Safety Relief Valves Sizing
Link: https://processpocket.streamlit.app/Safety%20Valves%20Sizing
This tool was developed for process engineers to quickly estimate the outcome of the safety relief valve sizing
equations on site. As a part of a larger project to develop what is similar to Carl Branan’s book “process
engineers Pocket Handbook” these tools would allow a process engineer to quickly calculate/estimate
equipment efficiencies or sizing using standardized calculations
The aim here is to take little-known data from the field (flow, pressures, temperatures, compositions..etc.) and
use it as input for a rough estimation without having to return to the office to use commercial software or
calculations Excel sheets to validate or to calculate. Additionally, these tools may also serve as a gathered data
validation tool.
Nomenclature
Tn
T
a
𝜆
H
Re
ρ
D
L
W
Q
Q
h
L1
C
U
Kd
KSH
Kv
Kc
Temperature (oK)
Temperature at relieving conditions (oK)
Temperature of insulation outer surface (1177 oK)
Latent heat of vaporization (kcal/kg)
Enthalpy (kcal/kg)
Reynold’s number
Density (kg/m3)
Diameter (m)
Length (m)
W Required relieving capacity (kg/hr)
Required relieving capacity (Nm3 /min or
L/min for liquids)
Relief Load (kW or kcal/hr)
Depth of wetted portion (m)
NLL in vessel/column (m)
Coefficient determined from an expression of
the ratio of specific heats of the gas or vapor
Heat transfer coefficient (kcal/(m2.h°C))
The effective coefficient of discharge
superheated correction factor (steam)
Viscosity correction factor (liquid)
Combination correction factor
P
P1/s/c/back
t
M
µ
k
αv
Cp
Aw
A/Acalc
Ae
G
Z
F
F2
L2
v
Kb
KN
Kw
Pressure (kPa)
Relief/Set/critical/back pressures (kPa)
Thickness of insulation (m)
Molecular weight M.wt
Viscosity (cP)
Gas specific heat ratio
cubical expansion coefficient (1/°K)
Heat Capacity (Kg/Kcal.hr. oC)
Wetted area (m2)
Minimum required effective discharge area (mm2)
Effective area (mm2)
Specific gravity
Compressibility factor
Environmental factor
Coefficient for subcritical gas flow sizing
equation
Elevation above grade (m)
Velocity (m/s)
Capacity correction factor due to backpressure
Correction factor for Napier equation (steam)
Backpressure correction factor (liquid)
Input Required
Table 1: Note 1: Input required depending on the case
1. Calculating Relieving/Set Pressure
2. Relief Loads Estimation (Cont.)
Case (non-fire/fire)
-
Closed Outlet (Heat Exchangers)
MAWP
kg/cm².g
Hot side inlet temperature
o
Design Pressure (if Set pressure
doesn’t equal MAWP)
Disc Installation Type (If multiple
device installation is chosen)
2. Relief Loads Estimation
kg/cm².g
Normal Cold Side rate
Kg/hr
One/additional/ Normal Cold Side composition
Supplemental
Normal Cold Side conditions (T&P)
External Fire (Vaporization)
C
%vol
o
C/ kg/cm².a
Inadvertent Control Valve opening
normal stream composition
%vol
Control valve size
inch
normal stream conditions (T&P)
o
C/ kg/cm².a
Control Valve opening
%
Aw calculations
(If the stream is liquid, it appears)
Type of Equipment
m2
%vol
Geometry inputs
m
Control valve inlet and outlet
stream composition
Control valve inlet and outlet
normal stream conditions (T&P)
Thermal Expansion
Heat Absorbed
kW
Relieved stream composition
%vol
External Fire (Gas expansion)
Relieved stream conditions (T&P)
o
Same input +
Max. Heat load
Kcal/hr
vessel maximum wall temperature
o
C
Closed Outlet (Vessel)
o
C/ kg/cm².a
C/ kg/cm².a
3. Gas or Vapor/ Steam
Mass flow rate
Kg/hr
Vessel Feed rate
Kg/hr
inlet/outlet stream composition
%vol
feed composition and
%vol
Inlet (relieved) stream conditions (T&P)
o
C/ kg/cm².a
feed stream conditions (T&P)
o
C/ kg/cm².a
Outlet (relief header) stream conditions (T&P)
o
C/ kg/cm².a
Feed vapor mass fraction (if not
calculated)
0-1 range
Kb, kd, kc input (optional)
-
Closed Outlet (Vessel with reboiler)
3. Liquid
Same +
Same +
Kw, kd, kc input (optional)
-
Output Obtained
1. Calculating Relieving/Set Pressure
3. Liquid
Max. accumulated pressure
kg/cm².g
Max. Flow Capacity
Kg/hr
Relief device set pressure
kg/cm².g
Kg/m3/cP
Allowable overpressure
Overpressure
Relieving pressure
2. Relief Loads Estimation
Calculated Relief Load
Calculated Relieving flow rate
3. Gas or Vapor/ Steam
Flow
Max. Flow Capacity
Physical properties used in
calculations: average cp/cv, µ, M.wt, Z
Kb,kd,kc + (kSH, kN) for steam
Minimum area
Selected Area
Orifice Designation
Permissible inlet/outlet nozzles
Table of Calculations
Specifications sheet
kg/cm²
%
kg/cm².a
Physical properties used in
calculations: Density/ µ
Kw,kd,kc
Minimum area
Selected Area
Orifice Designation
Permissible inlet/outlet nozzles
Table of Calculations
Specifications sheet
kW
Kg/hr
cm2/in2
cm2/in2
inches
-
Critical/Subcritical
Kg/hr
-/cP/-/cm2/in2
cm2/in2
inches
-
1. Introduction
Sizing pressure relief valves (PSV) requires a vivid understanding of the process where the safety valves are
installed, the sizing equations, and the numerous relevant standards. In this document, we’ll be exploring the
hand calculations required to preliminary size different safety valves. First, we’ll explore how to estimate the
relieving and set pressures according to standards. Secondly, we’ll explore the basic safety orifices sizing
equations (for gases, steam, or liquids) and learn how to estimate the required coefficients. Finally, we’ll take a
glance at how to estimate the required relief loads for different processes and contingencies as an introduction
to this complex matter. However, the back pressure calculations were not discussed in this document. The
backpressure used in safety calculations is the sum of superimposed backpressure and built-up back pressure.
The superimposed backpressure is the static pressure and the relief header before the valve opening, while the
built-up back pressure is the pressure increase due to the valve opening building up extra pressure to overcome
the outlet friction losses. The estimation of the built-up back pressure could be discussed later in the context of
flare systems calculations.
This document did not discuss the various safety valve types' working mechanisms, the rupture disc types and
sizing procedures, or guidelines for sizing the inlet/outlet piping of PSV. However, you may find the mentioned
topics in references and recommended reads.
2. Set/relief Pressure Calculations
Table 2.1: Relief Pressure estimation table (percentages are applied to MAWP’s gauge pressures) [1]
Contingency
Installation
Single-Valve Installations
Set Pressure
Max. Accumulated
(%)
pressure (%)
Multiple-Valve Installations
Set Pressure Max. Accumulated
(%)
pressure (%)
Non-fire only
First valve
100
110 [1]
100
116 [2]
Fire only
Additional valve(s)
First valve
--100
--121
105
100
116 [2]
121
Additional valve(s)
----105
121
Supplemental valve ----110
121
Note : All values are percentages of the maximum allowable working pressure.
(1) 10% or 3 psi (0.21 kglcm2), whichever is greater.
(2) 16% or 4 psi (0.28 kg/cm2), whichever is greater.
(3) A supplemental valve installation provides relieving capacity for an additional hazard created by exposure to
fire or other unexpected sources of external heat. Supplemental valves are used only in addition to valves sized
for operating (non-fire) contingencies. [3]
(4) In the case of ASME-application liquid service valves (that is, for protection of a liquid-full vessel), maximum
accumulated pressure is limited to 110% of the maximum allowable working pressure for operating
contingencies. In the case of non-ASME-application liquid service valves (for protection of piping without vessels
included), 25 % overpressure is generally specified. [3]
(5) The minimum pressure differentials between the set pressure of the valve and the operation pressure of the
vessel are recommended as follows:
Table 2.2: minimum differential pressure limitations [3]
Set Pressure Ps
Ps ≤ 70 psi (4.9 kg/cm2)
Ps ≤ 1000 psi (70 kg/cm2)
Ps > 1000 psi (70 kg/cm2)
Minimum recommended
Pressure differential
5 psi (0.35 kg/cm2)
10% of Ps
7% of Ps
Figure 2.1: Pressure Level Relationships for Pressure-relief Valves [1]
3. Safety Relief Valves Sizing
Gases
Steam
Subcritical Flow
𝐴=
𝐴=
𝐴=
Acalc
𝐹2 𝐾𝑑 𝐾𝑐 √𝑃1 (𝑃1 − 𝑃2 )
258 ∗ 𝑄 ∗ √𝑇𝐺𝑍
𝐹2 𝐾𝑑 𝐾𝑐 √𝑃1 (𝑃1 − 𝑃2 )
𝐴=
𝑊 ∗ √𝑇𝑍
𝐶𝐾𝑑 𝑃1 𝐾𝑏 𝐾𝑐 √𝑀
2.676 ∗ 𝑄 ∗ √𝑇𝑀𝑍
𝐶𝐾𝑑 𝑃1 𝐾𝑏 𝐾𝑐
14.41 ∗ 𝑄 ∗ √𝑇𝐺𝑍
𝐴=
𝐶𝐾𝑑 𝑃1 𝐾𝑏 𝐾𝑐
𝐴=
𝑃1
∗𝑇
𝑃𝑛 𝑛
𝑃𝐶𝑓
2 𝑘⁄(𝑘−1)
]
=[
𝑃1
𝑘+1
𝑇=
𝐶 = 0.03948√𝑘 [
𝐹2 = √[
Wmax[3]
Critical Flow
17.9 ∗ 𝑊 ∗ √𝑇𝑍
𝐹2 𝐾𝑑 𝐾𝑐 √𝑀𝑃1 (𝑃1 − 𝑃2 )
47.95 ∗ 𝑄 ∗ √𝑇𝑀𝑍
Liquids
𝐴=
190.5 ∗ 𝑊
𝑃1 𝐾𝑑 𝐾𝑠ℎ 𝐾𝑁 𝐾𝑏 𝐾𝑐
𝐴=
11.78𝑄√𝐺
𝐾𝑑 𝐾𝑤 𝐾𝑣 𝐾𝑐 √𝑃1 − 𝑃2
2 𝑘+1/𝑘−1
]
𝑘+1
𝑘
1 − 𝑟 (𝑘−1)/𝑘
] 𝑟 2/𝑘 [
]
𝑘−1
1−𝑟
𝑊𝑟𝑒𝑞 ∗ 𝐴𝑒
𝐴𝑐𝑎𝑙𝑐
A: mm2
W: kg/h
Units
Q: Nm3/min
P1,P2: kPa
T: Kelvin
W (kg/h ) = 0.044 * M.wt * Q (Nm3/hr)
Q (Nm3/min) = Q (Nm3/hr)/60
Conversion Q (L/min) = Q (m3/hr) *16.67
Notes
P (kPa) = P (kg/cm2) * 98.0665
A (cm2) = A (mm2)*0.01
A (in2) = A (cm2) * 0.155
𝑊𝑟𝑒𝑞 ∗ 𝐴𝑒
𝐴𝑐𝑎𝑙𝑐
A: mm2
W: kg/h
P1,P2: kPa
T: Kelvin
𝑊𝑟𝑒𝑞 ∗ 𝐴𝑒
𝐴𝑐𝑎𝑙𝑐
A: mm2
Q: L/min
P1,P2: kPag
T: Kelvin
Table 3.1: Table of single-phase relief valve sizing equations [1]
NOTE 1: The Napier coefficient KN must be considered when P1 ≥ 106.5 kg/cm2a.
NOTE 2: for gas equations
Kd = effective coefficient of discharge. For preliminary sizing, use the following values:
= 0.975 when a pressure relief valve is installed with or without a rupture disk in combination.
= 0.62 when a pressure relief valve is not installed and sizing is for rapture disk
Wrated = maximum rated flow rate through the valve
3.1 Gas PSV Sizing[1]
1. Estimate if flow is critical or sub-critical from the following equation
𝑃𝑐 = 𝑃1 ∗ [
2
𝑘+1
]
𝑘/𝑘+1
, where
Pc is the critical pressure, P1 is the upstream pressure (relieving), both in absolute units
k is the specific heats ratio for any ideal gas
2. Based on the flow condition, you can proceed with one of the following equations:
Sub-critical Flow
Pc < Pback
𝐴=
𝐴=
Critical Flow
Pc > Pback
17.9 ∗ 𝑊 ∗ √𝑇𝑍
𝐹2 𝐾𝑑 𝐾𝑐 √𝑀𝑃1 (𝑃1 − 𝑃2 )
47.95 ∗ 𝑄 ∗ √𝑇𝑀𝑍
𝐴=
𝐹2 𝐾𝑑 𝐾𝑐 √𝑃1 (𝑃1 − 𝑃2 )
258 ∗ 𝑄 ∗ √𝑇𝐺𝑍
𝐹2 𝐾𝑑 𝐾𝑐 √𝑃1 (𝑃1 − 𝑃2 )
𝑊 ∗ √𝑇𝑍
𝐴=
𝐶𝐾𝑑 𝑃1 𝐾𝑏 𝐾𝑐 √𝑀
2.676 ∗ 𝑄 ∗ √𝑇𝑀𝑍
𝐴=
𝐶𝐾𝑑 𝑃1 𝐾𝑏 𝐾𝑐
14.41 ∗ 𝑄 ∗ √𝑇𝐺𝑍
𝐴=
𝐶𝐾𝑑 𝑃1 𝐾𝑏 𝐾𝑐
Table 3.2: Gas PSV sizing equations
Where,
𝐶 = 0.03948√𝑘 [
2
𝑘+1
]
𝑘+1/𝑘−1
, refer to Figure 3.7
𝐹2 = 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑠𝑢𝑏𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑓𝑙𝑜𝑤 = √[
𝑘
] 𝑟 2/𝑘 [
𝑘−1
1−𝑟 (𝑘−1)/𝑘
1−𝑟
], refer to Figure 3.6
r: ratio of backpressure to upstream relieving pressure P2/P1
Balanced Pressure Relief Valves
Balanced pressure relief valves should be sized using critical-flow equations. The back pressure correction factor
in this application accounts for subcritical flow velocities and the tendency for the disc to drop below full lift (the
use of subcritical flow equations is appropriate only where full lift is maintained). For this application, the back
pressure correction factor, Kb, should be obtained from the manufacturer.
Figure 3.1: Kb for balanced bellows relief valves (Gas) [1]
[1]
3.2 Steam PSV Sizing
Pressure relief devices in steam service that operate at critical
low conditions may be sized using:
𝐴=
190.5∗𝑊
𝑃1 𝐾𝑑 𝐾𝑠ℎ 𝐾𝑁 𝐾𝑏 𝐾𝑐
, where
Kb: The capacity correction factor is due to backpressure.
Applied for balanced bellows valves only. Refer to Figure 1
For conventional valves, use a value for Kb equals 1.0.
KN: correction factor for Napier equation
= (0.1906 * P1- 1000)/(0.2292 *P1 - 1061)
where P1 in kPa and 10339 kPa < P1 ≤ 22057 kPa
KSH: Correction factor for superheated steam.
For saturated steam use KSH =1.0
3.3 Liquid PSV Sizing [1]
Pressure relief devices for liquid services may be sized using:
𝐴=
11.78 ∗ 𝑄 ∗ √𝐺
𝐾𝑑 𝐾𝑤 𝐾𝑣 𝐾𝑐 𝐾𝑝 √𝑃1 − 𝑃2
Kd: effective coefficient of discharge that should be obtained from the valve manufacturer. For preliminary sizing
estimation, a discharge coefficient of 0.65 can be used.
Kw: correction factor for back pressure. If the backpressure is atmospheric, Kw =1.0.
Balanced-bellow valves in backpressure service will require the correction factor obtained from
Figure 2 Conventional valves require no special correction.
Kv: correction factor for viscosity as determined from the following equation:
𝑘𝑣 = (0.9935 +
2.878
342.75 −1
𝑅𝑒
𝑅𝑒
0.5 +
1.5 )
170
or 𝑘𝑣 = (
𝑅𝑒
−0.5
+ 1)
When a pressure relief valve is sized for viscous liquid service, it should first be sized as if it were for non-viscous
type application (i.e., Kv = 1.0) so that a preliminary required discharge area, A, can be obtained from the previous
equation. From API standard orifice sizes (Table 3.3 may be used for preliminary estimation), the next larger
orifice size should be used in determining the Reynolds number, Re, the following equation:
𝑅𝑒 =
𝑄∗(18800∗𝐺)
𝜇√𝐴
,
µ: Liquid viscosity is cP
Q: flow rate in L/min
G: specific Gravity
A: selected area mm2
After Reynold’s number, Re, is determined, the factor Kv is obtained, and Kv is then applied in the liquid sizing
equation to correct the preliminary required discharge area. If the corrected area exceeds the chosen standard
orifice area, the above calculations should be repeated using the next larger standard orifice size.
Figure 3.2: Kw for kb for relief valves due to back pressure (liquid)
[1]
Table 3.3: Conventional and balanced-bellows valve selection table
(API RP 526 and GPSA Section 3) [3]
Figure 3.3: Kv for relief valves due to viscosity (liquid) [1]
Figure 3.5: KSH for steam at T&P[3]
Figure 3.4: Kb for conventional/pilot operated relief valves (Gas) [1]
Figure 3.6: F2 Values for Gas PSV Sizing (subcritical Flow)
Figure 3.7: C Values for Gas PSV Sizing (Critical Flow)
3.4 Calculating Equation Coefficients
1. Gas or Vapors
Kb Capacity correction factor
Kb = a + b(Pb /(Pset+POP)) 3 (abs. pressures)
(Conventional and pilot operated) [6]
γ
Range %
a
b
1.1
66-90
1.3026
-1.137*10-6
1.3
63-90
1.294
-1.1703*10-6
1.5
56-90
1.203
-1.143*10-6
1.7
51-90
1.148
-1.109*10-6
Kb =1/( a + b(PB/Ps)3) (gauge pressures)
(Balanced bellows) [6]
Overpressure Range
a
b
10
30-50
0.8707
4.724*10-6
20
30-50
0.976
8.36*10-7
1. The curves above represent a compromise of the values
[1]
recommended
several
relief
valve
manufacturers
and
Figure 3.6: C for by
Critical
flow gas
Sizing
equation
used when the make of the valve or the critical flow
pressure point for the vapor or gas is unknown. The curves
are for set pressures of 50 psig and above. They are limited
to back pressure below critical flow pressure for a given set
pressure. For set pressure below 50 psig or subcritical flow,
the manufacturer must be consulted for values of Kb. [1]
2. For 21% overpressure, Kb equals 1.0 up to PB/PS = 50%.[1]
3. For pilot-operated PRVs, the valve lift is not affected by
backpressure. For compressible fluids at critical
flow conditions, a backpressure correction factor of 1.0
should be used for pilot-operated PRVs.[1]
Alternatively, kb can be estimated for conventional and
pilot-operated Relief valves using Figure 3.4 (Subcritical
flow) [1]
Kd Effective coefficient of discharge for PSV
0.975 when a PRV is installed with or without a rupture disk
in combination;
0.62 when a PRV is not installed and sizing is for a rupture
disk
Kc combination correction factor
1.0 when a rupture disk is not installed.
Figure 3.7: F2 for Subcritical gas equation [1]
0.9 when a rupture
disk is installed with a pressure relief
valve and the combination does not have a published value.
2. Steam
KN Correction factor for Napier equation
= 1.0 where P1≤ 106.5 kg/cm2a or 1339 kPa
= (0.1906 * P1- 1000)/(0.2292 *P1 - 1061)
where P1 in kPa and
10339 kPa (106.5 kg/cm2a) < P1 ≤ 22057 kPa (226.1
kg/cm2A)
KSH Superheat steam correction factor
For saturated steam at any pressure, KSH = 1.0
KSH can be obtained from figure 3.5 or KSH tables published
in ref [1] P.86-90.
3. Liquid
Kw Correction factor due to back pressure
If the back pressure is atmospheric, Kw = 1.0. for
conventional and pilot-operated PSVs, kw =1. Otherwise.
Use Figure 3.2.
Kw = 1.1165-0.01*(PB/Ps) for (PB/Ps) > 17 [6]
Kv viscosity correction factor
2.878 342.75 −1
𝑘𝑣 = (0.9935 + 0.5 +
)
𝑅𝑒
𝑅𝑒1.5
170 −0.5
𝑘𝑣 = (1 +
)
𝑅𝑒
Or use Figure 3.3
1.Use the next larger orifice area to calculate Re
2.Correct calculated A without Kv by dividing it with new Kv
Kd Effective coefficient of discharge for PSV
0.65, when a PRV is installed with or without a rupture disk
in combination;
0.62, when a PRV is not installed, and sizing is for a rupture
disk
Notes on PSV sizing
PSV sizing could be an iterative procedure or a two-step process
After estimating the relieving capacity, you may want to check its impact on the relief header's total back
pressure. The increased back pressure due to the calculated relieved capacity could impact your
calculated/initially estimated Kb, resulting in another iteration/step to calculate the corrected relieved capacity.
Refer to section 5.3.4.2 on ref [1]
Inlet piping
inlet piping pressure losses due to friction should not be higher than 3% of set pressure and calculated using the
maximum rated capacity of the pressure relief device [1][3]. Exceptions were mentioned in recommended reads[II]
When two or more pressure relief devices are placed on one connection, the inlet piping internal cross-sectional
area shall be at least equal to the combined inlet areas of the pressure relief devices connected to it
Selection Criteria of PSV
1. Conventional PSVs
2. The sum of the maximum variable superimposed back pressure plus the built-up back pressure is less than
10% of the set pressure.
3. Fouling or corrosive conditions are not expected.
2. Bellows Type PSVs
1. The sum of the variable superimposed back pressure plus built-up back pressure exceeds 10% of set
pressure.
2. Fouling or corrosive conditions are expected and protection cannot be afforded by using alternative
materials or devices.
Backpressure Limitations on Bellows Type PSVs
Total backpressure shall not reduce differential pressure across the PSV to a value limiting PSV relieving capacity
to less than design capacity. This corresponds to a total backpressure of approximately 50% of set pressure for
gas services.
3.
1.
2.
3.
Pilot Operated PSVs
Pilot-operated PSVs are recommended when maximum set point accuracy is required
Pilot-operated PSVs shall generally be limited to clean gas service.
Tanks designed to API STD 650, which may also require pressure relief devices, may be protected by pilotoperated relief valves. Pilot-operated relief valves shall protect tanks designed to API STD 620.
More on the advantages and disadvantages of different PSV types can be found at recommended reads [II] [III]
4. Examining possible cases (Contingencies)
Estimating the required relief loads could be a grueling task that requires extensive heat and mass balance
calculations at relief conditions. It could be best to use simulation tools for this one. However, this section
aims to familiarize readers with the basis and variables needed for different scenarios. Moreover, manual
calculations could be an alternative option where minimum data are available for simulation in some cases.
All causes of overpressure, or contingencies, must be evaluated for each PSV installation in terms of the
pressures generated and the rates at which fluids must be relieved. Causes of overpressure in process
equipment can range from a single event to a complex combination of events. The basis for calculating a
valve size follows calculations of valid contingencies. The contingency that requires the largest effective area
dictates the size of the PSV.
More on “guidelines on estimating relief loads for different contingencies” can be found on recommended
reads [V][I][III]
Table 4.1: Guidelines on estimating relief loads for different contingencies [2]
Item
No. Condition
1 Closed outlets on vessels
Pressure Relief Device
(Liquid Relief)
Maximum liquid pumpin rate
Pressure Relief Device
(Vapor Relief)*
Total incoming steam and vapor plus that
generated therein at relieving conditions
Total vapor to condenser at relieving conditions
Total incoming steam and vapor plus that
generated therein at relieving conditions less
vapor condensed by side-stream reflux
Difference between vapor entering and leaving
section at relieving conditions
None, normally
Same effect in towers as found for Item 2; in
other vessels, same effect as found for Item 1
For towers, usually not predictable
2 Cooling water failure to condenser
3 Top-tower reflux failure
—
—
4 Side-stream reflux failure
—
5 Lean oil failure to absorber
6 Accumulation of noncondensables
—
—
7 Entrance of highly volatile
material: Water in hot oil or Light
hydrocarbons in hot oil
8 Overfilling storage or surge vessel
—
Maximum liquid
Pump-in rate
—
9 Failure of automatic controls
10 Abnormal heat or vapor input
—
—
11 Split exchanger tube
—
12 Internal Explosions
—
13 Chemical reaction
—
14 Hydraulic expansion
1. Cold fluid shut in
2. Line outside process area
3. Shut in
15 Exterior fire
16 Power failure (steam, electric, or
other)
Use Liquid expansion
equation (table 4.7)
Must be analyzed on a case-by-case basis
Estimated maximum vapor generation including
non-condensables from overheating
Steam or vapor entering from twice the crosssectional area of one tube; also same effects
found in Item 7 for exchangers
Not controlled by conventional relief devices
but by avoidance of circumstances
Estimated vapor generation from both normal
and uncontrolled conditions
—
—
—
Estimate by external fire equations (table 4.2)
Study the installation to determine the effect of
power failure; size relief valve for the worst
condition that can occur
1. Fractionators
—
2. Reactors
—
3. Air-cooled exchangers
—
4. Surge vessels
Maximum liquid inlet
rate
All pumps could be down, with the result that
reflux and cooling water would fail
Consider failure of agitation or stirring, quench
or retarding steam; size valves for vapor
generation from a runaway reaction
Fans would fail; size valves for the difference
between normal and emergency duty
—
* Considerations may be given to the suppression of vapor production as the result of the device’s relieving
pressure being above operating pressure, assuming constant heat input. (Procedures for sizing pressure relief devices
are presented in Section 4 of API-RP-520.)
After the specifications are determined, the next activity is to calculate a preliminary effective discharge area.
Figure 4.1 shows the inputs used to determine the basis for calculating the size of a PSV.
Figure 4.1: Sizing input flowchart [2]
Relief Loads Estimation for individual contingencies
External Fire
Overpressure due to vaporization [4]
External Fire
Overpressure due to Gas Expansion [4]
𝑄
∆𝐻
W: relieving load kg/hr
△H: Enthalpy difference between normal and relieving
conditions Kcal/kg
Q: total heat absorbed kcal/hr
NOTE: assuming to inlet or outlet flow
𝑄 = 𝑞𝑜 . 𝐹. 𝐴0.82
Q: total heat absorbed kcal/hr
F: Environmental factor
A: wetted surface m2
qo: 37130,
if drainage isn’t provided qo: 61000
Bare Vessel
F=1
Insulated Vessel
𝑘 ∗ (𝑎 − 𝑇)
𝐹=
𝐶. 𝑡
k: thermal conductivity of insulation ( W/m-K) at average of
904 oC and relieving temperature.
Tf: temperature of vessel contents at relieving condition ( oC)
a: temperature of insulation outer surface (904 oC)
C: constant that equals 66570
t: thickness of insulation (m)
Type of equipment
Factor F
Factor F
API RP521
NFPA 30
Bare Vessel
1.0
1.0
When the vessels that contain no liquid, such
as gas holders, are exposed to the fire
contingency, overpressure will occur due to the
gas expansion. The following equation can
obtain the relieving loads for this case:
𝑊 =
Water application
facilities on bare vessel
Water application
facilities on insulated
vessel
Depressurizing and
emptying facilities
Underground storage
Earth covered storage
above grade
1.0
0.3
1.0
0.15
1.0
-
0.0
0.03
0.3
-
Table 4.2: Relief loads guidelines for External Fire
𝐴 (𝑇𝑤 − 𝑇1 )1.25
𝑊 = 0.1406√𝑀𝑃1 (
)
𝑇11.1506
W: relieving load lb/hr
M: molecular weight
P1: relieving pressure psia
A: exposed surface area ft2
Tω: Vessel max. wall temperature, 593 for CS
(oR)
T1: relieving temperature (oR)
T ∗P
T1 = n 1⁄P
n
Pn: normal operating pressure (psia)
Tn: normal operating temperature (oR)
Closed Outlet
Drums / flashing drum with reboiler [4]
The vapor rate in the feed gas is treated as the relief
valve's relieving rate. The relief rate is determined by
estimating the emergency reboiler heat duty.
See Vaporizer notes on table 4.5
Reboiler Duty (steam)
Columns [4]
When all outlets from the equipment are blocked, the
relieving load should be at least as great as the capacity
of the sources of pressure. If all outlets are not blocked,
the capacity of the unblocked outlets may properly be
considered
(1) Valve block of reflux line
1
′
[(ℎ𝐹′ − ℎ𝐿 )𝑊𝐹′ − (ℎ𝐷
− ℎ𝐿 )𝑊𝐷′ − (ℎ𝐵′ − ℎ𝐿 )𝑊𝐵′
𝜆
+ ∆𝑄𝑅′ − ∆𝑄𝐶′ ]
λ /hL: latent heat of vaporization/Liquid enthalpy at the
top section of the tower (2 or 3 stages below the top tray)
h’F: feed stream enthalpy (relieving)
W’F: Feed stream flow rate (relieving)
h’D/ W’D: Top distillate enthalpy and flow rate (relieving)
h’B/ W’B: Bottom product enthalpy and flow rate
(relieving)
△Q’R: Reboiler duty (relieving)
△Q’C: Condenser duty (relieving)
𝑊=
𝑡2′ − 𝑡1′
𝑇 ′ − 𝑡1′
ln( ′
)
𝑇 − 𝑡2′
∆𝑇′ 𝑈
∆𝑄′ = ( )( 𝑐𝑎𝑙𝑐 )∆𝑄 (kcal/hr)
∆𝑇′ =
∆𝑇
∆𝑄′
𝑈𝐷
𝑊=
(kg/hr)
𝜆
Reboiler Duty (Oil)
(2) Valve block of fractionation column overhead vapor
product
1
[(ℎ𝐹′ − ℎ𝐿 )𝑊𝐹′ − (ℎ𝐵′ − ℎ𝐿 )𝑊𝐵′ + ∆𝑄𝑅′ ]
𝜆
Steam stripping is used:
1
𝑊𝐻𝐶 = [(ℎ𝐹′ − ℎ𝐿 )𝑊𝐹′ − (ℎ𝑠′ − ℎ𝑠′′ )𝑊𝑠′
𝜆
− (ℎ𝐵′ − ℎ𝐿 )𝑊𝐵′ ]
𝑊 = 𝑊𝐻𝐶 + 𝑊𝑠′
WHC: hydrocarbon relieved
W’s: steam relieved
h’s: steam inlet enthalpy (relieving)
h’’s: steam relieving enthalpy
estimate relieved steam based on a full open steam
control valve and pressure difference between the steam
header and relieving pressure
𝑊=
(𝑇1 ′ − 𝑡2′ ) − (𝑇2 ′ − 𝑡1′ )
𝑇 ′ − 𝑡2′
ln( 1 ′
)
𝑇2 − 𝑡1′
∆𝑇′ 𝑈
∆𝑄′ = ( )( 𝑐𝑎𝑙𝑐 )∆𝑄 (kcal/hr)
∆𝑇′ =
′
∆𝑄 = (
𝑊=
∆𝑇
𝑈𝐷
𝑇1 −𝑇2′
𝑇1 −𝑇2
∆𝑄′
𝜆
)∆𝑄 (kcal/hr)
(kg/hr)
Table 4.3: Relief loads guidelines for Drums and Columns
Discharge line of rotary machinery
Centrifugal pumps[4]
Centrifugal compressors[4]
An overpressure problem does not occur on
the discharge line of a centrifugal pump
because the centrifugal pump discharge
system normally has a design pressure equal
to or higher than the pump shut-off
pressure.
However, when the design pressure is set
lower than the pump shut-off pressure, an
overpressure problem will occur, and the
flow rate at the head, equivalent to the set
pressure of the PSV minus the maximum
suction pressure, should be read from the
pump performance curve for the relieving
load.
The relieving load should be determined
based on the pump’s maximum speed when
the steam turbine driver is provided.
If the design pressure for the compressor discharge system is
higher than the pressure of surge point at maximum speed,
overpressure does not occur. If the design pressure is lower
than that, overpressure protection should be considered. In
this case, the relieving load should be the flow rate (FD) at the
head equivalent to the design pressure (PD) at maximum
speed or should be the anti-surge flow (FS) at maximum
speed, whichever is greater. That value is usually obtained
from such compressor performance curve as shown below:
Reciprocating pumps[4]
The relieving load shall be equal to the
pump’s rated capacity.
The calculation procedure is as follows.
1. Assume the discharge pressure is 1.1 times the design
pressure. Based on the calculated discharge pressure,
estimate the suction pressure of the compressor assuming
the compressor is running on the surge control line. In
case of variable speed compressor, whole range of the
operating speed to be investigated.
2. Calculate weight flow through the compressor and
required power of the compressor based on the suction
and discharge pressures calculated in Step 1.
3. Check the calculated weight flow if it is available from
upstream side of the compressor.
4. Check the required power if it is available from the driver.
Relieving load is the maximum weight flow rate calculated in
Step 2 considering the limitation of available flow rate and
power checked in Step 3 and 4. In case the calculated suction
pressure is equal to or higher than the design pressure of the
suction side in Step 1, re-calculate the suction pressure
assuming that the compressor is still running on the surge
control line while the 1.1 times of the design
pressure is replaced with the design pressure of discharge
side.
Reciprocating compressors[4]
The relieving load should be equal to the
compressor’s rated capacity.
Table 4.5: Relief loads guidelines for Rotary Machinery
Heat Exchangers
Vaporization in Hex [4]
If the vapor pressure of the cold medium at the
inlet temperature of hot side is more than 1.3
times the design pressure of the cold side,
overpressure protection due to vaporization is
needed. If it is assumed that the outlet of the cold
side is blocked off, and the hot medium continues
to flow, the relieving load on the cold side should
be determined as follows :
𝑄 (𝑇1 − 𝑡𝑏𝑝 )
.
𝜆 (𝑇1 − 𝑡𝑎𝑣 )
𝑡1 + 𝑡2
𝑡𝑎𝑣 =
2
W : relieving load (kg/hr)
Q : normal heat exchanger duty (kcal/hr)
λ : latent heat of vaporization at tbp (kcal/kg)
T1: hot side inlet temperature (oC)
Tbp: cold side inlet temperature (oC)
tav: average cold side temperature (normal
operation) (oC)
t1/t2: cold side inlet/outlet temperature (oC)
𝑊 =
Vaporizer [4]
When the outlet of the cold side is blocked off, and the hot
medium continues to flow, overpressure will
occur, and the relieving load should be calculated based on the
vaporizer heat duty at the relieving condition obtained by the
procedure shown in Table 4.3
Steam Vaporizer
(1) Inlet and outlet temperatures of process fluid to/from
reboiler at relieving pressure will increase, because
the boiling temperature of process fluid increases, when the
operating pressure reaches the relieving pressure.
(2) When heating steam is supplied under steam flow control,
the saturated temperature of steam at the
pressure of supply header should be applied to ΔT calculation,
because the flow control valve tend to open to maintain the
steam flow at a constant. If the other control system is applied
to the steam supply, the normal operating temperature of
steam may be used.
(3) Ucalc (calculated overall heat transfer coefficient ) should be
used for recalculation.
Hot Oil Vaporizer
When the hot oil supply stops due to failures such as a hot oil
pump stop, overpressure does not occur because
of no heat input to the reboiler. If the hot oil supply continues,
the heat duty should be calculated based on the temperature
profile under the relieving conditions.
(1) Inlet and outlet temperatures of process fluid to/from the
reboiler will increase because the boiling temperature of
process fluid increases when the operating pressure reaches
the relieving pressure.
(2) The flow rate of hot oil is maintained the same as in normal
operation.
(3) UCALC (calculated overall heat transfer coefficient) should be
used for recalculation.
Based on the above conditions, assume the outlet temperature
of hot oil (T2’) and obtain the reboiler duty
(ΔQ’) by trial and error calculation using the following
equations :
Table 4.6: Relief loads guidelines for Heat Exchangers
Liquid Thermal Expansion [4]
Solar Radiation [4]
A 3/4-inch × 1-inch nominal pipe size (NPS) relief valve
is commonly used, even though it will be oversized,
since relieving load for thermal expansion will usually
be small.
If there is reason to believe that this size is not
adequate, the relieving load should be obtained
according to the following equation
𝛼𝑄
𝑉=
𝐶 ∗ 𝑆. 𝐺 ∗ 𝐶𝑝
V: volumetric flow rate at flowing temperature (m3lhr)
𝛼:cubical expansion coefficient (1/°K)
Q: total heat transfer rate. ( kW)
specific gravity, water = 1.0 (-)
Cp specific heat of the fluid
C: factor (1000)
𝑄 = 𝑞𝑠 𝜀𝐴
Q: heat absorbed by solar radiation (kcal/hr)
qs : heat flux by solar radiation (kcal/hr.m2)
ԑ : emissivity
A: projected heat transfer area (m2)
solar radiation
When the solar radiation data is not available, the noon values in
the following table can be applied to obtain the maximum heat
absorbed from solar radiation.
Maximum Expected Solar Radiation of Various North Latitudes
Latitude
(kcal/h.m2)
(kW/m2)
24-hr
N30°
353
0.41
average
Noon
value
N40°
N45°
N30°
353
353
990
0.41
0.41
1.15
N35°
N40°
N45°
Gravity of Oil [Deg API]
3 – 34.9
35 – 50.9
51 – 63.9
64 – 78.9
79 – 88.9
89 – 93.9
94 and lighter
Temperature °C
15.6
20
30
40
50
αv 1/°C or 1/K (1/°F)
0.00072 (0.0004)
0.00090 (0.0005)
0.00108 (0.0006)
0.00126 (0.0007)
0.00144 (0.0008)
0.00153 (0.00085)
0.00162 (0.0009)
αv 1/°C or 1/K
(water)
0.00018
0.00021
0.00030
0.00040
0.00047
976
1.14
950
1.1
922
1.07
Above table presents typical highest values of monthly average
solar radiation on a horizontal surface throughout the year,
based on analysis of Weather Bureau records for a number of
stations through the United States. Refer to Section 12 Table 12-5
of Perry’s Chemical Engineer’’ Handbook 7th Edition.
typical value of emissivity
Material
Emissivity, ε
0.1
Clean and polished metal
0.3
Metals, general
0.8
Rusty metal
0.95
Painted surface
For horizontal piping or vessels, vertical projected area on ground
is used. For vertical piping or vessels, horizontal projected area
may be used as conservative side.
Table 4.7: Relief loads guidelines for Liquid Thermal Expansion and Solar radiation
Inadvertent Control Valve Opening
Flashing Liquid [4]
(a) Calculate ΔP of the control valve at the relieving condition
(b) Breakthrough flow rate should be calculated on a liquid phase basis by using the selected CV value,
since LPG is in liquid phase at the inlet of the control valve.
(c) Calculate the flashed vapor flow rate (VF) by the flash calculation at the relieving pressure.
(d) If the vapor space is enough to accommodate the let down liquid for the operator’s response time, the
relieving load (VR) = VF – VN ( VN = vapor flow rate at normal operation).
(e) If the vapor space is not enough, consider the relieving of vapor-liquid mixture.
(f) In this case, pay attention to an occurrence of slug flow in two phase lines.
Gas Breakthrough [4]
(a) Calculate ΔP of the control valve at the relieving condition.
(b) Gas breakthrough flow rate (VB) should be calculated by using the selected CV value.
(c) Relieving load (VR) = VB – VN , ( VN = vapor flow rate at normal operation).
(d) In this case, pay attention to an occurrence of slug flow in two phase lines.
Liquid [Note 1] [7]
△𝑃
𝑄𝐿 = 0.86 ∗ 𝐶𝑣 . √
𝐺
QL in m3 /hr
△P in kg/cm2
G: Specific gravity (-)
Steam [7]
𝑄𝑠 = 394.155 ∗ 𝐶𝑣 . √
△ 𝑃. 𝑃2
𝑇
Estimation of control valve Cv[Note 2][7]
𝑣𝑎𝑙𝑣𝑒 𝐶𝑣 1
Single-seated
𝑑 (𝑖𝑛𝑐ℎ𝑒𝑠) = (
)2
valves
9
𝑑 (𝑖𝑛𝑐ℎ𝑒𝑠) = (
𝑣𝑎𝑙𝑣𝑒 𝐶𝑣 1
)2
12
Double-seated
valves
𝑣𝑎𝑙𝑣𝑒 𝐶𝑣 1
)2
20
Butterfly valve
sizes
Qs in kg/hr
△P and P2 in kg/cm2
T in oK
Gas [Note 1][7]
𝑄𝐺 = 386.67 ∗ 𝐶𝑣 √
△ 𝑃. 𝑃2
𝑍2 . 𝐺. 𝑇
3
Qs in Nm /hr
△P and P2 in kg/cm2
T in oK
G is the molecular weight divided by 29
𝑑 (𝑖𝑛𝑐ℎ𝑒𝑠) = (
Table 4.8: Relief loads guidelines for Inadvertent open control valve
NOTE 1: Assuming a subcritical and turbulent flow
NOTE 2: Shortcut mentioned in ref [8] were used in the tool (Cv =10*d2), d in inches
Wetted Area Calculations [5]
To determine vaporization rate, the surface
area wetted by a vessel's internal liquid and is
up to 7.6 m (25 feet) above grade, denoted as
"fire elevation", needs to be considered. The
term "grade" usually refers to ground level,
but may be at any level at which a sizable fire
could be sustained.
Semi-Ellipsoidal/Elliptical Heads
Or Torispherical/Dished Heads
z
D
Vessels
Cylindrical part
Vertical
h
𝐴𝑤
𝐷2 ℎ
(( − 0.5) 𝐵 + 1
8 𝐷
ℎ
4𝜀 ( − 0.5) + 𝐵
1
𝐷
+ ln(
))
4𝜀
2 − √3
= 𝜋
L
D
2
ℎ
√
𝐵 = 1 + 12 ( − 0.5)
𝐷
For 2:1 Elliptical head ε = 0.866,
elsewise:
Aw = 2πD*L
Horizontal
𝜀 = √1 −
D
z: inside dish depth
h
L
𝐴𝑤 = 𝐿𝐷 cos −1 (1 − (2ℎ/𝐷))
Heads
Hemispherical Heads
D
h
𝐴𝑤 = 𝜋ℎ
𝐷
2
4𝑧 2
𝐷2
𝜀 : Eccentricity of elliptical heads
Shortcut Calculations for various wetted Areas [4]
Figure 4.2: Heat exchanger U tube side Aw
Figure 4.3: Fixed Heat exchanger tube side Aw
Figure 4.4: Kettle reboiler Aw
Figure 4.5: Floating head Hex. Aw
Figure 4.6: Heat exchanger U shell-side Aw
Figure 4.7: Fixed heat exchanger Shell-side Aw
Figure 4.8: Spherical Tank Aw
Figure 4.9: Vertical vessel fixed head Aw
Figure 4.10: Vertical Vessel Elliptical Head Aw
Figure 4.11: Horizontal Vessel Aw
Figure 4.12: Trayed Column Aw
Examples
API RP 520 Example No. 1
Input
Mass flow
Molecular weight
Relieving Temperature
Design pressure of equipment
Units
Kg/hr
o
K
kPa / kg/cm2
API RP 520 Part I
24270
51
348
517
Tool
24271
51 (Using composition)
74.85 oC
5.272
Backpressure
Overpressure
kPa / kg/cm2
%
101.325
10
1.033
10 (Calculated)
670
0.9
392
1.11
1
1
0.975
36.98 / 5.73
41.16 / 6.38
P
0.98
1.05
1
1
0.975
39.5 / 6.12
41.16 / 6.38
P
Output
Relieving pressure
kPa / kg/cm2
Z
Critical Pressure
kPa / kg/cm2
Cp/Cv
Kb
Kc
kd
Acalculated
cm2/ in2
Aselected
cm2/ in2
Orifice Designation
1. Estimating Relief Pressure and constants
Relief pressure for one relief valve, no rupture disc, and non-fire case will equal 1.1 the equipment
design pressure
Pr = 1.1 * 517 = 670 kPa (6.8321 kg/cm2)
Kb = 1 as backpressure is atmospheric
Kc = 1, as there’s no rupture disc installed
Kd = 0.975
1. Checking whether the flow is critical
𝑃𝐶𝑓 = 𝑃1 ∗ [
1.11⁄(1.11−1)
2 𝑘⁄(𝑘−1)
2
]
]
= 670 ∗ [
= 670 ∗ 0.5825 = 390.33
𝑘+1
1.11 + 1
The PRV sizing is based on the critical flow equation since the backpressure (0 kPag) is less than the
critical flow pressure (291 kPag).
2. Calculating Orifice Area
𝐶 = 0.03948√𝑘 [
2
𝑘+1
]
(𝑘+1)/(𝑘−1)
=0.03948*√1.11 [
2
]
(1.11+1)/(1.11−1)
1.11+1
0.02489
Using The C graph provided earlier (Figure 2.7), C = 0.0249 for Cp/Cv of 1.11
= 0.03948 ∗ 0.63045 =
𝐴=
𝑊 ∗ √𝑇𝑍
𝐶𝐾𝑑 𝑃1 𝐾𝑏 𝐾𝑐 √𝑀
=
24270
348 ∗ 0.9
√
= 3698 𝑚𝑚2
0.0249 ∗ 0.975 ∗ 1 ∗ 1 ∗ 670
51
See API 526 for the selection of the proper orifice size. API 526 provides standard effective
orifice areas in terms of letter designations. For this example, a “P” size orifice should be selected since it
has an effective orifice area of 6.38 in.2 (4116 mm2)
Step 1: Calculate Relief Pressure
Step 2: Input mass flow rate and composition
Step 3: Input relief/back conditions (T&P)
Step 4: Download your calculations table!
API RP 520 Example No. 4
Input
Mass flow
Relieving Temperature
Design pressure of equipment
Units
Kg/hr
C
kPag / kg/cm2g
API RP 520 Part I
69615
427
11032
Tool
69615
427
112.5
Backpressure
Overpressure
kPag / kg/cm2g
%
101.325
10
1.033
10
12236 (124.77)
1
1
0.975
1.01
0.855
12.87 / 1.995
18.41 / 2.853
L
124.77
1
1
0.975
1.01
0.862
12.75 / 1.97
18.41 / 2.853
L
Output
Relieving pressure
kPa / kg/cm2
Kb
Kc
kd
KN
KSH
Acalculated
cm2/ in2
Aselected
cm2/ in2
Orifice Designation
1. Estimating Relief Pressure and constants
Relief pressure for one relief valve, no rupture disc, and non-fire case will equal 1.1 the equipment
design pressure
Pr = 1.1 * 11032 + 101.325 = 12236.5 kPa (124.77 kg/cm2)
Kb = 1 for conventional valve discharging to atmosphere
Kc = 1, as there’s no rupture disc installed
Kd = 0.975
KSH : 0.855 from tables
KN : P1 (124.77 kg/cm2.a) is > 106.5 kg/cm2.a
KN = (0.1906 *1774.7 - 1000)/(0.2292 *1774.7- 1061) = 1.01
2. Calculating Orifice Area
𝐴=
190.5 ∗ 𝑊
190.5 ∗ 69615
=
= 1287 𝑚𝑚2 (12.87 𝑐𝑚2 )
𝑃1 𝐾𝑑 𝐾𝑠ℎ 𝐾𝑁 𝐾𝑏 𝐾𝑐
12236.5 ∗ 0.975 ∗ 0.855 ∗ 1.01 ∗ 1 ∗ 1
See API 526 for the selection of the proper orifice size. API 526 provides standard effective
orifice areas in terms of letter designations. For this example, a “L” size orifice should be selected since it
has an effective orifice area of 2.853 in.2 (1841 mm2)
Step 1: Calculate Relief Pressure
Step 2: Input mass flow rate and composition
Step 3: Input relief/back conditions (T&P)
Step 4: Download your calculations table!
API RP 520 Example No. 5
Input
Mass flow
Specific Gravity
Viscosity
Units
L/min
Saybolt / cP
Design pressure of equipment kPag / kg/cm2g
Backpressure
kPag / kg/cm2g
Overpressure
%
Output
Relieving pressure
kPag / kg/cm2
Kc
Kd
Kw
Kv
Acalculated
cm2/ in2
Aselected
cm2/ in2
Orifice Designation
1. Estimating Relief Pressure and constants
API RP 520 Part I
6814
0.9
2000 / 388.5
Tool
368010 (kg/hr)
0.9
388.5
1724
345
10
17.58
3.52 (4.55 abs)
10
1896 (19.33 kg/cm2.g)
1.0
0.65
1
1 (initially) / 0.982
31.22 / 4.84
41.16 / 6.38
P
20.37 (19.337 gauge)
1
0.65
0.97
0.99
30.71 / 4.83
41.16 / 6.38
P
Relief pressure for one relief valve, no rupture disc, and non-fire case will equal 1.1 the equipment
design pressure
Pr = 1.1 * 1724 = 1896.4 kPa (kg/cm2)
Kw = 1 as backpressure is atmospheric
Kc = 1 as there’s no rupture disc installed
Kd= 0.975
Kv: initially assumed 1
2. Calculating Orifice Area
𝐴=
11.78𝑄√𝐺
𝐾𝑑 𝐾𝑤 𝐾𝑣 𝐾𝑐 √𝑃1 − 𝑃2
=
11.78 ∗ 6814
0.9
√
= 3066 𝑚𝑚2 (30.66 𝑐𝑚2 )
0.975 ∗ 1 ∗ 1 ∗ 1 1896 − 345
See API 526 for the selection of the proper orifice size. API 526 provides standard effective
orifice areas in terms of letter designations. For this example, a “P” size orifice should be selected since it
has an effective orifice area of 6.38 in.2 (4116 mm2)
3. Check Kv and recalculate Acalculated
𝑅𝑒 =
𝑄 ∗ (18800 ∗ 𝐺)
𝜇√𝐴
=
6814*18800*0.9
388.5√4116
−0.5
170
𝑘𝑣 = (
+ 1)
= 0.982
𝑅𝑒
𝐴=
𝐴𝑅
𝐾𝑣
=
3066
0.982
= 3122 𝑚𝑚2
= 4625
Step 1: Calculate Relief Pressure
Step 2: Input mass flow rate and composition
Step 3: Input relief/back conditions (T&P)
Step 4: Download your calculations table!
Fire Case Example: Benzene in a Horizontal Vessel
Input
Units
Reference [1]
Units Converted
Benzene
78.11
37.78 + 273.15 [Note]
1379
Atmospheric
21
Bare Vessel
Horizontal +
spherical heads
4.572
9.144
3.734
4.572
Tool
kPa / kg/cm2
kCal/kg
m2
Kg/hr
kPa / kg/cm2
-
1769.88
95.62(input)
83.7
14665
1 (input)
18.04 kg/cm2.g (1769.7 kPa)
146 [Note 1]
121
13020.15
0.81
Critical
1.12 (input)
1
1
0.975
Critical
0.97
1
1
0.975
cm2/ in2
cm2/ in2
6.787 / 1.052 in2
8.303 / 1.287 in2
J (nozzles 2”/3”)
8.20495 / 1.27177 in2
8.303 / 1.287 in2
J (nozzles 2”/3”)
Fluid
Molecular weight
Relieving Temperature
Design pressure of equipment
Backpressure
Overpressure
Vessel Geometry data
K
kPag / kg/cm2.g
kPa / kg/cm2
%
Diameter
T-T Length
Level (Normal liquid level)
Height above grade
m
m
m
m
Output
Relieving pressure
ΔH
Wetted Area (Aw)
Mass flow
Z
Critical Pressure
Flow condition
Cp/Cv
Kb
Kc
kd
C
Acalculated
Aselected
Orifice Designation
Notes:
Benzene
78.11
250 + 273.15 [Note 2]
14.06 kg/cm2.g (1379 kPa)
Atmospheric
21
Bare Vessel
Horizontal +
Cylindrical heads
4.572
9.144
3.734
4.572
1. Heat of vaporization is higher in the tool as a result of adding the heat required to bring the fluid
from the subcooled phase to saturation temperature
2. A temperature of 250 was assumed to obtain benzene at the vapor phase; assuming relived and
vaporized benzene at 37.78 C & 18 kg/cm2 is illogical. This, however, will increase Acalculaed.
3. Estimate Vessel wetted area
Level of the wetted area = 7.6 – 4.57 = 3.03 m
ratio of level = 3.03/4.57 = 0.663
Total Area of the horizontal vessel (spherical heads)
= (L+D)*πD = (9.1 + 4.57)*π*4.57 = 196.26 m2
9.1 m
Fraction of area (from Figure 4.11) = 0.6
Wetted area = Area fraction * total surface area
= 0.6*196.26 = 117.75 m2
4.57 m
7.6 – 4.57
Wetted Area
4.57 m
3.73+4.57 m 7.6 m
2ℎ
𝐴𝑤 (𝐶𝑦𝑙𝑖𝑛𝑑𝑟𝑖𝑐𝑎𝑙 𝑝𝑎𝑟𝑡) = 𝐿𝐷 cos −1 (1 − ( ))
𝐷
3.03
)) = 587 ∗ cos −1 (−0.326) = 79.14 𝑚2
4.57
𝐴𝑤 (2 ℎ𝑒𝑎𝑑𝑠) = 𝜋ℎ𝐷 = 3.14 ∗ 3.03 ∗ 4.057 = 38.6 𝑚2
𝐴𝑤 𝑡𝑜𝑡𝑎𝑙 = 79.147 + 38.6 = 117.74 𝑚2
4. Estimate Relief Load
= 9.1 ∗ 4.57 𝑐𝑜𝑠 −1 (1 − (2 ∗
Q = qoFA0.82
F = 1 for Bare vessel
qo = 37130 (adequate drainage is provided)
Q = 37130*1*117.750.82 = 1853159.92 kCal/hr
𝑊=
𝑄
1853159.92
=
= 12693 𝑘𝑔/ℎ𝑟
∆𝐻
146
3. Estimating Relief Pressure and constants
Relief pressure for one relief valve, no rupture disc, and fire case will equal 1.21 the equipment design
pressure
Pr = 1.21 * 1379 + 101.325 = 1770 kPa (18.05 kg/cm2)
Kb = 1 as backpressure is atmospheric
Kc = 1, as there’s no rupture disc installed
Kd = 0.975
4. Checking whether the flow is critical
1.12⁄(1.12−1)
2 𝑘⁄(𝑘−1)
2
]
]
𝑃𝐶𝑓 = 𝑃1 ∗ [
= 1770 ∗ [
= 1770 ∗ 0.5805 = 1027.5 𝑘𝑃𝑎
𝑘+1
1.12 + 1
The PRV sizing is based on the critical flow equation since the backpressure (0 kPag) is less than the
critical flow pressure (1027 kPag).
5. Calculating Orifice Area
𝐶 = 0.03948√𝑘 [
2
𝑘+1
]
(𝑘+1)/(𝑘−1)
=0.03948*√1.12 [
2
]
(1.12+1)/(1.12−1)
1.12+1
= 0.03948 ∗ 0.4 =
0.0249
Using The C graph provided earlier (Figure 2.7), C = 0.025 for Cp/Cv of 1.12
𝐴=
𝑊 ∗ √𝑇𝑍
𝐶𝐾𝑑 𝑃1 𝐾𝑏 𝐾𝑐 √𝑀
=
24270
348 ∗ 1
√
= 621 𝑚𝑚2
0.025 ∗ 0.975 ∗ 1 ∗ 1 ∗ 1770 78.11
See API 526 for the selection of the proper orifice size. API 526 provides standard effective orifice areas
in terms of letter designations. For this example, a “J” size orifice should be selected since it has an
effective orifice area of 1.287 in.2 (830 mm2)
Step 1: Calculate Relief Pressure
Step 2: Select estimate relief loads and choose “External Fire
due to vaporization”
Step 3: input relieved stream composition and conditions
Step 4: Input wetted Area required inputs
Step 5: check your results and calculations’ matrix
Step 6: go to “3. Gas or vapor” and use Calculated Relief Load
Step 7: Input mass flow rate and composition
Step 8: Download your calculations table!
Note: 250 oC was used to obtain the vapor phase
Definitions
Maximum operating pressure is the expected maximum pressure during operation of the system
upstream of the pressure relief valve.
Maximum allowable working pressure (MAWP) is the maximum gauge pressure permissible at the top of
a completed vessel in its operating position for a designated temperature. The pressure is based on
calculations for each element in a vessel using nominal thickness, exclusive of additional metal thickness
allowed for corrosion and loading other than pressure. The maximum allowable working pressure is the
basis for the pressure setting of the pressure relief devices that protect the vessel.
Design gauge pressure refers to at least the most severe conditions of coincident temperature and
pressure expected during operation. This pressure may be used in place of the maximum allowable
working pressure in all cases where the MAWP has not been established. The design pressure is equal to
or less than the MAWP.
Accumulation is the pressure increase over the maximum allowable working pressure of the vessel
during discharge through the pressure relief device, expressed in pressure units or as a percent.
Maximum allowable accumulations are established by applicable codes for operating and fire
contingencies.
Overpressure is the pressure increase over the set pressure of the pressure relief device, expressed in
pressure units or as a percent. It is the same as accumulation when the relieving device is set at the
maximum allowable working pressure of the vessel.
Rated relieving capacity is the portion of the measured relieving capacity permitted by the applicable
code regulation to be used as a basis for the application of a pressure relief device. Stamped capacity is
the rated relieving capacity that appears on the device nameplate.
The stamped capacity is based on the set pressure plus the allowable overpressure for compressible
fluids and the differential pressure for incompressible fluids. The stamped capacity shall not exceed 90%
of the average capacity of the valves tested.[ASME VIII Div. 1 UG-13 1 (d)(l)]
Set pressure is the inlet gauge pressure at which the pressure relief device is set to open under service
conditions.
Pressure differential is the difference between the set pressure of the pressure relief device and the
operating pressure of the protected vessel.
Cold differential test pressure is the pressure at which the pressure relief valve is adjusted to open on the
test stand. The cold differential test pressure includes corrections for the service conditions of back
pressure or temperature or both.
Back pressure is the pressure that exists at the outlet of pressure relief devices as a result of the pressure
in the discharge system. It is the sum of the superimposed and built-up back pressure.
Superimposed back pressure: The static back pressure that exists at the outlet of a pressure relief device
at the time the device is required to operate. It is result of pressure in the discharge system corning from
other sources and may be constant or variable. Built-up back pressure: The built-up back pressure is the
increase in pressure in the discharge header that develops as a result of flow after the pressure relief
device or devices open.
The built-up back pressure is caused by flow from the particular device and others, if any, which
simultaneously discharge into the disposal system. This type of back pressure is variable. The built-up
back pressure shall be less than the allowable back pressure, 10% of the set pressure for the
conventional type or 50% of the set pressure for the balanced-bellows type.
Constant Back Pressure: The static back pressure that exists under normal operation where no relief
device is operated; i.e. constant back pressure of the superimposed back pressure. The constant back
pressure is used to determine the spring set pressure of conventional type pressure relief valve as a
difference between the set pressure and the constant back pressure. Therefore, the opening pressure
will vary depend on the built-up back pressure. The opening pressure of balanced-bellows type is the set
pressure of the valve and is independent of any back pressure.
Blowdown is the difference between the set pressure and the closing pressure of a pressure relief valve,
expressed as a percent of the set pressure or in pressure units.
Opening pressures the value of increasing inlet static pressure at which there is a measurable lift of the
disc or at which discharge of the fluid becomes continuous.
Closing pressure is the value of decreasing inlet static pressure at which the valve disc reestablishes
contact with the seat or at which lift becomes zero.
Simmer is the audible or visible escape of compressible fluid between the seat and disc at an inlet static
pressure below the set pressure and at no measurable capacity
Leak-test pressure is the specified inlet static pressure at which a seat leak test is performed. The term
relieving conditions is used to indicate the inlet pressure and temperature on a pressure relief device at a
specific overpressure. The relieving pressure is equal to the valve set pressure plus the overpressure. The
temperature of the flowing fluid at relieving conditions may be higher or lower than the operating
temperature.
Chatter refers to the motion that causes the disc to contact the seat and damage the valve and
associated piping. Chattering may result in lowered capacity and damage to the seating surfaces.
Flutter refers to the abnormally rapid reciprocating motion of the movable parts of a pressure relief valve
in which the disc does not contact the seat
Atmospheric discharge is the release of vapors and gases from pressure relief or depressing devices to
the atmosphere.
Flare system is a means for the safe disposal of waste gasses by closed pipeline and combustion system.
With an elevated mre the combustion is carried out at the top of a pipe or stack where the burner and
igniter are located. A ground flare is similarly equipped except that combustion is carried out at or near
ground level. A burn pit differs from a flare in that it is normally designed to handle both liquids and
vapors.
Vent stack is the elevated vertical termination of a disposal system that discharges vapors into the
atmosphere without combustion or chemical conversion of the relieved fluid.
References
[1] API RP 520 Part I, 10th edition.
[2] Engineering Encyclopedia: Aramco desktop standards: sizing and selecting Pressure relief valves
[3] Pressure relief devices rev. 5, JGC standard practice 2002 JGS 210-120-1-61E
[4] Pressure Relieving design rev. 5, JGC standard practice 2008 JGS 210-120-1-40E
[5] Volume and Wetted Area of Partially Filled Horizontal Vessels, Link:
https://neutrium.net/equipment/volume-and-wetted-area-of-partially-filled-horizontal-vessels/
[6] Sizing Pressure-Relief Devices, Daniel A. Crowl and Scott A. Tipler. (AIChE)
[7] Elements of chemical process engineering chapter 1, Basic Process Engineering principles
[8] Chemical process engineering Vol. 1, Chapter 5 P. 246 By Kayode Coker
Other Recommended Reads
[I] EIEPD: PSV General Guideline: addresses the sizing procedures and guidelines, different relief
scenarios for relief load estimation, standards involved, and rupture disc types and sizing
procedures.
[II] The Safety Relief Valves Handbook by Marc Hellemans, Chapter 5: Design Fundamentals
[III] Applied Instrumentation in the Process Industries by W.G Andrew and H.B. Williams Vol 2, second
edition: Chapter 6: Pressure relief systems P. 130
[IV] API RP 520 Part II: Installation guidelines for PSVs.
[V] API 521: This standard specifies requirements and gives guidelines for examining the principal
causes of overpressure, determining individual relieving rates, and electing and designing disposal
systems, including such component parts as piping, vessels, flares, and vent stacks.