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Tecnomare code
PAP-002
originating division
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document codes
Process Activity Procedure
002
Two-Phase Relief PSV Sizing
distribution: PROS Dept.
supplementary notes: questo documento è da intendersi come COPIA NON CONTROLLATA.
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rev.
21/11/2014
date
Issue for Internal Use
description
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checked
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authorised
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Revision Sheet
Revision
Changes
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First Issue
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TABLE OF CONTENTS
1.
2.
3.
INTRODUCTION ................................................................................................................................4
1.1
SCOPE ................................................................................................................................................ 4
1.2
ACRONYMS ........................................................................................................................................ 4
SPREADSHEET ...................................................................................................................................5
2.1
GENERAL INPUT DATA ............................................................................................................................. 5
2.2
OMEGA METHOD CALCULATION PARAMETERS (1ST SHEET) ............................................................................. 6
2.3
HEM CALCULATION PARAMETERS (2ND SHEET)............................................................................................. 7
2.4
OUTPUT RESULTS ................................................................................................................................... 7
HOW TO USE ....................................................................................................................................8
3.1
SHEET 1 – OMEGA METHOD .............................................................................................................. 8
3.2
SHEET 2 – HEM METHOD ................................................................................................................... 9
APPENDIX A ‐ PROCEDURES.................................................................................................................... 13
A.1
GENERAL ............................................................................................................................................ 13
A.2
LEUNG OMEGA METHOD ....................................................................................................................... 14
A.2.1
Two‐phase Flashing or Non‐flashing Flow ............................................................................... 14
A.2.2
Subcooled Liquid ...................................................................................................................... 15
A.3
HOMOGENEOUS EQUILIBRIUM MODEL ..................................................................................................... 16
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1. INTRODUCTION
1.1 SCOPE
Scope of this document is to provide guidelines and procedure aimed to preliminarly size a
pressure safety valve for multiphase relief in case of overpressure, implementing the procedure
explained by the Std. API 520 8th Ed. - Annex C.
PSV Size spreadsheet is named “PSV 2-Phase_Calculation Sheet Rev0.xls” and it is contained in
the folder “PROS/Programmi Processo/PSVs” of internal library.
Task of process engineer shall be to define relief flow rate, physical properties of fluid at the
relieving conditions and line size of piping upstream and downstream PSV.
Futhermore, Pressure Safety Valve Datasheet is to be prepared by process engineer and provided
to STAU unit to finalize valve sizing choosing the suitable orifice type to be installed.
The following table explain how to fill the format items of the “PSV 2-Phase_Calculation Sheet
Rev0.xls” spreadsheet.
1.2 ACRONYMS
In this specification the following definition and abbreviations are applied.
API
American Petroleum Institute
HEM
Homogeneous Equilibrium Method
MAWP
Maximum Allowable Working Pressure
PED
Pressure Equipment Directive
PSV
Pressure Safety Valve
Std.
Standard
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2. SPREADSHEET
“PSV 2-Phase_Calculation Sheet Rev0.xls” is made by two separate sheets, respectively for
resolution using the Omega Resolution Method and Integral Resolution Method.
Spreadsheet cells highlighted with green colour represent the input of calculation. The remain cells
will be calculated though formulas specified inside and write-protected in order to prevent any
accidental change.
The selection of the right method will be explained in the following section. For further details refer
in Appendix A where the topic is more extensively discussed.
2.1 GENERAL INPUT DATA
Row
Name
Description
1
Item / Tag
The PSV tag number which the below column is
referring to has to be reported here
2
MAWP
Use design pressure when MAWP is not available
3
Contingency
Valve arrangement and relief design case shall be
specified here according to the corresponding note
4
Set Pressure Ps (barg)
PSV initial opening pressure
5
Overpressure Criteria
Corresponds to the standard used to calculate the
overpressure (API or PED)
6
Maximum Accumulated Pressure
(%)
Percentage of Ps corresponding to full lift open
pressure
7
Allowable Overpressure (%)
Percentage of set pressure aimed to calculate the
full-lift open pressure of PSV. It depends on the
contingency choosen for the relief case
8
Relieving Pressure P0 (barg)
Full-lift open pressure
9
Relieving Temperature T0 (°C)
Temperature estimated at the relieving start,
depending on the type of event leading to
overpressure
10
Bubble Point Pressure Pv (bara)
Vap-Liq equilibrium pressure at the relieving
temperature to be specified when the fluid is liquid at
the relieving conditions.
11
Total Backpressure (barg)
Build-up + Superimposed Backpressure. % total of
backpressure as a function of Ps will be calculated
12
Suggested Valve Type
Valve type (Balance bellow or Pilot-operated) is
automatically determined depending on total
backpressure specified
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Row
Name
Description
13
Relieving Liquid Flowrate (kg/h)
Estimated liquid flowrate to be relief shall be
specified into this cell
14
Relieving Gas Flowrate (kg/h)
Estimated liquid flowrate (or supercritical fluid) to be
relief shall be specified into this cell
15
Liquid Density (kg/m )
As specified in the note, when liquid phase is
present at the inlet of PSV, liquid density evaluated
at Pv shall be specified. Otherwise, liquid density at
P0,
16
Gas Density (kg/m3)
Gas density evaluated at P0 shall be specified
17
Liquid Viscosity (cP)
Liquid viscosity at relieving conditions (T0, P0) shall
be specified
18
Overall Fluid Density (kg/m3)
Overall fluid density evaluated at P0 is automatically
calculated here
3
2.2 OMEGA METHOD CALCULATION PARAMETERS (1ST SHEET)
19
P90% (bara)
90% of set pressure is calculated and shall be set in
Hysys simulation in order to estimate physical
properties for two-point Omega parameter
20
Overall Fluid Density @ P90%
(bara)
Overall fluid density evaluated at P90% shall be
estimated by isentropic expansion
21
Omega Parameter ω
22
Transition saturation pressure
ratio (ηst)
Depends on ω (2nd method only)
23
Saturation pressure ratio (ηs)
Depends on set pressure (2nd method only)
24
Flashing System
Show if the fluid to be relief flashes through the PSV
or not (2nd method only)
25
Subcooling Region
Show the region (low or high) in which the system
falls into (2nd method only)
26
Critical Pressure Ratio ηc
Depends on ηs and could be estimated by equation
or chart
27
Backpressure ratio ηa
Depends on the backpressure imposed on the
discharge of the PSV
28
Fluidodynamic Critical Pressure
(bara)
29
Fluidodynamic Flow Region
30
Maximum theoretical Mass Flux
(kg/m*s2)
authors: ESA/IGU
Depends on the specific
automatically calculated
volume
or
density,
Limit pressure above which a critical flux occurs
Show if the flux is critical or not
Mass flux can be relief by the PSV
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2.3 HEM CALCULATION PARAMETERS (2ND SHEET)
19-27
28
29
30
Representative Point Table
Maximum theoretical Mass Flux
(kg/m*s2)
Pressure at the throat of the
nozzle (bar a)
Overall Density at the throat of
the nozzle (kg/m3)
Some recapitulatory point from the table XX is listed
here with its pressure and density
Mass flux can be relief by the PSV
Pressure at which maximum max flux occurs
Density at which maximum max flux occurs
2.4 OUTPUT RESULTS
Relates the effective flow rate at the end of the PSV
nozzle with the theoretical one
Takes into accoun the possible presence of a
rupture disk upstream PSV
Related to the backpressure imposed downstream
the relief valve
It is the minimum orifice area required for the relief at
operating conditions
31
Discharge coefficient Kd
32
Combination correction factor Kc
33
Backpressure correction factor kb
34
Required PSV discharge Area
(mm2)
35
PSV orifice type
36
Selected PSV discharge Area
Effective PSV orifice area installed on the equipment
37
Selected PSV Rated Flowrate
Effective flow rate through PSV at relief conditions
38
Liquid Reynolds Number
Reynolds Number of liquid phase during the relief
39
Viscosity correction factor Kv
Related to the presence of liquid at the inlet of PSV
40
Effective required PSV discharge
Area
41
CHECK on Selected Area
42
Notes
Preliminary choice of orifice type by API 526
PSV discharge area recalculated using Kv
Check between line 36 and 40
In addiction to the above, it has to be noted that a control valve may be subjected to different
operating scenarios (e.g. operation with different fluids along the plant life). In such a case, a
different column shall be prepared and the analysed scenario specified in the notes.
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3. HOW TO USE
3.1 SHEET 1 – OMEGA METHOD
A preliminary check about the suitability of Leung Omega Method shall be done by checking if the
fluid falls into the thermodinamic supercritical region. Check is done automatically by the
spreadsheet, giving a warning as shown in Tab. 1. In this case, the use of HEM method is
recommended.
Check on Omega Method Validity:
Thermodynamic
bar a
Critical
Pressure:
Thermodynamic
°C
Critical
Temperature:
Omega Method
Validity:
WARNING!
9
93
NO
For fluid conditions near the
thermodynamic critical point, Omega
Method could underestimate PSV
orifice area. It is suggested to use
API 520 Integral Method in that case.
Table 1. Check Leung Method Validity
Relevant input data to be provided to the spreadsheet for PSV sizing are:
Design Parameters
MAWP, design case and number of PSV installed shall be specified. According to contingency,
relieving pressure will be calculated (line 8).
Physical Properties
Thermodinamic and physical properties at the relieving conditions and at the 90% of relieving
pressure shall be specified. Depending on the total backpressure imposed downstream PSV
(hypotized or estimated by Aspen Flare System Analyzer), pressure safety valve type is suggested
(line 12).
Material Balances
According to design scenario, gas and liquid flowrates to be relief shall be specified (lines 13-14);
Correction Factors
In order to estimate effective required discharge area, correction factors (lines 31-32-33-39) shall
be estimated.
Finally, preliminary choice of PSV orifice type and valve inlet/outlet diameter shall be done as
specified in Std. API 526.
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3.2 SHEET 2 – HEM METHOD
Homogeneous Equilibrium Model is suitable for PSV sizing for all the scenarios listed in Section
A.1, given that it depends on liquid/vapor (or gas) phase equilibrium during the relief through the
PSV orifice.
However, equilibrium physical properties to be put into “PSV 2-Phase_Calculation Sheet Rev0.xls Sheet 2 Tab 3” shall be achieved by isentropic expansion from relieving pressure up to maximum
mass flux will be calculated using Process Simulation (in this PAP, Hysys v8.3). In the following
description, procedure to be follow is reported:
Design Parameters
MAWP, design case and number of PSV installed shall be specified. According to contingency,
relieving pressure will be calculated (line 8).
Physical Properties
Thermodinamic and physical properties at the relieving conditions shall be specified. Depending on
the total backpressure imposed downstream PSV (hypotized or estimated by FlareNet Simulator),
pressure safety valve type is suggested (line 12).
Material Balances
According to design scenario, gas and liquid flowrates to be relief shall be specified (lines 13-14);
HYSYS Simulation
In order to obtain couple of Pressure vs Overall Density points (in the “PSV 2-Phase_Calculation
Sheet Rev0.xls - Sheet 2 Tab 3” can be specified maximum 50 points), a case sudy is to be set to
perform isentropic expansion of the flow stream, starting from its relieving pressure. In the following
screenshots, Aspen HYSYS v8.3 has been taken into account, but the same versions of HYSYS.
Once composition, pressure and temperature have been specified in the flow stream to be
relieved, molar entropy shall be specified as input (Fig 1) to be kept fixed during the expansion
Figure 1. Setting for Isentropic Expansion
Then, create new Case Studies: pushing the button “Add” in the interface “Set up” (Fig. 2), we can
select the variables “Pressure” (indepentent variable) and “Mass Density” (dependent variable)
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Figure 2. Set Up Interface Settings
Figure 3. Add New Variables
In the lower part of Fig. 2, we could select State Input Type = Nested, specifying low and high
bound, then specifying the step size equal to:
50
Ticking “Step Downward” and clicking on “Run”, from the interface “Results” (Fig. 4) the 50 pairs of
points are available to be copied and pasted in “PSV 2-Phase_Calculation Sheet Rev0.xls - Sheet
2 Tab 3” (Tab. 2). The calculation sheet will automatically select the row corresponding to the
maximum mass flux.
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Figure 4. Results Interface
Pressure
Overall
Density
Pressure
Integrand
Summation
Mass
Flux
bara
kg/m3
Pa
m2/s2
m2/s2
kg/s*m2
1
50.0
65.42
5000000
0
0
0
2
49.0
63.76
4900000
-1548
-1548
3548
….
33.0
39.15
3300000
-2508
-33436
10125
n
32.0
37.73
3200000
-2601
-36037
10130
….
2.0
2.00
200000
-39960
-300966
1549
50
1.0
0.99
100000
-66890
-367856
852
#
Table 2. Fluid Isentropic Path
N.B. copy and paste the results checking that decimal separator is set as dot, otherwise change
your Regional Options.
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Correction Factors
In order to estimate effective required discharge area, correction factors (lines 31-32-33-39) shall
be estimated.
Main design properties (maximum mass flux, related pressure and density) from “Tab. 3 – Fluid
Isentropic Path” will be automatically specified respectively into lines 28-29-30.
Finally, preliminary choice of PSV orifice type and valve inlet/outlet diameter shall be done as
specified in Std. API 526.
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APPENDIX A - PROCEDURES
A.1 GENERAL
PAP-002 refers to the sizing methodology described in Std. API 520 8th Ed. (Annex C), in which
Leung Omega Method (section A.2) and Homogeneous Equilibrium Method (section A.3) are
examined: in the first one, fluid physical properties are calculated through the Omega two-point
parameter, related to the fluid specific volume at the relieving conditions; the second method is
based on the thermal and mechanical equilibrium of the two phase fluid, assuming it as a “pseudosingle phase fluid”.
Leung Omega Method has been modified also to fit experimental data for subcooled liquid at the
PSV inlet (section A.2.2).
The procedure applies to all the scenarios (Tab.3) in which a relief of two-phase fluid occurs but,
according to the several scenarios could be verified, the following criteria shall be taken into
account for the choice of the right correlation to be used.
Two-phase Liquid/Vapour Relief Scenario
1 - Two-phase system (liquid vapor mixtures,
including saturated liquid) enters PSV and
flashes. No non-condensable gas present.
Example
Saturated Liquid/vapour
propane system enters PSV
and liquid propane flashes
2 - Two-phase system (highly subcooled liquid
and either non-condensable gas, condensable
vapour or both) enters PSV and does not flashes.
Highly subcooled propane
and nitrogen enters PSV and
the propane does not flash
Procedure
A.2.1 or A.3
3 - Two-phase system (the vapor at the inlet
contains some non-condensable gas and the
liquid is either saturated or subcooled) enters PSV
and flashes. Non-condensable gas enters PSV.
Saturated Liquid/vapour
propane system and nitrogen
enter PSV and the liquid
propane flashes
Procedure
A.2.1 or A.3
4 - Subcooled liquid (including saturated liquid)
enters PSV and flashes. No condensable vapour
or non-condensable gas enters PSV.
Subcooled propane enters
PSV and flashes
Procedure
A.2.2 or A.3
Table 3. Two-Phase Relief Scenarios
authors: ESA/IGU
Correlation
Procedure
A.2.1 or A.3
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A.2 LEUNG OMEGA METHOD
A.2.1
Two-phase Flashing or Non-flashing Flow
The first methodology is focused on estimating the two-point Omega parameter ω as follows:
9
1
.1
Where


is the specific volume evaluated at 90% of the PSV inlet pressure, m3/kg;
is the specific volume evaluated at the PSV inlet pressure, m3/kg.
According to the type of flux at the outlet of the PSV, maximum mass flux results on:
.2
2∗
∗ ln
1 1
∗
1
1
.
.3
1
Where
G
is the mass flux, kg/s*m2 ;
P0
is the pressure at PSV inlet, Pa;

is the specific volume evaluated at the PSV inlet pressure, m3/kg;
ηa
is the backpressure ratio, ηa=
Once the value of the maximum mass flux has been determined, the required orifice area can be
calculated using Equation (A.4):
277.8 ∗
.4
Where
A
is the required effective discharge area, mm2;
W
is the mass flow rate to be relief, kg/h;
Kd
is the discharge coefficient, preliminarly set as 0.85 in case of two-phase mixture or
saturated liquid entering the PSV inlet, 0.65 for a single phase (sub-cooled liquid);
Kb
is the backpressure correction factor;
Kc
is the combination factor, set to 1.0 if a rupture disk is not installed upstream PSV, 0.9
otherwise;
Kv
is the viscosity correction factor.
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A.2.2
Subcooled Liquid
The second method is applied to system in which presence of a subcooler or saturated liquid
occurs, whitout any presence of gas phase (condensable vapor or non-condensable gas) at the
inlet of PSV. The subcooled liquid either flashes upstream or downstream of the PSV throat
depending on which subcooling region the flow falls into, respectively low and high subcooling
region.
9
1
.5
Where

l
is the mass density evaluated at 90% of the PSV inlet pressure, kg/m3;
is the mass density evaluated at the PSV inlet pressure, kg/m3;
According to the type of flux at the outlet of the PSV, maximum mass flux results on:
2 1
2
ln
∗
1.414
.
1
1
∗
1
.6
.
.7
Where
G
is the mass flux, kg/s*m2;
P
shall be set to PS for critical flow, Pa for sub-critical flow, Pa;
η
is the backpressure ratio, set to ηc for critical flow, ηa for sub-critical flow;
Once the value of the maximum mass flux has been determined, the required orifice area can be
calculated using Equation (A.8):
16,67
∗
.8
Where
A
is the required effective discharge area, mm2;
Q
is the volumetric flow rate to be relief, l/h;
l0
is the mass density evaluated at the PSV inlet pressure, kg/m3;
Kd
is the discharge coefficient, preliminarly set as 0.85 in case of two-phase mixture or
saturated liquid entering the PSV inlet, 0.65 for a single phase (sub-cooled liquid);
Kb
is the backpressure correction factor;
Kv
is the viscosity correction factor.
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A.3 HOMOGENEOUS EQUILIBRIUM MODEL
HEM is the only procedure applicable for all the two-phase relief PSV sizing.
As a hypothesis, PSV inlet nozzle is assumed to be the limiting flow element of a fully opened relief
valve, through which an isentropic expansion occurs (so, adiabatic and reversible).
The general energy balance for isentropic nozzle flow is
2∗
∗
∗
2
.9
Where:
G
is the mass flux, kg/s*m2 ;
v
is the specific volume of the fluid, m3/kg;

is the mass density of the fluid, kg/m3;
P
is the stagnation pressure of the fluid, Pa;
P0
is the fluid condition at the inlet to the nozzle;
t
is the fluid condition at the throat of the nozzle where the cross-sectional area is minimized.
The integral (A.9) shall be evaluated numerically by direct summation over small pressure intervals
and using the hypothesis of isentropic expansion introduced above. The resolution of (A.1) shall be
made by means of “PSV 2-Phase_Calculation Sheet Rev0.xls - Sheet 2 Tab 3”, explained in
Appendix B.
Finally, the required orifice area can be calculated using Equation (A.4).
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