Evaluating PSV Requirements for Heat Exchanger Tube Rupture

Steam at 46 bar g in the tubes, process gas at 1 bar g in the shell, 52 bar g tube design, 5 bar g shell design, a 30-inch shell discharging through a 24-inch line with no valve in it. The relief question looks like a PSV sizing job. It is not. The open outlet is already the relief device, and the work is proving it stays adequate through both the steady state and the first few milliseconds after the tube lets go.

Resist the Reflex: Do Not Bolt a PSV onto the Shell

The fast answer under HAZOP pressure is to add a shell-side PSV and move on. It buys nothing here and it can make the file worse.

• A PSV on a shell that already vents to atmosphere through a full-bore 24-inch line relieves nothing. The open line passes the rupture flow at a lower pressure than any PSV set below 5 bar g would ever reach.
• Adding the valve creates a new inspection, testing and bench-set obligation, plus a nozzle, a flange and a body that can plug on a dirty process gas.
• Worse, it invites someone downstream to argue the vent line may now be isolated, because "the PSV protects it." That is how a permanently open path becomes a valved path in the next revamp.

The correct deliverable is a documented relief path, not a relief valve. Get the line qualified, then close the transient question the client actually asked.

Qualify the Open Path as a Relief Device

An atmospheric outlet is acceptable overpressure protection only if it is unobstructed and can never be obstructed. Walk it, do not read it off the P&ID.

1. Confirm no valve, blind, spectacle plate, orifice plate or spool break exists anywhere between the shell and atmosphere. A car-sealed-open valve is not the same thing as no valve; it is an administrative control and the client will challenge it.
2. Check the shell outlet nozzle size. The 24-inch run is irrelevant if the nozzle is 12-inch. The smallest cross-section in the path sets the backpressure.
3. Check the internal path from the likely break location to that nozzle. Baffle windows, a tight bundle-to-shell clearance and impingement plates are all restrictions the rupture flow has to pass through before it reaches the outlet.
4. Check the discharge end for screens, bird mesh, rain hats, silencers, knockout pots or a future tie-in to a scrubber. Any of these is a potential plug and moves you back into PSV territory.
5. Mark the line on the P&ID as a relief path with a no-isolation note and carry it into the management-of-change register.

Check before moving on: the minimum flow area from shell to atmosphere is identified, dimensioned, and free of any closable element.

Establish That Tube Rupture Is a Credible Scenario

Before sizing anything, run the screening criterion in your edition of API 521. The common screen exempts tube rupture when the low-pressure side design pressure is at least 10/13 of the high-pressure side design pressure. Here the ratio is 5 / 52 = 0.096 against a threshold of 10/13 = 0.769. The scenario is credible and must be evaluated. Verify the exact wording and basis (design pressure versus test pressure) against the standard you are working to, and record the result — that single line kills most of the argument about whether the study is required at all.

Calculate the Rupture Flow Rate

Use the full-bore double-ended break: one tube severs, and steam feeds out of both open ends. The upstream pressure ratio is 47 bar a / 2 bar a ≈ 23, far above the critical ratio for steam, so both ends are choked and the flow is set entirely by the tube-side condition and the open area.

A_total = 2 * (pi/4) * d_tube_ID^2

m_dot = Cd * A_total * P1 * sqrt( (k * M) / (Z * R * T1) * (2/(k+1))^((k+1)/(k-1)) )

where P1 = tube-side absolute pressure (Pa)
      T1 = tube-side absolute temperature (K), from steam tables at 46 bar g
      k  = ratio of specific heats
      Cd = discharge coefficient for the break geometry

Notes that change the answer:

• Take T1 off the steam tables at the operating pressure, not at the header design temperature. A saturated feed flashes across the break and the discharge is two-phase at the shell nozzle even though it is choked at the tube.
• Confirm whether the steam supply can actually sustain the flow. If the exchanger is fed through a long line or a control valve, the sustained rate is the smaller of the choked break flow and the supply line capacity; the initial peak is still the choked value.
• Add the normal process gas flow through the shell. The vent line has to pass both.

Check: a single mass flow number in kg/s, with the tube ID and discharge coefficient you used written next to it.

Size the Vent Line for That Flow and Prove the Steady-State Pressure

Run compressible flow through the minimum-area path at the combined rate. Work in absolute pressure, start from atmospheric at the discharge and march back to the shell.

1. Check the Mach number at the pipe exit first. If the line chokes at the outlet, the shell pressure is set by that choke and no amount of downstream length helps.
2. If not choked, use an adiabatic or isothermal compressible pipe method — not incompressible Darcy — with the fittings, the bend at the nozzle, and the exit loss included.
3. Compare the resulting shell pressure to 5 bar g. On a 24-inch line against a single ruptured tube, the number typically lands close to atmospheric, which is why this configuration has been built without PSVs for years.
4. Repeat with the mixed steam/process-gas properties, not pure process gas. Steam lowers the mixture molecular weight and raises the volumetric rate for the same mass rate.

Check: steady-state shell pressure documented with margin to 5 bar g. If the margin is thin, enlarge the nozzle or the line — that is the fix, not a valve.

Close the Transient Argument on the Gas-Filled Shell

The client's objection is the shock-tube case: open a high-pressure region into a low-pressure one and a wave propagates at roughly half the driver pressure. That model assumes a constant-area duct with a driver section comparable in size to the driven section. Neither holds here, and there are three independent reasons the shell does not see anything near 5 bar g.

• Area expansion. Compute A_shell / A_tube using your actual tube ID and the 30-inch shell bore. The number is in the hundreds to low thousands. The jet from a single severed tube expands into that volume as a decaying blast wave, not a plane shock; peak side-on overpressure falls off steeply with distance from the break, and the tube bundle itself sits in the way as an obstacle field.
• Impulse versus structural period. A shell responds to impulse, not to instantaneous peak pressure, when the pulse duration is short relative to its natural period. A wave that crosses a 30-inch shell in a fraction of a millisecond and reflects away carries negligible impulse against the mass of a 52 bar g-class tube-side/5 bar g-class shell assembly. Compare pulse duration to shell ring period before conceding the point.
• Fill rate. The bulk pressure rise is a mass balance, and it is slow:

  dP/dt = (R * T / (M * V_shell_free)) * (m_dot_in - m_dot_out)

  With V_shell_free as the gas-filled shell volume plus the vent line volume, integrate from 1 bar g and see how long the shell would take to reach 5 bar g with the outlet closed. It will be on the order of seconds. With the outlet permanently open there is no opening delay at all — the relief path is already flowing before the tube fails — so the vent starts passing the break flow in the same acoustic time the wave takes to reach it.

That last point is the one to lead with in the HAZOP close-out. A PSV scenario has an opening-time argument. An always-open vent has none.

Know the Case Where This Reasoning Fails

The transient concern the client is reaching for is real, but it belongs to a liquid-filled shell. When high-pressure gas or supercritical fluid breaks into liquid, the liquid is incompressible and its inertia prevents it from moving out of the way. The force reaches the shell wall in milliseconds. A PSV spring cannot accelerate off its seat in that time, and the liquid cannot flow to the valve anyway — hydraulically the shell might as well be filled with a solid. Only a large rupture disk responds fast enough.

Company thresholds for the shock case differ; the consensus band is a tube-side pressure above about 750–1000 psig. This unit runs 46 bar g, which is 667 psig — below that band even if the shell were liquid-filled. Confirm which criterion your own engineering standard uses and cite it.

Simulate It If the Client Wants a Number

When the qualitative argument does not close the action item, build the transient model. It is a short job in any pipeline transient package:

1. Model the shell as a 30-inch pipe of length equal to the shell tangent-to-tangent, with the correct free gas volume.
2. Attach the 24-inch outlet line to atmosphere with its real length, fittings and exit condition.
3. Impose the normal process gas flow through the shell that produces the 1 bar g operating pressure, so the model starts at the real initial condition.
4. Add a source at the break location set to the tube-side pressure and the tube flow area, behind a valve configured to open instantaneously.
5. Run it and plot shell pressure against time. Report the peak, the time to peak, and the settled steady-state value against the 5 bar g design.
6. Sensitivity-run the tube ID, the discharge coefficient and the outlet nozzle size. Those three move the answer; nothing else does much.

Check: peak transient pressure and steady-state pressure both below 5 bar g, with the model's initial condition matching the plant's normal operating pressure.

Verify End to End Before Closing the Action

• Minimum flow area from shell to atmosphere identified, dimensioned and unobstructable.
• 10/13 screening result recorded, showing why the scenario was evaluated rather than exempted.
• Double-ended choked break flow calculated with the tube ID and discharge coefficient stated.
• Steady-state shell pressure at combined break plus normal flow, below 5 bar g with margin.
• Transient peak below 5 bar g, either by the impulse and fill-rate argument or by simulation.
• Shell design temperature checked against the release temperature. A 46 bar g steam release into a shell rated for a 1 bar g process gas can exceed the shell's design temperature long before it exceeds its design pressure. Do not close the study on pressure alone.
• Atmospheric discharge location reviewed for a steam and process-gas plume at grade or near access ways.
• P&ID annotated and MOC raised to prevent future isolation of the vent path.

Stop and escalate if any of these turn up: the shell can be liquid-filled or liquid-blocked under any operating or upset case, the vent path contains a valve or a device that can plug, the outlet nozzle chokes at the rupture flow, or the release temperature exceeds the shell design temperature. In those cases the relief basis is no longer a plain vent-line hydraulics problem, and it needs the exchanger manufacturer's mechanical review plus a formal pressure-relief specialist before the unit runs. Take the same route if the client rejects a documented transient simulation — that becomes a standards interpretation question for the certifying authority, not a calculation to rework on shift.

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