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Validated sizing rule against chatter of relief valves during gas service
Journal of Loss Prevention in the Process Industries 14 (2001) 261–267 www.elsevier.com/locate/jlp
Validated sizing rule against chatter of relief valves during gas service J. Cremers, L. Friedel *, B. Pallaks Technische Universitat Hamburg, Department of Fluidmechanics, Eisendorfer Strasse 38, 21073 Hamburg, Germany
Abstract Spring loaded relief valves are commonly used for protecting pressure loaded vessels, piping, etc. against overpressure. If the relief valve is installed improperly it may chatter while discharging. This behaviour is defined as an extremely rapid full opening and closing of the valve. The associated mechanical loads can damage the piping, equipment and the relief valve with the result of loss of pressure relief protection, undirected process fluid release, danger of fire and/or explosion, etc. In the technical guidelines and in the literature, sizing rules for the proper installation of relief valves are recommended. Most commonly applied is the 3% pressure loss rule for the allowable inlet pipe pressure drop as recommended in the API RP 520 (API RP 520: Sizing, selection and installation of pressure-relieving systems in refineries, 1993) or AD A2 (AD-Merkblatt A2: Sicherheitseinrichtungen gegen Drucku¨berschreitung—Sicherheitsventile, 1993). Another recommendation is based on the transmission time and the amplitude of the pressure waves generated by the abrupt safety valve opening and closing. In addition to these elementary rules, sophisticated computer codes for numerical simulation of the valve behaviour during the discharge process need to include the interrelationship between the flow in the pipe and that in the safety valve. Experiments have been performed with the objective of checking the validity of the rules. Based also on results taken from the literature a modified pressure surge sizing method is recommended. The usefulness of supplementary measures to establish in industrial installations a posteriore valve stability, e.g., by increasing the inlet pipe diameter, reducing the safety valve lift or installation of an oscillation damper are also evaluated. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Relief valve; Gas flow; Valve chattering; Compression wave; Sizing rule; Oscillation damper
1. Design rules to avoid chatter In the literature, criteria are described for the different assumed reasons for the valve disc oscillation. The most commonly applied rules in practice are shown in Table 1. In the 3% loss rule, oscillations (of the open valve) induced as a consequence of a too high inlet pipe pressure loss are assumed. In this case, sizing of the valve inlet piping has to be performed in such a way that the pressure loss in the inlet piping, calculated with a presumed stationary flow through the fully opened valve, should not exceed 3% of the set pressure. Validation experiments by Kastor (1986) and Schmidt and Giesbrecht (1997) seem to allow for the conclusion that this rule is conservative and that the allowable pressure loss
* Corresponding author. Tel.: +49-40-77183052; fax: +49-4077182573.
in the inlet pipe may be up to 8 or 12% in the case of a valve reseating pressure difference of about 10% and moderate pressure increase rates. Indeed, in these experiments among others, the pressure drop was generated locally by a flow restriction in the inlet pipe, an arrangement which is not common. Additionally, the actual flow losses were introduced in the recalculation instead of the values, which would be obtained when using the recommended fitting loss coefficients. The sizing of pressure relief systems against chatter can be performed by numerical simulation of the flow during the transient pressure release process. While the 3% pressure loss rule is independent of the relief valve type and behavior, this numerical simulation also requires specific information on the valve characteristics. For example, the fluid force induced by the flow acting on the safety valve disc is required and may have to be determined by additional experiments. Also, although a variety of codes exists, no standard for quantification of valve stability is available. A practical approach for
0950-4230/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 0 - 4 2 3 0 ( 0 0 ) 0 0 0 5 4 - 1
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Nomenclature a h hmax t A AE C D L Lallow P P0 Pa PS S Z a z l ⌿
Isentropic speed of sound Valve lift Constructional limited valve lift Time Flow cross section Inlet pipe area Opening pressure difference Diameter Piping length Allowable inlet line length Pressure Set pressure Back pressure Reseating pressure Reseating pressure difference Real gas factor Actual discharge coefficient Isentropic coefficient Pressure loss coefficient Wall friction coefficient Density Discharge function
Indices 1 A o E U w
End of discharge pipe Discharge pipe Safety valve nozzle/seat Inlet line Surrounding Wave
Table 1 Characteristics of sizing rules to avoid full lift safety relief valve chatter and deduced allowable valve inlet pipe length Sizing rule
Oscillation origin
Allowable inlet pipe length
冘
AE Pa DE Flow induced , )⫺ zi) (zallow( inlet pipe aA0 P0 lpipe friction Equilibrium AE Pa 4 mvalvea2sound K ( , ) between spring p(Popen−Preseat)D0 DT aA0 P0 and flow force, unstable against small disturbances Pressure surge, Expansion wave ⌬P∗allow AE 1 P0−Pa t e.g., FDBR 153, in inlet pipe 2√2⌿ aA0√r √P0 open Fo¨ llmer (1992) and Frommann (1996) 3% Pressure loss API RP 520/AD A2 KDT number by B. Fo¨ llmer from Stability Diagram
冪
using the results of such a numerical simulation is presented by Fo¨ llmer (1981) in the form of a valve stability diagram based on the so called KDT number as a result of a parametric study, Fig. 1. The valve opening and closing is expected to be stable for a value equal to or less than the allowable KDT number. It is a function of the ratio of the inlet pipe cross section and the effective valve relief area, the KAD number, which stands for the sum of the opening and reseating pressure difference related to the set pressure, and the quotient of the back pressure and the set pressure. According to the so-called pressure surge criterion, a valve is expected to operate in a stable manner, resp., not to chatter if twice the transmission time tw of the expansion wave in the inlet pipe, generated by the abrupt valve opening, is shorter than the total opening time topen of the valve. In this case the stable valve opening will be supported by the returning compression wave, produced by reflection of the initial expansion wave at the vessel inlet. With the assumption that the related Jou-
J. Cremers et al. / Journal of Loss Prevention in the Process Industries 14 (2001) 261–267
Fig. 1.
263
Allowable KDT number as a function of back pressure ratio, effective cross sectional area quotient and KAD number.
kowsky pressure decay according to Joukowsky (1898) is a linear function of the valve opening time, i.e., ⌬PJouk 2tw ∗ ⬍⌬Pallow with 2tw⬍topen and tw⫽a/L (P0−Pa) topen
(1)
Here, a means the effective velocity of sound, L the inlet pipe length and ⌬P∗allow the allowable relative pressure decay. In the literature, there are various forms of this basic equation, differing by the definition of the opening time of the valve and in the magnitude of the allowable relative pressure decay caused by the expansion wave. Originally, Fo¨ llmer (1992) assumed an allowable relative pressure decay of 20 and 40% for gas and liquid flow respectively. The value valid for gas flow was reduced by Frommann (1996) to the actual reseating pressure difference on the basis of further experiments. In FDBR 153 (1989), on the other side, a 10 representing a 20% pressure decay for the case of a valve reseating pressure difference of maximally 5 and 10% is recommended for steam and water and the opening time is fixed to a period of 0.02 s. With a view to validating these methods by a systematic variation of the primary design parameters it is obvious from Table 1 that all the methods include the effective cross sectional area ratio Ae/(aA0), the back pressure ratio Pa/P0 and the reseating pressure difference S so besides changing these an allowable inlet line length can be calculated and compared with that measured. It is defined as that length, for which the safety valve does not chatter under all test conditions.
2. Testing procedure The experiments have been performed with air, carbon dioxide gas and helium with a view to checking the
effect of the respective properties of density, isentropic velocity of sound, resp., isentropic coefficient on the chatter behaviour and, thus, the allowable inlet line length. The test rig is shown in Fig. 2. It basically consists of a storage- and a pressure vessel, inlet and outlet piping, the safety valve and a back pressure regulator. The gas flows from the storage vessel into the pressure vessel, simulating the equipment to be protected against overpressure, and generates a pressure increase. If the set pressure of the valve is reached, the valve will open and release gas. This test is carried out in a systematic way for a given inlet line length and several pressure rise velocities. If the valve does not chatter in these tests, the inlet pipe length is increased in steps of 0.1 m and the procedure is, in each case, repeated until oscillations occur. On account of oscillations, the transient pressure in the vessel and in the pipe as well as the safety valve lift have been recorded. The maximum inlet pipe length at which definitely no chatter is observed is the experimentally determined allowable inlet pipe length.
3. Calculated and experimental allowable inlet line length In Table 2 a selection of the calculated and experimental allowable inlet line lengths is included for three types of full lift safety valves DN25/40, several combinations of the experimental parameters and gases. Three main results are evident: No sizing criterion is valid under all conditions because at least one experiment can be identified, in which the predicted allowable inlet pipe length is distinctly larger than the experimental one. The experimentally determined allowable inlet line length for otherwise identical conditions is shortest for carbon dioxide and longest for helium. This tendency coincides with the predictions according to the pressure
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Fig. 2.
Experimental set up for identification of the allowable inlet pipe length of a full lift safety valve.
Table 2 Experimental and predicted allowable inlet pipe length for full lift safety valves without bellows in air, carbon dioxide and helium flow Safety Inlet pipe Gas valve diameter DN25/40 DN
Experimental parameter
AE aA0
P0−Ps P0
Pa P0
P0
[-]
[%]
[%]
[bara]
A 25
B
25 40 25
C
40 25
Air Helium CO2 Air Air CO2 Air Air
Allowable inlet pipe length [m]
1.92
4.54 2.28 2.28 5.38
Exp.
New method
3% Pressure surge rule Pressure loss rule
KDT number
FDBR
Fo¨ llmer
From.
6.1 8.3 10.5 9.5 16.6 6.1 7.3 5.4 5.3 11.1
6.8 6.0 25.6 26.3 25.0 7.1 9.1 9.0 10.5 7.8
14.5 16.7 3.9 3.8 4.0 13.0 11.0 11.1 9.5 12.8
0.4 0.4 1.9 ⬎2.6 1.7 1.2 0.6 0.45 1.4 ⬎3.3
0 0 0 0 0 3.52 0.007 0.03 5.13 1.92
0.93 1.27 1.21 2.91 1.0 2.17 1.27 1.03 2.01 3.42
1.77 1.78 1.21 3.07 1.01 3.57 1.75 1.42 4.02 3.42
0.00 0.74 0.63 1.47 0.83 0.63 0.52 2.73
1.14 1.03 2.02 5.87 1.32 (1.34) 1.87 1.5 (2.23) 1.98
0.27 0.26 0.44 1.13 0.36 0.64 0.34 0.28 0.84 0.65
16.0
5.7
17.5
⬎3.3
1.99
3.51
3.51
3.42
(1.46)
0.62
4.37
surge criterion and the numerical simulation, but not with those obtained by applying the 3% pressure loss rule. The allowable inlet line length decreases with a higher back pressure ratio. This tendency can be experimentally resolved by increasing the back pressure while retaining a constant set pressure or vice versa, a constant back pressure and a lower set pressure. The first case is much more likely to produce chatter than the latter. Indeed, this tendency is only reproducible by numerical simulation. In view of the industrial demand for a reliable shortcut sizing criterion a modification or extension of one of the well-introduced sizing methods seems to be convenient and straightforward. It has already been shown by Botros (1997) with pilot operated safety valves and recently by the authors Cremers and Friedel (1998) for the case of full lift safety valves, that during chattering a standing wave establishes in the inlet pipe between
the valve and the pressure vessel, if it is free of flow obstructions and attains a sufficiently long length — a common arrangement in practice — the pressure surge criterion seems to be preferable as a basic model, though pipe flow friction may also be considered in an improved sizing criterion. 4. Improved sizing criterion The independent or primary design parameters in the pressure surge criterion are the effective cross sectional Pa AE , the back pressure ratio and the gas area ratio aA0 P0 density, all of which are determined by the process safety design case. The subsequently named modifications, introduced as submodels, are based on rational deliberations and experimental evidence, Cremers and Friedel (1999). As an example the maximum allowable
J. Cremers et al. / Journal of Loss Prevention in the Process Industries 14 (2001) 261–267
pressure decay ⌬P∗allow is fixed to the minimum value of the reseating pressure difference of 5% as allowed for popping safety valves in DIN 3320 (1984). The opening time of a valve is generally not accessible. From informal measurements of the valve suppliers it can be qualitatively deduced that the opening time decreases with a higher pressure difference across the valve and increases for larger valves due to the greater inertia of the moved mass. Based on these measurements and from data in EPRI PWR (1982) the relationship accounting for these tendencies for gas duty is:
冢
topen[s]⫽ 0.015⫹0.02
冣
冑D /DN15 0
2/3
(P0/PU) (1−PU/P0)2
·(h/hmax)0.7
with D0⬎DN15 and hⱕhmax
(2)
Here h denotes the actual lift and for reasons of simplicity, as well as provision, PU means the ambient pressure, even in the case of a substantial back pressure on the safety valve when installed or operated. The pressure loss in the inlet line is simply taken into account by a discharge coefficient for the mass flow as is usual in safety valve sizing. It is defined according to
aAe⫽
冪
1
1+
冘 冘 zi+
i
liL/Dinlet
with 0.57ⱕaAe⬍1
(3)
i
where li and zi are the usual pressure loss coefficients. The final dimensional equation for the allowable inlet line length on the basis of the pressure surge criterion and extended by the effect of the dissipation, etc. can be written as Lallow[m]⫽
冢
0.05 AEaAe 1 P0−Pa · 2冑2⌿ aA0 冑r 冑P0
· 0.015⫹0.02
冑D /DN15 0
(P0/PU)2/3(1−PU/P0)2
(4)
冣
(h/hmax)0.7
with D0⬎DN15, hⱕhmax, topen⬎2tw and tw⫽a/L
265
measured allowable length in all cases is underpredicted while still reasonable and technically realizable results are obtained, also if the results reported in EPRI PWR (1982) are recalculated according to Cremers (2000). With respect to the data by Kastor, however, the allowable inlet line length in the case of high local pressure losses caused by a restriction in the inlet line are overpredicted following Cremers (2000). Indeed, it is questionable if this arrangement is representative of industrial practice. Also, on following the recommendation in AD A2 (1993) a cross sectional area in the inlet line smaller than the valve inlet flange area is not considered as good engineering practice. The modified pressure surge criterion can be straightforwardly applied because all parameters are readily available for sizing and additional specific measurements are not necessary. The method has only been validated for gas flow. When applied to liquid flow, conservative inlet line lengths are expected in view of the relatively longer valve opening times. In view of the physical fundamentals being included in the modified criterion it should be possible to moderately extrapolate beyond and interpolate between the experimental range of the underlying data. An indication for this is the successful reproduction of the EPRI and Du Pont data. When sizing for the case of lift reduced safety valves, however, it is necessary that the valve supplier ensures the correct functional behavior. Under this condition a smaller valve reseating pressure difference can occur and the original stable flow field around the valve disc is adversely effected. To calculate the allowable inlet line length for a safety valve with adjacent outlet line, the established back pressure in the valve outlet is required. It can be obtained by starting a calculation with the pressure at the end of the outlet pipe P1 which is given by
冉 冊冑
P1⫽P0⌿a
D0 D1
2
(+1)冪Z 2
Z1
(6)
0
The back pressure in the outlet of the valve is obtainable by calculating in the counterflow direction to the valve outlet following Goβlau and Weyl (1994), either by using a numerical procedure as proposed by Ba¨ umer and Friedel (1996), even in the case of no multiple critical flow condition downstream of the valve in the discharge line according to Seynhaeve and Giot (1996), or following Pa⫽
(5) P0
In this correlation, ⌿, the so called discharge function accounting for the critical flow state is introduced. As is evident from Table 1 with the modified equation, the
(7)
冪冉P 冊 ⫹2冉冘lL /D ⫹冘z ⫹ ln 冉P 冊冊 ⌿ a 冉D 冊 Z . P1
2
2
A
0
A
pa
i
i
1
2
2
D 0 4Z 1 1
0
with the empirically imposed pressure ratio restriction for unbalanced safety valves of Pa/P0ⱕ10%. Where the
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length LA and the diameter DA refer to the downstream piping. From experiments by Ehrhardt (1997) and Kastor (1986) it can also be deduced that in the case of safety valves without bellows the back pressure should not exceed some 10% of the set pressure as is also recommended in API RP 520. If the back pressure is higher an oscillation damper should be installed to maintain valve stability. The usefulness of such an item is subsequently discussed.
5. Valve stability in case of damping A check of alternative measures to maintain a posteriore valve stability, e.g. by increasing the inlet pipe diameter, reducing the safety valve lift, installation of an oscillation damper or using a safety valve with bellow leads in most cases to the installation of an oscillation damper as the most effective, reliable and economic method Cremers and Friedel (1999). As an example of the achieved valve stability the opening and closing behavior of the valve A according to Table 2, with an allowable inlet line length for air flow of 0.4 m is shown in Fig. 3. The valve is now equipped with an oscillation damper and an increased inlet line length of 3.1 m. Though a longer inlet line and a relative back pressure of about 30% prevailed, the valve operation is absolutely stable. The basic elements of the installed oscillation damper are shown in Fig. 4. When the safety valve lift increases by opening, oil is forced by the piston to flow through a one-way flow restriction in the transmission line and so mechanical energy is dissipated. If the lift would decrease the oil can flow backward without restriction, hence, only the opening movement of the valve is damped. The main effect of the oscillation damper to maintain valve stability is supposed to rely on an extension of the opening time of the safety valve. As a result the amplitude of the associated expansion wave would be reduced following Cremers and Friedel (1999).
Fig. 4.
Elements of the full lift safety valve oscillation damper.
6. Conclusion
A comparison between measured and predicted inlet line lengths used in practice as a criterion for a stable safety valve opening and closing behaviour revealed that none of the sizing rules are adequate under all conditions during gas flow. As a consequence, a new sizing method based on the pressure surge criterion is proposed. It is validated with the results of new experiments and with those of others available from the literature for safety valves without bellows with an inlet flange diameter greater than DN15 and in case of a discharge line downstream of the valve, when the back pressure does not exceed 10% of the set pressure. An oscillation damper is an effective measure to maintain valve stability when the predicted inlet pipe length or the back pressure limit is exceeded in an industrial installation.
Fig. 3. Transient pressure and lift of a slightly damped valve with an inlet line length of 3.1 m and an excessively high relative back pressure during air flow.
J. Cremers et al. / Journal of Loss Prevention in the Process Industries 14 (2001) 261–267
References API RP 520: Sizing, selection and installation of pressure-relieving systems in refineries, 1993. AD-Merkblatt A2: Sicherheitseinrichtungen gegen Drucku¨ berschreitung - Sicherheitsventile -, 1993. Ba¨ umer, T., & Friedel, L. (1996). Auslegung von Abblaseleitungssystemen fu¨ r Gasstro¨ mungen mit multiplen kritischen Stro¨ mungsquerschnitten. 3R Intern., 35 (12), 713–719. Botros K. et al. (1997). Riser — Relief valve dynamic interactions. Attachm. 12th DIERS Users Group Meeting. Cremers, J. (2000). Auslegungsmethode zur Vermeidung von Schwingungen bei federbelasteten Vollhubsicherheitsventilen mit Zu- und Ableitung. Diss. Techn. Univ. Hamburg-Harburg. Cremers, J., & Friedel, L. (1998). Experimente zum Funktionsverhalten von Vollhubsicherheitsventilen bei Gasstro¨ mung. Vortrag Dechema Jahrestagungen, 2, 154. Cremers, J. & Friedel, L. (1999). Wirksamkeit konstruktiver Maβnahmen zur schwingungssicheren Installation von Vollhubsicherheitsventilen mit Zu- und Ableitung, Vortrag Dechema/GVC Arbeitsausschuβ Sicherheitsgerechtes Auslegen von Chemieapparaten, Frankfurt. DIN 3320, Teil 1: Sicherheitsventile, Sicherheitsabsperrventile, 1984. Ehrhardt, G. (1997). Durchfluβ und Funktion von Sicherheitsventilen bei Gegendruck in T. Lenzing, G. Ehrhardt, L. Friedel: Auslegung von Sicherheitsventilen samt Leitungen bei kompressibler Einphasen- und Zweiphasen-(Gas/Flu¨ ssigkeits)Stro¨ mung. BMBF Forschungsvorhaben 13 RG 9308.
267
EPRI PWR Safety and Relief Valve Test Program. NP-2628-SR, 1982. ¨ berpru¨ fung der Zuleitungen auf FDBR 153: Feder-Sicherheitsventile: U Druckschwingungen, 1989. Fo¨ llmer, B. (1981). Stro¨ mung im Einlauf von Sicherheitsventilen. Diss. RWTH Aachen. Fo¨ llmer, B. (1992). Die sichere Funktion bauteilgepru¨ fter Sicherheitsventile mit dem Einfluβ der Zufu¨ hrungsleitung. 3R Intern., 31 (7), 394–402. Frommann, O. (1996). Experimentelle und theoretische Untersuchung des dynamischen Verhaltens federbelasteter Vollhubsicherheitsventile bei anlaufender Stro¨ mung in der Zuleitung. Diss. Techn. Univ. Hamburg-Harburg. Goβlau, W. & Weyl, R. (1994). Stro¨ mungsdruckverluste und Reaktionskra¨ fte in Rohrleitungen bei Notentspannung durch Sicher¨ berwaheitsventile und Berstscheiben. Sonderdruck aus Techn. U chung 5/6/7-8/g (1989), 4. erga¨ nzte Auflage 1994. ¨ ber den hydraulischen Stoβ in WasserleiJoukowsky, N. (1898). U tungsrohren. Vero¨ ffentlichung der Kaiserlichen Akademie der Wissenschaften, Petersburg. Kastor, K. A. (1986). A dynamic stability model for predicting chatter in safety relief valve installations. Du Pont Eng Dept Rep., Accession No. 17131, Feb. 3. Schmidt, J., & Giesbrecht, H. (1997). Grenzen der sicheren Funktion von Vollhub-Sicherheitsventilen — Bewertung des 3% Druckverlust-Kriteriums (TRD 421/AD-A2). Chem.-Ing.-Tech., 69 (9), 1281. Seynhaeve, J.-M. & Giot, M. (1996). Choked flashing flow at multiple simultaneous locations. European Two-Phase Flow Group Meeting, Grenoble.
Validated sizing rule against chatter of relief valves during gas service J. Cremers, L. Friedel *, B. Pallaks Technische Universitat Hamburg, Department of Fluidmechanics, Eisendorfer Strasse 38, 21073 Hamburg, Germany
Abstract Spring loaded relief valves are commonly used for protecting pressure loaded vessels, piping, etc. against overpressure. If the relief valve is installed improperly it may chatter while discharging. This behaviour is defined as an extremely rapid full opening and closing of the valve. The associated mechanical loads can damage the piping, equipment and the relief valve with the result of loss of pressure relief protection, undirected process fluid release, danger of fire and/or explosion, etc. In the technical guidelines and in the literature, sizing rules for the proper installation of relief valves are recommended. Most commonly applied is the 3% pressure loss rule for the allowable inlet pipe pressure drop as recommended in the API RP 520 (API RP 520: Sizing, selection and installation of pressure-relieving systems in refineries, 1993) or AD A2 (AD-Merkblatt A2: Sicherheitseinrichtungen gegen Drucku¨berschreitung—Sicherheitsventile, 1993). Another recommendation is based on the transmission time and the amplitude of the pressure waves generated by the abrupt safety valve opening and closing. In addition to these elementary rules, sophisticated computer codes for numerical simulation of the valve behaviour during the discharge process need to include the interrelationship between the flow in the pipe and that in the safety valve. Experiments have been performed with the objective of checking the validity of the rules. Based also on results taken from the literature a modified pressure surge sizing method is recommended. The usefulness of supplementary measures to establish in industrial installations a posteriore valve stability, e.g., by increasing the inlet pipe diameter, reducing the safety valve lift or installation of an oscillation damper are also evaluated. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Relief valve; Gas flow; Valve chattering; Compression wave; Sizing rule; Oscillation damper
1. Design rules to avoid chatter In the literature, criteria are described for the different assumed reasons for the valve disc oscillation. The most commonly applied rules in practice are shown in Table 1. In the 3% loss rule, oscillations (of the open valve) induced as a consequence of a too high inlet pipe pressure loss are assumed. In this case, sizing of the valve inlet piping has to be performed in such a way that the pressure loss in the inlet piping, calculated with a presumed stationary flow through the fully opened valve, should not exceed 3% of the set pressure. Validation experiments by Kastor (1986) and Schmidt and Giesbrecht (1997) seem to allow for the conclusion that this rule is conservative and that the allowable pressure loss
* Corresponding author. Tel.: +49-40-77183052; fax: +49-4077182573.
in the inlet pipe may be up to 8 or 12% in the case of a valve reseating pressure difference of about 10% and moderate pressure increase rates. Indeed, in these experiments among others, the pressure drop was generated locally by a flow restriction in the inlet pipe, an arrangement which is not common. Additionally, the actual flow losses were introduced in the recalculation instead of the values, which would be obtained when using the recommended fitting loss coefficients. The sizing of pressure relief systems against chatter can be performed by numerical simulation of the flow during the transient pressure release process. While the 3% pressure loss rule is independent of the relief valve type and behavior, this numerical simulation also requires specific information on the valve characteristics. For example, the fluid force induced by the flow acting on the safety valve disc is required and may have to be determined by additional experiments. Also, although a variety of codes exists, no standard for quantification of valve stability is available. A practical approach for
0950-4230/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 0 - 4 2 3 0 ( 0 0 ) 0 0 0 5 4 - 1
262
J. Cremers et al. / Journal of Loss Prevention in the Process Industries 14 (2001) 261–267
Nomenclature a h hmax t A AE C D L Lallow P P0 Pa PS S Z a z l ⌿
Isentropic speed of sound Valve lift Constructional limited valve lift Time Flow cross section Inlet pipe area Opening pressure difference Diameter Piping length Allowable inlet line length Pressure Set pressure Back pressure Reseating pressure Reseating pressure difference Real gas factor Actual discharge coefficient Isentropic coefficient Pressure loss coefficient Wall friction coefficient Density Discharge function
Indices 1 A o E U w
End of discharge pipe Discharge pipe Safety valve nozzle/seat Inlet line Surrounding Wave
Table 1 Characteristics of sizing rules to avoid full lift safety relief valve chatter and deduced allowable valve inlet pipe length Sizing rule
Oscillation origin
Allowable inlet pipe length
冘
AE Pa DE Flow induced , )⫺ zi) (zallow( inlet pipe aA0 P0 lpipe friction Equilibrium AE Pa 4 mvalvea2sound K ( , ) between spring p(Popen−Preseat)D0 DT aA0 P0 and flow force, unstable against small disturbances Pressure surge, Expansion wave ⌬P∗allow AE 1 P0−Pa t e.g., FDBR 153, in inlet pipe 2√2⌿ aA0√r √P0 open Fo¨ llmer (1992) and Frommann (1996) 3% Pressure loss API RP 520/AD A2 KDT number by B. Fo¨ llmer from Stability Diagram
冪
using the results of such a numerical simulation is presented by Fo¨ llmer (1981) in the form of a valve stability diagram based on the so called KDT number as a result of a parametric study, Fig. 1. The valve opening and closing is expected to be stable for a value equal to or less than the allowable KDT number. It is a function of the ratio of the inlet pipe cross section and the effective valve relief area, the KAD number, which stands for the sum of the opening and reseating pressure difference related to the set pressure, and the quotient of the back pressure and the set pressure. According to the so-called pressure surge criterion, a valve is expected to operate in a stable manner, resp., not to chatter if twice the transmission time tw of the expansion wave in the inlet pipe, generated by the abrupt valve opening, is shorter than the total opening time topen of the valve. In this case the stable valve opening will be supported by the returning compression wave, produced by reflection of the initial expansion wave at the vessel inlet. With the assumption that the related Jou-
J. Cremers et al. / Journal of Loss Prevention in the Process Industries 14 (2001) 261–267
Fig. 1.
263
Allowable KDT number as a function of back pressure ratio, effective cross sectional area quotient and KAD number.
kowsky pressure decay according to Joukowsky (1898) is a linear function of the valve opening time, i.e., ⌬PJouk 2tw ∗ ⬍⌬Pallow with 2tw⬍topen and tw⫽a/L (P0−Pa) topen
(1)
Here, a means the effective velocity of sound, L the inlet pipe length and ⌬P∗allow the allowable relative pressure decay. In the literature, there are various forms of this basic equation, differing by the definition of the opening time of the valve and in the magnitude of the allowable relative pressure decay caused by the expansion wave. Originally, Fo¨ llmer (1992) assumed an allowable relative pressure decay of 20 and 40% for gas and liquid flow respectively. The value valid for gas flow was reduced by Frommann (1996) to the actual reseating pressure difference on the basis of further experiments. In FDBR 153 (1989), on the other side, a 10 representing a 20% pressure decay for the case of a valve reseating pressure difference of maximally 5 and 10% is recommended for steam and water and the opening time is fixed to a period of 0.02 s. With a view to validating these methods by a systematic variation of the primary design parameters it is obvious from Table 1 that all the methods include the effective cross sectional area ratio Ae/(aA0), the back pressure ratio Pa/P0 and the reseating pressure difference S so besides changing these an allowable inlet line length can be calculated and compared with that measured. It is defined as that length, for which the safety valve does not chatter under all test conditions.
2. Testing procedure The experiments have been performed with air, carbon dioxide gas and helium with a view to checking the
effect of the respective properties of density, isentropic velocity of sound, resp., isentropic coefficient on the chatter behaviour and, thus, the allowable inlet line length. The test rig is shown in Fig. 2. It basically consists of a storage- and a pressure vessel, inlet and outlet piping, the safety valve and a back pressure regulator. The gas flows from the storage vessel into the pressure vessel, simulating the equipment to be protected against overpressure, and generates a pressure increase. If the set pressure of the valve is reached, the valve will open and release gas. This test is carried out in a systematic way for a given inlet line length and several pressure rise velocities. If the valve does not chatter in these tests, the inlet pipe length is increased in steps of 0.1 m and the procedure is, in each case, repeated until oscillations occur. On account of oscillations, the transient pressure in the vessel and in the pipe as well as the safety valve lift have been recorded. The maximum inlet pipe length at which definitely no chatter is observed is the experimentally determined allowable inlet pipe length.
3. Calculated and experimental allowable inlet line length In Table 2 a selection of the calculated and experimental allowable inlet line lengths is included for three types of full lift safety valves DN25/40, several combinations of the experimental parameters and gases. Three main results are evident: No sizing criterion is valid under all conditions because at least one experiment can be identified, in which the predicted allowable inlet pipe length is distinctly larger than the experimental one. The experimentally determined allowable inlet line length for otherwise identical conditions is shortest for carbon dioxide and longest for helium. This tendency coincides with the predictions according to the pressure
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Fig. 2.
Experimental set up for identification of the allowable inlet pipe length of a full lift safety valve.
Table 2 Experimental and predicted allowable inlet pipe length for full lift safety valves without bellows in air, carbon dioxide and helium flow Safety Inlet pipe Gas valve diameter DN25/40 DN
Experimental parameter
AE aA0
P0−Ps P0
Pa P0
P0
[-]
[%]
[%]
[bara]
A 25
B
25 40 25
C
40 25
Air Helium CO2 Air Air CO2 Air Air
Allowable inlet pipe length [m]
1.92
4.54 2.28 2.28 5.38
Exp.
New method
3% Pressure surge rule Pressure loss rule
KDT number
FDBR
Fo¨ llmer
From.
6.1 8.3 10.5 9.5 16.6 6.1 7.3 5.4 5.3 11.1
6.8 6.0 25.6 26.3 25.0 7.1 9.1 9.0 10.5 7.8
14.5 16.7 3.9 3.8 4.0 13.0 11.0 11.1 9.5 12.8
0.4 0.4 1.9 ⬎2.6 1.7 1.2 0.6 0.45 1.4 ⬎3.3
0 0 0 0 0 3.52 0.007 0.03 5.13 1.92
0.93 1.27 1.21 2.91 1.0 2.17 1.27 1.03 2.01 3.42
1.77 1.78 1.21 3.07 1.01 3.57 1.75 1.42 4.02 3.42
0.00 0.74 0.63 1.47 0.83 0.63 0.52 2.73
1.14 1.03 2.02 5.87 1.32 (1.34) 1.87 1.5 (2.23) 1.98
0.27 0.26 0.44 1.13 0.36 0.64 0.34 0.28 0.84 0.65
16.0
5.7
17.5
⬎3.3
1.99
3.51
3.51
3.42
(1.46)
0.62
4.37
surge criterion and the numerical simulation, but not with those obtained by applying the 3% pressure loss rule. The allowable inlet line length decreases with a higher back pressure ratio. This tendency can be experimentally resolved by increasing the back pressure while retaining a constant set pressure or vice versa, a constant back pressure and a lower set pressure. The first case is much more likely to produce chatter than the latter. Indeed, this tendency is only reproducible by numerical simulation. In view of the industrial demand for a reliable shortcut sizing criterion a modification or extension of one of the well-introduced sizing methods seems to be convenient and straightforward. It has already been shown by Botros (1997) with pilot operated safety valves and recently by the authors Cremers and Friedel (1998) for the case of full lift safety valves, that during chattering a standing wave establishes in the inlet pipe between
the valve and the pressure vessel, if it is free of flow obstructions and attains a sufficiently long length — a common arrangement in practice — the pressure surge criterion seems to be preferable as a basic model, though pipe flow friction may also be considered in an improved sizing criterion. 4. Improved sizing criterion The independent or primary design parameters in the pressure surge criterion are the effective cross sectional Pa AE , the back pressure ratio and the gas area ratio aA0 P0 density, all of which are determined by the process safety design case. The subsequently named modifications, introduced as submodels, are based on rational deliberations and experimental evidence, Cremers and Friedel (1999). As an example the maximum allowable
J. Cremers et al. / Journal of Loss Prevention in the Process Industries 14 (2001) 261–267
pressure decay ⌬P∗allow is fixed to the minimum value of the reseating pressure difference of 5% as allowed for popping safety valves in DIN 3320 (1984). The opening time of a valve is generally not accessible. From informal measurements of the valve suppliers it can be qualitatively deduced that the opening time decreases with a higher pressure difference across the valve and increases for larger valves due to the greater inertia of the moved mass. Based on these measurements and from data in EPRI PWR (1982) the relationship accounting for these tendencies for gas duty is:
冢
topen[s]⫽ 0.015⫹0.02
冣
冑D /DN15 0
2/3
(P0/PU) (1−PU/P0)2
·(h/hmax)0.7
with D0⬎DN15 and hⱕhmax
(2)
Here h denotes the actual lift and for reasons of simplicity, as well as provision, PU means the ambient pressure, even in the case of a substantial back pressure on the safety valve when installed or operated. The pressure loss in the inlet line is simply taken into account by a discharge coefficient for the mass flow as is usual in safety valve sizing. It is defined according to
aAe⫽
冪
1
1+
冘 冘 zi+
i
liL/Dinlet
with 0.57ⱕaAe⬍1
(3)
i
where li and zi are the usual pressure loss coefficients. The final dimensional equation for the allowable inlet line length on the basis of the pressure surge criterion and extended by the effect of the dissipation, etc. can be written as Lallow[m]⫽
冢
0.05 AEaAe 1 P0−Pa · 2冑2⌿ aA0 冑r 冑P0
· 0.015⫹0.02
冑D /DN15 0
(P0/PU)2/3(1−PU/P0)2
(4)
冣
(h/hmax)0.7
with D0⬎DN15, hⱕhmax, topen⬎2tw and tw⫽a/L
265
measured allowable length in all cases is underpredicted while still reasonable and technically realizable results are obtained, also if the results reported in EPRI PWR (1982) are recalculated according to Cremers (2000). With respect to the data by Kastor, however, the allowable inlet line length in the case of high local pressure losses caused by a restriction in the inlet line are overpredicted following Cremers (2000). Indeed, it is questionable if this arrangement is representative of industrial practice. Also, on following the recommendation in AD A2 (1993) a cross sectional area in the inlet line smaller than the valve inlet flange area is not considered as good engineering practice. The modified pressure surge criterion can be straightforwardly applied because all parameters are readily available for sizing and additional specific measurements are not necessary. The method has only been validated for gas flow. When applied to liquid flow, conservative inlet line lengths are expected in view of the relatively longer valve opening times. In view of the physical fundamentals being included in the modified criterion it should be possible to moderately extrapolate beyond and interpolate between the experimental range of the underlying data. An indication for this is the successful reproduction of the EPRI and Du Pont data. When sizing for the case of lift reduced safety valves, however, it is necessary that the valve supplier ensures the correct functional behavior. Under this condition a smaller valve reseating pressure difference can occur and the original stable flow field around the valve disc is adversely effected. To calculate the allowable inlet line length for a safety valve with adjacent outlet line, the established back pressure in the valve outlet is required. It can be obtained by starting a calculation with the pressure at the end of the outlet pipe P1 which is given by
冉 冊冑
P1⫽P0⌿a
D0 D1
2
(+1)冪Z 2
Z1
(6)
0
The back pressure in the outlet of the valve is obtainable by calculating in the counterflow direction to the valve outlet following Goβlau and Weyl (1994), either by using a numerical procedure as proposed by Ba¨ umer and Friedel (1996), even in the case of no multiple critical flow condition downstream of the valve in the discharge line according to Seynhaeve and Giot (1996), or following Pa⫽
(5) P0
In this correlation, ⌿, the so called discharge function accounting for the critical flow state is introduced. As is evident from Table 1 with the modified equation, the
(7)
冪冉P 冊 ⫹2冉冘lL /D ⫹冘z ⫹ ln 冉P 冊冊 ⌿ a 冉D 冊 Z . P1
2
2
A
0
A
pa
i
i
1
2
2
D 0 4Z 1 1
0
with the empirically imposed pressure ratio restriction for unbalanced safety valves of Pa/P0ⱕ10%. Where the
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length LA and the diameter DA refer to the downstream piping. From experiments by Ehrhardt (1997) and Kastor (1986) it can also be deduced that in the case of safety valves without bellows the back pressure should not exceed some 10% of the set pressure as is also recommended in API RP 520. If the back pressure is higher an oscillation damper should be installed to maintain valve stability. The usefulness of such an item is subsequently discussed.
5. Valve stability in case of damping A check of alternative measures to maintain a posteriore valve stability, e.g. by increasing the inlet pipe diameter, reducing the safety valve lift, installation of an oscillation damper or using a safety valve with bellow leads in most cases to the installation of an oscillation damper as the most effective, reliable and economic method Cremers and Friedel (1999). As an example of the achieved valve stability the opening and closing behavior of the valve A according to Table 2, with an allowable inlet line length for air flow of 0.4 m is shown in Fig. 3. The valve is now equipped with an oscillation damper and an increased inlet line length of 3.1 m. Though a longer inlet line and a relative back pressure of about 30% prevailed, the valve operation is absolutely stable. The basic elements of the installed oscillation damper are shown in Fig. 4. When the safety valve lift increases by opening, oil is forced by the piston to flow through a one-way flow restriction in the transmission line and so mechanical energy is dissipated. If the lift would decrease the oil can flow backward without restriction, hence, only the opening movement of the valve is damped. The main effect of the oscillation damper to maintain valve stability is supposed to rely on an extension of the opening time of the safety valve. As a result the amplitude of the associated expansion wave would be reduced following Cremers and Friedel (1999).
Fig. 4.
Elements of the full lift safety valve oscillation damper.
6. Conclusion
A comparison between measured and predicted inlet line lengths used in practice as a criterion for a stable safety valve opening and closing behaviour revealed that none of the sizing rules are adequate under all conditions during gas flow. As a consequence, a new sizing method based on the pressure surge criterion is proposed. It is validated with the results of new experiments and with those of others available from the literature for safety valves without bellows with an inlet flange diameter greater than DN15 and in case of a discharge line downstream of the valve, when the back pressure does not exceed 10% of the set pressure. An oscillation damper is an effective measure to maintain valve stability when the predicted inlet pipe length or the back pressure limit is exceeded in an industrial installation.
Fig. 3. Transient pressure and lift of a slightly damped valve with an inlet line length of 3.1 m and an excessively high relative back pressure during air flow.
J. Cremers et al. / Journal of Loss Prevention in the Process Industries 14 (2001) 261–267
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