API 521 §4.4.12.4 · Norouzi & Rahimi Mofrad (2008)

Liquid Thermal Expansion & Thermal Relief Valves

Complete guide for junior process engineers — from decision to sizing to discharge
Step 1 of 70%
Step 1 — Initial check
Three conditions that must ALL be true before thermal expansion is even possible

Before asking "do I need a TRV?", first check whether thermal expansion can actually occur. If any one of these three initial conditions is absent, thermal expansion will not take place — and no TRV is needed.

Box 1 — Initial requirements (all three must be yes)
  • 1
    System is ≥95% liquid-full. Two-phase systems with significant vapour pockets do not qualify — gas absorbs the volume increase. Caution: small vapour pockets can disappear on heating due to compression or solubilisation. Multi-component mixtures with wide boiling range may always retain sufficient vapour.
  • 2
    The line or equipment is normally blocked in for operational or emergency purposes. Exception: lines handling sub-ambient fluids are treated as blocked-in even if not normally isolated, because warm-up will always occur.
  • 3
    A heat source is present whose temperature exceeds the liquid operating temperature. Sources: solar (max ~60–70 °C), steam/hot-fluid heat tracing, heating coils/jackets, ambient warm-up, flare radiation. Electrical tracing is excluded — it is thermostatically controlled and maintains temperature rather than raising it. For piping-only systems, external fire is NOT considered a heat source for thermal expansion purposes.
↓ All yes → continue to Box 2  |  Any no → no TRV required (thermal expansion will not occur)
Process plant vs. off-plot pipingOn-plot process lines are rarely blocked in continuously and operators usually drain them — TRVs are uncommon. Off-plot storage and transport lines are regularly shut in without draining — TRVs are far more common there.
Check your understanding
An insulated steam-traced hydrocarbon line on a process unit is blocked in for maintenance. Only an electrical heat-tracing system is active (no steam). Does condition 3 (heat source present) apply?
Step 2 — Existing safeguards
Can existing measures eliminate the need for a TRV?

If all Box 1 conditions are met, check Box 2. If any one of these applies, no TRV is required — though thermal expansion will still occur, the rupture risk is removed by the safeguard.

Box 2 — Safeguards & alternatives (any one yes → no TRV needed)
  • 4
    Pressure rise stays within design limits. Use API 521 Eq. 4 or the simplified equation to calculate the final pressure p₂. If p₂ ≤ design pressure — criterion met, no TRV needed. Document the calculation.
  • 5
    Another pressure safety device already protects the system (e.g. a PSV sized for another relief scenario). Thermal relief flow rates are very small — even a minimally-sized existing PSV will handle it by opening momentarily.
  • 6
    Administrative procedure ensures liquid is drained before block-in. Draining just 10% of the liquid volume is sufficient to prevent dangerous thermal expansion. Must be captured in a formal shutdown or maintenance procedure. Lock-open (LO) drain valves qualify as a reliable safeguard.
  • 7
    Engineering provision prevents full liquid blockage: ¼ in. (6 mm) hole drilled in gate valve disc; small bypass with an open or LO valve; reverse-check valve around one block valve; or a three-way valve instead of a standard block valve.
  • 8
    A weak point exists where pressure can relieve without major consequence. Note: API 521 §4.4.12.4.2 takes no credit for reverse back-flow through a check valve — it must be assumed to hold. Other references do accept check valve leakage as a safeguard; align with your project's governing standard.
¼ in. hole in gate
Drilled through gate valve disc — the simplest provision
Bypass + LO valve
Small bypass line locked open during normal operation
Three-way valve
Replaces block valve — the system can never be fully isolated
Note on check valves (API 521 §4.4.12.4.2)API 521 explicitly prohibits taking credit for reverse flow through a check valve. Assume it holds tight. Norouzi & Rahimi Mofrad note that other industry references accept check valve leakage as sufficient — always align with your project's governing document.
Check your understanding
A blocked-in pump suction line has a spring-loaded check valve on the inlet. A colleague says "the check valve will leak and relieve any pressure build-up — no TRV needed." Is this acceptable per API 521?
Step 3 — Consequence assessment
If no safeguard applies — assess the rupture consequences

When Box 2 provides no safeguard, you must assess Box 3: the consequences of a pipe or equipment rupture. If any one of the following applies, a TRV is required.

Box 3 — Rupture consequences (any yes → TRV required)
  • 9
    Liquid is lethal, toxic or corrosive — rupture is not tolerable from a personnel health perspective.
  • 10
    Liquid is combustible or explosive — rupture risk is unacceptable from a plant safety viewpoint.
  • 11
    Liquid has major environmental impact — release to grade is unacceptable; TRV must discharge to a closed system.
  • 12
    Liquid is highly volatile — releases continue until the full inventory is vaporised, causing extended downtime, material loss, and VOC emissions.
  • 13
    Line/equipment is critical to plant operation — it cannot be bypassed without a major process interruption.
  • 14
    Pipe is large — diameter >1½ in. (DN40) or length >30 m — rupture repair cost exceeds TRV cost. For liquid-full equipment: TRV required if blocked volume >0.5 m³.
↓ All no → no TRV required, but consider consequence management (spill containment, bunding)
If all Box 3 answers are noThe rupture risk is considered acceptable and no TRV is required. Document the assessment. Some provisions for managing rupture consequences (bunding, drain routing, spill containment) should still be considered during detailed design.
Check your understanding
A 2-in. cooling water line, 15 m long, blocked between two manual valves. Non-hazardous fluid, no environmental concern, non-critical service. No drain procedure in place. Box 2 provides no safeguard. Does Box 3 require a TRV?
Step 4 — Pressure rise calculation
Quantifying the pressure build-up: API 521 Eq. 4 and the simplified approach

Two approaches are available. Use the rigorous API 521 Eq. 4 when all parameters are known. When data is limited, the simplified form gives a conservative first-pass estimate.

Rigorous — API 521 Equation 4 (Karcher / CCPS)

Final gauge pressure
p₂ = p₁ + [ (T₂−T₁)(βᵥ − 3αₗ) − (qₗₗ·t/V) ]
          ──────────────────────────────────────
               κ + d/(2·E·w)·(2.5 − 2ν)

Set qₗₗ = 0 (assume block valve seats perfectly) for conservative calculation. This removes the leakage term from the numerator.

SymbolDescriptionUnit (SI)
p₁ / p₂Initial / final gauge pressurekPa
T₁ / T₂Initial / final temperature°C
βᵥCubic expansion coefficient of liquid1/°C
αₗLinear expansion coefficient of pipe wall1/°C
κIsothermal compressibility of liquid1/kPa
d / wInternal diameter / wall thicknessm
EModulus of elasticity of wall at T₂kPa
νPoisson's ratio (use 0.3 for metals)
qₗₗLiquid leakage across block valve (usually set to 0)m³/s
VPipe volume

Pipe wall material data — API 521 Table 3

Materialαₗ (1/°C)E (kPa)
Carbon steel (1020)1.21×10⁻⁵207×10⁶
304 stainless steel1.73×10⁻⁵193×10⁶
316 stainless steel1.60×10⁻⁵193×10⁶
Alloy 6001.1–1.66×10⁻⁵172–221×10⁶
Nickel-copper alloy1.01–1.42×10⁻⁵169–213×10⁶

For other materials → Perry's Chemical Engineers' Handbook. For βᵥ and κ → Lange's Handbook (12th ed.) or your process simulator.

Simplified approach — when API 521 parameters are unavailable

Simplified pressure rise (Norouzi & Rahimi Mofrad, 2008)
P_f = P_i + αᵥ · (T_f − T_i) / χ

where: χ = (1/v₁) · (v₁ − v₂) / (P₂ − P₁)

This form ignores pipe wall elasticity — it is conservative for rigid piping. Use it for quick screening. For water at 20°C: ΔP/ΔT ≈ 2.1×10⁻⁴ / 4.56×10⁻⁵ ≈ 4.6 bar/°C — a 5–10°C rise can push a blocked-in water line to design pressure.

Practical note on T_fThe TRV will open long before the liquid reaches the heat source temperature. In practice, a 5–10°C rise above initial temperature is often sufficient to push the pressure from operating to design pressure. Do not use the heat source temperature as T_f for TRV setting — the valve will have already acted well before that.
Check your understanding
Why is setting qₗₗ = 0 in API 521 Eq. 4 described as conservative?
Step 5 — Relief rate & TRV sizing
How much needs to be relieved — and what size valve do you need?

TRV volumetric relief rate (SI) — Norouzi & Rahimi Mofrad Eq. 4

Volumetric relief rate
q = (αᵥ · φ) / (1,000 · d · C)
SymbolDescriptionUnit
qVolumetric relief ratem³/s
αᵥCubic expansion coefficient of liquid1/°C
φHeat transfer rate to the blocked-in systemW
dLiquid relative density (ref. water at 15.6 °C)dimensionless
CSpecific heat capacity of trapped liquidJ/(kg·K)

Key assumptions when determining heat input φ:

TRV sizing guidance (Norouzi & Rahimi Mofrad)

  • Default for most piping applications: NPS ¾ × NPS 1 (DN20 × DN25). Almost always oversized but is the standard industry default for piping thermal relief — the calculated flow rate is typically tiny.
  • !
    Perform a full relief rate calculation and size check for: large-diameter, uninsulated, above-ground pipelines and large liquid-full vessels or heat exchangers.
  • !
    For equipment operating liquid-full: a TRV is required if the blocked volume >0.5 m³, and sizing must be verified.
Check your understanding
You are specifying a TRV for a DN50 cooling water line. The calculated relief rate is 0.00008 m³/s. What valve size do you specify?
Step 6 — Location & discharge routing
Where to install the TRV and where to route the discharge

Follow these six installation rules every time you position a TRV on a blocked-in system:

The discharge destination depends on the fluid properties. Use this table:

ConditionRequired discharge destination
Liquid temperature above flash pointClosed system — flare header, slop system, or closed drain vessel
Liquid temperature >300 °CClosed system — flare or closed drain; risk of autoignition or severe burn injury
Toxic, corrosive, volatile, or environmentally harmful (Q9–12 yes)Closed system — flare header, slop system, or closed drain as approved for the fluid service
Liquid is the same as stored in a nearby vesselBack to vessel — or connect to the downstream side of the block valve so the TRV acts as a bypass
Non-hazardous, non-volatile, below flash point (Q9–12 all no)Open to grade — acceptable with project and authority approval; confirm with local regulations
General rule on discharge routingRoute the TRV discharge to a closed drain, slop system, flare header, or other approved disposal system appropriate for the fluid service. The discharge line must always be capable of accepting the relieved material at any time — consider the position of downstream valves and whether the receiving system is pressured or depressured at the moment of relief. Keep the discharge line as short and as low in back-pressure as possible.
Check your understanding
A TRV is required on a light naphtha line (flash point −40 °C, boiling point 35 °C at atmospheric pressure). Where should the discharge be routed?
Step 7 — Complete workflow
Your 8-step TRV decision checklist — use this on every project
Quick field rule of thumbAny off-plot transport or storage line carrying a flammable, toxic, or highly volatile fluid, diameter >1½ in., length >30 m → almost certainly needs a TRV. On-plot process lines → start with the drain procedure check first. When in doubt, calculate p₂ and let the numbers decide.
Check your understanding
A ¾-in. cooling water line, 10 m long, blocked in between two manual valves during a shutdown. No heat tracing. Ambient temperature. No drain procedure documented. Does this line need a TRV?
References
API Standard 521, 7th Edition (2020) — Pressure-relieving and Depressuring Systems, §4.4.12.4 Piping.
Norouzi, S. & Rahimi Mofrad, S. (2008) — "What you should know about liquid thermal expansion." Hydrocarbon Processing, November 2008, pp. 67–69.
CCPS / Karcher — cited in API 521 as basis for Equation 4.
Perry's Chemical Engineers' Handbook — material property data for αₗ and E.
Lange's Handbook of Chemistry, 12th Ed. — isothermal compressibility data.