Introduction
A thermal relief PSV — sometimes called a minor relief valve — is a small pressure relief device designed to handle limited, well-defined overpressure scenarios rather than a major process upset. Sizing these devices correctly is a precision exercise: undersizing risks system failure, while oversizing introduces unnecessary mechanical complexity and cost.
This post walks through the key steps in sizing a thermal relief PSV. If you are not yet sure that a thermal relief valve is the right device for your scenario, start with when a thermal relief PSV is needed — and for how the device fits the wider relief and depressuring picture, see the pressure relief and flare systems overview.
Understanding the Relief Case
Before any calculation begins, you must define the credible overpressure scenario the valve is protecting against. For thermal relief applications, the most common case is thermal expansion — where a trapped liquid volume increases in temperature and, because it is incompressible, generates significant pressure rise even with small temperature changes.
Common scenarios requiring thermal relief:
- Liquid-filled piping sections that can be blocked in by valves (e.g., between two block valves)
- Equipment that can be isolated from the system while containing liquid subject to heat input (solar, steam tracing, exothermic reaction)
- Heat exchangers where tube-side flow can be blocked while shell-side heat input continues
Clearly define:
- The fluid and its properties at relieving conditions
- The heat input rate (W or BTU/hr)
- The maximum allowable accumulated pressure (MAAP = 110% of MAWP for non-fire cases per API 520)
Key Sizing Parameters
1. Relief Rate
For a thermal expansion case, the volumetric relief rate is determined by:
Q = (β × H) / (ρ × Cp)
Where:
- Q = volumetric flow rate (m³/s or gpm)
- β = cubic expansion coefficient of the liquid (1/°C or 1/°F)
- H = heat input rate (W or BTU/hr)
- ρ = liquid density at relieving conditions (kg/m³ or lb/ft³)
- Cp = specific heat capacity (J/kg·°C or BTU/lb·°F)
For water at typical pipeline temperatures, β ≈ 0.00025/°C, which means even modest heat input can generate meaningful pressure in a blocked-in system.
2. Set Pressure
The set pressure must not exceed the MAWP of the protected equipment. For thermal relief valves protecting piping, this is typically the piping class pressure rating. Common choices:
- Set at MAWP for lines with no other overpressure protection
- Set at 90–95% of MAWP to provide margin above normal operating pressure
Ensure adequate differential between normal operating pressure and set pressure to prevent simmering (chatter). A minimum differential of 10% is recommended.
3. Valve Orifice Area
Using the calculated relief rate, fluid properties, and allowable overpressure, the required orifice area is calculated using API 520 Part I methodology:
A = Q / (Kd × Kw × Kc × Kb × √(2g × ΔP/ρ))
Where:
- Kd = discharge coefficient (typically 0.65 for liquid service)
- Kw = back pressure correction factor
- Kc = combination correction factor (if in-line rupture disc)
- Kb = back pressure correction factor (for balanced bellows valves)
- ΔP = differential pressure across valve at relieving conditions
Select the next standard API orifice size above the calculated required area. API 526 lists standard orifice designations (D, E, F, G, H, J, K, L, M, N, P, Q, R, T).
4. Back Pressure Evaluation
Confirm the built-up back pressure at maximum relief flow does not exceed allowable limits:
- Conventional valves: back pressure ≤ 10% of set pressure
- Balanced bellows: typically ≤ 30–50%
- Pilot-operated: varies by design
For thermal relief valves discharging to atmosphere or a low-pressure header, back pressure is usually not a governing constraint.
Liquid, Flashing, or Two-Phase — Know Which You Are Sizing
The clean thermal-expansion equation above assumes the trapped fluid stays liquid as it is heated and relieved. That assumption is what makes the relief rate tiny — you are only displacing the expansion volume of an incompressible liquid. It quietly breaks in two common situations, and getting it wrong undersizes the valve by orders of magnitude:
- The liquid can flash at relieving pressure. If the fluid is near its bubble point — a light condensate, a volatile NGL, a liquid close to its saturation pressure — then as the valve opens and pressure falls, part of the inventory boils. You are now generating vapour, not just displacing liquid, and the required relief rate is governed by the vaporisation rate, which is far larger. Size this as a vapour or two-phase case per API 520, not as thermal expansion.
- There is a vapour space or gas blanket. A blocked-in segment that is not completely liquid-full behaves differently — the gas cushion absorbs some expansion, but a heated gas blanket also adds its own pressure rise. Confirm the fill state.
The practical test: check the relieving temperature and pressure against the fluid's saturation curve. If the relieving point sits in the two-phase region, abandon the simple liquid expansion model. This single check is the difference between a correctly sized "D" orifice and a dangerously undersized valve — and it is the most common way a "thermal relief" case turns out to be something larger in disguise (the same trap covered in when a thermal relief PSV is needed).
Worked Example — Solar Thermal Expansion, End to End
Scenario (illustrative): a 6-inch water injection line, ~30 m long, blocked between two isolation valves in full tropical sun. MAWP = 50 barg, operating pressure = 40 barg, set pressure = 50 barg. Discharge is to a low-pressure drain header.
Step 1 — heat input. Take the solar flux absorbed by the bare line as ≈ 0.63 kW/m² of plan (projected) area per the API 521 solar guidance. A 6-inch line (≈ 168 mm OD) over 30 m presents a projected area of 0.168 × 30 ≈ 5.0 m², so:
H = 0.63 kW/m² × 5.0 m² ≈ 3.2 kW (≈ 3,200 W)
Step 2 — fluid properties at relieving conditions (water near 50 °C): ρ = 988 kg/m³, Cp = 4,183 J/kg·°C, cubic expansion coefficient β = 0.000457 /°C.
Step 3 — volumetric relief rate (the API 521 thermal-expansion expression):
Q = (β × H) / (ρ × Cp)
Q = (0.000457 × 3200) / (988 × 4183)
Q ≈ 3.5 × 10⁻⁷ m³/s ≈ 0.021 l/min ≈ 0.0056 USgpm
Step 4 — required orifice area (API 520 Part I liquid sizing, non-certified-capacity form):
A = Q / [ Kd · Kw · Kc · √( 2·ΔP / ρ ) ]
With Kd = 0.65 (liquid), Kw = Kc = 1.0, and ΔP taken as the relieving pressure above back-pressure ≈ 55 bar = 5.5 × 10⁶ Pa:
√(2·ΔP/ρ) = √(2 × 5.5e6 / 988) ≈ 105 m/s
A = 3.5e-7 / (0.65 × 105) ≈ 5.1 × 10⁻⁹ m² ≈ 0.005 mm²
Step 5 — select a standard orifice. The calculated area is vanishingly small — orders of magnitude below the smallest API 526 letter orifice. The smallest standard "D" orifice is 0.110 in² (71 mm²), already ~14,000 times the calculated requirement. The conclusion is the important part: every standard thermal-relief valve is hugely oversized for this duty on area alone. You select the smallest available orifice (D or E), and the real engineering is making sure it will not chatter — which means a generous margin between operating (40 barg) and set (50 barg) pressure, and confirming the valve manufacturer's minimum stable flow.
This is the defining feature of thermal relief sizing: the area calculation almost never governs valve selection. It exists to prove the case is small and to rule out a high-flow scenario hiding in the system. Once that is established, mechanical stability and seat tightness drive the choice. (Contrast this with a fire or blocked-outlet case, where the area really does govern — see emergency depressurisation and blowdown.)
Common Pitfalls
- Using fire-case heat input for a thermal relief valve. Fire-case sizing per API 521 produces enormously larger relief rates and valves. Confirm the governing credible case is genuinely thermal expansion, not fire.
- Ignoring viscosity correction. For viscous fluids the Kv viscosity correction per API 520 reduces effective capacity; omitting it undersizes the valve.
- Selecting too large an orifice. Because the calculated area is tiny, the temptation is to "add margin" by upsizing. An oversized valve lifts, dumps a surge, drops below set, and re-seats — a chatter cycle that rapidly destroys the seat.
- Set pressure too close to operating pressure. Less than ~10% differential creates chronic simmering and seat degradation; in this example the 40→50 barg margin is healthy.
- Forgetting the line can be liquid-full and gas-blocked at once. If trapped liquid can flash to vapour at relieving conditions, the case is no longer a simple incompressible thermal expansion — re-evaluate as a two-phase or vapour case.
- Treating it as a process relief valve. A thermal relief PSV supplements primary protection; it is not the vessel's main relief device. Document its basis in the relief philosophy and cause-and-effect matrix.
Conclusion
Sizing a thermal relief PSV correctly requires a clear, justified definition of the relief case, careful calculation of the required relief rate, and disciplined selection of the appropriate standard orifice. The calculation itself is straightforward — the discipline lies in properly defining the scenario and resisting the temptation to add unnecessary margin by upsizing.
Thermal relief valves are small devices with a specific job. Size them precisely for that job.
