Cavitating Feed Valve to a Reboiler

Required Cv

Cv = Q √(SG/ΔP) = 150 × √(1.0 / 50) = 150 / 7.07 = 21.2

With a rated Cv of 40, the design point sits at 21.2/40 ≈ 53% of rated capacity. For a linear trim, Cv is roughly proportional to lift above the leakage floor, so the valve runs near mid-stroke at design flow.

Cavitation check

ΔP at design = 60 − 10 = 50 psi.

Allowable (incipient-cavitation) ΔP = FL² (P1 − Pv) = 0.90² × (60 − 0.25) = 0.81 × 59.75 ≈ 48.4 psi

Actual ΔP (50 psi) exceeds the allowable 48.4 psi, so the valve is cavitating at design flow. The choked-flow limit, FL²(P1 − Ff·Pv) = 0.81 × (60 − 0.25) ≈ 48.4 psi, is also essentially reached - the trim is at the point where further pressure drop buys almost no additional flow.

That matches the symptoms: cavitation collapse downstream of the vena contracta gives the noise, body vibration and the unsteady downstream gauge. The process engineer sized on ΔP alone and stopped there.

Turndown calculation

At 25 gpm the required Cv = 25 × √(1/50) = 3.54, which is 3.54/40 ≈ 9% of the rated Cv.

Two problems:

1. Rangeability and resolution. A linear-characteristic globe at ~9% of rated Cv sits near the seat, where the installed characteristic is steep and small stroke changes produce large flow changes. Control at low rates will be coarse, and the positioner resolution, deadband and packing friction all become a large fraction of the required stroke.
2. ΔP is not constant. On a centrifugal pump curve, lowering the flow raises the valve ΔP above the design 50 psi, so the required Cv at 25 gpm is even smaller than the calculation - pushing the valve closer to the seat.

Recommendation

• Specify equal-percentage trim so the gain falls away as the valve closes, and a body/trim combination where the design point lands around 60–70% lift and the minimum flow lands above ~20% lift. In practice: a 2-inch body with reduced-area trim (e.g. rated Cv ≈ 25–30, equal percentage) rather than a full-Cv 40 linear trim.
• Split the pressure drop. Take 15–25 psi in a fixed restriction (orifice plate, additional line loss, or a pump impeller trim) so the valve sees ~25–35 psi. This simultaneously fixes the cavitation margin and lets a smaller trim handle the same flow.
• If the ΔP split is not possible, use an anti-cavitation cage trim or hardened (Stellite) trim and accept the noise, but that treats the symptom.

The stated hazard drives the answer: loss of feed overheats the reboiler tubes within minutes.

• Fail-closed on air or signal loss stops feed immediately while the heating medium may still be valved in - that is a direct route to dry-out, tube overheating and possible rupture. Fail-closed looks 'safe' by reflex but is wrong here.
• Fail-open keeps the tubes wetted on instrument-air or signal failure, which is the safer default for this specific consequence.

Caveats to close out with the HAZOP team:

• Fail-open floods the column with cold feed, which creates its own upset (level, flooding, loss of separation). That must be shown to be tolerable, and the high-level / flooding safeguards confirmed.
• The robust answer is usually fail-open plus a trip on the heating medium, so that loss of feed is detected by low flow and the reboiler duty is cut. Verify the trip is independent of the feed valve and that its response time is faster than the tube dry-out time.
• Confirm the actuator is actually sized to stroke the valve open against the spring on air failure, and that the positioner is set up for the correct air-fail action - a fail-open specification that the actuator cannot deliver is a paper safeguard.