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Pressure Relief Valve (PSV) Sizing Calculator

API 520 Part I | API 521 Fire | API 526 Orifices | Metric + Imperial | v1.0

API 520·521·526
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Gas / Vapor Relief — API 520 §5.6

Critical & subcritical flow | C(k) | Kb | F₂ | orifice D–T

Protected System
Fluid Properties at Relief
Use properties at the RELIEVING condition (P₁, T₁), not normal operating. Pick a library fluid to auto-fill M & k and enable Auto-Z: the server computes Z with the Peng-Robinson EOS at relieving pressure & temperature (same engine as the EOS & control-valve calculators) and runs a phase-stability check — it warns if the "vapor" is actually liquid or near its dew point. If k unknown, k = 1.0 gives C = 315 (conservative).
Valve & Installation
Sizing Result — API 520 Gas/VaporPASS
📖 New to PSV sizing? Plain-language guide to every field

A pressure safety valve (PSV) is the last line of defence: if pressure in your vessel rises too high, it pops open and lets gas escape until things are safe again. This tab answers one question: how big must the valve opening be to let enough gas out fast enough?

Set Pressure — the pressure at which the valve starts to open. Almost always equal to the vessel's design pressure (stamped on its nameplate). Not the normal operating pressure.from vessel nameplate / U-1 datasheet
Relief Rate W — how much gas the valve must release, in kg/h. This comes from your worst credible upset: e.g. if the outlet is blocked, W = everything the compressor or upstream plant can push in. Not sure? Build it in the Scenarios tab, which can estimate loads for you.
Relieving Temperature — gas temperature at the moment the valve is open, which is usually hotter than normal operation (pressure went up, and often temperature with it). If unsure, use the highest credible temperature — it gives a safely larger valve.
Fluid / M / k / Z — just pick your gas from the list; molecular weight (M), heat-capacity ratio (k) and compressibility (Z) fill in automatically. Z is computed by a real equation of state at relieving conditions — this matters because guessing Z wrong is the classic sizing mistake. Only touch these numbers for a gas not in the list.
Overpressure / Scenario — how far above set pressure the vessel is allowed to climb while the valve is blowing. Code allows 10% for a normal (process) case, 21% for fire. Leave the default unless your datasheet says otherwise.
Valve Style — Conventional: simple spring valve, fine when the discharge pipe is short and open to air. Balanced bellows: has an internal bellows that shields the spring from discharge-pipe pressure — needed when back pressure is significant. Pilot-operated: a small pilot valve controls a big main valve — for high back pressure or when operating close to set.
Back Pressure — the pressure sitting in the pipe downstream of the valve, pushing back against it. Discharging straight to atmosphere through a short pipe? Enter 0. Discharging into a flare header that runs at, say, 2 barg? Enter 2. High back pressure squeezes valve capacity — the tool applies the correction (Kb) automatically. Not sure of the number? The Inlet/Outlet Lines tab calculates it from your pipe dimensions.
Kd — Discharge Coefficient — an efficiency factor for the valve nozzle. Leave the default 0.975 for preliminary sizing; the vendor's certified value replaces it at purchase time.
Rupture Disc — select "yes" only if a bursting disc is installed underneath the valve inlet (done for corrosive or dirty service). It costs 10% capacity (Kc = 0.9).

Reading the result: the tool computes the required orifice area, then picks the next standard API 526 orifice letter (D = smallest … T = largest). "Q orifice, 78% used" means: buy a Q-orifice valve, and your load uses 78% of what it can pass — the spare margin is normal and healthy.

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Steam Relief — API 520 §5.8

Napier equation | Kn high-pressure | Ksh superheat

Steam Conditions
Valve & Installation
Sizing Result — API 520 SteamPASS
📖 Plain-language guide — steam relief

Sizing a safety valve for a steam boiler, steam drum, or steam line. Same idea as the gas tab, but steam gets its own dedicated formula (with two extra correction factors handled automatically).

Set Pressure — the boiler/vessel design pressure from the nameplate, where the valve must start opening.
Relief Rate W — the steam flow the valve must dump. For a fired boiler this is the maximum continuous rating (peak steam generation) — the valve must handle everything the burners can make with the outlet blocked.from boiler datasheet MCR
Saturated vs Superheated — saturated steam is at its boiling temperature for the pressure (fresh from a drum, still "wet-capable"). Superheated steam has been heated further in a superheater and is hotter than boiling. If your steam comes straight off a drum: saturated. If it passed a superheater: superheated — enter its actual temperature, and the tool applies the superheat correction (Ksh) from the full API table. Superheated steam is less dense, so the valve must be a little bigger.
Kn — Napier correction — only kicks in above about 103 barg (1,500 psia); the tool applies it automatically. You'll see it in the results at very high pressure.
Back Pressure / Valve Style / Kd / Rupture Disc — same meaning as on the Gas tab (tap its guide). Steam valves usually discharge to open air through a short vent: back pressure 0, conventional style.
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Liquid Relief — API 520 §5.10

Certified valves (Kd = 0.65) | Kw bellows | Kv viscosity iteration

Liquid Conditions
Kv viscosity correction is iterated against the NEXT standard orifice per API 520 practice (Re = Q·2800·G / (μ·√A)). Valid for Re ≥ 20.
Valve & Installation
Sizing Result — API 520 LiquidPASS
📖 Plain-language guide — liquid relief

For valves protecting liquid-full systems: pump discharge lines, blocked-in liquid piping, thermal-relief on pipelines. Liquid valves work differently from gas valves (liquid doesn't expand), so they use their own certified formula.

Flow Q — the liquid flow the valve must pass. Classic case: pump keeps running against a blocked outlet → Q = the pump's flow at relieving pressure, read from its curve (deadhead region).from pump curve
Specific Gravity G — how heavy the liquid is vs water. Water = 1.0, ammonia ≈ 0.62, diesel ≈ 0.84, brine > 1.from fluid datasheet
Viscosity — how "thick" the liquid is, in cP. Water = 1, light oils 5–50, heavy oils hundreds. Thick liquids squeeze through the valve less easily, so the tool automatically iterates a viscosity correction (Kv) and enlarges the valve if needed. For water-like liquids the correction is negligible.
Overpressure — liquid valves are certified at 10% overpressure; the tool defaults correctly. (Older 25% sizing is obsolete.)
Kd — liquid valves use 0.65 (not the gas value 0.975). Already the default here.
Back Pressure & Kw — if you chose a bellows valve and there's back pressure, capacity drops; the tool applies the liquid bellows correction (Kw) automatically.

Tip: thermal expansion of blocked-in liquid (sun or heat tracing warming a full pipe) produces tiny flows — usually a ¾"×1" valve. The Scenarios tab can calculate that load for you.

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Fire Case — API 521

Wetted: Q = C·F·Aw⁰·⁸² → W = Q/λ | Unwetted: A = F′·A′/√P₁

Vessel Exposure Mode
Wetted vessel: pool fire boils the liquid inventory — relief load W = Q/λ, then sized as vapor at 21% accumulation. Wetted area limited to 7.6 m (25 ft) above the fire source.
Wetted Area
Fire Environment & Fluid
λ near the critical point → W = Q/λ diverges. For NH₃ storage relief use λ at relieving pressure, e.g. ≈ 1,050 kJ/kg near atmospheric. Water spray gives NO credit for F per API 521.
Sizing Result — API 521 FirePASS
📖 Plain-language guide — fire case

If a pool fire burns under your vessel, the flames boil the liquid inside and the vapor must escape through the PSV. This tab first works out how much heat the fire puts in, converts that to a vapor flow, then sizes the valve. It's often the governing case for storage vessels.

Wetted vs Unwetted — Wetted: the vessel contains liquid; fire boils it; the valve relieves the vapor. This is the normal case. Unwetted: the vessel holds only gas; there is no liquid to boil, the wall just heats up and the gas expands. Careful — a PSV often cannot save a gas-filled vessel (the wall weakens before enough pressure builds); the tool will tell you when that happens and point to depressuring instead.
Wetted Area Aw — the outside surface of the vessel that has liquid behind it, up to 7.6 m above the fire (flames don't effectively heat higher). Easiest: pick your vessel shape and enter diameter, length and liquid level — the tool does the geometry. Already have the number from a datasheet? Use direct entry.
Environment Factor F — credit for fireproof insulation. Bare vessel = 1.0. Good insulation can cut the heat to 0.3, 0.15 or 0.075 — but only if the insulation and its jacketing survive a fire and fire-hose impact. When in doubt, use 1.0 (safe side).
Drainage & Firefighting — if the area under the vessel slopes away so burning liquid drains off, and firefighting exists, the fire is less severe (C = 21,000). No drainage → C = 34,500 and a bigger valve. Ask your fire-protection team which applies.
Latent Heat λ — the energy needed to boil 1 kg of your liquid. Water ≈ 2,257 kJ/kg, ammonia ≈ 1,050 near ambient. The relief load is simply fire heat ÷ λ.from fluid property tables at relieving pressure Warning: λ shrinks near the critical point — if your relieving pressure is close to critical, this simple method understates the load; get specialist input.
Fluid / T / M / k — properties of the vapor being relieved, used for the final valve sizing at 21% overpressure (the code allows more accumulation in fire).
Unwetted inputs — exposed area, normal operating P & T, and maximum wall temperature (default 593 °C = carbon steel limit). The tool heats the trapped gas at constant volume and checks whether the valve can even help.
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Two-Phase Relief — API 520 Annex C (Omega)

Leung ω-method | ω = 9·(v₉/v₀ − 1) | critical ratio η꜀ | mass flux G

Two-Phase Mixture
Flash the inlet mixture isentropically (or isenthalpically) from P₀ (relieving pressure, absolute) to 0.9·P₀ and read both mixture specific volumes from your process simulator or steam/fluid tables. ω = 9·(v₉/v₀ − 1).
Sizing Result — Two-Phase OmegaWARN
📖 Plain-language guide — two-phase relief

Sometimes what comes out of the valve isn't clean gas or clean liquid but a froth of both — like opening a shaken soda bottle. Classic causes: a vessel of hot liquid that flashes to vapor as pressure drops, or gas bubbling through liquid. Standard gas/liquid formulas undersize badly here; this tab uses the industry-standard omega (ω) method instead.

When do I need this tab? — flashing liquids (liquid stored above its atmospheric boiling point: LPG, ammonia, hot condensate), reboiler blowthrough, foamy/reactive systems. If the phase check on the Gas tab warned "stable phase is LIQUID", you likely belong here or on the Liquid tab.
Direct v₀/v₉ mode — the rigorous route: your process simulator flashes the mixture from relieving pressure P₀ down to 90% of P₀, and you type in the mixture specific volume at both points. Most accurate; use it when you have simulation access.
Frozen mode — for a gas + liquid mixture where no new vapor forms as pressure drops (e.g. nitrogen-padded oil, air + water). You enter the vapor fraction x₀ and liquid density; the tool computes the vapor behaviour itself. No simulator needed.
Flashing mode (Leung) — for a boiling liquid at its saturation point (the soda-bottle case). Enter vapor fraction (0 for pure saturated liquid), liquid Cp and latent heat — the tool builds ω with the published Leung correlation. No simulator needed.
Kd — two-phase flow uses 0.85 by convention (between the gas 0.975 and liquid 0.65). Already the default.
ω, η꜀, G in the results — internals of the method: ω describes how much the froth expands, η꜀ is the choking pressure ratio, G is the mass flow per unit area. You don't need to act on them — they're shown so a reviewer can check the work.

Honest limit: this is a screening method. Reactive (runaway) systems and severely foamy fluids need a DIERS-type dynamic analysis by a specialist.

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Built-up Back Pressure & Inlet 3% Check

Isothermal compressible tailpipe hydraulics per API 521 §5.5 / API 520 Pt II

Valve & Relief Flow
Fluid Properties
Tailpipe flow is low-pressure so Z ≈ 1 is usually fine; Auto-Z evaluates PR EOS at the destination state.
Tailpipe (Valve Outlet → Destination)
ΣK: include exit loss (K = 1.0) + elbows (~0.3–0.5 each) + tees. Typical schedule-40 IDs: 3″ = 77.9 mm, 4″ = 102.3 mm, 6″ = 154.1 mm, 8″ = 202.7 mm, 10″ = 254.5 mm.
Inlet Line — 3% Rule Check (optional)
API 520 Pt II: non-recoverable inlet loss at rated valve capacity must not exceed 3% of set pressure — otherwise chatter/rapid-cycling risk. Leave inlet ID blank to skip.
BACK PRESSURE EVALUATIONPASS
📖 Plain-language guide — why pipes around the valve matter

A perfectly sized valve can still fail in service if the pipes around it are wrong. Two silent killers: a too-small inlet pipe makes the valve slam open and shut rapidly ("chatter" — destroys the valve in minutes), and a too-small outlet pipe builds pressure behind the valve and chokes its capacity. This tab checks both from simple pipe dimensions.

Back pressure — the concept — pressure in the discharge pipe pushing against the back of the valve. Two parts: superimposed (already there before the valve opens — e.g. the flare header runs at 2 barg) and built-up (created by the valve's own flow rushing through the pipe). The tool computes built-up from your pipe size and length.
The rules of thumb it checks — total back pressure ≤ 10% of set pressure → an ordinary (conventional) valve is fine. 10–50% → you need a balanced-bellows valve (and it loses some capacity, shown as Kb). Above 50% → pilot-operated territory or, better, a bigger discharge pipe.
Outlet inputs — tail-pipe inside diameter, its length, fittings (each elbow ≈ K 0.3–0.5, pipe exit = 1.0 — add them up into ΣK), and where it discharges: open atmosphere or a flare header (enter header pressure).
Inlet 3% rule — pressure lost in the short pipe between vessel and valve inlet must stay below 3% of set pressure, measured at the valve's rated (not required) flow. Break it and the valve chatters. Inputs: inlet pipe ID, length, fittings, and rated flow (≈ the selected orifice's full capacity — the sizing tabs show it).
Choked exit — if flow reaches the speed of sound at the pipe exit, the pipe itself becomes the bottleneck no matter what's downstream. The tool flags it; the fix is a bigger tail pipe.
Reaction force — when the valve fires, the escaping jet kicks the pipework like a rocket nozzle. The result (in kN) goes to your piping/civil engineer for support design — multiply by up to 2 for the opening shock.
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Overpressure Scenario Manager — Governing Case

PSV-datasheet workflow: compare all credible scenarios, size on the governing area

Common Valve Data
Each scenario is evaluated at this set pressure with its own ASME accumulation — 10% process (single valve), 21% fire — then the orifice is selected on the largest required area (the governing case). Typical credible scenarios per API 521 §4.4: blocked outlet, control-valve failure, external fire, tube rupture, thermal expansion, utility failure, abnormal heat input.
Scenarios (2–8)
Governing-Case ComparisonWARN
📖 Plain-language guide — scenarios & the governing case

Real relief design never asks "how big a valve for this flow?" — it asks "what's the worst thing that can credibly happen, and is the valve big enough for that?" This tab is that workflow: list every credible upset, size each one, and buy the valve for the biggest (the governing case).

What's a scenario? — a specific credible failure: outlet valve accidentally closed (blocked outlet), a control valve fails wide open and high-pressure gas floods in (CV blowby / gas blowby), fire under the vessel, an exchanger tube bursts and the high-pressure side blows into the low-pressure side, sun heating a blocked-in liquid line (thermal expansion). API 521 lists them; add every one that can physically happen to your vessel.
Load Basis — the tool can compute loads for you — for CV blowby, enter the failed valve's Cv (from its datasheet) and upstream pressure: the tool calculates the blowby flow. For tube rupture: tube bore and shell-side pressure. For thermal: heat input in kW. For blocked outlet, enter the flow manually — it equals whatever your upstream pump/compressor can deliver (read from its curve; only you know that machine).
Why each row shows a different accumulation — code allows the vessel to climb 10% above set during a process upset but 21% during fire, so the fire row legitimately relieves at higher pressure. Handled automatically per row.
Reading the table — the ★ row is the governing case; the orifice is chosen for it. The % column shows how small every other case is by comparison — useful sanity check (thermal expansion at 0.1% of governing is normal; fire at 99% of a blocked-outlet governing case deserves a second look).
One valve, every case — the selected valve must also work (not just be big enough) for the small cases: a huge valve relieving a tiny thermal load may chatter. That's why tiny loads usually get their own small ¾"×1" valve instead.
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Reference — API 526 Orifices & Rules

Letter orifices D–T | ASME accumulation | Kd guide | formulas

API 526 Standard Letter Orifices
OrificeArea (in²)Area (mm²)Typical Inlet × Outlet
D0.110711"×2", 1½"×2", 1½"×2½"
E0.1961261"×2", 1½"×2", 1½"×2½"
F0.3071981½"×2", 1½"×2½", 2"×3"
G0.5033251½"×2½", 1½"×3", 2"×3"
H0.7855061½"×3", 2"×3"
J1.2878302"×3", 2½"×4", 3"×4"
K1.83811863"×4"
L2.85318413"×4", 4"×6"
M3.6023234"×6"
N4.3428004"×6"
P6.3841164"×6"
Q11.0571296"×8"
R16.0103236"×8", 6"×10"
T26.0167748"×10"
ASME VIII Accumulation Limits
CaseMax AccumulationMax Set Pressure
Single valve, non-fire10% (min 3 psi)100% MAWP
Multiple valves, non-fire16%First: 100%, supplemental: 105% MAWP
External fire (any number)21%≤ 110% MAWP
Discharge Coefficient Guide
ServicePreliminary KdNote
Gas / vapor / steam0.975Use certified Kd from vendor for final sizing
Liquid (certified valve)0.65API 520 §5.10 certified liquid trim
Two-phase0.85API 520 Annex C recommendation
PSV + upstream rupture discKc = 0.9Combination capacity factor (unless certified)
Governing Equations
GAS (critical):  A = W·√(T·Z/M) / (C·Kd·P₁·Kb·Kc)   C = 520·√(k·(2/(k+1))^((k+1)/(k−1)))
GAS (subcritical):  A = W·√(T·Z/M) / (735·F₂·Kd·Kc·√(P₁·(P₁−P₂)))
STEAM:  A = W / (51.5·P₁·Kd·Kb·Kc·Kn·Ksh)   Kn = (0.1906·P₁−1000)/(0.2292·P₁−1061) for P₁ > 1500 psia
LIQUID:  A = Q/(38·Kd·Kw·Kc·Kv) · √(G/(P₁−P₂))   Kv = f(Re), Re = Q·2800·G/(μ·√A)
FIRE wetted:  Q = C·F·Aw⁰·⁸² (C = 21000 / 34500),  W = Q/λ
FIRE unwetted:  A = F′·A′/√P₁,  F′ = 0.1406/(C·Kd)·[(Tw−T₁)¹·²⁵/T₁⁰·⁶⁵⁰⁶],  T₁ = Tn·P₁/Pn
TWO-PHASE:  ω = 9·(v₉/v₀−1),  G꜀ = η꜀·√(P₀/(v₀·ω)),  A = W/(Kd·Kb·Kc·G)
US customary internal basis: W lb/h, T °R, P psia, A in², Q gpm, μ cP. All conversions handled server-side. Areas reported are EFFECTIVE areas for API 526 preliminary selection — final selection uses the vendor's certified actual area & Kd (ASME "K") per API 520 §5.2.