PSV Relief Rate Sizing: How Much Flow Must a Gas PSV Pass?

A relief rate is not a property of the valve, the line size, or the operating pressure. It is an output of a contingency analysis. Picking 10,000 m3/day for a 12 in line carrying 2 MMSCMD sets the required capacity at 0.5% of throughput, which no credible upset in a gas pipeline will respect. Before anything else, separate the two quantities that get collapsed into the phrase "discharge flow rate."

Required Relief Rate Versus Installed Discharge Capacity

Two different numbers share the same units and get swapped constantly.

• Required relief rate (W_req) — the mass flow that must leave the protected system to hold pressure at or below the allowable accumulation during the governing upset. It comes from the process, not from the valve.
• Installed capacity (W_cap) — what the PSV actually passes at relieving conditions, a function of effective orifice area, relieving pressure, gas molecular weight, temperature, and compressibility.

Sizing means finding an orifice where W_cap ≥ W_req. Rating an existing valve means solving the same equation the other direction. Both use the same API 520 Part I vapor relation; only the unknown changes. If the question is "what discharge rate should I assume," the answer is always: the one the worst credible contingency imposes on you.

Why 10,000 m3/day Fails Immediately

Run the ratio. The line moves 2,000,000 Sm3/day, or 83,333 Sm3/h, roughly 23.1 Sm3/s. An assumed relief of 10,000 Sm3/day is 417 Sm3/h. If the downstream outlet blocks and the upstream source keeps delivering, the PSV would pass one two-hundredth of the inflow while the remaining 99.5% packs the line. Pressure climbs to whatever the source can deliver, and the valve is decoration.

There is also a common inversion worth killing here: the idea that a PSV relieves after inflow stops. The opposite defines the case. A shutdown that removes inflow removes the overpressure source. The relieving scenario is inflow continuing while the exit path disappears — blocked outlet, closed ESD valve, failed pressure control valve wide open, downstream isolation on a slug catcher or filter.

Approaches Available, Compared

Use the third. The second is a check you run afterward against the first. The first is not an engineering method — API 521 is explicit that the designer investigates the credible causes of overpressure, quantifies the inflow for each, and takes the largest as the governing relief load.

Contingency List for a 12 in Gas Line

On a dry gas pipeline segment, the list is short and blocked outlet almost always governs. Work it in this order:

1. Blocked outlet. Downstream valve closes, upstream keeps flowing. The relief load is the maximum sustained inflow the source can deliver into the segment at relieving pressure — not the normal operating rate, unless the source is genuinely rate-limited to that value. With 2 MMSCMD entering and nothing leaving, 2 MMSCMD is the starting point.
2. Control valve failure. Regulator or PCV fails full open with a higher-pressure source upstream. Compute wide-open capacity from the valve Cv at the upstream supply pressure and the relieving downstream pressure. This case frequently exceeds normal throughput.
3. Thermal expansion. Blocked-in liquid-full sections only; for dry gas it is negligible but the isolatable spool must still be checked.
4. External fire. Applies to vessels and blocked-in inventory within a credible fire zone. Fire exposure uses a different accumulation allowance than the other cases — take that limit from API 521 and the applicable ASME code, and treat it as a separate sizing run.
5. Gas breakthrough / heat exchanger tube rupture. Applies where a high-pressure gas stream can enter a lower-rated system.

Do not move on until every credible cause has a number or a documented reason for exclusion. The governing rate is the maximum of the list, not the sum, unless a single initiating event produces two loads simultaneously.

Is a PSV Even Required Here?

The two stated cases matter for this decision.

If the segment is designed for 1000 psi and merely operated at 400 psi, protection is only required where the supply can push it above MAWP on a control failure. A source physically incapable of exceeding the design pressure — a compressor with a maximum discharge below MAWP, or an upstream system with a lower rating — removes the overpressure cause. Document the source's maximum capability; that record is what justifies either the PSV or its absence.

Note also which number belongs where. Set pressure and accumulation are gauge quantities, because overpressure protection is a differential problem: upstream gauge plus atmospheric minus atmospheric returns upstream gauge. The flow equation, however, takes relieving pressure in absolute units. Mixing the two is the most common arithmetic error in a relief calculation, and at 400 psia the 14.7 psi offset is 3.7% of the answer.

Choked Flow and the Relieving Pressure Basis

Every case here discharges to atmosphere or to a flare header at low back pressure, so the orifice is choked. Velocity at the throat sits at the local speed of sound, fixed by gas composition and relieving temperature, and it does not change with upstream pressure once upstream absolute pressure exceeds the critical value — roughly atmospheric divided by 0.6, about 24.5 psia for a typical specific heat ratio. Both 400 psia and 1000 psia are far above that threshold.

Mass flow still changes with pressure, because mass flux is density times velocity and density scales with upstream absolute pressure. That is why the same required standard volumetric rate produces two different orifice areas across the two cases: at 385 psig relieving conditions the gas is roughly 2.5 times less dense than at 985 psig, so the area must grow accordingly.

The critical-flow vapor relation from API 520 Part I:

A = W / (C * Kd * P1 * Kb * Kc) * sqrt( (T * Z) / M )

A  = required effective discharge area
W  = required relief mass flow
C  = coefficient from the k (Cp/Cv) table in API 520 Part I
Kd = effective coefficient of discharge (valve manufacturer / API default)
Kb = back pressure correction (1.0 for unbalanced valve, atmospheric discharge)
Kc = rupture disc combination factor (1.0 if no disc upstream)
P1 = relieving pressure, ABSOLUTE = set (gauge) + overpressure + atmospheric
T  = relieving temperature, absolute
Z  = compressibility at relieving conditions
M  = gas molecular weight

Rearranged to rate an installed valve:

W_cap = A_installed * C * Kd * P1 * Kb * Kc / sqrt( (T * Z) / M )

All terms on the right are known once the orifice designation and gas properties are fixed, which makes rating existing hardware straightforward algebra.

Sizing Procedure

1. Fix MAWP and set pressure. Set pressure at or below MAWP, both in gauge. Record which component sets the MAWP for the segment — flange class, pipe wall, or an attached vessel.
2. Fix the allowable accumulation. For non-fire contingencies, allowable build-up is 110% of MAWP. Fire exposure uses its own limit from API 521 / ASME; run it as a separate case.
3. Compute relieving pressure. P1 = 1.10 × MAWP (gauge) + 14.7 psi, absolute. Confirm the units before it enters the flow equation.
4. Convert the governing volumetric load to mass. W = Q_std × ρ_std, with ρ_std taken from the gas composition at the standard reference conditions your contract uses. Confirm whether the 2 MMSCMD figure is referenced to 15 °C or 0 °C; the two bases differ by about 5% and the difference propagates straight into the orifice area.
5. Establish relieving temperature and Z. Use the flowing temperature at the relieving condition, not ambient. For blocked-in gas under continued compression, temperature rises; take the value from the heat and material balance for that upset.
6. Pull k and C. Compute Cp/Cv at relieving conditions from the composition, then read C from the API 520 Part I table.
7. Solve for A, then round up to the next standard API orifice letter. Never round down. Check that the selected orifice is not so oversized that it will chatter at the expected relief load — if the required area is far below the smallest available letter, evaluate a modulating pilot-operated valve instead.
8. Check inlet and outlet piping. Non-recoverable inlet loss at rated capacity is limited to 3% of set pressure for a conventional spring valve; exceeding it produces chatter regardless of correct orifice sizing. Verify built-up back pressure in the discharge header against the valve type.
9. Repeat for both operating cases. The 385 psig case will drive the larger orifice for the same standard volumetric rate. Size on that one if both are credible operating states under the same MAWP.

Verification Before Sign-Off

1. Recompute W_cap for the selected orifice using the rearranged equation and confirm W_cap ≥ W_req with the actual manufacturer Kd, not the API default.
2. Confirm that the governing scenario in the relief calculation matches the largest single entry in the contingency list, and that every excluded cause carries a written justification.
3. Confirm every pressure in the datasheet is labeled gauge or absolute, and that P1 in the flow equation is absolute.
4. Confirm the standard-condition reference for the 2 MMSCMD load matches the reference used for ρ_std.
5. Confirm the relief mass rate against the source's maximum deliverable capability — if the source cannot physically deliver the assumed load, document the limiting element; if it can deliver more, resize to the higher figure.
6. Check inlet pressure drop ≤ 3% of set pressure and back pressure within the valve type's limit at the rated capacity, then release the orifice designation to the datasheet.

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