Liquid Thermal Expansion Relief Sizing

Professional Engineering Sizing for Relief Valves protecting liquid-filled equipment from solar, ambient, or fire heat inputs. Based on API 520/521.

US CUSTOMARY METRIC / SI

1. Project Data

Project Name

Tag Number

Engineer

2. Relief Requirements

PRESSURE CONDITIONS

Set Pressure ($P_{set}$, psig)

Overpressure (%)

Back Pressure ($P_2$, psig)

Relieving Pressure ($P_1$, psig)

HEAT INPUT SCENARIOS

Active Scenario

Total Heat Input ($\Phi$, BTU/h)

3. Fluid Properties

Liquid Type

Relief Temp ($T$, °F)

Vapor Press ($P_v$, psia)

Sp. Gravity ($G$)

Viscosity ($\mu$, cP)

Exp. Coeff ($\alpha_v$, 1/°F)

Sp. Heat ($c$, BTU/lb·°F)

* Vapor pressure ($P_v$) is dynamically calculated via the Antoine Equation for library liquids based on relief temperature to check for flashing.

4. Valve Constants

Rupture Disk Installed Upstream?

Discharge Coeff ($K_d$)

Backpressure Factor ($K_w$)

Comb. Factor ($K_c$)

Viscosity Factor ($K_v$) Auto-Iterated via Re#

5. Trapped Volume Exemption Check

Many company standards and API 521 indicate thermal relief may not be mandatory for small trapped liquid volumes (typically < 132 gal / 500 L) as natural pipe elasticity safely absorbs the expansion.

Pipe Dia (in)

Pipe Length (ft)

Trapped Piping Volume: 0 gal

Sizing Summary

Recommended API Orifice

3/4" x 1"

Required Area ($A$) -

Actual API Area -

Capacity Used -

Req. Flow Rate ($q$) -

Relieving Press. ($P_1$) -

Note: Calculated API orifice is the minimum standard size that satisfies the required area. For very small loads, a "D" orifice is the minimum available standard.

Engineering Reference & Technical Basis

1. Thermal Relief Flow Rate & Pool Fire

The liquid expansion volume flow rate due to heat absorption is calculated per API 520 Part I (US Customary):

q = \frac{\alpha_v \cdot \Phi}{500 \cdot G \cdot c}

For API 521 Fire Case (Liquid Filled), heat input is calculated by:

\Phi = 21,000 \cdot A_{wetted}^{0.82}

$q$ = Required volumetric flow rate (US gpm)

$\alpha_v$ = Cubical expansion coefficient ($1/^\circ F$)

$\Phi$ = Total heat transfer rate (Btu/hr)

$A_{wetted}$ = Total wetted surface area ($ft^2$)

2. Relief Valve Area Sizing (Liquid)

Once the required relief flow rate is known, the required orifice area is calculated by:

A = \frac{q}{38 \cdot K_d \cdot K_w \cdot K_v \cdot K_c} \sqrt{\frac{G}{P_1 - P_2}}

$A$ = Required effective discharge area ($in^2$)

$P_1$ = Upstream relieving pressure ($psig$)

$P_2$ = Backpressure ($psig$)

$K_d$ = Effective discharge coefficient (usually 0.65)

$K_c$ = Combination factor (0.9 with Rupture Disk)

$K_w$ = Backpressure Correction factor

$K_v$ = Viscosity correction factor

3. Guidelines & DIERS Flashing Alert

Trapped Volume Rule of Thumb: API 521 states that for piping segments with small liquid inventory (e.g. less than 500 liters), detailed PSV sizing is often unnecessary. Thermal expansion can be safely absorbed by pipe elasticity.

Flashing / Two-Phase Flow: The liquid sizing equation assumes the fluid does not boil. If the Relieving Pressure ($P_1$) falls below the fluid's Vapor Pressure ($P_v$) at relieving temperature, the liquid will flash. In this case, DIERS Two-Phase methodology must be used.

Overpressure Allowance: Typically, a 10% overpressure is utilized for non-fire thermal relief. Higher overpressures (up to 33%) are permitted for fire scenarios depending on design codes.

Rupture Disks: If a rupture disk is installed upstream of the relief valve, ASME Section VIII requires a 10% capacity de-rating ($K_c = 0.9$).

4. Valve Constant Selection Guidelines

1. Discharge Coefficient ($K_d$)

Standard Default: Use 0.65 for preliminary sizing of liquid relief valves when the specific valve make/model is unknown (API 520 default).

Certified Valves: Use the manufacturer's certified value (typically 0.70 to 0.85) if a specific valve with ASME/National Board certification is selected.

2. Backpressure Factor ($K_w$)

Conventional Valves: Use 1.0 if discharging to the atmosphere or a system with constant, very low superimposed backpressure.

Balanced Bellows: If variable built-up backpressure exceeds 10-15% of set pressure, $K_w < 1.0$. Derive from manufacturer curves based on backpressure ratio.

3. Viscosity Factor ($K_v$) Auto-Iteration

API 520 Iteration: $K_v$ is dependent on the Reynolds Number ($Re$), which depends on Required Area ($A$). The tool iteratively solves for $K_v$ utilizing the Blevins correlation:

K_v = \left( 0.9935 + \frac{2.878}{\sqrt{Re}} + \frac{342.75}{Re^{1.5}} \right)^{-1}

If $Re > 100,000$, viscosity drag is negligible and $K_v = 1.0$.

References

API Standard 520 Part I: Sizing, Selection, and Installation of Pressure-Relieving Devices.
API Standard 521: Pressure-relieving and Depressuring Systems.
ASME Boiler and Pressure Vessel Code (Section VIII): Rules for Construction of Pressure Vessels.
DIERS (Design Institute for Emergency Relief Systems): Methodology for two-phase flashing flow.