t = wall thickness of pipe (in.).
Di = inside diameter of pipe (in.).
T = temperature rise of the trapped liquid (°F).
P = pressure rise of the trapped liquid resulting from T rise (psig).
Equation 8 considers the elasticity of the pipe, but assumes isothermal fluid temperature. Other methods for protecting low-heat-flux systems from thermal expansion involve the use of hydropads or compensators.14 However, these devices can be much more expensive than PRVs and have their own periodic testing requirements. They offer an advantage primarily in situations in which a discharge collection system such as a scrubber or a flare is not available.
Compressibility of liquids
Although a fluid’s thermal expansion has a stronger influence in determining ultimate pressure than does a fluid’s ability to compress, Equation 8 shows that the ultimate pressure is indeed a function of the pipe’s elasticity and the fluid’s compressibility (or elasticity). Because liquid molecules are spatially farther apart than the molecules in solid matter, a liquid’s compressibility (or lack of) plays a bigger role than the pipe’s elasticity in determining the final pressure.
Analyses show that for 2-in. Schedule 40 carbon-steel or stainless-steel pipe, trapped water will reach an ultimate pressure of 1,200 psig with only a 30°F temperature rise or 40 psi/°F, not the 50 psi/°F suggested by Equation 7. Typical compressibility values are given in Table 2.
Table 2 shows a strong correlation between the relative compressibility of the liquid and the molecule’s geometry. It stands to reason that the lowest compressibility values in Table 2 are for elemental mercury and water. Straight-chain molecules appear to be much more compressible than aromatic compounds of similar molecular weight and composition. Therefore, one could draw the conclusion that long-chain polymers compress very well under pressure, although no data were collected to support this theory. A word of caution: Liquid compressibility varies over a wide range, and no substitute can replace experimental data.
The engineer should be overly cautious when making PRV determinations in situations in which the handled fluid potentially could impact human health, cause severe environmental consequences or bring about a large economic impact. Furthermore, caution should be used with systems having a design that cannot be compared to similar piping systems.
Overpressurization resulting from thermal expansion is unlikely to happen in a system with a high design pressure or in pipe runs under 100 feet. However, for low- to moderate-pressure systems located outside in direct sunlight, with pipe runs greater than 100 feet and operating as a batch system (often isolated), engineers should provide PRVs in piping systems if the fluid has a low boiling point (i.e., is cryogenic), regardless of pipe length; is a hazardous fluid; or is part of a large-volume system.
The most accurate formula takes into account the thermal expansion of the pipe and the relative compressibility of the fluid. However, the value of operating experience far outweighs that of quantitative analysis. Thermal relief of high-heat-flux systems should be sized based on vaporization of the trapped fluid, not on expansion. A simple energy balance around the trapped fluid will determine the vapor generation rate and, therefore, the appropriate PRV size, although the effect of two-phase flow should be considered.
1. ASME B31.3, Process Piping, 1999, p. 11.
2. Woods and Baguley. Practical Guide to B31.3, 5th Ed., p. 7.
3. ASME B31.3, Process Piping, Appendix F, 1999.
4. API RP 520, Part 1, "Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries," 2000.
5. API RP 521, "Guide for Pressure-Relieving and Depressuring Systems," 1997.
6. ASME B31.3, Process Piping, 1999, p. 13
7. ASME B16.5, Pipe Flanges and Flange Fittings, 1996.
8. United Electric. Process Measurement and Contol,D Version, p. 19.
9. ASME B16.34, "Valves ¾ Flanged, Threaded, and Welding End," 1996.
10. Wong. "Safer Relief Valve Sizing," Chemical Engineering, May 1989, p. 137.
11. Bravo and Beatty. "Decide Whether To Use Thermal-Relief Valves," Chemical Engineering Progress,December 1993, p.35.
12. Brahmbhatt. "Are Liquid Thermal-Relief Valves Needed?" Chemical Engineering,May 14, 1984, p. 69.
13. Copenhaver, Coppari and Rochelle. "Forestall Pipe Burst," Chemical Engineering,January 2001, p. 84.
14. Boteler. "Save Pipes from Bursting with a Compensator," Chemical Engineering,December 1998, p. 98.
Eskridge is a principal engineer with Jacobs, Louisville, Ky. He can be reached at email@example.com or (502) 339-7006.