Introduction
A token relief PSV — sometimes called a thermal relief or 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 token relief PSV.
Understanding the Relief Case
Before any calculation begins, you must define the credible overpressure scenario the valve is protecting against. For token 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 token 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 token 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 token relief valves discharging to atmosphere or a low-pressure header, back pressure is usually not a governing constraint.
Practical Sizing Example
Scenario: A 6-inch water injection line blocked between two isolation valves with solar heat gain estimated at 500 W. MAWP = 50 barg. Operating pressure = 40 barg. Set pressure = 50 barg.
Fluid properties at 50°C: ρ = 988 kg/m³, Cp = 4,183 J/kg·°C, β = 0.000457/°C
Relief rate:
Q = (0.000457 × 500) / (988 × 4183) = 5.5 × 10⁻⁸ m³/s = 0.0033 l/min
This is an extremely small flow rate — confirming that a "D" or "E" orifice token relief valve is appropriate. Do not oversize to a larger orifice: an oversized valve will chatter due to insufficient lift at such low flow rates.
Common Sizing Mistakes
- Using fire case heat input for a thermal relief valve: Fire case sizing produces enormously larger valves. Confirm your basis is the correct credible case.
- Ignoring viscosity correction: For viscous fluids (Kv correction per API 520), failure to apply the correction leads to undersizing.
- Selecting too large an orifice: Oversized valves lift, relieve a surge, drop below set pressure, and re-seat — this chatter cycle rapidly destroys seating surfaces.
- Set pressure too close to operating pressure: Creates chronic simmering and seat degradation.
Conclusion
Sizing a token 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.
Token relief valves are small devices with a specific job. Size them precisely for that job.