DIERS Omega Two-Phase Relief — Engineering Fundamentals
Why single-phase sizing fails for flashing relief, Leung's Omega closed-form, choked vs subcritical regime.
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
For a saturated-liquid inlet:
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:
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
| Scenario | System | ω range |
|---|---|---|
| Runaway exotherm (BPC reactor) | Liquid + light vapor | 1 – 10 |
| Fire on liquid-full vessel | Sat. hydrocarbon | 0.5 – 5 |
| Loss of cooling on refrigerated drum | Sat. propane / butane | 1 – 20 |
| Power failure on cryogenic NGL | NGL, low T | 5 – 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.