API 521 Fire Case: Why Does Relieving Temp Shrink Orifice?

A vapor-filled vessel in a pool fire has no latent heat sink. The wall absorbs flux, the gas inside expands at constant volume, and the pressure rise per degree is governed by the gas law alone. Run that arithmetic against a Class 600 design pressure and the calculated relieving temperature lands in four figures Fahrenheit — not because the calculation is wrong, but because it is telling you the steel fails before the valve lifts. The sections below build the analysis in the order it has to be done, each ending with the check that proves the step before you move on.

Pressure and Temperature Definitions That Must Not Be Mixed

Four numbers control this problem and three of them get conflated routinely.

• Operating pressure — 326 psig, the normal gas pressure in the vessel.
• MAWP / design pressure — 1432 psig at the 140 °F design temperature, taken here from the ASME B16.5 Class 600 pressure-temperature rating table for the flange material group.
• Set pressure — where the PSV lifts. It may sit at or below MAWP, never above.

The term "design temperature" here means the metal temperature the vessel was designed and stamped for: 140 °F. Relieving temperature T1 is the gas temperature at the instant of relief. They are separate quantities and a fire case drives them hundreds of degrees apart.

B16.5 rates flanges. It does not rate the shell, the heads, or the nozzle necks. Anchoring the design pressure to the flange rating is common practice, but the failure mode in a fire is shell metal losing strength, not a flange leaking.

Check 1:Expect the stamped pair to be 1432 psig at 140 °F or lower. If a nozzle or the shell governs, the B16.5 number is not your MAWP and every downstream calculation shifts.

What Equation 11 Actually Computes

API 521 Eq (11) is the constant-volume ideal gas ratio: T1 = Tn × (P1 / Pn), with all pressures absolute and all temperatures in degrees Rankine. It says nothing about fire, heat flux, or vessel geometry. It only states that a fixed mass of gas in a fixed volume must get hot in proportion to how much you let the pressure rise.

Working the case at hand, with normal conditions taken as Pn = 326 + 14.7 = 340.7 psia and Tn = 90 + 459.67 = 550 °R:

• Set at MAWP, 1432 psig, 21 % accumulation: P1 = 1.21 × 1432 + 14.7 ≈ 1747 psia. T1 = 550 × 1747 / 340.7 ≈ 2820 °R ≈ 2360 °F.
• Set at 627 psig: P1 = 759 + 14.7 ≈ 774 psia. T1 = 550 × 774 / 340.7 ≈ 1249 °R ≈ 790 °F, which brackets the 819 °F reported and differs only by how the normal state was referenced.

2360 °F is above the melting point of carbon steel, so the intuition that the vessel is gone before the valve lifts is correct. The failure mechanism is worse than that description implies: carbon steel does not need to melt. It loses a large fraction of its room-temperature yield strength by 1000–1100 °F and enters creep, so a pressurized shell tears open at a fraction of the melting temperature. Rupture is the design limit, not fusion.

The most frequent arithmetic error in this equation is feeding it gauge pressure or degrees Fahrenheit. Both make the ratio meaningless and both produce answers that look plausible. Where composition matters — heavy hydrocarbons, anything that may drop condensate, significant departure from ideal — replace Eq (11) with a series of constant-volume (V-P) flash calculations on the real composition, stepping pressure from the operating state to the relieving state. That returns a true T1 with real compressibility and tells you whether the relief is single-phase or two-phase before you pick a sizing equation.

Check 2: Recompute T1 with set pressure equal to MAWP. Expect a value far above 1100 °F. Any result in that range is a finding, not an input: it means a pressure relief device cannot be the fire-case protection layer for this vessel.

Screening the Fire Case for Credibility

Before sizing anything, establish whether a pressure relief device has a physical job to do. Find the credible operating scenario that maximizes liquid inventory in the vessel — startup holdup, slug catcher carryover, level controller failure, shutdown drain-back. Then run a boiling calculation: vaporize that entire liquid inventory into the vapor space and see whether the resulting pressure reaches MAWP.

If it does, the fire case is a wetted-wall problem. Use the API 521 wetted heat-input correlation of the form Q = C × F × A^0.82, with the coefficient selected for prompt firefighting and adequate drainage versus neither, and the exposed area taken over the fire zone footprint and elevation limits given in API 521. The latent heat of the boiling liquid is a genuine sink, the relief rate is real, and a PSV earns its place.

If total vaporization does not reach MAWP, the fire case reduces to gas thermal expansion and the real gas law has nowhere near enough capacity to raise pressure to the set point before the metal flows. That is the situation described by a 1432 psig design pressure sitting on a 326 psig vapor service.

Check 3: Vaporize the maximum credible liquid inventory at constant volume. Expect either a pressure at or above MAWP (wetted case, size the PSV normally) or a pressure well below it (unwetted case, the PSV is a code device only). Record which result you got in the relief study.

Why a Higher Relieving Temperature Shrinks the Orifice

Two equations are pulling in opposite directions and the confusion comes from comparing them without holding the same variable fixed.

API 520 Part I Eq (2) for critical vapor flow gives A = W / (C · Kd · P1 · Kb · Kc) × sqrt(T · Z / M). At a fixed relief load W, area scales with the square root of temperature: hotter gas is less dense, so more area is needed to pass the same pounds per hour. That is the behavior most engineers carry in their heads.

The unwetted-wall route in API 521 does not hold W fixed. It computes the required effective area directly from the environmental factor F', exposed area A', and relieving pressure: A = F' × A' / sqrt(P1), where F' is built from (Tw − T1)^1.25 / T1^0.6506. Tw is the vessel wall temperature, commonly taken as 1100 °F for carbon steel per API 521's recommendation — confirm the value and the material basis in the edition you are working to.

Raise T1 and both terms move against the orifice: the wall-to-gas driving temperature difference shrinks to the 1.25 power, and the divisor grows. The required area collapses. The physics behind the algebra: the relief requirement is set by the rate at which the gas is absorbing heat and expanding. Hotter gas is less dense, so a given volumetric expansion carries fewer pounds out of the vessel, and a smaller wall-to-gas gradient drives less heat into it. As T1 approaches Tw, the gas has come to equilibrium with the wall, there is no further expansion, and the calculated requirement goes to zero. API 521 imposes a floor on F' (0.01 is the conventional minimum) precisely because the formulation would otherwise return nothing.

A shrinking orifice is therefore not a favorable trend. It is the arithmetic reporting that the steel has already reached its rupture temperature.

Check 4: Hold set pressure at MAWP and sweep T1 from operating temperature to Tw. Expect the required area to fall monotonically until it hits the F' floor. That confirms you are in the unwetted regime and not sizing against a physical relief demand.

The Set-Pressure Trap

Dropping the set pressure to 627 psig so that the relieving point lands on the B16.5 Class 600 rating curve is geometrically tidy and operationally wrong for four reasons.

1. It caps the vessel at roughly 560–570 psig operating pressure for the life of the installation, once normal operating margin below set is allowed. The Class 600 rating was specified to accept a future high-pressure feed. The two decisions cancel each other.
2. It does not protect. At 759 psig relieving the gas is near 800 °F and the shell metal is hotter still, well outside the 140 °F design temperature and into the range where allowable stress has dropped sharply.
3. It produces a larger, more expensive orifice, because both the lower P1 and the lower T1 push the area up.
4. Re-setting the valve later is not a spring change. It invalidates the relieving temperature, the required area, the inlet pressure drop check, the tailpipe backpressure calculation, and the entire relief study for that scenario.

Also settle whether this vessel is genuinely a separate protected system. If it cannot be isolated from the upstream PSV that covers blocked outlet, that device may already provide code compliance for the vessel, subject to inlet line size and pressure drop.

Check 5: Trace the path from the vessel vapor space to the upstream PSV on the P&ID. Expect zero closable block valves, or car-sealed-open valves with a management-of-change record. Any isolatable valve in that path means the vessel needs its own device.

Protection Layers That Change Time to Failure

For a vapor-filled vessel, the layers that actually move the failure clock are the ones that either remove inventory or keep flux off the wall.

• Passive fire protection. Fire-resistant insulation applied to the vessel, verified for the fire duration and jacketed against water washout.
• Drainage and spacing. Grading that carries pool inventory away from the vessel footprint changes the fire scenario itself.

Install the PSV where the applied code requires one on an ASME VIII vessel. Then state plainly in the relief study, in the same document where the sizing appears, that the device does not mitigate fire exposure on a vapor-filled vessel and that time to rupture is essentially unchanged whether the valve is large, small, or absent. Hand the owner a risk assessment so the decision on additional layers is made with the facts visible. Sizing a valve and letting the paperwork imply protection is the failure mode that matters more than any orifice selection.

Check 6: Confirm the depressuring path is credited in the cause-and-effect matrix against a confirmed fire signal, and that the flare header and knockout drum were rated for that simultaneous blowdown load. Expect the depressuring case, not the PSV case, to govern the header.

End-to-End Verification

1. T1 from Eq (11) recomputed with absolute pressure and Rankine at set = MAWP. Expect a value far above the assumed Tw, confirming the PSV cannot lift in time.
2. Maximum credible liquid inventory vaporized at constant volume. Expect a peak pressure below MAWP for the unwetted conclusion, at or above it for the wetted conclusion.
3. Area sensitivity swept over T1. Expect monotonic decrease to the F' floor, and expect the API 520 Eq (2) result at fixed W to move the opposite way — the two are not in conflict.
4. Set pressure held at MAWP in the final case, not tuned downward to reach a flange rating intersection. Expect the required area to be small and to be documented as code-compliance sizing.
5. Isolation path to the upstream PSV verified as non-closable or car-sealed open.
6. Depressuring valve orifice checked against the API 521 pressure-and-time criterion, with wall temperature evaluated over the blowdown transient.
7. Relief study text states the fire-case limitation explicitly, names the credited layers (depressuring, deluge, passive fire protection, drainage), and carries the owner's acceptance of the residual risk.

Check 8 is the one that closes the job. If the study reads as though the PSV protects the vessel from fire, none of the preceding checks were worth running.

Frequently Asked Questions