Performance of a safety relief valve under back pressure conditions

Performance of a safety relief valve under back pressure conditions Y.

s. Lai

Dresser Industries,

Valve and Controls Division,

Alexandria,

LA 71309, USA

By the nature of its design, the performance of a spring-loaded safety relief valve, especially a conventional valve, is influenced by back pressure. A bellows safety relief valve, since its disc is subjected to a much smaller downward force resulting from back pressure, is able to remain stable under much higher back pressure conditions. Due to the wide range of bellows manufacturing tolerances, the bellows safety relief valves can substantially reduce, but cannot totally eliminate, the back pressure effects on its set point and relieving capacity. Set point change in a conventional safety relief valve, due to constant superimposed back pressure, can be easily negated by cold differential set. For a bellows safety relief valve, however, set point change must be corrected by the set point correction factor which is a linear function of the back pressure to the set pressure ratio, R. There exists an allowable back pressure to set pressure ratio, I%, and a critical back pressure to set pressure ratio, R,, for each conventional and each bellows safety relief valve. When total back pressure exceeds R,, the relieving capacity will be reduced, mainly resulting from the valve lift being reduced, and the capacity reduction factor should be applied in valve sizing. Once the R, is exceeded, the safety relief valve becomes unstable and will totally lose its overpressure protection capability. For a given back pressure to set pressure ratio, R, the capacity reduction factor is a function of system overpressure, but its relationship is non-linear in nature. (Keywords: relief valves; back pressure; device performance)

The spring-loaded safety relief valve is the most widely used overpressure protection device in refinery, process, and power generating plants. There are two basic types of spring-loaded safety relief valve in use today: the conventional valve and the balanced bellows valve, as shown in Figures I and 2, respectively. ASME Code Section VIII’ specifies basic design, construction and performance requirements for a safety relief valve. In actual installations, however, safety relief valves are subjected to many adverse field conditions, such as pressure drop in inlet piping, vibration and back pressure, which are not addressed by the ASME Code. Excessive pressure drop in inlet piping can cause a safety relief valve to chatter*. Mechanical and flowinduced vibrations can lower the set point, cause seat leakage and damage valve parts3-5. Excessive back pressure in the downstream piping can change the set point, reduce the relieving capacity and induce the instability of the valve@. By the nature of its design, the safety relief valve will cease to function properly once the back pressure exceeds its allowable limit. One way to reduce the adverse back pressure effects on the safety relief valve is to install a balanced bellows in the valve: this reduces the magnitude of undesirable downward force on the

Received 3 May 1991; revised 25 July 1991 095cM230/%?/010055-05 @ 1992 Butterworth-Heinemann

valve disc. The metallic bellows is a delicate mechanical element which has a rather wide range of manufacturing tolerances and makes the design of the bellows safety relief valve very complicated. To assist process system engineers in designing an optimum overpressure protection system at lowest cost, safety relief valve back pressure performance data were developed through extensive flow tests of both conventional and bellows valves. The flow tests were carried out on air under a wide range of back pressure conditions. Theoretical force analysis, test data and summaries are presented in this paper.

Forces in safety relief valves Forces on the disc/holder assembly before the valve opens are shown in Figure 3 and represented in the equation: F1 + F, = F, + A,P

+ (Ab - Ad)Pb

(1)

where F1 = initial helical spring force; F2 = initial bellows spring force (zero for conventional valve); F, = seating force; Ad = effective disc area; Ab = effective bellows area (zero for conventional valve); P = system pressure; Pb = superimposed back pressure . When the valve pops open, P is equal to the set point, P,, and F, = 0. Equation (1) then becomes:

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J. Loss Prev. Process

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Performance

of safety relief valve:

Figure 1 Conventional

FI

+

F2 = AdP,

Y. S. Lai

Figure 2 Balanced

safety relief valve

+ (Ab -

Ad) P,,

(2)

i.e. (F, + F,) and Pb together determine the set point of the valve. Moreover, if and only if A,, = Ad, the set point of a safety relief valve will not be affected by superimposed back pressure Pt,. When a safety relief valve pops open, discharging medium will fill up the valve body and generate built-up back pressure. The disc/holder assembly is then subjected to a new set of forces as illustrated in Figure 4. After the valve pops open, the disc/holder assembly motion will closely follow slow system pressure transients and can be assumed to be in a quasi-static condition. Its equation of motion can be expressed as:

j-,, PldA + A -

P,dA

ldcmu) -

(F, + Fz) - (k, + WY

= 0

where kl and k2 are the spring rates of the helical spring and bellows, respectively, y is valve lift Al and A2 are pressure areas of pressures PI and P2, respectively, and mu is the momentum of the discharging medium. [I PldA + AId( is the total upward force on the disc/holder assembly resulting from the

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J. Loss Prev. Process Ind., 1992, Vol5, No 1

bellows

safety relief valve

pressure PI and the discharging medium. [(F, + F2) + is the total downward force (k, + kz)y + 1 PrdAl resulting from the helical spring, bellows and the pressure P2 in the valve body. The lift and stability of the safety relief valve depend on the relative magnitude of the total upward force and the total downward force. When P2 is within the allowable limit of the valve, the total upward force can overcome the total downward force and the valve can reach its rated lift. When P2 exceeds the allowable limit but is less than the critical limit of the valve, the total downward force will be excessive and prevent the valve from achieving its rated lift. If P2 increases further to the critical limit of the valve, the downward force becomes too high to allow the valve to stay open. The valve will consequently attempt to close before the system pressure is sufficiently relieved. This adverse condition will cause the valve to chatter and totally lose its overpressure protection capability. The functions PI, P2 and mv in Equation (3) are complicated and are unique for each design. Since they have not yet been satisfactorily formulated, complete theoretical solution of Equation (3) is not available. The performance of safety relief valves under back pressure conditions can only by studied by actual tests.

Performance

Figure 3 Forces when for

conventional

Fs

bellows

valve is closed (A,

= 0 and

F2 = 0

valve)

I( F1

Y. S. Lai

Effects on set point

I F2

F S

of safety relief valve:

+ kly)

For a conventional safety relief valve, superimposed back pressure will raise the valve set point. From Equation (Z), it can be easily seen that the amount of set point increase is equal to the magnitude of the superimposed back pressure. This back pressure effect on set point can be easily negated by applying the cold differential set technique, i.e. to set the valve at (PS - Pb) on the test stand for an installation in which the valve is to pop at P, under constant superimposed back pressure Ps. Again referring to Equation (2), the presence of Ab of the bellows substantially reduces the back pressure effect on a bellows valve. Due to manufacturing tolerance, the effective area of the bellows could vary by as much as 10%. Therefore, it is not economically feasible to produce a bellows safety relief valve having effective disc area exactly equal to the effective bellows area. In other words, the bellows safety relief valve cannot be totally balanced and superimposed back pressure swing can cause the set point to drift. To determine the amount of set point change under various back pressures, a typical G-orifice bellows valve was tested on a flow test stand as depicted in Figure 5. During the back pressure test, the outlet piping is enclosed and pressurized which makes valve opening almost inaudible. Therefore, the set point was defined by the valve spindle motion of 0.025 mm as measured by linear variable differential transformer. The set point change data are plotted in Figure 6 in terms of per cent back pressure, R, = Ps/P,, and set point correction factor, K,, = Psb/P,, where P, is set point of the valve when Pb = 0 and Psb is set point under back pressure Pb. All pressures are gauge pressures. The K, value in Figure 6 is less than one; however, it is important to realize that the K, value can also be greater than or equal to unity for a different valve.

Effects on stability and relieving capacity Figure4 Forces when k2 = 0 for conventional

bellows valve)

valve

is relieving

(F2 = 0 and

/-

TEST

To study the stability and relieving capacity of a safety relief valve under back pressure conditions, four different sizes of conventional valve and five different

VALVE

PREsslAtE GAUGE

PRESSURE

GAUGE 753 FLOU METER

ACC WLATU? I-

Figure

5

Back pressure

test stand

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Performance I

of safety relief valve:

Y. S. Lai

;,;I

7

1.0

1

I 9

7 0

0.9

0

0

5

BACK

Figure 6 Typical

PRESSURE

10 TOSETPRESSURE

set point correction

20

15 RATIO.

R (Xl

V

factor

sizes of bellows valve of the same make were flow tested on a flow test stand depicted in Figure 5. Test valves and test pressures are summarized below. Conventional valves Set pressures Back pressures Overpressure Bellows valves Set pressures Back pressures Overpressure

F, G, H and J orifices; l-28 barg ; 5-40% of set pressure; 0.2 bar or 10%) whichever is greater. F, G. H, J and K orifices; l-14.5 barg; 40-90% of set pressure; lo,16 and 21%.

3

F -

ORIFICE

>

G -

ORIFICE

\

H -

ORIFICE

7

J - ORIFICE

O

I-

VI

0.5

10

5

BACK

Figure 7 Capacity

V

m

20

15

PRESSURE

reduction

TO

25

30

SET PRESSURERATIO.R (X)

factors for conventional

valves

1.0

All flow tests were performed in accordance with the following procedures using air as test medium. Mount test valve on test stand. Set opening pressure, P,. Adjust test valve to achieve proper action. Actuate test valve to desired overpressure. Establish the desired back pressure Pb in the discharge pipe at 10 diameters downstream of the test valve by adjusting the pressure regulator. 6. Measure relieving capacity Q by flow meter.

1. 2. 3. 4. 5.

The relieving capacity of conventional and bellows valves under various back pressure conditions are plotted in Figures 7 and 8, respectively, in terms of R and Kb; Kb = capacity reduction factor = Q/Q, where Q, is rated capacity. Lower bound data of each test only are shown in the figures.

Summary Wide scattering bands noted in Figures 7 and 8 indicate that the spring-loaded safety relief valve is a rather complicated piece of equipment. Slight design variation could result in quite different performance. There exists an allowable back pressure to set pressure ratio, R,, and a critical back pressure to set pressure ratio, R,, for each spring-loaded safety relief valve. Before R, is exceeded, the valve will remain stable and relieve the rated capacity. Once R, is reached, the valve will become unstable and will totally lose its overpressure protection capability. The balanced bellows safety relief valve is not totally balanced, i.e. excessive back pressure does cause the set point to drift and the valve lift to drop.

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0.5 L

90

40 BACK

50 PRESSURE

60 TO SET

70 PRESSURE

RATIO.

80 R ,X1

For a conventional valve, the effect of constant superimposed back pressure on its set point can be negated by applying the cold differential set technique. For a bellows valve, on the other hand, the set point correction factor, K,, shall be used to adjust the back pressure effect, i.e. Psb = K,P,. Inability to achieve rated lift under excessive back pressure is responsible for all of the relieving capacity reduction for a conventional valve and the large majority of capacity reduction for a bellows valve. For conventional valves, the relieving capacity falls off rapidly once the built-up back pressure exceeds the R,, and hence it is not advisable to have conventional valves subjected to built-up back pressure exceeding R, in installation. The recommended built-up back pressure limit of 10% for a typical conventional safety relief

Performance valve, given by the American Petroleum Institute, is a sound design guide. The bellows valve can take substantially higher back pressure and remain more stable than the conventional valve. Moreover, the R, of bellows valves is greater than the R, by more than 30% ; therefore it is safe to allow a bellows valve subjected to built-up back pressure exceeding the R,. When the R, limit is exceeded, the relieving capacity, Q, should be downrated by Kb from the rated capacity Q,, i.e.

Q = KbQ,.

For bellows valves, the capacity reduction factors under 16% overpressure are substantially higher than those under 10% overpressure. However, the capacity reduction factors under 21% overpressure are only slightly better than those under 16% overpressure. Capacity reduction factor is not a linear function of system overpressure; for example, capacity reduction factor will not increase by 50% when overpressure is increased by 50%. Capacity reduction factors of bellows safety relief

of safety relief valve:

Y. S. Lai

valves can vary substantially between different makes, and therefore they must be developed individually by tests. It has been observed that capacity reduction factors of some makes of bellows safety relief valves are lower than those given in Figure 27 of Reference 6, i.e. the Figure 27 data are not necessarily conservative.

References 1 ASME Boiler and Pressure Vessel Code Section VIII, Pressure Vessels, American Society of Mechanical Engineers, 1989 2 API Recommended Practice 520, Part II - Installation, American Petroleum Institute, 1988 3 Lai, Y. S. Tram. Am. Nudeor Sm. 1978,30,495 4 Bernstein, M. D. and Bloomfield, W. J. paper presented at ASME PVP Conference, 23-27 July 1989, Honolulu 5 Baldwin, R. M. and Simmons, H. R. J. Pressure Vessel Technol. 1986,108,267 6 API Recommended Practice 520, Part I - Sizing and Selection, American Petroleum Institute, 1990 7 Huff, J. E. paper presented at API 48th Mid-Year Meeting, 10 May 1983, Los Angeles 8 Lai, Y. S. in Proc. of ASME PVP-180,1989, pp. 111-118

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