Assessing Pressure Relief Needs

Evaluating thermal expansion and overpressure protection.

By Chip Eskridge, P.E.

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However, if the temperature of the heat source is above the boiling point of the trapped fluid at the PRV’s set pressure, vaporization will prevail. An energy balance across the trapped fluid’s boundary will determine the necessary relieving rate.  The PRV should be sized by:

(5) 

where:

 Wcold = PRV’s relieving rate in lb/hr.
 Qhot = heat input by the hot fluid in Btus/hr.
 DHvcold = heat of vaporization of the cold fluid in Btus/lb at the PRV’s set pressure.

Therefore, a Tubular Exchanger Manufacturers Association (TEMA) 28-240 heat exchanger with a rated duty of 10 x 106 Btus/hr, trapped water on the cold side, a PRV set at 150 psig and a hot-side temperature of at least 365°F would generate:

(6) 

Therefore, a 2J3 or a 3K4 PRV would be selected. Slight variations exist in the nozzle sizes of PRVs offered by various manufacturers. A word of caution: As the relieving fluid flashes from liquid to steam through the nozzle, two-phase flow will occur. Simple sizing of the nozzle for single-phase flow might provide erroneous results, so the engineer should investigate sizing methodologies to handle this scenario, such as those covered in API RP 520.

Low-heat-flux systems.Overpressurization of low-heat-flux systems (e.g., from solar heating) is much harder to calculate accurately. Even API RP 520 and 521 suggest Equation 3 does not apply. Factors affecting the calculation include:

Seat leakage. A block valve’s seat can leak, and such leakage is allowed by ASME standards.9  This leakage curtails the rise in pressure.

Shading effects. Piping can be exposed to any combination of light, which makes it difficult to determine actual heat flux.

Nonisothermal fluids. Viscous fluids (1,000 centipoise) such as polymers generally do not conduct heat very well, so heating and expansion of the fluid are dampened. Also, polymers have a complex molecular geometry; therefore, they might compress better than a simple molecule.

Piping layout. A piping system usually has high points that will prevent the system from filling completely with liquid or long instrument sensing lines that entrap gases such as air or nitrogen. This small vapor space will act as a pressure absorber, reducing ultimate pressure.

Administrative procedures. Based on the sequence in which block valves are closed, fluids can drain partially from the system, creating a small vapor space.

Protection by design. Piping systems designed with heavy-rated components withstand higher pressures.

For piping systems in which isothermal conditions can be assumed and having a layout that does not lend itself to trapping noncondensables, a quick rule-of-thumb has been suggested that is based on the ratio of the fluid’s thermal expansion coefficient and its liquid compressibility.  For water, the value determined through the following equation would be used to determine pressure rise:


(7) 
where:
 B = cubical thermal expansion coefficient of the fluid (°F-1).
 ß = liquid compressibility (vol./vol. atm.-1).

However, this equation can lead to erroneous results because it does not account for the elasticity of the pipe. A more rigorous formula recently has been suggested.  It states:
 
(8) 

where:
 E = modulus of elasticity of pipe (psi).
 K = bulk modulus of liquid (psi) = 1/ß.
 n = Poisson’s Ratio (dimensionless).
 aL = linear thermal expansion coefficient of liquid (in./in./°F) equal to 1/3 the cubical thermal expansion coefficient (B).
 aP = cubical thermal expansion coefficient of pipe (in./in./°F) equal to 1/3 the cubical thermal expansion coefficient (B).

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