Gas Flow Choking: A Process Design Guide

Choked flow (also called critical or sonic flow) happens when gas velocity reaches the speed of sound at a pipe restriction. Once you choke, decreasing downstream pressure does not increase flow. That sounds theoretical until you find your PSV is not passing what you sized it for, or your flare header throttles at the T-joint you added during a revamp.

Quick rule of thumb: if P2/P1 < 0.528 for air or diatomic gas (gamma = 1.4), you are choked. For natural gas (gamma ~= 1.30), the critical ratio is ~0.546. For steam (gamma ~= 1.30), same.

Where Choked Flow Actually Bites You

PSV discharge. Spring-operated valves are sized for critical flow by default. API 520 Part I Eq. 3.6 assumes choked vapor flow at the valve throat. If your backpressure climbs too high, you lose sonic flow and the PSV capacity drops — not by a small amount.
Flare tip exit. Flare tips are usually sized for Mach 0.2 at peak flow (API 521 guidance). Push beyond Mach 0.5 and you get unstable flame and noise.
Control valves in vapor service. When valve pressure drop exceeds the critical pressure drop (ΔP_choked = FL^2 · (P1 - FF·Pv) per ISA 75.01), Cv does not scale with added pressure drop.
Orifice plates and restriction orifices. RO's sized at sonic give you a predictable flow rate independent of downstream pressure — that's actually useful for metering, but it's a trap if you expected the downstream process to control flow.
Compressor anti-surge and recycle lines. The recycle often chokes at the trim. That's by design — gives you predictable flow — but you must account for it in capacity calcs.

The Three Numbers to Check

For any gas flow design review, I check three numbers before anything else:

Check	What it tells you	Limits
Mach at pipe outlet	Is the main line approaching choking?	Target M < 0.3 design; M < 0.5 short-term; M < 0.7 absolute max
Mach at any restriction (reducer, valve, tee)	Localized choking that degrades downstream performance	Same — M < 0.3 preferred
Critical pressure ratio at each dP element	Will this element choke and decouple flow from downstream pressure?	If P2/P1 < (2/(gamma+1))^(gamma/(gamma-1)), choked

Critical Pressure Ratio by Gas

The critical ratio r_c = (2/(gamma+1))^(gamma/(gamma-1)) is a function of gamma only:

Gas	gamma (typical)	Critical P2/P1
Monatomic (He, Ar)	1.67	0.487
Diatomic (H2, N2, O2, air)	1.40	0.528
Natural gas (CH4-rich)	1.30	0.546
Propane, butane	1.13	0.576
Steam (saturated)	1.30	0.546
Steam (superheated high-T)	1.33	0.540

Common Mistakes

1. Using incompressible Darcy-Weisbach when you shouldn't

If the pressure drop across the line is more than ~10% of inlet absolute pressure, compressibility matters. Use Crane TP-410 isothermal Eq. 1-6 or adiabatic Eq. 1-8. The Weymouth / Panhandle equations are shortcuts for long pipeline networks.

2. Forgetting upstream temperature drop

Gas expansion in a pipe (especially across a restriction) is closer to isothermal over long distances but locally adiabatic. Temperature drops reduce sonic velocity: a = sqrt(gamma · R · T / M). A sonic line that looked OK at 100 degF can choke at -40 degF downstream of a JT valve.

3. Ignoring valve/fitting equivalent length

Crane TP-410 has tabulated K and L/D values. A single gate valve fully open is roughly L/D = 8, a ball valve is 3, a 90-deg elbow standard radius is 30. Add them up before computing friction.

4. Choked flow at the PSV outlet pipe

API 520 Part II recommends PSV outlet piping be sized so built-up backpressure < 10% of set for conventional, < 50% for balanced-bellows. Exceed that and the valve chatters or fails to reclose — worse than losing capacity.

Back-of-Envelope Sonic Velocity

For natural gas (MW 18, gamma 1.30) at 100 degF:

a = sqrt(1.30 * 32.174 * 1545.3 * 560 / 18)
a ~= 1430 ft/s

Design for v < 400 ft/s (Mach 0.28) to stay in the safe subsonic region.

Decision Matrix

Situation	Design Target	Why
Process piping, continuous service	Mach <= 0.3	Erosion, noise
Flare header (main)	Mach <= 0.5	API 521 §7.3.3
Flare sub-header laterals	Mach <= 0.6	Short duration only
Flare tip exit	Mach <= 0.2	Flame stability per API 537
PSV body (inside valve)	Sonic by design	Required for standard API 520 sizing
PSV outlet tailpipe	Mach <= 0.7 at peak	Prevents standing wave / backpressure spikes
Compressor suction	Mach <= 0.1 (50 ft/s typ)	NPSH-like requirement for centrifugals
Instrument air supply piping	100 ft/s max	Noise and rider-valve issues

Practical Review Checklist

Inlet static pressure, temperature, MW, Z — all three independently verified
Peak flow case includes PSV simultaneous relief, trip cases, and upset scenarios
Mach calculated at pipe inlet AND outlet (they differ)
Every restriction (orifice, RV, control valve, tee, reducer) checked for P2/P1 ratio
If P2/P1 < 0.546 anywhere, explicitly size the restriction for sonic flow
Outlet sonic velocity verified against downstream process fluid temperature (not inlet temperature)
PSV outlet tailpipe velocity with worst simultaneous relief, NOT nominal flow

References

Crane TP-410 (2013), Flow of Fluids, Chapter 1
API Standard 520 Part I (2020), Sizing Selection and Installation
API Standard 521 (2020), Pressure-relieving and Depressuring Systems
API Standard 537, Flare Details for General Refinery and Petrochemical Service
ISA 75.01.01, Flow Equations for Sizing Control Valves
Perry's Chemical Engineers Handbook, 8th Ed., Section 6