Tube Rupture Relief Valve Sizing

Professional Engineering Sizing for Relief Valves protecting low-pressure shell sides from high-pressure tube ruptures. Supports Liquid and Gas/Vapor phases based on API 520/521.

US CUSTOMARY METRIC / SI

1. Project Data

Project Name

Tag Number

Engineer

2. Exchanger Pressures

HIGH PRESSURE (TUBE) SIDE

Design Pressure ($P_{HP,d}$, psig)

Normal Operating Press. ($P_{HP,op}$, psig)

Driving force for rupture flow calculation.

LOW PRESSURE (SHELL) SIDE & PSV

Design Pressure ($P_{LP,d}$, psig)

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

Overpressure (%)

Back Pressure ($P_2$, psig)

Relieving Pressure ($P_1$, psig)

3. Tube Geometry & Rupture

Tube OD (in)

Wall Thickness (in)

Tubes Ruptured

Rupture $C_d$

Calculated Tube ID: 0.782 in

Total Rupture Area (2 open ends per tube): 0.961 in²

4. HP Fluid Properties

Fluid Phase Scenario

Fluid Type

Sp. Gravity ($G$)

Viscosity ($\mu$, cP)

5. Valve Constants

DISCHARGE COEFF. ($K_d$) BASIS

API 520 Prelim ASME Certified

Discharge Coeff ($K_d$)

Backpressure Factor ($K_w$)

Rupture Disk Installed Upstream?

Comb. Factor ($K_c$)

Visc. Factor ($K_v$)

Sizing Summary

Recommended API Orifice

3" x 4"

Required Area ($A$) -

Actual API Area -

Capacity Used -

Rupture Flow ($q$) -

Rupture Area ($A_r$) -

Relieving Press. ($P_1$) -

Rule of Thumb: API 521 traditionally assumes that a tube failure results in a flow equivalent to twice the cross-sectional area of one tube (fluid flowing from both the tube stub and the open tube length).

Engineering Reference & Technical Basis

1. API 521 Exemption (10/13ths Rule)

Per API 521, a pressure relief device may not be required to protect the low-pressure side of a heat exchanger from a tube rupture if the low-pressure side design pressure is greater than or equal to a specific fraction of the high-pressure side design pressure.

For equipment designed to ASME Section VIII Div. 1 (hydrotest = 1.3x Design):

P_{LP,design} \ge \frac{10}{13} P_{HP,design}

This implies the LP side test pressure (1.3 $\times$ LP Design) is greater than or equal to the HP design pressure, so structural failure from a tube break is highly unlikely.

2. Tube Rupture Liquid Flow Rate

When the HP fluid is a non-flashing liquid, the volumetric flow rate ($q$) through the ruptured tube is calculated via standard orifice flow mechanics based on the pressure differential ($\Delta P = P_{HP,op} - P_{LP,rel}$):

q = 38 \cdot A_r \cdot C_{d,rup} \sqrt{\frac{P_{HP,op} - P_{LP,rel}}{G}}

$q$ = Flow rate through rupture (US gpm)

$A_r$ = Rupture area (typically $2 \times$ tube ID area, in²)

$C_{d,rup}$ = Rupture discharge coefficient (typically 0.6)

$G$ = Specific gravity of HP fluid at relieving conditions

3. Relief Valve Area Sizing (Liquid)

Once the required relief flow rate ($q$) is established from the liquid rupture calculation, the required PRV orifice area is calculated per API 520 Part I:

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 (0.65 for preliminary API)

$K_v$ = Viscosity correction factor (Iterated based on Re)

4. Gas/Vapor Flow and Sizing

When the HP fluid is a gas/vapor, the mass flow rate ($W$) across the rupture and the required PRV area are calculated using the appropriate API 520 gas equations based on critical or subcritical flow conditions:

A = \frac{W}{C \cdot K_d \cdot P_1 \cdot K_b \cdot K_c} \sqrt{\frac{T Z}{M}} \quad \text{(Critical)}

Where $C = 520 \sqrt{k \left( \frac{2}{k+1} \right)^{(k+1)/(k-1)} }$.

For Subcritical Flow: The constant $C$ in the equation above is replaced by $735 \cdot F_2$.
For Rupture Flow ($W$): The mass flow rate escaping through the broken tube is calculated using this exact same critical/subcritical logic, but utilizing the rupture area ($A_r$) instead of the valve area ($A$).

References

API Standard 521: Pressure-relieving and Depressuring Systems (6th Ed, Sec 4.4.8).
API Standard 520 Part I: Sizing, Selection, and Installation of Pressure-Relieving Devices.
ASME Boiler and Pressure Vessel Code (Section VIII): Rules for Construction of Pressure Vessels.