KasperCalc: Pressure Relief Valve Sizing Calculator

Configuration

Service

Device

Rupture Disk Upstream

Contingency

This Device

Overpressure (% of set)

Fluid

Sizing Equations In

Load a Worked Example

Fluid properties come from the CoolProp tables in Thermodynamics Land (gases, steam and liquids) or this site's own digitized liquid data (Multi-Fluid Property Charts). Every property box can be typed over; blank boxes use the fluid data (shown in grey). Pick "Manual entry" to type all of them yourself.

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Warnings & Status

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psig

barg

kPag

psig

barg

kPag

psig

barg

kPag

Barometric Pressure

psia

kPa

Use the value for the site elevation.

deg F

deg C

Kelvin

deg R

Required Relieving Rate (W)

lb/h

kg/h

or gas volume at standard conditions

scfm

Nm³/min

scfm at 14.7 psia and 60 °F; Nm³/min at 101.325 kPa and 0 °C. Converted to mass flow with M, using the factors in API 520 eq. (3) and (6).

Required Relieving Rate (Q)

GPM

L/min

m³/hr

Volume flow at the flowing temperature.

Steam Condition

K_SH

Saturation temp. at P₁ (°F)—

Liquid Properties at Relief

Viscosity at T₁

v₀ at the inlet

ft³/lb

m³/kg

v₉ at 90 % of inlet pressure

ft³/lb

m³/kg

K_d

K_b

K_w

K_c

Relieving Conditions

Max. accumulated pressure—

Allowable overpressure—

Relieving pressure P₁ (psia)—

Relieving pressure P₁ (kPa)—

Back pressure P₂ (psia)—

Back pressure, % of set (gauge)—

Critical flow pressure P_cf (psia)—

Flow—

Sizing Factors

—

Required Effective Area

Required area (in²)—

Required area (mm²)—

API 526 orifice letter—

Letter effective area—

Required / letter area—

Sizing equation (API 520)—

API 526 Orifice Letters

Letter	in²	mm²

Effective areas for preliminary sizing with the API 520 equations. Check the chosen valve's actual area and rated coefficient with the manufacturer.

Preliminary sizing with the API Standard 520 Part I (8th edition) equations and the API 526 effective orifice areas. The selected valve's certified capacity must still be checked with its actual area and rated coefficient of discharge.

Also See:

Orifice Flow Rate Calculator

Also See:

Gas Flow Safety Calculator

Also See:

Thermo Land (Fluid Property Lookup)

Reference Guide — Relief Valve Sizing

What Sizing a Relief Valve Means

A pressure relief valve (PRV) opens when the pressure in a vessel or line reaches its set pressure and passes enough flow to stop the pressure rising past what the code allows. Sizing finds the smallest effective discharge area that passes the required relieving rate at the relieving pressure, then picks the standard orifice that is at least that big.

The steps on this page follow API Standard 520 Part I:

Find the worst-case relieving rate W (or Q) for the contingency: blocked outlet, control valve failure, fire and so on. API 521 lists the common causes. This page takes that rate as an input.
Fix the relieving pressure P₁ from the set pressure, MAWP and the allowable accumulation (card 02).
Calculate the required effective area A with the equation for the service: gas or vapor, steam, liquid or two-phase (cards 03 to 07).
Choose the API 526 orifice letter whose effective area is equal to or larger than A (card 08).

Pressure levels for a relief valve: operating pressure below set pressure, set pressure at or below MAWP, and the maximum accumulated pressure 10, 16 or 21 percent above MAWP; relieving pressure P1 is the accumulated pressure plus atmospheric pressure

Pressure levels for a single relief device

Preliminary sizing. The API 520 coefficients (K_d = 0.975 for gas and steam, 0.65 for liquid) and the API 526 effective areas are nominal values for choosing a valve size. They are not a particular valve's certified values. Once a valve is chosen, its rated capacity must be checked with that valve's actual orifice area and rated coefficient of discharge (API 520 5.2).

Set Pressure, Accumulation & Relieving Pressure

Accumulation is the pressure rise above MAWP allowed while the device relieves. Overpressure is the rise above the set pressure. When the set pressure equals MAWP they are the same; when the valve is set lower, the overpressure is larger.

Relieving pressure (absolute) \[ P_1 = P_{set} + \Delta P_{over} + P_{atm} = P_{accum,max} + P_{atm} \]

For liquids the sizing equation uses gauge pressures, so P₁ there is the set pressure plus the overpressure, without the atmospheric term.

When the MAWP is between 15 and 30 psig (103 and 207 kPag), the allowable accumulation for operating contingencies is 3 psi (21 kPa) for a single device and 4 psi (28 kPa) for multiple devices. This calculator uses the larger of that and the percentage.

Contingency	Device	Max. set pressure, % MAWP	Max. accumulated pressure, % MAWP
Operating, single device	First	100	110
Operating, multiple devices	First	100	116
Operating, multiple devices	Additional	105	116
Fire	First	100	121
Fire	Additional	105	121
Fire	Supplemental	110	121

Set pressure and accumulation limits for ASME Section VIII vessels, from API 520 Part I Table 1.

Example (API 520 Table 2): MAWP 100 psig, set 100 psig, single device. Maximum accumulated pressure 110 psig, overpressure 10 psi, P₁ = 110 + 14.7 = 124.7 psia. With the valve set at 90 psig the overpressure is 20 psi and P₁ is the same.

Gas or Vapor: Critical & Subcritical Flow

Gas speeding up through the valve nozzle reaches the speed of sound when the outlet pressure is low enough. Below that critical flow pressure, lowering the back pressure further does not increase the flow, and the flow depends only on the inlet conditions.

Critical flow pressure ratio, eq. (1) \[ \frac{P_{cf}}{P_1} = \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}} \]

If P₂ ≤ P_cf the flow is critical (choked):

Critical flow, eq. (2) USC / (5) SI \[ A = \frac{W}{C\,K_d\,P_1\,K_b\,K_c}\sqrt{\frac{T\,Z}{M}} \] \[ C = 520\sqrt{k\left(\frac{2}{k+1}\right)^{\frac{k+1}{k-1}}}\ \text{(USC)},\qquad C = 0.03948\sqrt{k\left(\frac{2}{k+1}\right)^{\frac{k+1}{k-1}}}\ \text{(SI)} \]

USC: A in², W lb/h, P₁ psia, T °R. SI: A mm², W kg/h, P₁ kPa, T K. M is the molecular weight. If k is not known, API 520 suggests C = 315 (0.0239), the value at k = 1, which is conservative.

If P₂ > P_cf the flow is subcritical. For conventional and pilot-operated valves the area is:

Subcritical flow, eq. (12) USC / (15) SI \[ A = \frac{W}{735\,F_2\,K_d\,K_c}\sqrt{\frac{Z\,T}{M\,P_1\,(P_1-P_2)}}\qquad A = \frac{17.9\,W}{F_2\,K_d\,K_c}\sqrt{\frac{Z\,T}{M\,P_1\,(P_1-P_2)}} \] \[ F_2 = \sqrt{\left(\frac{k}{k-1}\right) r^{2/k}\left[\frac{1-r^{(k-1)/k}}{1-r}\right]},\qquad r = \frac{P_2}{P_1} \]

Balanced-bellows valves are sized with the critical-flow equation and the manufacturer's K_b, even when the flow is subcritical (5.6.4.3).

Which k? Use the ideal-gas k at the relieving temperature. A real-gas Cₚ/Cᵥ at high pressure is not a good model of the isentropic expansion, and using it can undersize the valve (5.6.2.4). This page takes k and M from the CoolProp data at the lowest tabulated pressure (the ideal-gas limit) and Z from the density at P₁ and T₁. Where Z is below about 0.8 or above about 1.1, API 520 Annex B covers sizing for strongly non-ideal fluids.

Back Pressure & Valve Types

Simplified cross-sections of a conventional spring-loaded relief valve, where outlet pressure acts on the top of the disc, and a balanced-bellows valve, where a bellows shields the disc from outlet pressure

Conventional vs. balanced-bellows valve (simplified)

Conventional valve. Back pressure in the outlet pushes on the back of the disc. Superimposed back pressure raises the opening pressure, so the spring is set lower to suit (the cold differential test pressure). Built-up back pressure should stay under 10 % of the set pressure at 10 % overpressure; above that the valve can chatter. No K_b correction is used for gas at critical flow or for liquid (5.3.3.1.3).

Balanced-bellows valve. A bellows keeps the back pressure off the disc, so it can usually take a total back pressure up to about 50 % of the set pressure. High back pressure still reduces lift, so the capacity is corrected with K_b (gas and steam) or K_w (liquid) from the manufacturer (5.3.3.2).

Pilot-operated valve. Lift is not affected by back pressure; for gas at critical flow K_b = 1.0 (5.3.3.3).

Rupture disk upstream of a valve. The combination's capacity is multiplied by K_c: the certified value for that disk and valve pair, or 0.9 when the combination has no certified value (5.11.2).

Steam (Napier Equation)

Steam at critical flow is sized with the Napier equation rather than the general gas equation:

Steam, eq. (21) USC / (22) SI \[ A = \frac{W}{51.5\,P_1\,K_d\,K_b\,K_c\,K_N\,K_{SH}}\qquad A = \frac{190.5\,W}{P_1\,K_d\,K_b\,K_c\,K_N\,K_{SH}} \]

Napier correction, eq. (23) to (25) \[ K_N = 1.0 \quad (P_1 \le 1500\ \text{psia} = 10\,339\ \text{kPa}) \] \[ K_N = \frac{0.1906\,P_1 - 1000}{0.2292\,P_1 - 1061}\ \text{(psia)},\qquad K_N = \frac{0.02764\,P_1 - 1000}{0.03324\,P_1 - 1061}\ \text{(kPa)} \]

The second form applies from 1500 to 3200 psia (10 339 to 22 057 kPa).

K_SH corrects for superheat. It is 1.0 for saturated steam at any pressure, and for superheated steam it comes from API 520 Table 9 by set pressure and temperature (15 to 3000 psig, 300 to 1200 °F). This page interpolates linearly between the table's rows and columns. Where the point falls next to a blank (“—”) cell of the table, there is no tabulated value to interpolate from, and the page asks for K_SH.

Above 1200 °F, API 520 says to size steam with the gas equations (card 03).

Example (API 520 5.7.2): 153 500 lb/h saturated steam, set 1600 psig, 10 % accumulation. P₁ = 1774.7 psia, K_N = 1.01, A = 1.705 in² (1100 mm²): a K orifice (1.838 in²).

Liquid Relief & Viscosity Correction

For valves with ASME capacity certification in liquid service, the liquid is treated as incompressible:

Liquid, eq. (28) USC / (29) SI \[ A = \frac{Q}{38\,K_d\,K_w\,K_c\,K_v}\sqrt{\frac{G_l}{P_1 - P_2}}\qquad A = \frac{11.78\,Q}{K_d\,K_w\,K_c\,K_v}\sqrt{\frac{G_l}{P_1 - P_2}} \]

USC: Q in US gal/min, P in psig. SI: Q in L/min, P in kPag. G_l is the specific gravity at the flowing temperature, referred to water at standard conditions. This page uses water at 60 °F (999.01 kg/m³), the same reference as the site's other fluid pages. For preliminary sizing K_d = 0.65.

Viscous liquids flow less than the equation predicts. API 520 sizes first with K_v = 1, takes the next larger standard orifice, finds its Reynolds number, and corrects the area by K_v. If the corrected area is larger than that orifice, the steps repeat with the next size up. This page runs that loop for you.

Reynolds number, eq. (31) to (34); K_v, eq. (30) \[ Re = \frac{Q\,(2800\,G_l)}{\mu\sqrt{A}}\ \text{or}\ \frac{12\,700\,Q}{U\sqrt{A}}\ \text{(USC)},\qquad Re = \frac{Q\,(18\,800\,G_l)}{\mu\sqrt{A}}\ \text{or}\ \frac{85\,220\,Q}{U\sqrt{A}}\ \text{(SI)} \] \[ K_v = \left(0.9935 + \frac{2.878}{Re^{0.5}} + \frac{342.75}{Re^{1.5}}\right)^{-1} \]

μ in centipoise, U in Saybolt universal seconds (the SSU forms are not recommended below 100 SSU). API 520 Figure 37 stops at K_v = 1.0, which the equation passes near Re = 10⁵, so the page holds K_v at 1.0 there.

Example (API 520 5.8.2): 1800 gal/min crude, G = 0.90, 2000 SSU, set 250 psig, back pressure 0 to 50 psig on a balanced-bellows valve (K_w = 0.97). A_R = 4.752 in², Re = 4525 on the P orifice, K_v = 0.964, A = 4.93 in²: a P orifice.

Two-Phase Relief: Omega Method

A liquid that flashes, or a mixture of liquid and vapor, can pass much less mass through a valve than the liquid equation predicts. API 520 Annex C gives Leung's omega method, a form of the homogeneous equilibrium model, for flashing or non-flashing two-phase flow with no non-condensable gas at the inlet. ω describes how fast the mixture expands as the pressure falls, from two specific volumes:

Omega parameter, eq. (C.12) \[ \omega = 9\left(\frac{v_9}{v_0} - 1\right) \]

v₀ is the specific volume at the inlet and v₉ is the specific volume at 90 % of the inlet pressure, from a flash calculation in a process simulator.

Critical pressure ratio, eq. (C.14) \[ \eta_c^2 + (\omega^2 - 2\omega)(1-\eta_c)^2 + 2\omega^2\ln\eta_c + 2\omega^2(1-\eta_c) = 0 \]

If P_c = η_cP₀ ≥ P_a (the back pressure), the flow is critical:

Mass flux, eq. (C.16) USC / (C.18) SI, and subcritical (C.17) / (C.19) \[ G = 68.09\,\eta_c\sqrt{\frac{P_0}{v_0\,\omega}}\ \text{(USC)},\qquad G = \eta_c\sqrt{\frac{P_0}{v_0\,\omega}}\ \text{(SI)} \] \[ G = \frac{\left\{-2\left[\omega\ln\eta_a + (\omega-1)(1-\eta_a)\right]\right\}^{1/2}}{\omega\left(\frac{1}{\eta_a}-1\right)+1}\sqrt{\frac{P_0}{v_0}},\qquad \eta_a = \frac{P_a}{P_0} \]

Area, eq. (C.20) USC / (C.21) SI \[ A = \frac{0.04\,W}{K_d\,K_b\,K_c\,K_v\,G}\qquad A = \frac{277.8\,W}{K_d\,K_b\,K_c\,K_v\,G} \]

USC: P psia, v ft³/lb, G lb/(s·ft²), W lb/h, A in². SI: P Pa, v m³/kg, G kg/(s·m²), W kg/h, A mm². For preliminary sizing K_d = 0.85. The subcritical USC form carries the same 68.09 factor.

No pressure relief valve has a certified two-phase capacity, and these methods have not been validated by test (API 520 C.1.1, 5.10.2). Treat the result as an estimate.

API 526 Orifice Letters

API 526 is the purchase specification for flanged steel relief valves. It names each orifice size by a letter, from D (smallest) to T (largest), and gives each letter an effective area to be used with the API 520 equations. The required area from the calculator is rounded up to the next letter.

Effective areas are not the area of any real valve. A manufacturer's valve with a given letter has its own actual orifice area and rated coefficient of discharge, chosen so that its certified capacity meets or exceeds what the API equations predict for that letter (API 520 5.2.5, 5.2.6).

If the required area is larger than a T orifice, the relief load has to be split between several valves; API 520's two-phase example ends with two Q orifices and one R orifice. Multiple valves use the 116 % accumulation (card 02).

Letter	Effective area, in²	Effective area, mm²

API 526 effective orifice areas as printed in the Baker Hughes Consolidated and LESER sizing guides; mm² = in² × 645.16. API 520 quotes the K, M, P, Q, R and T areas in its examples.

Notes, Limitations & Sources

This calculator does not decide the relieving rate, check inlet pressure loss or discharge piping, or size for fire heat input; API 520 Part II and API 521 cover those. K_b for balanced-bellows valves and K_w are left for you to enter from the manufacturer, since the API 520 curves (Figures 30 and 31) are typical values only. Liquid valves without capacity certification (API 520 5.9) and rupture-disk sizing by the flow-resistance method (5.11.1.3) are not covered.

The worked examples in the Configuration list load the inputs from API 520 Part I. Two of them read a factor off a figure (F₂ = 0.86 in Example 2, η_c = 0.66 in Annex C) where this page calculates it from the equation (0.855 and 0.656), so those results differ slightly from the printed ones. The SI results in API 520's examples are the USC answers converted to mm², so the SI equations, whose constants are rounded, agree with them to about 0.2 %.

Sources

American Petroleum Institute, API Standard 520, Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries, Part I: Sizing and Selection, 8th ed., Dec. 2008: equations (1) to (34), Tables 1 and 7 to 9, Annex C. Newer editions exist; check against the edition your project calls for.
Baker Hughes, Consolidated Valve Sizing and Selection, Technical Specification Rev. E, Feb. 2022: API 526 effective areas (Table 6), accumulation rules.
LESER, Design of Safety Valves, Design Standard ASME VIII / API 520, Rev. 00, June 2018: API 526 effective areas, API K_d values.
Fluid properties: CoolProp tables via Thermodynamics Land; digitized liquid densities and viscosities via Multi-Fluid Property Charts.

Pressure Relief Valve Sizing Calculator — API 520 Required Effective Area and API 526 Orifice Letter for Gas, Steam, Liquid and Two-Phase Relief

Also See:

Also See:

Also See:

What Sizing a Relief Valve Means

Set Pressure, Accumulation & Relieving Pressure

Gas or Vapor: Critical & Subcritical Flow

Back Pressure & Valve Types

Steam (Napier Equation)

Liquid Relief & Viscosity Correction

Two-Phase Relief: Omega Method

API 526 Orifice Letters

Notes, Limitations & Sources

Cite This Work