the same as accumulation when the relieving device is set at the maximum allowable working pressure of the vessel. Rated relieving capacity is the portion of the measured relieving capacity permitted by the applicable code regulation to be used as a basis for the application of a pressure relief device. Stamped capacity is the rated relieving capacity that appears on the device nameplate. The stamped capacity is based on the set pressure plus the allowable overpressure for compressible fluids and the differential pressure for incompressible fluids. The stamped capacity shall not exceed 90% of the average capacity of the valves tested.[ASME VIII Div. 1 UG-13 1 (d)(l)] Set pressure is the inlet gauge pressure at which the pressure relief device is set to open under service conditions. Pressure differential is the difference between the set pressure of the pressure relief device and the operating pressure of the protected vessel. Cold differential test pressure is the pressure at which the pressure relief valve is adjusted to open on the test stand. The cold differential test pressure includes corrections for the service conditions of back pressure or temperature or both. Back pressure is the pressure that exists at the outlet of pressure relief devices as a result of the pressure in the discharge system. It is the sum of the superimposed and built-up back pressure. Superimposed back pressure: The static back pressure that exists at the outlet of a pressure relief device at the time the device is required to operate. It is result of pressure in the discharge system corning from other sources and may be constant or variable. Built-up back pressure: The built-up back pressure is the increase in pressure in the discharge header that develops as a result of flow after the pressure relief device or devices open. The built-up back pressure is caused by flow from the particular device and others, if any, which simultaneously discharge into the disposal system. This type of back pressure is variable. The built-up back pressure shall be less than the allowable back pressure, 10% of the set pressure for the conventional type or 50% of the set pressure for the balanced-bellows type. Constant Back Pressure: The static back pressure that exists under normal operation where no relief device is operated; i.e. constant back pressure of the superimposed back pressure. The constant back pressure is used to determine the spring set pressure of conventional type pressure relief valve as a difference between the set pressure and the constant back pressure. Therefore, the opening pressure will vary depend on the built-up back pressure. The opening pressure of balanced-bellows type is the set pressure of the valve and is independent of any back pressure. Blowdown is the difference between the set pressure and the closing pressure of a pressure relief valve, expressed as a percent of the set pressure or in pressure units. Opening pressures the value of increasing inlet static pressure at which there is a measurable lift of the disc or at which discharge of the fluid becomes continuous. Closing pressure is the value of decreasing inlet static pressure at which the valve disc reestablishes contact with the seat or at which lift becomes zero. Simmer is the audible or visible escape of compressible fluid between the seat and disc at an inlet static pressure below the set pressure and at no measurable capacity Leak-test pressure is the specified inlet static pressure at which a seat leak test is performed. The term relieving conditions is used to indicate the inlet pressure and temperature on a pressure relief device at a specific overpressure. The relieving pressure is equal to the valve set pressure plus the overpressure. The temperature of the flowing fluid at relieving conditions may be higher or lower than the operating temperature. Chatter refers to the motion that causes the disc to contact the seat and damage the valve and associated piping. Chattering may result in lowered capacity and damage to the seating surfaces. Flutter refers to the abnormally rapid reciprocating motion of the movable parts of a pressure relief valve in which the disc does not contact the seat Atmospheric discharge is the release of vapors and gases from pressure relief or depressing devices to the atmosphere. Flare system is a means for the safe disposal of waste gasses by closed pipeline and combustion system. With an elevated mre the combustion is carried out at the top of a pipe or stack where the burner and igniter are located. A ground flare is similarly equipped except that combustion is carried out at or near ground level. A burn pit differs from a flare in that it is normally designed to handle both liquids and vapors. Vent stack is the elevated vertical termination of a disposal system that discharges vapors into the atmosphere without combustion or chemical conversion of the relieved fluid. References [1] API RP 520 Part I, 10th edition. [2] Engineering Encyclopedia: Aramco desktop standards: sizing and selecting Pressure relief valves [3] Pressure relief devices rev. 5, JGC standard practice 2002 JGS 210-120-1-61E [4] Pressure Relieving design rev. 5, JGC standard practice 2008 JGS 210-120-1-40E [5] Volume and Wetted Area of Partially Filled Horizontal Vessels, Link: https://neutrium.net/equipment/volume-and-wetted-area-of-partially-filled-horizontal-vessels/ [6] Sizing Pressure-Relief Devices, Daniel A. Crowl and Scott A. Tipler. (AIChE) [7] Elements of chemical process engineering chapter 1, Basic Process Engineering principles [8] Chemical process engineering Vol. 1, Chapter 5 P. 246 By Kayode Coker Other Recommended Reads [I] EIEPD: PSV General Guideline: addresses the sizing procedures and guidelines, different relief scenarios for relief load estimation, standards involved, and rupture disc types and sizing procedures. [II] The Safety Relief Valves Handbook by Marc Hellemans, Chapter 5: Design Fundamentals [III] Applied Instrumentation in the Process Industries by W.G Andrew and H.B. Williams Vol 2, second edition: Chapter 6: Pressure relief systems P. 130 [IV] API RP 520 Part II: Installation guidelines for PSVs. [V] API 521: This standard specifies requirements and gives guidelines for examining the principal causes of overpressure, determining individual relieving rates, and electing and designing disposal systems, including such component parts as piping, vessels, flares, and vent stacks.