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Design and Calculation of the Pressure Relief Valves and Rupture Disks System
Prakash Thapa
Centre for Risk, Integrity and Safety Engineering (C-RISE)
Faculty of Engineering & Applied Science
Memorial University, St John’s, NL, A1B 3X5, Canada
Abstract
Oil and gas production facilities handle gas and liquids under pressure conditions where the
improper use or failure of certain components may cause an overpressure of various facility
components. Economic considerations do not allow the facility engineer to design all components to
withstand the maximum pressure to which they may be exposed. To provide a safe yet economic
design, pressure relieving devices are used.
This tutorial deals with the design, selection, operation, and maintenance of pressure relief devices
for the protection of pipe, valves, fittings, vessels, and other components. Pressure safety valves and
rupture disks are discussed, along with a variety of installation methods and testing techniques.
Downstream gas disposal methods are discussed in the tutorial EPT 04-T-02 on Flare and Vent
Systems. Most definitions required for an understanding of pressure relieving devices can be found
in Part 1 of API RP 520 I.
Introduction
Code Requirements for Pressure Relief
There are five primary codes which address the use of pressure relieving components. The pressure
vessel code, whether American, Canadian, or British, requires the presence of a relief device on all
code approved vessels. The American Petroleum Institute (API) provides API RP 520 I, “Sizing,
Selection, and Installation of Pressure Relieving Devices in Refineries”. This RP is often applied to
production facilities and provides a guide for sizing and analysis of safety relief devices. API RP
14C, “Analysis, Design, Installation and Testing of Basic Surface Safety Systems for Offshore
Production Platforms”, recommends the installation of relief valves for various components within a
production system. API RP 14E, “Design and Installation of Offshore Production Platform Piping
Systems”, discusses the use, in conjunction with API RP 14C, of pressure relieving devices to
protect piping systems. Finally API RP 521, “Guide for Pressure-Relieving and Depressuring
Systems”, discusses design of the overall relieving system. Piping systems are covered in the
tutorial EPT 09-T-01 on Facilities Piping, while relieving systems are covered in the tutorial EPT
04-T-02 on Flare and Vent Systems.
Types of Pressure Relief Devices
All of the following devices relieve pressure automatically, actuated by upstream static pressure.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Relief Valves
Relief valves are spring loaded pressure relief devices. At the set pressure, the inlet pressure force
overcomes the spring force and the valve disk begins to lift off the seat. As inlet pressure increases,
the lift of the disk increases proportionally to allow an increase in the flow. The closing pressure is
less than the set pressure and shall be reached after the blowdown phase is complete.
These devices are used primarily for liquid service (incompressible fluids) and open in proportion to
increasing pressure over opening pressure. Relief capacities are usually rated at 10 or 25 percent
overpressure, depending on the application.
Safety Valves
Safety valves are also spring loaded pressure relief devices, but they are designed to provide full
opening with minimum overpressure. Static pressure and the kinetic energy of the gas or vapor are
utilized to overcome the spring force on the disk as it lifts, resulting in a popping action. These
devices are used primarily for steam and air services (compressible fluids) and provide rapid full
opening or pop action with little overpressure.
Safety Relief Valves
Safety relief valves provide the characteristics of safety valves in gas or vapor service and the
characteristics of relief valves in liquid service.
They may be pilot operated - controlled by an auxiliary (pilot) valve - or spring loaded. Spring
loaded safety relief valves are of either of two types, conventional (performance depends on back-
pressure) or balanced (minimizes the effect of back-pressure).
Rupture Disks
Rupture disks are non-reclosing differential pressure relief devices. A “rupture disk device” is
defined as both the rupture disk itself and the rupture disk holder.
Types of Pressure Relief Valves
Valves that activate automatically to relieve pressure are called “safety valves”, “relief valves”, or
“safety relief valves”. Safety valves are spring loaded and characterized by a rapid full opening or
“pop” action. They are used primarily for steam or air service. Sometimes they are referred to as
“pop valves”. Relief valves are spring loaded and open more slowly. They reach full opening at 10
or 25 percent above set pressure and are used primarily for liquid services. Safety relief valves can
be either spring loaded or pilot operated. Most automatically actuating relief devices used in
production facilities are actually safety relief valves; however, they are commonly referred to as
relief valves or safety valves. In this tutorial the term “relief valve” is used in the generic sense of
any automatically actuating pressure relieving device with reclosing capabilities. There are three
types of relief valves: conventional (spring loaded), balanced bellows, and pilot operated.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Conventional
Figure 1 shows a cross section of a conventional relief valve, while Figure 2 is a schematic that
shows the valve's operation. A vented bonnet configuration is one that consists of a spring which
creates a closing force that overcomes both the pressure in the vessel, P1, and the back-pressure
downstream of the valve, P2. At the set point, the force of P1 and P2 acting on their respective areas
equals the spring force, and the valve opens. If the valve is installed in a header system with other
valves, then the set point required to overcome the spring force decreases if P 2 is increased.
Figure 1: Cross Section of a Conventional Relief Valve (Courtesy of API)
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Figure 2: Schematic Showing Operation of Conventional Relief Valves (Courtesy of API, API
RP 520 I)
In a non-vented bonnet type conventional relief valve, the back-pressure acts downward on the entire
disk area but also acts upward on a portion of the disk area. In this case, an increasing back-pressure
shall cause an increase in the valve set point.
Where the discharge is routed independently to atmosphere, conventional relief valves shall be used.
If this type of device is installed in a header system, when one device is relieving, thereby creating a
header back-pressure, the set point of every other device in the header system shall be affected.
Conventional relief valves are normally used in an open system or in a closed flare header system
designed so that the back-pressure does not exceed 10 percent of the relief valve set pressure.
Conventional relief valves may be equipped with lifting levers or screwed caps. The lifting lever
permits mechanical operation of the valve for testing or cleaning out foreign material from under the
seat. Screwed caps prevent leakage from the valve, but they also prevent overriding the spring if
foreign material or ice becomes lodged under the disk. Relief valves for steam and air service are
required by code to be furnished with lifting levers.
Balanced Bellows
Balanced bellows relief valves are a variation of spring-loaded valves. They contain a bellows
arrangement to prevent back-pressure from affecting the set point. Figure 3 shows a cross section of
a balanced relief valve, and Figure 4 is a schematic that shows how the valve operates. The bonnet
is vented to atmosphere, providing a constant force downward on the disk. The bellows is installed
in such a manner that the back-pressure acts both downward and upward on equal areas of the disk.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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This means that the forces created by the back- pressure cancel and therefore do not affect the set
point.
Figure 3: Cross Section of a Balanced Bellows Relief Valve (Courtesy of API)
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Figure 4: Schematic Showing Operation of a Balanced Bellows Relief Valve (Courtesy of API,
from API RP 520 I)
Balanced bellows valves are normally used where the relief valves are piped to a closed flare system
and the back-pressure exceeds 10 percent of the set pressure. They cost more than conventional
relief valves. In sour service, the bonnet vent shall be piped to a safe location.
Pilot-Operated
There is no spring in a pilot operated relief valve the Instead a pilot valve, shown in Figure 5, senses
vessel pressure. Under normal conditions, vessel pressure is routed through the pilot to the upper
side of the disk. The area exposed to this pressure is larger than the disk area exposed to the inlet
nozzle. Therefore the seating force on the disk is greater than the lifting force. In fact, as the vessel
pressure approaches the set point, the closing force increases to assure a tight seal and to prevent
valve “chatter”. When the set point is reached, the pilot shifts, blocking the pressure from the vessel,
venting pressure from above the disk, and allowing the disk to rise.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Figure 5: Cross Section of a Pilot Operated Relief Valve
Pilot-operated valves have several advantages besides not allowing operation near the set point to
cause chatter. The set point is not affected by back- pressure as the upper portion of the disk is
isolated. With proper auxiliary valves in the pilot lines, the pilot may be tested without venting
vessel pressure. This may be useful if the vessel contains toxic materials. However, it shall be
realized that corrosion between the disk and seat or other obstructions in the valve body may prevent
the disk from lifting. Periodic bench testing may be required to assure the main valve will function
properly.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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One disadvantage of pilot operated valves is that, if there is no pressure in the vessel, back-pressure
on the valve could cause the disk to lift. If a vessel was shut-in and depressured for maintenance,
and the relief valve outlet was tied into a relief header, when another valve in the header was opened,
back-pressure would be applied to the disk. Figure 6 shows an arrangement of two check valves in
the sensing system to assure that either vessel pressure or header pressure, whichever is greater, is
always present above the disk. Such an arrangement provides “backflow protection”. Additionally,
pilot operated valves shall not function if the pilot fails. If the sensing line fills with hydrates or
solids, the valve shall not open until the vessel pressure is 25 percent greater than the pressure
trapped above the disk (usually the normal operating pressure of the vessel). For this reason pilot
operated valves shall be used with care in dirty gas service and liquid service.
Figure 6: Pilot Operated Valve Backflow Protection by Means of Check Valves
Rupture Disks
Rupture disks are thin diaphragms held between flanges and designed to burst at a specific static
inlet pressure. A conventional rupture disk is shown in Figure 7. These devices cannot reseal when
the pressure declines. If the disk ruptures and flow continues into the vessel, the relief system shall
be designed for the anticipated flow rate. The disk shall be replaced before the pressure vessel can
be placed back in service. Figure 8 shows the relationship between vessel Maximum Allowable
Working Pressure (MAWP), and single and multiple rupture disk applications.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Figure 7: Conventional Rupture Disk (Courtesy of API, from API RP 520 I)
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Figure 8: Pressure Level Relationships for Rupture Disk Devices (Courtesy of API, from API
RP 520 I)
Rupture disks can be manufactured from a variety of materials and with coatings for corrosion
resistance. The most common disk materials are aluminum, monel, inconel, stainless steel, and
plastic.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Rupture disks may be used alone, or as a backup in parallel with a relief valve. If used as a backup,
the disk may be set to relieve at approximately 115 percent MAWP (See Figure 7). This ensures that
the disk ruptures only if the relief valve fails or is inadequately sized so that when the pressure rises
above 110 percent MAWP, the relief valve does not have enough capacity.
A rupture disk can also be used in series with a relief valve. Located at the valve inlet to protect the
valve from corrosion conditions within the vessel, a rupture disk allows the use of a less expensive
valve. Valve internals are protected from the corrosive materials, so specialized metallurgy is not
required. Fugitive emissions that pass through pressure relief valves are also eliminated. When
properly designed, the rupture disk bursts first, with the relief valve immediately opening. When the
pressure declines, the relief valve reseals, limiting additional flow.
Additional instrumentation shall be provided so the operator will be advised to replace the ruptured
disk. This is also true if the rupture disk develops a small pinhole leak, because the pressure on the
back of the disk can build up. Since the rupture disk is designed to fail at a specified differential
pressure across the disk, any back-pressure shall cause it to fail at a system pressure higher than the
intended relieving pressure. ASME Code requires a free vent, a try-cock, a pressure gauge, or
suitable telltale indicator to relieve or sense back-pressure buildup. These shall be monitored so the
rupture disk can be replaced if failure occurs.
In this application, the relief valve capacity shall be derated by 20 percent unless the manufacturer
has established a certified capacity factor for the specific rupture disk/valve combination per ASME
SEC VIII D1. The rupture disks shall be non-fragmenting so that pieces of the rupture disk do not
block the valve or prevent it from opening. Figure 9 shows a scored, tension-loaded rupture disk,
which is normally non-fragmenting.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Figure 9: Scored Tension–Loaded Rupture Disk (Courtesy of API, from API RP 520 I)
1. Pressure Relief Valve Sizing
General
For safe production facility design, all of the following conditions shall be considered to determine
which one governs the size of the relief valve:
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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1. Blocked discharge. If all outlets from the vessel are assumed to be shut- in, the total
design inlet mass flow rate shall be handled by the relief valve. This condition could
occur if, after the equipment has been shut- in and isolated, the operator opens the inlet
prior to opening the outlet valving.
2. Fire. An external fire can result in vapors evolving from the liquids and in thermal
expansion of the gas, which the relief valve shall be able to accommodate. A procedure
for calculating this is presented in API RP 520 I. This condition may be critical for large,
low-pressure vessels and tanks, but it does not normally govern for most other pressure
vessels.
3. Gas blowby. Gas blowby is a critical condition in production facility design. This
condition occurs when an upstream liquid control valve fails in the open condition or an
upstream manual drain valve is inadvertently left in the open position. The relief valve
shall then handle the maximum gas flow rate into the downstream component during this
upset condition. For example, if a high-pressure separator were to experience gas
blowby, the downstream lower-pressure separator relief valve may have to handle the
total design gas flow rate of the high-pressure separator. While this flow may be
restricted by an orifice or piping pressure drop, this would not be a conservative
assumption. Accidents involving overpressuring of low pressure separators are often a
result of relief valves being inadequately sized to handle the gas blowby condition.
4. Thermal Relief. Equipment that is completely full of liquid presents a problem of liquid
hydraulic expansion if it is blocked in while heat is added. In many cases, this potential
risk can be controlled by design or procedures (see API RP 521). To protect piping or
equipment against overpressure resulting from ambient temperature changes, a nominal-
size relief device (for example, a 19 by 25 mm, or 3/4 by 1 in, relief valve) will normally
suffice.
Figure 10 shows the relationships between vessel Maximum Allowable Working Pressure (MAWP)
and the safety relief valve set pressure for single and multiple relief valve installations. For a single
relief valve installation, the primary relief valve shall be set to open at no more than 100 percent of
the MAWP and sized to relieve the worst case flow rate, either blocked discharge or gas blowby
(exclusive of fire), at a pressure of 1.10 MAWP. If two or more relief valves are used to handle the
worst case flow rates, the first valve still shall be set no higher than 100 percent MAWP, while the
second or last may be set for 1.05 MAWP. Their combined capacity shall relieve the same worst
case flow rates at 1.16 MAWP.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Figure 10: Pressure Level Relationships for Pressure Relief Valve (Courtesy of API, from API
RP 520 I)
The maximum pressure for fire relief rates 1.21 MAWP. Under these relief conditions, the pressure
in the vessel shall actually exceed the MAWP. Such occurrences are taken into account by the
various safety factors in the ASME Pressure Vessel Code. This situation is one reason the vessel is
tested to 1.5 MAWP prior to receiving the code stamp.
The relief valve shall be installed so that discharged gases and/or liquids are routed to a safe
location. In small facilities and remote locations where no liquids are discharged, this may be
accomplished with a simple “tail pipe”, which points the discharge vertically upward. A jet in
excess of 150 m/sec (500 ft/sec) dilutes the discharge gases to below the lower flammable limit in
approximately 120 pipe diameters.
Large facilities and offshore platforms where the escaping gases and liquids could present a source
of pollution or ignition often route the relief valve discharges into a common header that discharges
at a safe location. A vent scrubber is installed in this header to separate the bulk of the liquids and to
minimize the possibility of liquid discharges to the surroundings. For relief systems with a common
header, the back- pressure developed in the header shall be checked for various relieving scenarios.
When reliefs discharge into a common header, the header pressure shall increase. As discussed
previously, this back-pressure can adversely affect relief valve performance by causing the valve to
open at a higher pressure, or it may restrict the flow capacity. The effect depends on the type of
relief valve and the severity of the back-pressure. The design of headers, scrubbers, and vent or flare
systems is beyond the scope of this tutorial and is covered in API RP 521. Specific header sizing
information is included in the tutorial EPT 04-T-02 on Flare and Vent Systems.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Gas or Vapor Service
General
1. The maximum flow of a compressible fluid through an orifice occurs at sonic velocity. Sonic
velocity is maintained as long as the pressure drop through the orifice is sufficiently high.
2. Critical Pressure Ratio (c) is the largest ratio of downstream pressure to upstream pressure
capable of producing sonic velocity. It is dependent on the specific heat ratio of the fluid:
Equation 1
psia kPa pressure, inlet P
psia kPa pressure, outlet flow critical P
C/C ratio, heat specific k
ratio pressure critical
:where
1k 2
P
P
1
cf
vp
c
1-kk
1
cf
c
3. Values of k and molecular weights for common gases are shown in Table 1. Critical
Flow Pressure is slightly greater than half of the inlet pressure for gases with specific heat
ratios < 1.5.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Table 1: Molecular Weights and k=CP/CV for Common Gases
Gas
Molecular Weight
Specific Heat Ratio (k = Cp/Cv)
at 15.6°C and 100 kPa (60°F and
1 Atmosphere)
Methane
16.04
1.31
Ethane
30.07
1.19
Ethylene
28.03
1.24
Propane
44.09
1.13
Propylene
47.08
1.15
Isobutane
58.12
1.18
n-Butane
58.12
1.19
Isopentane
72.13
1.08
n-Pentane
72.15
1.08
n-Hexane
84.17
1.06
Benzene
78.11
1.12
n-Heptane
100.20
1.05
Toluene
92.13
1.09
n-Octane
114.22
1.05
n-Nonane
128.23
1.04
n-Decane
142.28
1.03
Air
28.96
1.40
Ammonia
17.03
1.30
Carbon dioxide
44.01
1.29
Hydrogen
2.02
1.41
Hydrogen sulfide
34.08
1.32
Sulfur dioxide
64.04
1.27
Steam
18.01
1.33
Source: API 520 (with Isobutane molecular weight corrected)
4. The rate of gas flow through an orifice or nozzle is a function solely of the inlet pressure
when the back-pressure is less than the critical flow pressure (critical flow). When the outlet
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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back-pressure is greater than the critical flow pressure, the gas rate is then also a function of
outlet pressure (subcritical flow).
The value of k can be accurately calculated as described in the tutorials EPT 07-T-03A and
EPT 07-T-03B on Reciprocating Compressors, provided the gas composition is known.
When this is not the case, k can be estimated from Figure 11, based on:
Equation 2
volume constant at heat specific C
pressure constant at heat specific C
weightmolecular gas MW
air to relativegravity specificgas SG
:where
MW
5.1
1
SG29
5.1
1~
C
C
k
V
P
V
P
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Figure 11: Specific Heats Ratio Versus Molecular Weight for Hydrocarbon Gases (Courtesy
of API, from API RP 520 I)
6. The sizing equations for pressure relief valves in vapor service fall into two general
categories, critical or subcritical.
7. If the pressure downstream of the throat is less than or equal to the critical flow pressure,
Pcf, then critical flow shall occur, and the procedures in Section 7.2.2 shall be applied.
8. If the downstream pressure exceeds the critical flow pressure, Pcf, then subcritical flow
shall occur, and the procedures in Section 7.2.3 shall be applied.
Sizing for Critical Flow
Pressure relief valves in vapor service may be sized using Equations (3) through (5) when
governed by critical flow. Each equation may be used to calculate the effective pressure
relief valve discharge area, a, required to achieve the design flow rate.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Equation 3
MW
TZ
K P K C W
a
:Customary
MW
TZ
KPCK
13,157W
a
:Metric
b1d
b1d
Equation 4
b1d
b1d
K P K C 6.32 MW ZTV
a
:Customary
KPCK TZMW555.79V
a
:Metric
Equation 5
b1d
b1d
K P K C 1.175 SG ZTV
a
:Customary
KPCK TZSG2993V
a
:Metric
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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100 reoverpressu percent
P
psig kPa re,overpressu P
psig kPa pressure, set P
psi 14.7PP kPa 100PP
pressure. atmosperic plus reoverpressu allowable the plus pressure
setthe is This .psia kPa pressure, relieving upstream P
0.92. K operated, pilot 33 and 23 type
AGCO For 0.975. K operated, springedConsolidat and Farris
For .ermanufactur valve from discharge of tcoefficien valve K
2. Table or 12 Figure from
obtained be can This .conditions standardat vapor or gas the
of heats specificthe of ratio the from determined tcoefficien C
hr/lb hr/kg valve, the through flow required W
in mm valve, of area discharge effective required a
:where
set
ov
set
avsetovset
1
d
d
d
22
air to relative gas ofgravity specificG S
F60 and psia 14.7 at SCFM C15.56 and
kPa 100 at hr/m stdvalve, the through flow required V
valves. relief safety
bellows balanced for 13 Figure use or available, when
ermanufactur valve from factor correction this Obtain
factor. correction pressure-back K
R K e,temperatur flowing T
factorility compressib Z
gas of weightmolecular MW
condition relief fire 20
condition relief loperationa for 10 reoverpressu Percent
oo
3
b
o
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
21 of 53
Figure 12: Coefficient C Versus Specific Heats Ratio (Courtesy of API, from API RP 520 I)
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Table 2: Value of Coefficient C
k
C
k
C
k
C
1.01
316.56
1.31
347.91
1.61
373.32
1.02
317.74
1.32
348.84
1.62
374.09
1.03
318.90
1.33
349.77
1.63
374.85
1.04
320.05
1.34
350.68
1.64
375.61
1.05
321.19
1.35
351.60
1.65
376.37
1.06
322.32
1.36
352.50
1.66
377.12
1.07
323.44
1.37
353.40
1.67
377.86
1.08
324.55
1.38
354.29
1.68
378.61
1.09
325.65
1.39
355.18
1.69
379.34
1.10
326.75
1.40
356.06
1.70
380.08
1.11
327.83
1.41
356.94
1.71
380.80
1.12
328.91
1.42
357.81
1.72
381.53
1.13
329.98
1.43
358.67
1.73
382.25
1.14
331.04
1.44
359.53
1.74
382.97
1.15
332.09
1.45
360.38
1.75
383.68
1.16
333.14
1.46
361.23
1.76
384.39
1.17
334.17
1.47
362.07
1.77
385.09
1.18
335.20
1.48
362.91
1.78
385.79
1.19
336.22
1.49
363.74
1.79
386.49
1.20
337.24
1.50
364.56
1.80
387.18
1.21
338.24
1.51
385.39
1.81
387.87
1.22
339.24
1.52
366.20
1.82
388.56
1.23
340.23
1.53
367.01
1.83
389.24
1.24
341.22
1.54
367.82
1.84
389.92
1.25
342.19
1.55
368.82
1.85
390.59
1.26
343.16
1.56
369.41
1.86
391.25
1.27
344.13
1.57
370.21
1.87
391.93
1.28
345.08
1.58
370.99
1.88
392.59
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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1.29
346.03
1.59
371.77
1.89
393.25
1.30
346.98
1.60
372.55
1.90
393.91
Source: API 520
Figure 13: Variable or Constant Back-Pressure Sizing Factor, Kb, for Balanced Bellows Safety
Relief Valves (Vapors and Gases) (Courtesy of API, from API RP 520 I)
2. A standard orifice size may be selected from Table 3.
Table 3: Standard Orifice Areas and Designations
(From API Standard 526)
Orifice
Area (Square in)
D
0.110
E
0.196
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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F
0.307
G
0.503
H
0.785
J
1.287
K
1.838
L
2.853
M
3.60
N
4.43
P
6.38
Q
11.05
R
16.0
T
26.0
3. Alternately, Equations (3), (4), and (5) may be rearranged to solve for flow rates for a given
area:
Equation 6
TZ
MW
K P K C a W
:Customary
TZ
MW
13,157
KPaCK
W
:Metric
b1d
b1d
Equation 7
MW ZT
K P K C a 6.32
V
:Customary
TZMW555.79
KPaCK
V
:Metric
b1d
b1d
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
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Equation 8
SG ZT
K P K C a 1.175
V
:Customary
TZSG2993
KPaCK
V
:Metric
b1d
b1d
1.1.1. Sizing for Subcritical Flow
1. If the ratio of back-pressure to inlet pressure exceeds the critical pressure ratio Pcf/P1, the
flow through the pressure relief valve is then subcritical. Equations (9) through (11) are used
to calculate the required effective discharge area for conventional relief valves that have
springs adjusted to compensate for superimposed back-pressure or to calculate the required
effective discharge area for a pilot-operated relief valve. Sizing of balanced-bellows relief
valves under conditions of subcritical flow shall be done using Equations (3) through (5).
For these valves, the back-pressure correction factor shall be obtained from the manufacturer.
Equation 9
211d2
211d2
P-P P MW ZT
K F 735W
a
:Customary
P-PMWPZT
KF
17.90W
a
:Metric
Equation 10
211d2
211d2
P-P P MWZT
K F 4645.2
V
a
:Customary
P-PPZTMW
KF
0.756V
a
:Metric
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
26 of 53
Equation 11
211d2
211d2
P-P P SGZT
K F 863.63
V
a
:Customary
P-PP SGZT
KF
4.07V
a
:Metric
psig kPa pressure,-back P
psia 14.7P kPa 100P
psia kPa pressure,-back P
P/P pressure, relieving upstream to pressure-back of ratio r
r-1r-1
r
1-kk
values for 14 Figure see flow al subcriticof tcoefficien F
:where
b
bb
2
12
k1-k
k
2
2
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
27 of 53
Figure 14: Values of Subcritical Flow Coefficient F2 (Courtesy of API, from API RP 520 I)
1. Equations (9), (10), and (11) may be solved for flow rates for a
given area:
Equation 12
T Z P-P P MW
K F a 735 W
:Customary
ZT P-PMWP
17.90
KaF
W
:Metric
211
d2
211
d2
Equation 13
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
28 of 53
MWT Z P-P P
K F a 4645.2 V
:Customary
MWZT P-PP
0.756
KaF
V
:Metric
211
d2
211
d2
Equation 14
SGT Z P-P P
K F a 863.63 V
:Customary
SGZT P-PP
4.07
KaF
V
:Metric
211
d2
211
d2
Steam Service
Pressure relief valves in steam service are sized as follows:
Equation 15
SHNd1
SHNd1
K K K P 51.5 W
a
:Customary
KKKP190.42W
a
:Metric
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
29 of 53
1.0. K pressure,any at steamrated satu
For .K Factors, Correction Superheat10, Table 520, RP
API from obtained be can This factor. correction steam superheat K
psia 3215Ppsia 1515 where
1061-P 0.2292 1000-P 0.1906
kPa 22,167PkPa 10,446 where
1061-P 0.0337 1000-P 0.0280
psia 1515 kPa 10,446P where1
equation Napier for factor correction K
0.92. K operated, pilot 33 and 23 type
AGCO For 0.975. K operated, springedConsolidat and Farris
For .ermanufactur valve from discharge of tcoefficien valve K
:where
SH
SH
SH
1
1
1
1
1
1
1
N
d
d
d
Alternately, the mass flow rate may be calculated from the valve discharge area:
Equation 16
SHNd1
SHNd1
K K K P a 51.5 W
:Customary
190.42
KKKaP
W
:Metric
Liquid Service
The procedure for obtaining capacity certification per ASME SEC VIII D1 includes determination of
the coefficient of discharge for the design of liquid relief valves at 10 percent overpressure. Valves
that require a capacity in accordance with the ASME Code are sized using:
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
30 of 53
Equation 17
21
L
VWd
21
L
VWd
P-P
SG
K K K 38 Q
a
:Customary
P-P
SG
KKK
196.3Q
a
:Metric
waterto
relative e,temperatur flowing at liquid ofgravity specific SG
16. Figure from determined asvicosity to due factor correction K
.correction specialno require valves alConvention 15.
Figure from determined factor correction the require willce servi
pressure-back in valves bellows-Balanced 1. K c,atmospheri
is pressure-back the If pressure.-back to due factor correction K
used. be can 0.65 of tcoefficien discharge
a estimation y sizingpreliminar a For er.manufactur valve the
from obtained be shouldthat discharge of tcoefficien effective K
gpm hr/m e,temperatur flowing at rate flow Q
:where
L
V
W
W
d
3
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
31 of 53
Figure 15: Correction Factor Due to Back-Pressure on Balanced Bellows Pressure Relief
Valves in Liquid Service (Courtesy of API, from API RP 520 I)
For viscous liquid service, a relief valve shall first be sized as if it were for nonviscous service to
obtain a preliminary required discharge area, a. The next larger standard orifice size shall then be
used in determining the Reynolds number, R, from either of the following relationships:
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
32 of 53
Equation 18
a
SG2800 Q
R
:Customary
a
313.13QSG
R
:Metric
L
L
Equation 19
SUS100U for
aU
Q 12700
R
:Customary
aU
1,420,000Q
R
:Metric
secUniversal
Saybolt
s/mm e,temperatur flowing the atviscosity U
areas orifice standard
ser'manufactur from
in mm area, discharge effective a
cp sPa e,temperatur theflowing atviscosity absolute
number Reynolds R
:where
2
22
After the value of R is determined, the factor Kv is obtained from Figure 16. K v is used to find the
required discharge area. If the corrected area exceeds the chosen standard orifice area, the
calculation shall be repeated using the next larger standard orifice size.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
33 of 53
Figure 16: Capacity Correction Factor Due to Viscosity (Courtesy of API, from API RP 520 I)
Two-Phase Flow
In production operations many relief valves shall be sized for handling fluids containing both liquid
and gas. In addition, most liquid reliefs will produce flashing and vapor generation as the fluid
moves through the valve. The vapor generation shall be considered since it may reduce the effective
mass flow capacity of the valve.
There are presently no precise formulas for calculating orifice area for two- phase flow. The
common convention is to calculate the area required for the gas and liquid flows separately as single
phase flows. The two areas are then added to approximate the area required for two-phase flow.
When liquids that are at their vapor pressure are to be relieved, the designer shall calculate the
backpressure downstream of the relief valve due to two-phase flow in the relief header. The flow
rate of vapor generated due to pressure drop through the relief valve can then be determined and the
relief valve sized for two phase flow. This is an iterative solution, as the amount of vapors generated
by pressure drop through the relief valve depends upon the backpressure, which is a function of two-
phase pressure drop in the header.
The designer shall also consider the effect of any auto refrigeration that may be caused by the
flashing of liquid. Materials of construction shall be adequate for the outlet temperatures involved.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
34 of 53
In addition, the possibility of flow blockage occurring from hydrates or other blockages shall be
considered in the installation design when auto refrigeration conditions exist.
Effects of Back-pressure on Capacity
Reduced relief valve capacity occurs when back-pressure exceeds the following approximate
percentage of set pressure plus allowable overpressure:
1. Spring loaded 60 percent
2. Balanced bellows 35 percent
3. Pilot operated 60 percent
In relief valves other than balanced bellows relief valves, liquid flow capacity is proportional to
pressure drop across the valve. Bellows valves have a further reduction in capacity with back-
pressure. Where high back-pressure exist, therefore, this type of relief valve has a potential
disadvantage when compared to the other two types.
Installation
Relief valve inlet piping shall be as short as practical, and each relief valve shall be equipped with
inlet piping no smaller than the valve inlet flange size. The inlet piping pressure drop from the
source to the relief valve inlet flange shall not exceed 3 percent of the valve set pressure.
Where relief valves are vented to the atmosphere, they shall have “tail pipes” equal to or larger in
diameter than the relief valve outlet. These pipes shall extend vertically a minimum of 0.3 m (1 ft)
above building eaves or, in operating areas with adjacent platforms, 2.4 m (8 ft) above the platform
level. The tail pipe shall be provided with a small drain hole to keep rainwater or condensed liquids
from accumulating in the tailpipe. The drain hole shall be located such that the exhaust through the
drain hole does not impinge on vessels, piping, other equipment, or personnel.
Piping shall be installed in such a manner that liquid in the relief valve piping shall drain into the
relief header. This liquid is removed in the vent scrubber (see tutorial the EPT 04-T-02 on Flare and
Vent Systems for information on header design.) Unavoidable low spots in the piping shall be
equipped with drain valves piped to a safe location.
Relief valves shall be tested on a periodic basis even if testing is not required by regulations. Pilot
operated valves can be tested by sending a test signal to the pilot through a test connection in the
pilot sensing line. Spring loaded relief valves shall either: (1) be removed from service; (2) be
tested by subjecting the equipment being protected to set pressure; or (3) have an upstream block
valve provided, which can isolate the relief valve from the equipment being protected, and a test
connection between the block and relief valves installed. There is no industry consensus on which
of these three test methods provides the highest level of safety. Therefore, some relief valves are
installed with upstream block valves and some without.
If relief valves discharge to a common header, it is sometimes convenient to install downstream
block valves so that the relief valve can be removed for repairs without shutdown of all equipment
tied into the common header. The increase in operating flexibility may not be worth the decrease in
safety if the downstream block valve is inadvertently left closed.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
35 of 53
Where either upstream or downstream block valves are used they shall be full open gate or ball
valves with a device that enables them to be locked open and sealed. These are referred to as “car-
seal-open” valves.
Various arrangements employing three-way valves and multiple relief valves are sometimes used to
provide the benefits of being able to isolate the relief valve for testing and maintenance without the
disadvantage of decreasing safety through inadvertent closing of a block valve. Three-way valve
arrangements are much more costly than ordinary block valves. Table 1 in MP 70-P-06 provides
guidance for Mobil installations.
As much as possible, relief valves shall be accessible from platforms. Where relief valves must be
removed for testing, those with 100 mm (4 in) and larger inlet sizes often have davits or other lift
equipment nearby for lowering them to the ground. Relief valve connections to equipment and all
relief piping shall be designed to withstand the high impact forces that occur when the valve opens.
Discharge piping supports shall be arranged to minimize moments at the connection to the
equipment being protected.
Rupture Disk Sizing
Rupture Disk Devices Used Independently
1. Rupture disk devices may be used alone or in combination with a pressure relief valve in
vapor service or in liquid service. For all fluids an effective coefficient of discharge Kd =
0.62 shall be used in the equation for relief valves when sizing a rupture disk for stand-
alone service.
2. The required discharge area, a, is calculated using the appropriate equation for the
flowing medium (see Equations [3] through [14] for vapor and Equation [17] for liquid).
The rupture disk shall be selected so that the area is equal to or greater than the required
discharge area calculated by the appropriate equation.
3. For rupture disk devices that have a structural member (for example, a knife blade or
vacuum support) that reduces the effective discharge area after bursting, the projected
area of the structural member shall be deducted from the flow area of the pipe. This
gives a net discharge area for the rupture disk to be used in the calculations.
4. Users shall be aware that, when using Kd = 0.62 to determine the capacity of a given size
of rupture disk or, conversely, the required area for a given flow quantity:
a) The rupture disk device shall be selected in a size and pressure range that the
manufacturer has determined will give a satisfactory opening for the style of rupture disk
in the particular fluid service.
b) The rupture disk device shall be installed in a piping system short enough that it does not
add significantly to the flow resistance of the burst rupture disk device.
5. If a rupture disk device discharges into a vent system or a closed relief system, it will
usually not contribute significantly to the pressure drop in the piping system. Sizing of
the disk becomes a line sizing problem that uses the relieving rate and the maximum
allowable inlet pressure defined by the code. In general, the rupture disk can be
considered to have an equivalent length of 75 pipe diameters. The manufacturer shall be
consulted if more accurate values are required.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
36 of 53
Rupture Disks Used with Relief Valves
1. One important application of a rupture disk device is at the inlet of a pressure relief valve.
The sizing of the pressure relief valve/rupture disk device combination requires that the
pressure relief valve first be sized to meet the required relieving capacity. The certified
and published capacity of the pressure relief valve used alone is then multiplied by the
combination capacity factor, Kc, to determine the capacity of that combination. Kc = 0.80
unless the manufacturer has established another certified value in accordance with ASME
SEC VIII.
2. The nominal size of the rupture disk device installed at the inlet of the pressure relief
valve shall be equal to or greater than the nominal size of the inlet connection of the
valve to permit sufficient flow capacity and valve performance.
3. The design of the piping from the protected vessel to the inlet of the pressure relief valve
is crucial to the proper functioning of the valve. The frictional pressure loss from the
vessel to the relief valve inlet, including the loss through the rupture disk, shall be less
than 3 percent of the relief valve set pressure. An inlet pipe and rupture disk sized larger
than would be necessary if the pressure relief valve alone were used for relief are often
necessary.
37 of 53
Appendix A–Nomenclature
Operating Pressure
The operating pressure is that pressure normally exerted on the
component or system. Because fluctuations in process pressure can
occur as the control system reacts to changes in flow rate,
temperature, etc., the design pressure shall always be higher than
the operating pressure.
Huddling Chamber
The huddling chamber results from the shape of the seat disk and
the outlet of the relief valve inlet nozzle. Because the disk is larger
than the nozzle outlet with sides that come down around the nozzle
throat, an annular area is created, forming the huddling chamber.
When the seat lifts, higher pressure from the nozzle escapes into
the huddling chamber. Although the nozzle area pressure may be
somewhat reduced, the seat is forced open because higher pressure
is applied to the additional area of the disk in the huddling
chamber. This action increases the reliability of the relief valve
opening.
Gag
When the relief valve body is pressure tested, it is necessary to
prevent the seat disk from lifting off the seat. This is accomplished
by use of a threaded rod or “gag” which is inserted into the top of
the bonnet and depresses the seat disk so that the valve remains
closed against the test pressure.
Flutter
The condition when the set pressure/relieving characteristics of a
relief valve cause the seat disk to reciprocate rapidly without
contacting the valve seat is called flutter.
Chatter
The condition when the set pressure/relieving characteristics of a
relief valve cause the seat disk to repeatedly lift and reseat, thereby
damaging the seat and associated piping, is called chatter.
a = effective discharge area of valve, mm2, in2
C = coefficient determined from the ratio of specific heats
CP = specific heat at constant pressure
CV = specific heat at constant volume
F2 = coefficient of subcritical flow
k = specific heat ratio, Cp/Cv
Kb = back-pressure correction factor
Kd = valve coefficient of discharge
KN = correction factor for Napier equation
Kp = correction factor for overpressure
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
38 of 53
KSH = superheat steam correction factor
Kv = correction factor due to viscosity
KW = correction factor for liquid due to back-pressure
MW = gas molecular weight
Po = upstream vessel maximum pressure, kPa (A), psia
P1 = inlet pressure, kPa (A), psia
P2 = (absolute) back-pressure = Pb + 101.3 kPa (A), = Pb + 14.7 psia
Pb = back-pressure, kPa (g), psig
Pcf = critical flow outlet pressure, kPa (A), psia
POV = overpressure, kPa (g), psig
Pset = set pressure, kPa (g), psig
Q = liquid flow rate, m3/h, (gpm)
R = Reynolds number
r = ratio of absolute back-pressure to upstream relieving pressure, P2/P1
SG = gas specific gravity relative to air
SGL = specific gravity of liquid relative to water
T = flowing temperature, K, °R
U = viscosity, mm2/sec, Saybolt Universal seconds
V = flow through valve, standard m3/hr, SCFM
W = flow through valve, kg/hr, lb/hr
Z = gas compressibility
c = critical pressure ratio
= absolute viscosity, Pa-sec, cp
39 of 53
Appendix B–Example Problems - Metric Units
2. Two-Phase Flow
Given:
V
=
Maximum gas flow rate
=
52,000 std m3/hr
MW
=
Molecular weight of gas
=
23.2
Z
=
Compressibility factor
=
0.75
k
=
Ratio of specific heats
=
1.245
T
=
Flowing temperature
=
38°C
P set
=
Set pressure
=
8270 kPa
P b
=
Back-pressure
=
3450 kPa
Q
=
Liquid Rate
=
2.38 m3/hr
SG L
=
Specific gravity of liquid (Water = 1)
=
0.63
K d
=
Valve coefficient of discharge for conventional and
bellows
=
0.975
Kd
=
Valve coefficient for pilot
=
0.92
Kd
=
Valve coefficient for liquid service
=
0.65
Kv
=
Viscosity correction factor
=
0.95
Determine whether gas flow is critical or subcritical
Calculate orifice size for:
1. Conventional safety relief valve (bonnet vented to atmosphere)
2. Balanced bellows safety relief valve
3. Pilot operated valve
3. Two-Phase Flow
Determine whether gas flow is critical or subcritical
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
40 of 53
kPa 5113
11.245
2
101.38278270 P
1k 2
P
P
1-1.245
1.245
cf
1-kk
1
cf
c
Pcf is greater than the back-pressure of 3450 kPa, so flow through relief valve is critical.
Conventional Safety Relief Valve (Vented Bonnet)
Calculate Orifice Size for Gas
23
Vp
1
b
b1d
in 1.075 mm 693.7 a
19198.30.975341.71 23.20.7538273 52,000 555.79
a
2 Table from 341.71,
2342.19341.22
C/C heats specificof ratio on based constant Gas C
kPa 9198.3 101.38278270 P
1
factor correction pressure-Back K
:where
K P K C MW ZTV 555.79
a
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
41 of 53
Calculate Orifice Size for Liquid
22
21
21
L
VWd
in 0.012 mm 8.0
5647
0.63
0.95 1 0.65 2.38 196.3
a
kPa 5647 3450-8278270 P-P
:where
P-P
SG
K K K Q 196.3
a
Calculate Total Orifice Size
J'' sizevalve Use : 1.088in701.7mm
8.0693.7
aa a
22
GLTOTAL
Balanced Bellows Safety Relief Valve
Calculate Orifice Size for Gas
b1d K P K C MW ZTV 555.79
a
Determine Kb
23
b
in 1.265 mm 816.2
0.859198.30.975341.71 23.20.7538273 52,000 555.79
a
reoverpressu percent 10 with13 Figure from 0.85 K
percent 41.7
8270
100 3450
100
GkPa Pressure, Set G kPa Pressure,-Back
Pressure-Back Gauge Percent
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
42 of 53
Calculate Orifice Size for Liquid
22
W
21
L
VWd
in 0.016 mm 10.4
5647
0.63
0.950.770.65 2.38 196.3
a
15 Figure
from pressure-back gauge percent 41.6 for 0.77
pressure-back for factor Correction K
:where
P-P
SG
K K K Q 196.3
a
Calculate Total Orifice Size
K'' sizevalve Use : 1.281in826.6mm
10.4816.2
aa a
22
GLTOTAL
Pilot Operated Valve
Calculate Orifice Size for Gas
22
b1d
in 1.140 mm 735.2
19198.30.92341.71 23.20.7538273 52,000 555.79
a
K P K C MW ZTV 555.79
a
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
43 of 53
Calculate Orifice Size for Liquid
22
21
L
VWd
in 0.012 mm 8.0
5647
0.63
0.9510.65 2.38 196.3
a
P-P
SG
K K K Q 196.3
a
Calculate Total Orifice Size
J'' sizevalve Use :in 1.152 mm 743.2
8.0735.2 a
22
TOTAL
Gas Subcritical Flow
Given:
V
=
Maximum gas flow rate
=
30,000 std m3/hr
MW
=
Molecular weight of gas
=
23.2
Z
=
Compressibility factor
=
0.75
k
=
Ratio of specific heats
=
1.245
T
=
Flowing temperature
=
21°C
P set
=
Set pressure
=
690 kPa
P b
=
Back-pressure
=
410 kPa
K d
=
Valve coefficient of discharge for conventional and
bellows
=
0.975
Kd
=
Valve coefficient for pilot
=
0.92
Determine whether gas flow is critical or subcritical
Calculate orifice size for:
4. Conventional safety relief valve (bonnet vented to atmosphere)
5. Balanced bellows safety relief valve
6. Pilot operated valve
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
44 of 53
Subcritical Flow Example Problem
Determine whether gas flow is critical or subcritical
kPa 478
11.245
2
101.369690 P
1k 2
P
P
1-1.245
1.245
cf
1-kk
1
cf
c
Pcf is greater than the back-pressure of 517 kPa, so flow through relief valve is subcritical.
Permitted build-up back-pressure of 10 percent of Pset is 69 kPa, so total back- pressure = 410
+ 69 = 479 kPa (G).
Conventional Safety Relief Valve (Vented Bonnet)
211d2 P-P P MWZT
K F V 0.756
a
From Figure 14, for r = P 2/P1 = (410 + 69 + 101.3)/(690 + 69 + 101.3) = 0.67, coefficient of
subcritical flow F2 = 0.79.
Q'' sizevalve Use :in 6.651 mm 4291.0
580.3-860.3860.3 23.2212730.75
0.9750.79 30,000 0.756
a
22
Balanced Bellows Safety Relief Valve
b1d K P K C MW ZTV 555.79
a
Assume Kb = 0.65 for this application. This value would normally be obtained from the
manufacturer.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
45 of 53
Q'' sizevalve Use :in 9.922 mm 6401.1
0.65860.30.975341.71 23.20.7521273 30,000 555.79
a
22
Pilot Operated Valve
Q'' sizevalve Use :in 7.049 mm 4547.5
580.3-860.3860.3 23.2212730.75
0.920.7930,000 0.756
a
P-P P MWZT
K F V 0.756
a
22
211d2
Appendix C–Example Problems - Customary Units
Two-Phase Flow
Given:
V
=
Maximum gas flow rate
=
44 MMSCFD
MW
=
Molecular weight of gas
=
23.2
Z
=
Compressibility factor
=
0.75
k
=
Ratio of specific heats
=
1.245
T
=
Flowing temperature
=
100°F
Pset
=
Set pressure
=
1200 psig
Pb
=
Back-pressure
=
500 psig
Q
=
Liquid Rate
=
360 BPD
SGL
=
Specific gravity of liquid (Water = 1)
=
0.63
Kd
=
Valve coefficient of discharge for conventional and
bellows
=
0.975
K d
=
Valve coefficient for pilot
=
0.92
K d
=
Valve coefficient for liquid service
=
0.65
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
46 of 53
K v
=
Viscosity correction factor
=
0.95
Determine whether gas flow is critical or subcritical.
Calculate orifice size for:
7. Conventional safety relief valve (bonnet vented to atmosphere)
8. Balanced bellows safety relief valve
9. Pilot operated valve
Two-Phase Flow Example Problem
Determine whether gas flow is critical or subcritical.
psia 742
11.245
2
14.71201200 P
1k 2
P
P
1-1.245
1.245
cf
1-kk
1
cf
c
Pcf is greater than the back-pressure of 515 psia, so flow through relief valve is critical.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
47 of 53
Conventional Safety Relief Valve (Vented Bonnet)
Calculate Orifice Size for Gas
J'' sizevalve Use : in 1.073
113350.975341.71 6.32 23.20.75460100 30,556
a
psia 1335 14.71201200 P
min
ft
30556
min 60hr
hr 24
day
day
ft
1044 V
1
factor correction pressure-Back K
2 Table from 341.71,
2342.19341.22
C/C heats specificof ratio on based constant Gas C
:where
K P K C 6.32 MW ZTV
a
2
1
33
6
b
VP
b1d
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
48 of 53
Calculate Orifice Size for Liquid
2
21
21
L
VWd
in 0.012
820
0.63
0.95 1 0.65 38 10.5
a
psi 820 500-1201200 P-P
gpm 10.5
min 60hr
hr 24
day
barrel
gal 42
day
barrels
360 Q
:where
P-P
SG
K K K 38 Q
a
Calculate Total Orifice Size
J'' sizevalve Use :in 1.085
1.0730.012
aa a
2
GLTOTAL
Balanced Bellows Safety Relief Valve
Calculate Orifice Size for Gas
b1d K P K C 6.32 MW ZTV
a
Determine Kb
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
49 of 53
2
b
in 1.262
0.8513350.975341.71 6.32 23.20.75560 30556
a
reoverpressu percent 10 with13 Figure from 0.85 K
percent 41.6
1200
100 500
100
psig Pressure, Set psig Pressure,-Back
Pressure-Back Gauge Percent
Calculate Orifice Size for Liquid
2
W
21
L
VWd
in 0.016
820
0.63
0.950.770.65 38 10.5
a
15 Figure
from pressure-back gauge percent 41.6 for 0.77
pressure-back for factor Correction K
:where
P-P
SG
K K K 38 Q
a
Calculate Total Orifice Size
K'' sizevalve Use :in 1.278
1.2620.016 a
2
TOTAL
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
50 of 53
Pilot Operated Valve
Calculate Orifice Size for Gas
2
b1d
in 1.137
113350.92341.71 6.32 23.20.75560 30,556
a
K P K C 6.32 MW ZTV
a
Calculate Orifice Size for Liquid
2
21
L
VWd
in 0.012
820
0.63
0.9510.65 38 10.5
a
P-P
SG
K K K 38 Q
a
Calculate Total Orifice Size
J'' sizevalve Use :in 1.149
1.1370.012 a
2
TOTAL
Gas Subcritical Flow
Given:
V
=
Maximum gas flow rate
=
25 MMSCFD
MW
=
Molecular weight of gas
=
23.2
Z
=
Compressibility factor
=
0.75
k
=
Ratio of specific heats
=
1.245
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
51 of 53
T
=
Flowing temperature
=
70°F
Pset
=
Set pressure
=
100 psig
Pb
=
Back-pressure
=
60 psig
K d
=
Valve coefficient of discharge for conventional and
bellows
=
0.975
Kd
=
Valve coefficient for pilot
=
0.92
Determine whether gas flow is critical or subcritical.
Calculate orifice size for:
10. Conventional safety relief valve (bonnet vented to atmosphere)
11. Balanced bellows safety relief valve
12. Pilot operated valve
Subcritical Flow Example Problem
Determine whether gas flow is critical or subcritical
psia 69.3
11.245
2
14.710100 P
1k 2
P
P
1-1.245
1.245
cf
1-kk
1
cf
c
Pcf is greater than the back-pressure of 517 kPa, so flow through relief valve is subcritical.
Permitted build-up back-pressure of 10 percent of Pset is 10 psi, so total back- pressure = 60 +
10 = 70 psig.
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
52 of 53
Conventional Safety Relief Valve (Vented Bonnet)
min
ft
17,361
min 60hr
hr 24
day
day
ft
1025 V
:where
P-P P MWZT
K F 4645.2 V
a
33
6
211d2
From Figure 14, for r = P 2/P1 = (60 + 10 + 14.7)/(100 + 10 + 14.7) = 0.68, coefficient of
subcritical flow F2 = 0.80.
Q'' sizevalve Use :in 6.651
84.7-124.7124.7 23.2704600.75
0.9750.804645.217,361
a
2
Balanced Bellows Safety Relief Valve
b1d K P K C 6.32 MW ZTV
a
Assume Kb = 0.65 for this application. This value would normally be obtained from the
manufacturer.
Q'' sizevalve Use :in 9.769
0.65124.70.975341.71 6.32 23.20.7570460 17,361
a
2
Design and Calculation of the Pressure Relief Valves and Rupture Disks System
53 of 53
Pilot Operated Valve
Q'' sizevalve Use :in 6.905
84.7-124.7124.7 23.2704600.75
0.920.804645.2
17,361
a
P-P P MWZT
K F 4645.2
V
a
2
211d2
References
The following Mobil guides and industry publications shall be considered a part of this EPT. Refer
to the latest editions unless otherwise specified herein.
MEPS–Mobil Engineering Practices
API–American Petroleum Institute
API RP 14C
Recommended Practice for Analysis, Design, Installation, and
Testing of Basic Surface Safety Systems for Offshore Production
Platforms Fifth Edition; Errata - 1994
API RP 14E
Recommended Practice for Design and Installation of Offshore
Production Platform Piping Systems Fifth Edition
API RP 520 I
Sizing, Selection and Installation of Pressure-Relieving Devices in
Refineries, Part I - Sizing and Selection
API RP 521
Guide for Pressure-Relieving and Depressuring Systems Fourth
Edition
ASME–American Society of Mechanical Engineers
ASME SEC VIII
D1
SISI Units (Boiler and Pressure Vessel Codes)