The model resolves when the rupture is treated as a transient, compressible long-pipeline problem and the selected expansion method is compatible with the solver’s conservation-of-energy formulation. A large reservoir-to-atmosphere pressure ratio alone does not prove that the rupture plane is choked.
Flow-regime mechanism
The term choked flow here means that the gas reaches Mach 1 at a controlling section, so reducing downstream pressure no longer increases mass flow through that section under the same upstream state. For an ideal gas flowing isentropically through a short restriction, the critical downstream-to-upstream absolute-pressure ratio is:
Pdown/Pup = [2/(k+1)]^(k/(k-1))
Here, k is the gas-specific ratio of specific heats. For k = 1.4, the critical ratio is approximately 0.528. For k = 1.28, it is approximately 0.549. Use the value calculated from the modeled gas state rather than treating a 2:1 upstream-to-downstream ratio as a universal threshold.
That critical-pressure test applies across a short controlling plane such as an orifice, vessel opening, or directly connected valve. A long pipeline adds distributed friction, gas inventory, pressure-wave travel, and position-dependent upstream pressure. The pressure at the rupture plane—not merely the remote source pressure—controls the local Mach number.
Check 1: Solver-message classification
Read the complete calculation log from the first warning through the first fatal or terminating entry. The messages Long Pipeline calculation ignoring Atmospheric expansion method and as this calculation always assumes Conversation of Energy indicate that the long-pipeline calculation is selecting its own energy treatment and declining the requested atmospheric-expansion method. The second message appears to refer to conservation of energy, but retain the displayed wording when reporting the diagnostic.
| Reading | Meaning | Next action |
|---|---|---|
| Results exist and only these messages appear | The messages describe method selection rather than a failed choked-flow test. | Proceed to Check 2 and validate the physical case. |
| A later fatal or terminating message appears | That later entry identifies the calculation failure. | Correct its named input or model conflict before diagnosing choking. |
| No results and no later diagnostic appears | The calculation setup may contain an incompatible or incomplete option. | Record the case inputs and selected methods, then isolate the option that invokes atmospheric expansion. |
Check 2: Rupture-plane pressure ratio
Obtain absolute pressure immediately upstream of the rupture and the atmospheric backpressure used by the model. Gauge pressure cannot be inserted directly into the critical-ratio equation. Calculate r = Pdown/Pup, then calculate the critical ratio using the gas property k at the relevant state.
-
Check 2A: Expect
rgreater than the critical ratio when the short-opening criterion does not predict choking. Continue to Check 3 because pipeline friction may still create a sonic controlling location elsewhere. -
Check 2B: Expect
requal to or below the critical ratio when a short, isentropic opening can choke. Continue to Check 3; the long-pipeline pressure loss still determines whether the rupture plane actually receives that upstream pressure. -
Check 2C: If
kis unavailable, read it from the gas-property calculation at the modeled pressure and temperature. Substituting the air value for methane or a natural-gas mixture can move the predicted critical ratio.
A remote pressure ratio can be misleading. In the cited limiting example, a 10,000 m long, 25 mm inside-diameter air line supplied at 10 bar gauge and open to atmosphere produced an outlet velocity of about 33 m/s, despite an approximately 11:1 absolute-pressure ratio. A rupture 9,000 m from the source increased velocity only to about 35 m/s; sonic velocity occurred only for rupture positions within approximately 130 m of the source. These values belong to that stated example and are not methane design limits.
Check 3: Distributed pipeline restriction
Compare the rupture location with the source, pipe length, inside diameter, and frictional pressure profile. In adiabatic, constant-area gas flow with wall friction, the Fanno-flow mechanism drives the Mach number toward one. The available pipe length and friction can therefore limit mass flow before the remote source pressure is communicated to the opening.
| Observed model condition | Controlling mechanism | Decision |
|---|---|---|
| Short connection or rupture near the pressure source | The opening-plane pressure ratio can dominate. | Evaluate the critical ratio and local sonic state. |
| Long, small-diameter path to the rupture | Distributed friction lowers pressure and limits mass flow. | Use the long-pipeline compressible-flow calculation. |
| Rupture position changes the calculated flow materially | Pipe resistance and upstream inventory are controlling. | Retain location as an explicit scenario variable. |
| Steady and initial-release results differ sharply | Pressure-wave and inventory depletion effects are significant. | Proceed to Check 4. |
Do not describe Fanno flow as isenthalpic. The standard idealization is adiabatic, constant-area flow with friction; stagnation enthalpy remains constant when there is no heat transfer or shaft work, while static properties change along the pipe.
Check 4: Transient versus steady state
A full-bore rupture begins as an unsteady depressurization. A pressure wave propagates into the pipeline, the local gas accelerates, and the pressure available at the opening changes as upstream inventory responds. The initial acoustic choking condition and the later friction-limited condition are different calculation states.
Under the narrow assumptions of a perfect gas, constant specific heat, zero initial velocity, and negligible friction, the cited transient derivation gives:
Pexit/Pinitial = [2/(k+1)]^(2k/(k-1))
For k = 1.4, this expression gives (1/1.2)^7 = 0.279. This transient result must not replace the steady, short-restriction critical ratio of 0.528. The formulas answer different questions. A long-pipeline rupture model must track the transition rather than applying either ratio to the entire event.
- Check 4A: Expect the initial release rate to reflect the local pre-rupture inventory and pressure.
- Check 4B: Expect the release rate and controlling location to evolve as the pressure wave travels and frictional losses develop.
- Check 4C: If the model reports only a steady result, do not use it as the initial full-bore rupture rate without a separate transient calculation.
Resolving and verification procedure
- Define methane or the actual gas composition and use the model-calculated thermodynamic properties at the relevant state.
- Enter absolute source and atmospheric pressures, pipeline length, inside diameter, rupture position, and the friction inputs required by the long-pipeline model.
- Select the long-pipeline transient calculation for a full-bore rupture. Remove or disable the conflicting atmospheric-expansion selection if the solver explicitly states that it ignores that method.
- Run at least two rupture positions when location is uncertain: one near the source and one farther downstream. Compare local upstream pressure, Mach number, and mass-release rate.
- Verification Check 1: Expect the log to proceed beyond the two method-selection messages without a later fatal entry.
- Verification Check 2: Expect the reported energy balance to close within the software’s stated acceptance criterion; obtain that criterion from the calculation report or product documentation.
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Verification Check 3: Expect any reported choked location to have Mach number
1, subject to the solver’s numerical tolerance, rather than inferring choking solely from the remote pressure ratio.
Frequently asked questions
What happens if the upstream pressure is more than twice atmospheric pressure?
A short opening may choke, but a long pipeline may not deliver the remote pressure to the rupture plane. Calculate the local absolute-pressure ratio and inspect the pipeline pressure profile and Mach number.
What happens if PHAST ignores the Atmospheric expansion method?
The long-pipeline solver is applying its conservation-of-energy treatment instead of that expansion selection. Search the subsequent log entries for the first fatal message; the quoted entries alone describe the method choice.
What happens if I use 0.5 as the critical pressure ratio?
You introduce a gas-property error. Calculate [2/(k+1)]^(k/(k-1)); it is approximately 0.528 for k = 1.4 and 0.549 for k = 1.28.
What happens if the rupture model reports choked flow?
Perform the final verification at the reported controlling section: expect Mach number 1 within the solver’s numerical tolerance and confirm that the pressure, mass-flow, and energy-balance results correspond to the same transient time step.