Relief Scenarios — What Actually Sets the PSV

The drum nobody could explain

Turnaround walkdown. A butane surge drum, 2.4 m diameter × 6 m tangent-to-tangent, design 10 barg. Its feed line is 3″, the normal vapour make off the top is 4 t/h — and bolted to the crown is a 3″ × 4″ J-orifice relief valve, big enough to swallow twice the plant's normal vapour rate. A graduate asks the obvious question: what is that valve actually for?

Guess first. Which of these do you think set that orifice? (a) the feed control valve failing wide open · (b) the vapour outlet being blocked · (c) a fire under the drum · (d) the upstream exchanger springing a tube leak.

It was (c), by a comfortable margin — and the plant's own process upsets came third and fourth. That is the normal result, not an oddity.

The belief this kills is the comfortable one:

"The PSV protects the vessel."

It does not. It protects the vessel against exactly one failure mode — overpressure caused by an excess of mass or energy that has nowhere else to go. It is blind to everything else:

• Vacuum — a PSV opens outward only. Steam-out then cool-down will collapse a tank while the PSV sits there, shut and satisfied. That is a vacuum breaker's job.
• Runaway reaction — a PSV sized for a normal upset cannot pass a runaway's vapour. Rupture discs, quench, dump and emergency depressuring do that.
• Mechanical failure — a cracked nozzle weld, a brittle fracture, a corroded-through shell. Pressure never exceeded MAWP; the vessel failed anyway.
• Dry-wall failure in a fire — the shell above the liquid level has no boiling liquid to cool it. It runs to creep temperature and ruptures below set pressure. The PSV never lifts. Fireproofing and depressuring answer that one, not the PSV.

And even inside its one job, it is not sized for "everything". API 521's method is narrower and much more useful: list the credible causes of overpressure, quantify the relief load for each, size for the largest single one, and then design the system that carries it away.

The pressure it is allowed to reach while doing that is fixed by code (ASME VIII Div 1, UG-125):

Non-fire, single relief device:     accumulation ≤ 10 %   →   P_rel = 1.10 × MAWP
Non-fire, multiple devices:         accumulation ≤ 16 %   →   P_rel = 1.16 × MAWP
External fire (supplemental):       accumulation ≤ 21 %   →   P_rel = 1.21 × MAWP

Symbol key — every symbol on this sheet

• MAWP — maximum allowable working pressure: the vessel's design pressure at temperature; the PSV set pressure normally sits at or below it · barg
• accumulation — pressure rise above MAWP while relieving, as a percentage of MAWP · %
• P_rel — relieving pressure = MAWP + accumulation (absolute, for gas sizing) · bara, kPa abs
• P_b — built-up back pressure in the tailpipe and flare header · barg
• A — required effective orifice area — the number you carry to the API 526 letter table · mm²
• W — relief load as mass flow (vapour cases) · kg/h
• Q — relief load as volumetric flow (liquid cases) · L/min, m³/h
• A_ws — wetted surface area: shell and head in contact with liquid, up to 7.6 m above grade · m²
• λ (lambda) — latent heat of vaporisation at relieving conditions · kJ/kg
• F — environment factor: insulation credit; 1.0 for a bare vessel, ~0.3 well insulated · –
• k — ratio of specific heats, Cp/Cv · –
• C — gas sizing coefficient, a function of k alone · –
• K_d — effective discharge coefficient: 0.975 vapour, 0.65 liquid · –
• K_b, K_c, K_w, K_v — corrections for back pressure, an upstream rupture disc, liquid back pressure and viscosity · –
• Z — compressibility factor at relieving conditions · –
• M — molecular mass · kg/kmol
• C_v, K_v — control-valve capacity coefficients; K_v = 0.865 · C_v · –
• C_d — orifice discharge coefficient for a ruptured tube, taken as 0.7 · –
• β (beta) — cubic thermal expansion coefficient of a trapped liquid · 1/°C
• DLF — dynamic load factor applied to the PSV reaction force (see the DLF topic) · –

The credible scenarios — and which one usually wins

Seven causes cover most of what you will ever list on a relief study:

The fire case has its own correlation, because it is a heat-transfer problem rather than a hydraulic one:

Adequate drainage + firefighting:   Q = 43.2 · F · A_ws^0.82      (Q in kW, A_ws in m²)
Without adequate drainage:          Q = 70.9 · F · A_ws^0.82
Relief load:                        W = 3600 · Q / λ              (kg/h)

Only the wetted wall counts, and only up to 7.6 m above grade. Two independent reasons. The wetted part is where boiling liquid pulls heat through the wall and turns it into vapour you must relieve; the dry part has no such mechanism, so it contributes no load. And 7.6 m is roughly as high as a ground pool fire licks — above that, the flame is not touching your steel. That single rule is why a half-full drum and a nearly-empty one relieve completely differently, and why level is a relief-sizing input, not just an operating number.

Once you have a load, API 520 Part I turns it into an area:

Vapour, critical flow:
    A = 13160 · W · √(T·Z/M) / (C · K_d · K_b · K_c · P_rel)      [mm²; W kg/h; P_rel kPa abs]
    C = 519.6 · √( k · (2/(k+1))^((k+1)/(k-1)) )                  [356 at k = 1.4]

Liquid:
    A = 11.78 · Q · √(G/(P_1 − P_2)) / (K_d · K_w · K_c · K_v)    [mm²; Q L/min; P kPa gauge]

Notice what these two formulas force on you: you cannot rank scenarios by kg/h. 8000 kg/h of butane vapour and 70 m³/h of butane liquid are not comparable quantities. The only common currency is required orifice area in mm² — and once you rank in mm², the winner is frequently not the one people expect. Run the cases side by side and watch the ranking flip as you move the sliders: ▶ open the interactive: process relief scenarios calc

And then the rule that saves the most money on a relief study: two scenarios never add. A fire and a blocked outlet are independent events; the probability of both in the same hour is negligible, so you size for the larger and the smaller comes free. The single exception is a common cause — a power failure that simultaneously stops the cooling-water pumps and the condenser fans is one event with several effects, and those effects do combine.

Worked example — the C4 surge drum, case by case

Horizontal drum Ø2.4 m × 6 m T/T, 2:1 heads, 50 % liquid. MAWP 10 barg. Butane: λ = 300 kJ/kg, M = 58, k = 1.09, relieving T = 373 K, Z = 0.9, liquid SG 0.58. Feed from a 40 barg header through a C_v = 25 level valve; normal liquid outlet 80 m³/h; normal vapour make 4000 kg/h; the feed passes a 25 barg exchanger. Flare back pressure 0.5 barg. Bare vessel, drainage adequate.

Fire. Wetted area = shell arc + wetted fraction of both heads. The surface area of one 2:1 semi-ellipsoidal head is 1.084 · D² (that constant already contains the π — do not multiply it by πD²/4 as well, or you lose 22 % of the head area): = 1.2 × π × 6 + 2 × (1.084 × 2.4²) × 0.5 = 22.6 + 6.2 = 28.9 m². Q = 43.2 × 1.0 × 28.9^0.82 = 681 kW; W = 3600 × 681/300 = 8169 kg/h. Fire gets 21 %: P_rel = 1.21 × 10 = 12.1 barg = 1311 kPa abs. C at k = 1.09 = 325. → A = 622 mm² → J orifice (830 mm²).

Blocked outlet. 4000 kg/h of vapour, 10 % accumulation → P_rel = 11 barg = 1201 kPa abs. → A = 332 mm² → H.

Control valve fails open. K_v = 0.865 × 25 = 21.6; ΔP = 40 − 11 = 29 bar; Q = 21.6 × √(29/0.58) = 153 m³/h in, less the 80 m³/h the open liquid outlet still passes = 73 m³/h = 1215 L/min of liquid relief. → A = 518 mm² → J.

Tube rupture. One 15.75 mm bore tube, double-ended, C_d = 0.7, ΔP = 25 − 11 = 14 bar: Q = 0.7 × 2 × (π/4 × 0.01575²) × √(2 × 1.4×10⁶/650) = 0.0179 m³/s = 64 m³/h. → A = 484 mm² → H. (The ⅔ rule would have excused this case entirely if the drum's 10 barg design had been ≥ ⅔ × 25.)

Thermal expansion. 6 m of blocked-in 8″ line in the sun, Φ ≈ 1.05 kW, q = β·Φ/(ρ·c) = 0.0011 × 1.05/(580 × 2.2) = 3.3 L/h → A = 0.02 mm². (ρ is the blocked-in fluid — butane at SG 0.58, not the 650 kg/m³ exchanger-side liquid.)

Ranked in mm²: fire 622 > CV failure 518 > tube rupture 484 > blocked outlet 332 > thermal 0.02. Fire governs. Note that it beats the CV case by only 20 % — nudge the C_v to 30 and the ranking flips. That is why this is a comparison, not a lookup.

And note the bottom of the list. Thermal expansion needs roughly thirty thousand times less area than the governing case — and it is still mandatory. Nobody makes a valve that small; you fit the smallest one that exists, a ¾″ × 1″ D orifice, because a liquid-full line with both ends shut and the afternoon sun on it will part a flange gasket or split a pipe. Small is not the same as optional, and "it's only a thermal relief" is how blocked-in lines get missed on P&IDs.

Then the second half of the job, which the orifice letter does not touch. Relief load sizes the valve. Relief system design is everything downstream of it, and it is governed by different numbers:

• Inlet line — non-recoverable loss ≤ 3 % of set pressure, or the valve chatters itself apart.
• Tailpipe and header — built-up back pressure ≤ 10 % of set for a conventional valve (a balanced-bellows or pilot-operated valve buys you more), plus the flare load this valve contributes to the common header when it is one of several lifting together.
• Reaction force — the discharging jet pushes the tailpipe backwards, and it arrives in milliseconds. Take the API 520 Part II steady thrust and multiply it by a dynamic load factor (DLF ≤ 2 for a single ramp, and the ramp is the valve's opening time — see the DLF topic). This is a pipe-stress load, and it is where relief work hands over to the stress engineer.

See all of it in one place — where the energy enters for each scenario, the wetted band under a fire, the relief path lighting up through the valve and tailpipe, and the reaction arrows at the elbow and the riser: ▶ open the interactive: process relief scenarios 3d

Common pitfalls

• Sizing for the normal flow. Blocked outlet is not "a bit more than normal" — it is all of normal, with the exit removed, and it is often the governing process case.
• Using total surface area for fire. Only wetted, only to 7.6 m. Using total area over-sizes the valve; forgetting that the dry wall can still fail under-protects the vessel.
• Adding two independent scenarios "to be safe". An over-sized PSV chatters at low load, hammers its own seat and leaks. Conservatism in the wrong place buys you a new failure mode.
• Ranking in kg/h. Vapour and liquid loads only become comparable after they are converted to required area.
• Forgetting tube rupture because the exchanger is "someone else's equipment". Check the ⅔ rule explicitly and write down the answer, even when it excuses you.
• Treating a power failure like a single-effect scenario. It is common-cause: cooling stops, pumps stop, fans stop, and the effects do combine.
• Stopping at the orifice letter. 3 % inlet loss, 10 % built-up back pressure, flare load and reaction force are all still ahead of you, and any one of them can force a different valve type.
• Omitting a thermal relief on a blocked-in liquid leg because the calculated area rounds to zero. It is the cheapest valve on the plant and the most commonly missing one.

Outcome

• A PSV answers overpressure only — never vacuum, runaway, brittle fracture, corrosion or a dry shell in a fire. Naming what it does not do is half the competence.
• API 521's method is: list credible causes → quantify each load → size for the largest single one → then design the relief system. Two independent scenarios never add; one common cause does.
• Accumulation limits: 10 % single device, 16 % multiple, 21 % fire — and the higher fire allowance makes the fire orifice smaller than the same load would need on a process case.
• Fire load comes from Q = 43.2·F·A_ws^0.82 on the wetted area only, to 7.6 m. Level is a relief input.
• Rank scenarios in mm² of required orifice, never in kg/h. The governing case is usually fire or blocked outlet, not the process upset everyone talks about.
• Thermal relief valves are trivially small and absolutely mandatory.
• Interactive: ▶ open the interactive: process relief scenarios calc — five scenarios computed, ranked and sized live; slide the design pressure and watch which case governs change hands.
• 3D: ▶ open the interactive: process relief scenarios 3d — where the energy enters, per scenario, with the relief path and the tailpipe reaction force.

Open items

• Add a two-phase / flashing relief case (Omega method, API 520 Annex C) — the comparator is single-phase only, and real hydrocarbon relief is very often flashing.
• Add the inlet-line 3 % and built-up back-pressure checks to the comparator so the valve type (conventional / bellows / pilot) falls out of the same tool.
• Worked flare-header case: several valves lifting on one common-cause event, and the header sizing that follows.

Educational teaching material — simplified and illustrative. Not for engineering design use.
© EPiC Circle · provided by PipeAxis