Two-Phase Relief Sizing

DIERS Omega Two-Phase Relief — Engineering Fundamentals

Why single-phase sizing fails for flashing relief, Leung's Omega closed-form, and the choked vs subcritical regime.

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Method

Leung (1986) Omega

Closed-form simplification of the DIERS two-phase model.

Applies when

0.1 ≤ ω ≤ 100

Two-phase regime where single-phase API 520 sizing fails.

Discharge coeff.

K_d = 0.65

Standard DIERS convention for the mass-flux area relation.

Contents

Use this guide when you need to:

  • Decide whether two-phase sizing applies to a relief case.
  • Compute the Omega parameter for a saturated-liquid inlet.
  • Check choked vs subcritical flow and size PSV area.

1. When two-phase matters

API 520 single-phase sizing assumes either pure gas (compressible critical flow) or pure liquid (Bernoulli). Relief from a saturated liquid system flashes inside the valve nozzle — the working fluid is two-phase by the time it reaches the throat. Single-phase gas sizing under-predicts the required area (treats it as gas-only); single-phase liquid over-predicts because it ignores the vapor expansion.

DIERS (Design Institute for Emergency Relief Systems, AIChE 1976–1995) developed the rigorous two-phase model. Leung (1986) gave the closed-form Omega simplification that turns the iterative DIERS solution into a single equation.

2. The Omega parameter

The Leung (1986) ω is dimensionless. With inlet specific volume vo = vl + xo·(vg − vl):

ω = xo·vg/vo + 0.18505 · (cp · To · Po / vo) · ((vg − vl) / hfg)²

For a saturated-liquid inlet (xo = 0), vo = vl and the first term drops. The factor 0.18505 = 144/778.17 converts psia·ft³ to Btu so the Po·v term is energy-consistent (US units); the flashing term is divided by the inlet specific volume vo. ω captures the compressibility of the two-phase mixture during expansion through the nozzle:

  • ω < 0.1 — essentially incompressible (liquid-dominated). Use API 520 liquid sizing.
  • 0.1 ≤ ω ≤ 100 — DIERS Omega applies; use this calc.
  • ω > 100 — essentially gas-only. Use API 520 gas sizing.

3. Choked / subcritical

The critical pressure ratio ηc from Leung's fit:

ηc ≈ 0.55 + 0.217·ln(ω) − 0.046·(ln ω)² + 0.004·(ln ω)³

If backpressure P_b/P_o ≤ η_c → choked flow (mass flux = G_crit). Otherwise non-choked; G is reduced via a square-root subcritical correction.

Mass flux G then drives area via A = W/(3600·G·K_d), with K_d = 0.65 standard DIERS convention.

4. Common scenarios

ScenarioSystemω range
Runaway exotherm (BPC reactor)Liquid + light vapor1 – 10
Fire on liquid-full vesselSat. hydrocarbon0.5 – 5
Loss of cooling on refrigerated drumSat. propane / butane1 – 20
Power failure on cryogenic NGLNGL, low T5 – 50

5. References

  • DIERS Project Manual (CCPS / AIChE 1995). Two-Phase Relief and Vent Systems.
  • Leung, J.C. (1986). "A generalized correlation for one-component homogeneous equilibrium flashing choked flow." AIChE J. 32(10), 1743–1746.
  • API Std 520 Part I §A.3 — Two-phase sizing guidance.
  • Fauske, H.K. (1985). "Flashing flows or: some practical guidelines for emergency relief vent design." Plant Oper. Prog. 4(3), 132–134.

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Frequently Asked Questions

When does single-phase relief sizing fail?

When a saturated-liquid system flashes inside the valve nozzle, the fluid is two-phase at the throat. Single-phase gas sizing under-predicts the required area, while single-phase liquid sizing over-predicts it by ignoring vapor expansion.

What does the Omega parameter represent?

Omega captures the compressibility of the two-phase mixture as it expands through the nozzle. Below 0.1 the flow is essentially incompressible (use API 520 liquid sizing); above 100 it is essentially gas-only (use API 520 gas sizing); between 0.1 and 100 the DIERS Omega method applies.

How is choked flow determined in the Omega method?

The critical pressure ratio η_c is computed from Leung's fit to Omega. If the backpressure ratio P_b/P_o is at or below η_c the flow is choked at the critical mass flux; otherwise it is non-choked and the mass flux is reduced by a square-root subcritical correction.