# Assessing Pressure Relief Needs

## Evaluating thermal expansion and overpressure protection.

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t = pipe wall thickness (inches [in.]).
S = maximum allowable stress per code (psi).
E = pipe joint efficiency (dimensionless).
D = outside diameter of the pipe (in.).
Y = factor = 0.4 for pipe less than 900°F.

For 2-in. carbon-steel pipe (Schedule 40 SA-53, Grade B electric-resistance-welded [ERW]), the maximum design pressure (P) can be calculated by:

(2)

Equation 2 accounts for 12.5 percent of mill under-run, an Ej (joint efficiency) of 0.85 for ERW (nonseamless) pipe, a corrosion allowance of 1/16 in., and 20 percent overpressurization resulting from occasional variance. Because trapped fluids usually are associated with batch or transfer systems, which operate a lower velocities, a corrosion/erosion allowance of 1/32 in. generally is appropriate. Therefore: P = 1,850 psig, which accounts for a 1/32-in. corrosion allowance. For 2-in. stainless-steel pipe (Schedule 40S SA-312, Grade 304L ERW) with no corrosion allowance, P = 2,860 psig.

This usually dictates that some other component must determine the system’s design pressure, including:

Block valves. A 1,000-lb.-rated threaded-end ball valve has a maximum working pressure of 1,000 psig up to 100°F and derates with temperature primarily because of its elastomeric seat material. However, small nonflanged valves can be procured at higher ratings (e.g., 2,000 psig).

Instrumentation. Usually only instruments with bellows, diaphragms or other thin metallic parts need be considered during system design pressure determination. Generally, pressure gauges have burst pressures greater than 2,000 psig, although needle damage will occur at lower pressures. On the other hand, a temperature switch with a small dead-band can have a pressure rating of only 100 psig.
Fittings. Forged elbows, couplings and other fittings manufactured to ASME B16.11 for piping systems are specified at an ASME Class 2000 minimum and will not be the weakest component.

#### Overpressurization scenarios

High-heat-flux systems. API RP 520 and 521 standards discuss in detail 16 bases for overpressurization for pressure vessels and storage tanks. Although they are written for process equipment, some of the concepts can be applied to piping systems.

Thermal expansion of a trapped liquid is discussed only briefly in API RP 520 and 521. The standards are written mainly for equipment such as heat exchangers, which have large heat fluxes, but their concepts can be extended to similar high-heat-flux piping systems such as steam-traced lines, jacketed pipe and immersed cooling coils. API RP 520 suggests using the following formula to determine relieving capacity in gallons per minute (gpm):

(3)

where:
B = cubical expansion coefficient per degree Fahrenheit for the trapped liquid (°F-1).
H = heat transfer rate or flux (British thermal units [Btus]/hr).
G = specific gravity of the liquid (dimensionless).
C = specific heat of the trapped fluid (Btus/lb°F).

Cubical expansion coefficients are easy to determine, for any chemical, as long as the density of the fluid is known at the initial and final temperature. The thermal expansion coefficient (B) can be calculated by:

(4)

where:
Bavg = average cubical expansion coefficient.
n2 = specific volume of the liquid at t2.
n1 = specific volume of the liquid at t1.
t2 = final fluid temperature.
t1 = initial fluid temperature.
Therefore, for water heated from 60°F to 110°F:

B = 0.00017°F-1

Other useful coefficients are provided in Table 1.

For high-heat-flux systems, the decision is not whether a PRV should be installed, but what size the PRV should be. A ¾-in. x 1-in. PRV should handle any trapped fluid with a vapor pressure that remains below the PRV’s set pressure (i.e., the fluid does not flash).

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