Diameter Basis for Rupture Disk KR

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Diameter Basis for Rupture Disk KR

Monday, October 10, 2016

ASME Section VIII §UG-127(a)(2)1 indicates that the relieving capacity of a rupture disk used independently (that is, not on the inlet or outlet of a pressure relief valve) can be determined based on one of two methods:  the flow resistance method or the coefficient of discharge method.  For the flow resistance method, two additional options are presented based on the calculation methodology used:  nozzle flow equations or piping flow equations.

To employ the nozzle flow equations for the flow resistance method, one needs a discharge coefficient and an effective cross-sectional area available for flow.  UG-127(a)(1)(c) specifies the use of a discharge coefficient of 0.62, and indicates that “the area A in the theoretical flow equation shall be the minimum net flow area50 as specified by the rupture disk device Manufacturer.”  Note 50 defines the minimum net flow area [MNFA]:

The minimum net flow area is the calculated net area after a complete activation of the rupture disk or pin device with appropriate allowance for any structural members which may reduce the net flow area through the device. The net flow area for sizing purposes shall not exceed the nominal pipe size area of the rupture disk device.

To employ the pipe flow equations for the flow resistance method, one needs a derating factor and an equivalent velocity head factor.  UG-127(a)(2) specifies the use of a derating factor of 0.90 or less, and indicates that “This analysis shall take into consideration the flow resistance of the rupture disk device…”, and indicates the use of the “…certified flow resistance51 KR for the rupture disk device…”  Note 51 defines the certified flow resistance:

The certified flow resistance KR is a dimensionless factor used to calculate the velocity head loss that results from the presence of a nonreclosing pressure relief device in a pressure relief system.

When performing pipe flow calculations, the equivalent velocity head loss factor is associated with a specific diameter in the piping system.2, 3, 4, 5  For systems with a constant cross-sectional area, this diameter is easy to specify; however, for systems with varying cross-sectional area, one must indicate the diameter for which the equivalent velocity head loss factor is associated.6

From this perspective, an interesting question arises as to the diameter to employ when using the pipe flow equations for the flow resistance method to calculate the relief capacity of a rupture disk, specifically for cases where the minimum net flow area is noticeably different than the cross-sectional area of the inlet pipingShould the diameter associated with KR be specified based on the MNFA?

ASME Section VIII UG-127 and UG-131 do not provide a explicit answer to this question, and a search of the ASME code interpretations7 yielded no pertinent results; however, based on our further research, the answer is “no”.  The key to understanding our assertion lies in the methodology for determining the KR factor in the first place, as detailed in the ASME Performance Test Code for Pressure Relief Devices.8

PTC-25 Figure 3-9-1 shows the test rig recommended for use in testing nonreclosing pressure relief device flow resistance, §5-5.7 provides the calculation methodology itself, and Test Report Form 5-5.7 is used for computing the results of the analysis.  In the PTC-25, the calculation of KR is clearly based on the inner diameter of the piping of the test rig attached to the rupture disk device.  As a result, any effects of resistance to flow that are associated with the rupture disk having a MNFA that is different than the cross-sectional area of the pipe attached to the rupture disk (which we specifically take as the inlet pipe size) are already accounted for in the calculation of the certified KR factor.

Excerpt from ASME PTC-25 Figure 3-9-1 [8] (purposefully truncated to fit space)

Excerpt from ASME PTC-25 Form 5-5.7 [8]

[1] American Society of Mechanical Engineers. “2010 ASME Boiler & Pressure Vessel Code, 2011a Addenda, Section VIII, Division 1 – Rules for Construction of Pressure Vessels”. Jul 2011; New York: ASME.

[2] Benedict RP. Fundamentals of Pipe Flow. 1980; New York: John Wiley & Sons.

[3] Darby R. Chemical Engineering Fluid Mechanics. 2001; Boca Raton: CRC Press.

[4] Tilton JN. “Fluid and Particle Dynamics”. In Perry RH and Green DW. Perry’s Chemical Engineers’ Handbook (pp. 6.1-6.54). 1997; New York: McGraw Hill.

[5] Hooper WB. “The Two-K Method Predicts Head Losses in Pipe Fittings”. Chemical Engineering. 24 Aug 1981: 96-100.

[6] Hooper WB. “Calculate Head Loss Caused By Change in Pipe Size”. Chemical Engineering. 7 Nov 1988: 89-92.

[7] American Society of Mechanical Engineers. ASME Interpretations Database, Standard Designation “BPV Section VIII Div 1”, Subject “UG-127”. Retrieved September 28, 2016 from ASME: https://cstools.asme.org/Interpretation/SearchInterpretation.cfm

[8] American Society of Mechanical Engineers. “ASME PTC 25-2014, Pressure Relief Devices, Performance Test Code”. 17 Jun 2014; New York: ASME.

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