26/12/2019
Forces due to Safety or
Relief Valve Discharge
Considerations and methods of
calculating piping forces due to
relief or safety valve opening
Abstract
Normative definitions, types, considerations, and formulas for
calculating discharge of the PSVs, PRVs or PVs in pipelines
José F. Vianna Pereira
vianna@jfvp.com.br
Pipe Forces due to Relief Valve Discharge
Contents
1 – Introduction .............................................................................................................................................5
2 – A Word of Advice ......................................................................................................................................5
3 – API and ASME B31.3 - Normalized Aspects ................................................................................................5
3.1 – API RP520 and API RP521 - Definitions and Nomenclatures ......................................................................... 5
Pressure Relief systems: ..................................................................................................................................... 5
Relief Valve: ........................................................................................................................................................ 6
PRV = Pressure Relief Valve: ............................................................................................................................... 6
PSRV = Pressure Safety Relief Valve: .................................................................................................................. 6
PSV = Pressure Safety Valve: .............................................................................................................................. 6
PV = Pressure Valve: ........................................................................................................................................... 6
3.2 – Definitions Contained in ASME B31.3............................................................................................................ 6
301.2.2 - Pressure Required for Containment or Relief. .................................................................................... 6
301.5 – Dynamic Effects. (See Appendix F, paragraph F301.5) .......................................................................... 6
301.5.1 – Impact ................................................................................................................................................. 6
301.5.5 – Discharge Reactions............................................................................................................................ 6
4 – Types of PRVs ...........................................................................................................................................7
4.1- PRV with a Single Adjusting Ring for Blowdown Control ................................................................................ 7
4.2 - PRV with Balanced-Bellows Pressure Relief Valve ......................................................................................... 7
4.3 - PRV – Balanced-Bellows Pressure Relief Valve with an Auxiliary Piston........................................................ 8
4.4 - Pilot-Operated Valve (Flowing-Type) ............................................................................................................. 8
4.5 – Rupture Disk Device in Combination with a PRV ........................................................................................... 8
5 – Operation details of a PRV ........................................................................................................................9
5.1 - PRV Operating with Steam or Gas .................................................................................................................. 9
5.2 - PRV Operating with Liquid.............................................................................................................................. 9
6 – Typical PRV Installation: Atmospheric (Open) Discharge .......................................................................... 10
7 - Typical PRV Installation: Closed System Discharge .................................................................................... 10
8 – Typical Pilot-Operated PRV Installation ................................................................................................... 11
9 - Examples of PRVs Installation with 3-Way Valves to Change Flow Direction .............................................. 11
10 – Systems with PSVs, PRVs or PVs – Basic Considerations ......................................................................... 12
10.1 – Systems open to atmosphere .................................................................................................................... 12
10.2 – Closed Systems – Collected into a Blowdown Vessel ................................................................................ 12
10.3 - Auxiliary Methodology for Verification of the Effects of Relief Systems – Practical Simplifications in
Stress Assessment and Analysis in Closed Systems .............................................................................................. 12
10.4 – Approaches and Considerations in a Dynamic Excitation Piping System .................................................. 13
1st - Accurate Calculation .................................................................................................................................. 13
2nd - Simplified Calculation ............................................................................................................................... 13
3rd - Particularities of Dynamic Systems ........................................................................................................... 14
4th - Maximum Distance of Straight Runs of Pipelines Subject to Dynamic Analysis. ...................................... 14
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Pipe Forces due to Relief Valve Discharge
11 – Safety Valve Operating Phenomena........................................................................................................ 15
11.1 - CHATTERING: .............................................................................................................................................. 15
11.2 - SIMMERING: ............................................................................................................................................... 15
11.3 - FLUTTERING: ............................................................................................................................................... 15
12 – The Reason Why the 2 Hz are Requested in Modal Dynamic Calculation ................................................... 15
For Gases - Conclusion...................................................................................................................................... 16
For Liquids - Conclusion .................................................................................................................................... 17
13 – Step by Step in Pressure Wave Development in a Closed System ............................................................ 17
14 – Calculation Example in an Open Atmosphere System ............................................................................. 24
14.1 – Model Evidence in Caesar II – Isometric calculation of the lines used in this example. ........................... 25
14.2 – Process Data .............................................................................................................................................. 26
14.3 – Line Geometry Data – Diameter, Schedule, Insulation, and Materials ..................................................... 26
14.4 – Datasheet of the Safety Valves .................................................................................................................. 26
14.5 – Calculation of Forces According to Caesar II’s Relief Load Synthesis ........................................................ 27
Location of forces in an open system (Caesar II Manual)................................................................................. 27
Types of calculation contained in relief load synthesis .................................................................................... 27
Caesar II Calculation Report ............................................................................................................................. 28
Summary of the forces calculated above in Newtons (N) and Pounds*Force (lbf) ......................................... 28
14.6 – Calculation of Forces According to ASME B31.1 Formulas ........................................................................ 28
Formulas of ASME B31.1 “Safety Relief Valve Thrust” ..................................................................................... 28
a & b Values According to Table II-2.2.1 of ASME B31.1 – Used in the above formula ................................... 28
Steam properties according to Sarco’s program .............................................................................................. 29
Table II-2.2.1 (B31.1) for setting the values of a and b .................................................................................... 29
Valve data for calculation ................................................................................................................................. 29
Calculated Values ............................................................................................................................................. 29
14.7 – Calculation of Forces According to API RP520 Formulas ........................................................................... 30
Sketch for force location .................................................................................................................................. 30
Variables used in this calculation step ............................................................................................................. 30
API RP520 formulas used in force calculation .................................................................................................. 30
Calculation Data and Determined Values......................................................................................................... 31
Summary of forces calculated according to API RP520 .................................................................................... 31
14.8 – Comparison of Values Calculated by the Three Methods Above .............................................................. 31
14.9 – Determination of Force x Time graphics encoded in Caesar II (Dynamic Module) ................................... 31
Data to determine the graphics ....................................................................................................................... 31
Graphics plotted for encoding with the highest values ................................................................................... 31
14.10 – Inputted Static and Dynamic Cases ......................................................................................................... 32
14.11 – Dynamic Input and Calculated Natural Frequencies ............................................................................... 32
14.12 – Calculated Maximum Stresses – Static and Dynamic .............................................................................. 35
Static – Permanent Loads ................................................................................................................................. 35
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Pipe Forces due to Relief Valve Discharge
Static – Thermal Effects .................................................................................................................................... 35
Dynamic – PSV A open – Combination 1 (Sus 13+D1) ...................................................................................... 35
Dynamic – PSV B open – Combination 2 (Sus 14+D2) .................................................................................... 35
Dynamic – PSVs A&B open – Combination 3 (Sus 16+D3) ............................................................................... 35
15 – Calculation Example in a Closed System – Fluid Collected into a Blowdown Vessel ................................. 36
15.1 – Caesar Coded Model and Isometric Line Calculation. ............................................................................... 36
Mathematical model taken from Caesar II ....................................................................................................... 36
Detailed calculation Isometrics ........................................................................................................................ 37
15.2 – Process Data .............................................................................................................................................. 38
15.3 – Line Geometry Data – Diameter, Schedule, Insulation, and Materials ..................................................... 38
15.4 – Datasheet of the PSV-29615 & PSV-29616 ................................................................................................ 39
15.5 – Assumptions Adopted in Determining Dynamic Forces ............................................................................ 40
15.6 – Calculation of the Dynamic Forces in the Inlet Pipes Due To a Liquid Hammer from the PSV-29615 &
PSV-29616............................................................................................................................................................. 41
Basic data for the calculation = PSV-29615/16 ................................................................................................ 41
Process data for the calculation (PSV-29615/16) ............................................................................................. 41
Calculation of the velocity of sound in the liquid through the pipe (C = m/s) ( PSV-29615/16) ...................... 41
Calculation of flow rate variation (V) for the PSV-29615/16 ......................................................................... 41
Calculation of P and wavelength L as defined by the PSV-29615/16 ............................................................ 41
Calculation of maximum unbalanced force (F) for the PSV-29615 & 29616.................................................... 42
Determination of values for each pipe section for the PSV-29615 .................................................................. 42
Determination of values for each pipe section for the PSV-29616 .................................................................. 42
Caesar II inputted force x time graphics in the PSVs entry sections ................................................................ 42
15.7 - Calculation of the Dynamic Forces in the Discharge Pipes Due To the Shock of “Flashing” Liquid from the
PSV-29615 & PSV-29616 by the Approximate Method........................................................................................ 44
Basic data for the calculation of the PSV-29615/16 forces .............................................................................. 44
Process data for the calculation = PSV-29615/16 ............................................................................................ 45
Calculation of the speed of sound in the liquid through the pipe (C = m/s) = PSV-29615/16 ......................... 45
Time the wave goes from one curve to the adjacent one (ts) ......................................................................... 45
Calculation of specific fluid weight () ............................................................................................................. 45
Calculation of flow rate variation (V) for PSV-29615/16 ............................................................................... 46
Calculation of P and wavelength L as defined by PSV-29615/16 ................................................................... 46
Calculation of maximum unbalanced force (F) for the PSV-29615 & 29616.................................................... 46
Determination of values for each pipe run for the PSV-29615&PSV-29616 .................................................... 46
Caesar II encoded graphics in the PSVs’ outputs.............................................................................................. 46
15.8 – Inputted Static and Dynamic Cases ........................................................................................................... 47
15.8.1– Static Cases .............................................................................................................................................. 47
15.8.2– Dynamic Cases ......................................................................................................................................... 47
15.9 – Dynamic Input............................................................................................................................................ 47
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Pipe Forces due to Relief Valve Discharge
15.10 – Calculated Maximum Stresses ................................................................................................................. 61
15.10.1 – Greater relationships of static stresses ............................................................................................ 61
15.10.2 – Greater relationships of dynamic stresses ....................................................................................... 62
15.11 – Resulting Natural Frequencies................................................................................................................. 62
15.12 – Details of Drains and Vents, and Proposed Supports .............................................................................. 63
16 - Conclusions ........................................................................................................................................... 64
17 – Reference Documents ........................................................................................................................... 64
18– Biography .............................................................................................................................................. 64
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Pipe Forces due to Relief Valve Discharge
1 – Introduction
The purpose of this article is to elucidate the differences in piping calculations due to the discharge of the PVRs
in open and closed systems. It provides a methodology for evaluating and calculating the forces developed in the
pipes receiving the discharge of these valves, reviews the types of assembly, proposes a few rules to be
observed in the project, and analyzes the process phenomena that can happen in these systems.
2 – A Word of Advice
The difference in PVRs’ discharge in systems open to atmosphere and closed systems is immense.
In systems open to atmosphere there are no wave reflections within the pipe, only a reactive force on the valve
due to the jet flow in the orifice and another force on the outlet in the discharge pipe perpendicular to the
discharge pipe section.
In closed systems (collected into a blowdown vessel), the dynamics of the forces is quite different. The valve
discharges within a very short time (hundredths of a second) a certain amount of fluid, and as a result of this
rapid opening time, a blow is caused to the stagnant fluid downstream of the valve. A fluid “cork” is formed
downstream of the valve. Two speeds occur, a subsonic and a second supersonic wave speed, both flow towards
the blowdown vessel. As the fluid “cork” propagates toward the vessel, the supersonic wave - finding an
element with significant capacitance - is reflected back toward the valve. This supersonic wave is “banging”
between the “cork” and the damping vessel, imposing a dynamic excitation on the pipe, acting on the various
sections of the valve’s downstream pipe, until this “cork” of fluid reaches the blowdown vessel. In practice,
when an opening of a PVR occurs, a rumble is heard, meaning that the sound barrier has been breached, and
then the “squeak” of the flow going towards the vessel, ending when this “cork” reaches the vessel.
The correct evaluation of these forces and the consequent application of the correct form is fundamental in pipe
stress analysis. Pretending that these forces do not exist, or confusing the calculation from closed systems
with open systems, demonstrates total ignorance of the fluid dynamics in piping systems. If the piping is
assembled and the PVR opens, surely the scornful reviews will come later.
There is an approximate calculation method, according to the JOUKOWSKY equations, which makes the
evaluation of these forces very easy. There are no acceptable reasons for the “make-believe”, which is very
common in piping projects.
An acceptable method consists in determining these forces, analyzing the path through which they will be
applied, and the following conclusion as to whether or not their application is important in an approximate or
accurate calculation. It is thus defined whether the force is significant or not. The “make-believe”, the result of
ignorance, is meaningless and may later result in a price to be paid.
3 – API and ASME B31.3 - Normalized Aspects
3.1 – API RP520 and API RP521 - Definitions and Nomenclatures
Pressure Relief systems:
It is an arrangement of a pressure relief system on pipes or equipment. A mechanism intended for safe relief,
transport and disposal of steam, liquid or gaseous phase fluids. A relief system may consist of only one pressure
relief valve or rupture disc, with or without a discharge pipe, for a single container either in a line or to
atmosphere. A more complex system may involve many pressure relief devices distributed in common headers
to terminal disposal equipment.
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Pipe Forces due to Relief Valve Discharge
Relief Valve:
A valve for pressure relief in pipes or equipment. It is spring-loaded due to static pressure upstream of the valve.
The valve opens normally in proportion to the increase in static pressure when the opening pressure is
exceeded. A relief valve is mostly used with incompressible fluids.
PRV = Pressure Relief Valve:
A generic term applied to relief valves, safety valves or relief and safety valves. A pressure relief valve is designed
to automatically close and prevent fluid flow. The load from the PRVs in stress analysis is considered as an
occasional load (OCC).
PSRV = Pressure Safety Relief Valve:
A spring-loaded pressure relief valve that can be used as a relief or pressure relief valve, depending on its
application. Load from the PSRVs in stress analysis is considered to be an occasional load (OCC).
PSV = Pressure Safety Valve:
A spring-loaded pressure relief valve driven by the static pressure upstream of the valve, characterized by a
quick opening. A safety valve is typically used with compressible fluids. The load from the PSVs in stress analysis
is considered as an occasional load (OCC).
PV = Pressure Valve:
A pressure control valve that operates whenever the upstream valve pressure of a system exceeds the control
pressure set on the valve. The load from the PVs in stress analysis is considered as a permanent load (SUS). The
PVs are used only on closed circuits.
3.2 – Definitions Contained in ASME B31.3
301.2.2 - Pressure Required for Containment or Relief.



Measures must be taken to safely contain or relieve (see paragraph 322.6.3) any expected pressure that
the pipes may be subjected to. Piping not protected by a pressure relief device, or which may be isolated
from a pressure relief device, should be designed for at least the highest pressure that can be
developed.
Sources of pressure to be considered include ambient influences, pressure fluctuations and surges,
improper operation, unstable fluid decomposition, static head and control device failure.
Emission licenses in paragraph 302.2.4 (f) are permitted as long as the other requirements in paragraph
302.2.4 are also met.
301.5 – Dynamic Effects. (See Appendix F, paragraph F301.5)
301.5.1 – Impact
Impact forces caused by external or internal conditions (including changes in flow, hydraulic shock, liquid or solid
displacement, intermittency and gasification) must be taken into account in piping design.
301.5.5 – Discharge Reactions
Piping should be designed, arranged and supported to withstand reaction forces due to valve discharge or fluid
discharge.
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Pipe Forces due to Relief Valve Discharge
4 – Types of PRVs
4.1- PRV with a Single Adjusting Ring for Blowdown Control
4.2 - PRV with Balanced-Bellows Pressure Relief Valve
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Pipe Forces due to Relief Valve Discharge
4.3 - PRV – Balanced-Bellows Pressure Relief Valve with an Auxiliary Piston
4.4 - Pilot-Operated Valve (Flowing-Type)
4.5 – Rupture Disk Device in Combination with a PRV
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Pipe Forces due to Relief Valve Discharge
5 – Operation details of a PRV
5.1 - PRV Operating with Steam or Gas
5.2 - PRV Operating with Liquid
9
Pipe Forces due to Relief Valve Discharge
6 – Typical PRV Installation: Atmospheric (Open) Discharge
7 - Typical PRV Installation: Closed System Discharge
10
Pipe Forces due to Relief Valve Discharge
8 – Typical Pilot-Operated PRV Installation
9 - Examples of PRVs Installation with 3-Way Valves to Change Flow Direction
11
Pipe Forces due to Relief Valve Discharge
10 – Systems with PSVs, PRVs or PVs – Basic Considerations
The difference between systems open to atmosphere and closed systems where fluid is collected into a
blowdown vessel should always be taken into consideration.
10.1 – Systems open to atmosphere
In systems open to atmosphere, the act of two forces are considered in the calculation.
One of the forces is located on the valve on the outlet flange, in the axial direction of the discharge pipe in the
opposite way to the flow (backward), which occurs due to sudden outflow of fluid through the valve orifice. This
force is similar to the reaction of a firearm called “recoil”.
The second force acts on the pipe at the exit point to atmosphere, normal to the cut surface of the pipe. This
force is dynamic, but it excites the pipe only at this point and imposes no forces on the intermediate curves
because there are no reflections inside the pipe.
The evaluation of these forces can be done with the support of Caesar II’s dynamic modeler, called “Relief Loads
Synthesis”.
The API-520 Part II also calculates these forces.
Annex II of B31.1, too, contains rules for calculating such forces.
10.2 – Closed Systems – Collected into a Blowdown Vessel
In closed systems that are collected into a blowdown vessel, the forces propagate from the valve opening point
(PSV, PRV or PV) to the blowdown vessel.
As it is a closed system, there is a reflection of waves that generate forces that are “banging” between the valve
and the blowdown vessel, thus exciting the various sections through which these shock waves pass.
In hydraulic transients due to safety valve opening, in general, the pressure difference between upstream and
downstream of the valve is very high. The pressure wave resulting from the valve opening is highly nonlinear and
the formation of a shock wave occurs immediately downstream of the valve. In this case, the shock wave
separates the fluid still at rest inside the pipe from the one that has already suffered the action of the pressure
force that set it in motion. It is clear that in this situation, the resting fluid portion does not perceive the
existence of the shock (due to valve opening) prior to the passage of this shock wavefront. In relation to a fixed
reference, two wave fronts propagate - a subsonic and a supersonic wave front - whose forces are defined as a
function of the speed of the two wave fronts. The flow on one side of the shock is supersonic and on the other is
subsonic.
Although the determination of these forces makes it necessary to apply thermodynamics and fluid flow theories,
they can be evaluated in a simplified way using the JOUKOWSKY equations. Coade’s paper, for example,
calculates the P that occurs downstream of the PRV and propagates this force at the speed of sound in the fluid
in question. This force is applied section by section along the discharge lines to the disposal vessel.
10.3 - Auxiliary Methodology for Verification of the Effects of Relief Systems – Practical
Simplifications in Stress Assessment and Analysis in Closed Systems
The practice of several systems that have been carried out over the years has defined a methodology for
simplifying the calculation of closed systems, which we are proposing here. Naturally, the use of the
methodology defined here and contemplated by this item is the responsibility of an analyst engineer, and should
be the reason for the agreement between the interested parties.
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Pipe Forces due to Relief Valve Discharge
Gas or Steam Discharge
In flare lines from PSVs, PRVs or PVs with gas or steam discharge with an outlet diameter less than or equal to
8” and ΔP ≤ 10kgf/cm2, this discharge is considered to impose forces which are not significant. However, at least
one modal dynamic analysis should be performed and the means of support designed so that the first natural
frequency of the system is greater than 2 Hz.
It is thus assumed that we are not expecting significant forces due to this opening. Therefore, the prediction of a
two-way support acting on X, Y and Z, and the use of an elastometer between the support and the pipe – made
of material compatible with the design temperatures of these lines – is sufficient to consider these systems as
acceptable.
Liquid, Gas or Steam Discharge Not Listed Above
In flare lines from gas or steam discharge PSVs, PRVs or PVs, with an outlet diameter greater than 8” and ΔP >
10kgf/cm2 , or from PRVs, PSVs or PVs with liquid discharge, in addition to performing modal dynamic analysis,
the loads due to the opening of these valves must be calculated. If these forces show significant values, a timehistory or equivalent dynamic analysis should be performed to evaluate their effects on the system.
The calculated force is assumed to be significant when the modulus of this force is greater than or equal to the
frictional force corresponding to the supports that exist during the course of these forces. It’s considered the
weight of the pipe on the support with a vertical load and the corresponding frictional force = Vertical force x
friction coefficient. Being the force due to opening greater than or equal to this frictional force, the pipe will
“detach” from this support, thus imposing forces and stress on the pipes. More accurately, if we have the line
arrangement we can calculate the frictional forces on the supports through which this pressure wave will pass,
and verify whether the force due to opening is greater than or equal to these frictional forces.
10.4 – Approaches and Considerations in a Dynamic Excitation Piping System
1st - Accurate Calculation
It’s focused on determining the discharge forces of the PSVs, PRVs or PVs from a fluid dynamics (fluid shock)
point of view using, for example, a fluid program or the theoretical method for analysis and definition of force x
time profiles acting on the various sections during the transient. The result of this calculation defines the
variations of the forces inside the pipes per unit of time, section by section.
This evaluation should be followed by a dynamic Time-History analysis or equivalent. Traditional piping system
programs should be used to reflect these Force x Time variations in displacements, support loads and nozzles,
and stresses on piping and fittings.
2nd - Simplified Calculation
It’s focused on determining the discharge forces of the PSVs, PRVs or PVs by an approximate methodology that
replaces the one above. Consider the difference between open systems and closed systems. The walk-through in
this approach comes down to:





Modal Dynamic Analysis, keeping in mind that the first modal is 2 Hz.
Equivalent Static Analysis or Spectral Dynamic Analysis, with the discharge forces of the PSVs, PRVs or
PVs applied at specific nodal points. In the case of evaluation using the equivalent static method, a DLF =
2 should be used. Dynamic Spectral Analysis calculates the DLF.
Adoption of some support procedures that guarantee model fidelity, especially the rigidity of the
supports.
Determination of maximum pipe length so that system discretization is adequate.
Adoption of discretization procedure in the calculation to ensure that the distribution of masses from
the pipe fittings is as real as possible.
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Pipe Forces due to Relief Valve Discharge
3rd - Particularities of Dynamic Systems
Piping systems subjected to dynamic effects should preferably be analyzed with the aid of a computer program
that performs dynamic calculations. Dynamic pipeline calculations are linear so, for example, there are no
distributed loads in these calculations, only concentrated loads that are generated by the calculation program.
As a methodology to be used in the dynamic calculation, we indicate the following rules:








All supports must be two-way acting.
One-way supports should not be used due to nonlinearity.
We cannot consider the friction of the supports because it is a nonlinearity.
We cannot consider GAPs in the supports because it is a nonlinearity as well.
“Snubbers”, when necessary, should be minimized as much as possible due to the cost.
All supports, including gravity direction, must act both ways in calculation, design and construction.
Support standards for dynamic systems should not contain GAPs beyond mounting clearance.
Preferably, they should have a resilient element, such as an elastometer, between the support and the
pipe in the horizontal and upward directions.
If there are Loops in the system on lines subjected to fluid shock, care must be taken so that the section
furthest from the Loop is locked in the longitudinal direction.
4th - Maximum Distance of Straight Runs of Pipelines Subject to Dynamic Analysis.
The maximum distance (L) between two consecutive nodal points should be calculated with the equation below:
0.5
  
E I 
L  0.5  


 m 
2

f

max 
0.25
Where:
fmax = upper frequency limit up to which natural frequencies must be taken into account in the calculations:
f Max = 33 HZ
E = modulus of elasticity (N/m²);
I = moment of inertia (m4);
m = mass per unit length (Kg / m);
L = maximum span (m):
In order to facilitate its use, we reduce the constant terms and allow the right entry with unit weight (W)
through the formula:
E* I
L  1,08565 * 
 W 
0 , 25
Where:
L in mm
E in N/mm²
I in mm4
W in N/mm
OBS.: Between two consecutive supports, there must be at least one point defined as a node, even if the gap
between the supports does not reach the distance “L” defined by the above formula. Coade’s Mass Space
14
Pipe Forces due to Relief Valve Discharge
program, which is Freeware, calculates this maximum span to equal values if the number of concentrated
masses equals 1.
11 – Safety Valve Operating Phenomena
These phenomena can occur regardless of line design, and can happen due to the process. They are classified as:
“Chattering”, “Simmering” and “Fluttering”. These are operational phenomena that may exist due to the process
and occur in relief and/or safety valves. Below are the definitions of these phenomena and their causes.
11.1 - CHATTERING:
The most common phenomenon encountered in installations, and characterized by the rapid and abnormal
movement of the moving parts of a relief and safety valve where the disc contacts the nozzle. It’s a very strong
vibration that occurs with compressible fluids, however, in liquids it can be encountered when the inlet piping to
the relief valve is too long and induces the liquid at high flow velocities.
The main causes for “chattering” are:




Oversized valve.
Nozzle ring too high.
Poorly designed discharge piping.
Very high load drop in inlet pipe when the load drop is greater than 3%.
11.2 - SIMMERING:
An audible or visible leak that occurs in a safety valve operating with compressible fluids. Normally this occurs at
98% of valve set pressure. The main damage is wear on the sealing surfaces due to erosion caused by the high
velocity of fluid flowing at this time, as well as spring fatigue and wear on the guide surfaces.
11.3 - FLUTTERING:
A phenomenon similar to “chattering”, but there is no physical contact between the disc and the nozzle.
Therefore, the sealing surfaces of these parts are not damaged, but the guide surfaces may be.
The opening course and consequently the valve flow ends up “fluttering”.
Because it is a phenomenon similar to “chattering”, but with less intensity.
12 – The Reason Why the 2 Hz are Requested in Modal Dynamic Calculation
If we go into the theory of structural dynamics, we can elucidate the differences between damped and free
systems. With this, we can conclude the different ways to solve these oscillatory motion equations, which bring
different approaches to these systems.
We know that the evaluation of a system through a dynamic calculation, be it spectral, harmonic or “timehistory”, does not raise the concern with resonance, because resonance is one of the portions that solves the
problem, so it is considered in this calculation. The resulting displacements, stresses and loads calculated meet
this premise.
The adoption of Modal Analysis as a dynamic effects verification tool and the consequent minimum frequency
evaluation are usual for fluid shock systems evaluation when the propagated dynamic force has lower values
than the friction of the supports through which this wave front spreads. In this premise we are avoiding
“resonance”, considering possible points that are not contemplated in the project, such as supports not
adequately sustained, etc.
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Pipe Forces due to Relief Valve Discharge
In systems with fast flow operation, the distance between the element that produces the shock wave (Valve)
and the element that receives and returns the shock wave (Vessel) “capacitor” is considered equal to the length
L (m).
The velocity of the supersonic shock wave propagation sound is usually referred to as the letter C (m/s).
The time with which this shock wave travels from the point of generation of this wave to the receiving vessel is
called t (s).
t(s) = L(m) / C(m/s)
The time T with which this wave goes and returns to the origin point is calculated as:
T (S) = 2* t(s)
This time T is the period of the supersonic wave action, the inverse of this period and the acting frequency
imposed on the system by the shock wave.
f (hz) = 1 / T (s)
The determination of the sound velocity in the fluid depends on some variables and must be calculated properly.
However, by approximation we have the following values:
Water at room temperature

C = 1252m/s
Methane at 200ºC

C = 565 m/s
Superheated steam (400ºC)

C = 633 m/s
Oil at 35ºC

C= 1306 m/s
Creating a table of frequency x distance, considering two basic fluids, with water representing liquids and
methane representing torch gases, we will then have the following values.
Fluido
Água
Metano
V Som
C
1252
1252
1252
1252
1252
1252
Distância
L
100
300
470
500
1000
2000
Periodo
s
0,160
0,479
0,751
0,799
1,597
3,195
Imposta
1/s
6,26
2,09
1,33
1,25
0,63
0,31
Mínima
1/s
9,39
3,13
2,00
1,88
0,94
0,47
565
565
565
565
565
565
565
100
150
212
300
500
1000
2000
0,354
0,531
0,750
1,062
1,770
3,540
7,080
2,83
1,88
1,33
0,94
0,57
0,28
0,14
4,24
2,83
2,00
1,41
0,85
0,42
0,21
For Gases - Conclusion
The fluid from flare systems being gas or steam, according to the table above - distances less than 212 m require
natural piping frequencies greater than 2 Hz as minimum frequency. For systems with distances from 212 m to
100 m, the frequency of 5 Hz can be considered as the minimum design frequency for these systems.
For those systems whose distance from the blowdown vessel to the shock generating valve is greater than or
equal to 212 m. The minimum natural pipe frequency ≥ 2 Hz removes possible resonances. This value is a
‘wildcard’ value used as the minimum frequency in flare system design.
16
Pipe Forces due to Relief Valve Discharge
For Liquids - Conclusion
The conclusion from the table above is that in liquid discharge the minimum distance to maintain the minimum
frequency of 2 Hz is 470 m. For distances between 470 m and 100 m, the minimum natural frequency of the
analyzed piping should be 10 Hz.
13 – Step by Step in Pressure Wave Development in a Closed System
1st Step
In the normal flow state, pressures at different pipe runs are balanced, so no unbalanced force due to pressure
excites the pipe. This first section we will call Loop.
2nd Step
The valve opens suddenly, throwing in the downstream pipe a quantity of fluid moving forward, in this example,
upwards. Yellow represents an overpressure front developed inside the pipe when the valve opens. At this time,
there are no horizontal forces in the horizontal section 20 - 30, until the pressure wave reaches the 1st curve.
17
Pipe Forces due to Relief Valve Discharge
3rd Step
‘
After the wavefront enters the section 20 - 30, there is a pressure unbalance in this section, so in Node 20 we
have a part of the wave causing an overpressure and in Node 30 the normal pressure. Then a horizontal force is
generated due to the pressure unbalance in the section 20 - 30, which lasts until the wavefront reaches node 30
and balances the pressure, ending the pressure unbalance, and consequently the force ceases to act on this
section.
4th Step
18
Pipe Forces due to Relief Valve Discharge
When the wave passes the Node 30 curve, the unbalanced wave force at section 20 - 30 is zero. If L is the length
of section 20 - 30 between curves and C is the velocity of sound in the fluid, the unbalanced force acts during the
time Td = L/C. When it enters the section after Node 30, the overpressure of Node 30 causes an unbalance of
pressure and the consequent vertical force on the section after Node 30 begins to act at Time > Td and lasts the
same as Td of the subsequent section (30 – 40).
After the wavefront passes Node 30, the horizontal force is zero, but the pipe corresponding to this portion (20 30) is still deflected, continuing to vibrate for a time depending on damping. Due to the horizontal force that
acted on the pipe run between Nodes 20 - 30, the loop is deformed in the horizontal direction towards the
unbalanced forces. It passes through the neutral point, is deformed in the opposite direction and returns again
to be deformed in the direction of force.
5th Step
19
Pipe Forces due to Relief Valve Discharge
When the pressure wave leaves the loop, entering section 40 – 50, it moves forward, exciting the other
subsequent sections.
This phenomenon repeats itself segment by segment, exciting the piping along the sections where the wavefront
passes. Notice in the sketches that the red arrow represents the direction of the flow and the green arrow
represents the direction of the force, and we remember that the excitation in the section continues for a time
that depends on damping.
6th Step
When the wavefront reaches a high acoustic capacitance element, such as a vessel, a tank, a pump, or a closed
valve, it is reflected.
20
Pipe Forces due to Relief Valve Discharge
7th Step
If the reflection point is an open end, a rarefaction wave (low pressure) will be reflected through the system. If
the reflection point is a positive displacement machine, for example, a higher-pressure wave will move from the
reflected point back to the source. In fact, most boundary conditions have some attributes of one boundary and
the other, so the reflected wave has hybrid properties and is positioned between one condition and the other.
21
Pipe Forces due to Relief Valve Discharge
8th Step
The unbalanced load in the horizontal direction is zero, however, the vertical leg of the loop pipe suffers a
vertical unbalanced load while the wave is at 40 – 30.
9th Step
Depending on the distance of the reflection point, the wave may enter the loop while still oscillating back and
forth due to the original impact on the system, and subsequent recurrence may occur.
The horizontal load in the loop begins to increase as the reflected wave enters the first curve.
22
Pipe Forces due to Relief Valve Discharge
10th Step
If the wave comes in at the right time, the displacement due to the newly developed horizontal force may
increase the displacement of the oscillation. The reflected wavelength has a period equal to the length between
the loop and the reflection point divided by the speed of the moving wavefront.
The magnitude of the unbalanced load remains acting as long as the wavefront is in the horizontal range. The
over pressured one will act on the left curve and the one under pressure will act on the right curve, causing an
unbalanced load. The duration of this load is equal to the length between curves divided by the speed of the
traveling wavefront.
11th Step
23
Pipe Forces due to Relief Valve Discharge
When the wavefront leaves the corresponding curve-to-curve section in the horizontal direction, the unbalanced
load drops to zero.
As seen earlier, the system can remain oscillating back and forth. As the frontwave travels in the pipe to the left
of the discharged loop, it continues to pass the neutral (discharged) position.
12th Step
Eventually, the reflected wave on the left side of the system will return to the loop and the unbalanced loads will
act on the system again, but this time, still in the oscillating condition left by the previous passage.
14 – Calculation Example in an Open Atmosphere System
The determination of the forces acting on pipelines in systems open to atmosphere can be performed by
different methods. In this article, we included through this calculation example the determination of forces by
the following methods:



As calculated by Caesar II in the dynamic force calculation module due to safety valve opening called
“Relief Load Synthesis”
As defined in ASME B31.1
As defined in API RP520
In the following example, the end is open and is mounted on a silencer.
24
Pipe Forces due to Relief Valve Discharge
14.1 – Model Evidence in Caesar II – Isometric calculation of the lines used in this example.
25
Pipe Forces due to Relief Valve Discharge
14.2 – Process Data
14.3 – Line Geometry Data – Diameter, Schedule, Insulation, and Materials
14.4 – Datasheet of the Safety Valves
26
Pipe Forces due to Relief Valve Discharge
14.5 – Calculation of Forces According to Caesar II’s Relief Load Synthesis
Location of forces in an open system (Caesar II Manual)
Types of calculation contained in relief load synthesis
27
Pipe Forces due to Relief Valve Discharge
Caesar II Calculation Report
Summary of the forces calculated above in Newtons (N) and Pounds*Force (lbf)
FExit = 12.413,927 N
= 2.790,76 lbf
FInterface = 34.974,176 N
= 7.862,51 lbf
14.6 – Calculation of Forces According to ASME B31.1 Formulas
Formulas of ASME B31.1 “Safety Relief Valve Thrust”
a & b Values According to Table II-2.2.1 of ASME B31.1 – Used in the above formula
28
Pipe Forces due to Relief Valve Discharge
Steam properties according to Sarco’s program
Table II-2.2.1 (B31.1) for setting the values of a and b
a:
831
b:
4,33
ho (Stagnation enthalpy), BTU/lbm:
1201,76
gc, (Gravity Acceleration), lbm-ft/lbf-sec2:
J (Enthalpy), ft-lbf/Btu:
W (Mass flow) lbm/sec:
Pa (atmospheric pressure), psia:
32,2
778
70,4155556
14,7
A1 (Exit area at point 1), in2:
188,69
Valve data for calculation
Relief Valve set pressure, psig:
Steam operating temperature, °F:
Orifice size, in2
Actual flow capacity of valve at
10% accumulation, lbm/hr:
Valve inlet I.D., in:
Valve outlet I.D., in
Valve discharge elbow OD, in:
Discharge elbow nom wall, in:
692,70
504,34
6,38
:
253.496
4
6
16
0,250
:
Calculated Values
P1=
13,88
psia
V1=
1557,27
F1=
3251
lbf
(Without DLF)
F=
7.825
lbf
(Without DLF)
ft/sec
29
Pipe Forces due to Relief Valve Discharge
14.7 – Calculation of Forces According to API RP520 Formulas
Sketch for force location
Variables used in this calculation step
API RP520 formulas used in force calculation
C  kgoRT F1  ( W / 366) * kT/(k  1)M  AoP2
P2  W / Ao  / 366x T1 /(k k  1M)  Pa
30
Pipe Forces due to Relief Valve Discharge
Calculation Data and Determined Values
Input
Valores calculados
P2' = -14,6957
Ao
W
k
T
T1
M
go
R
C
P2
188,69
253.496
1,2746
964
933
18,02
32,2
85,68
1841
0,00
F1
DLF x F1
d
ρ
Ma
3792
7584
15,5
1,542
0,019
P
693
AORIF
6,38
o
V ORIF
F
0,000892 1030,992 6675,933
Summary of forces calculated according to API RP520
F1 FINAL
= 3.792,15 lbf
16868,3 N
FFINAL
= 6.675,93 lbf
29.696,0 N
14.8 – Comparison of Values Calculated by the Three Methods Above
Local da Força Variável
F
na PSV
F1
na Interface
CII
7.862
2.791
B31.1
7.825
3.251
RP-520
6.676
3.792
Maior Valor
7.862
3.792
Unidade
lbf
lbf
14.9 – Determination of Force x Time graphics encoded in Caesar II (Dynamic Module)
Data to determine the graphics
PSV opening time
=
8 msec
(Milliseconds)
PSV closing time
=
8 msec
(Milliseconds)
Relief Duration
=
1000 msec
(Milliseconds)
Distance from the PSV to interface point
=
78,98 ft
Fluid velocity inside the discharge pipe
=
1557,27 ft/sec
Time it takes for the force to reach the open section to atmosphere
=
50,71664 msec
Theoretical induced frequency
=
9,858697 Hz (Hertz)
Graphics plotted for encoding with the highest values
31
Pipe Forces due to Relief Valve Discharge
14.10 – Inputted Static and Dynamic Cases
Static = CASE 3 – Analysis under Hydrostatic Test conditions
Static = CASE 4/11/18 - Analysis of Operating conditions with PSV A operating
Static = CASE 5/12/19 - Analysis of Operating conditions with PSV B operating
Static = CASE 6/13/20 - Analysis of Project conditions with PSV A operating
Static = CASE 7/14/21 - Analysis of Project conditions with PSV B operating
Static = CASE 8/15/22 - Analysis of Operating conditions with PSVs A & B operating
Static = CASE 9/16/23 - Analysis of Project conditions with PSVs A & B operating
Static = CASE 10/17/24 - Analysis of Operating conditions with PSVs A & B off
Dynamics 1  Force Graph with PSV – A (Open)
IMPOSED FORCES:
34327 Node 260
16868 Node 410
Dynamics 2  Force Graph with PSV – B (Open)
IMPOSED FORCES:
34327 Node 150
16868 Node 720
Dynamics 3  Force Graph with PSVs – A & B (Open)
IMPOSED FORCES:
34327 Node 260
16868 Node 410
34327 Node 150
16868 Node 720
14.11 – Dynamic Input and Calculated Natural Frequencies
----- DYNAMIC ANALYSIS INPUT DATA
S2
<----- Analysis Type (HARMONIC/SPECTRUM/MODES/TIMEHISTORY)
10
<----- Static Load Case for Nonlinear Restraint Status
0.0
<----- Stiffness Factor for Friction (0.0-Not Used)
50
<----- Max. No. of Eigenvalues Calculated (0 - Not Used)
33
<----- Frequency Cutoff (Hz)
0.1
<----- Closely Spaced Mode Criteria
N
<----- Re-use Last Eigensolution (Frequencies and Mode Shapes)
MODAL
<----- Spatial or Modal Combination First
SRSS
<----- Spatial Combination Method (SRSS/ABS)
GROUP
<----- Modal Combination Method (Group/10%/DSRSS/ABS/SRSS)
Y
<----- Include Missing Mass Components (Y/N)
SRSS
<----- Missing Mass Combination Method (SRSS/ABS)
ABS
<----- Directional Combination Method (SRSS/ABS)
LUMPED
<----- Mass Model (LUMPED/CONSISTENT)
Y
<----- Sturm Sequence Check on Computed Eigenvalues (Y/N)
6
<----- Estimated No. of Significant Figures in Eigenvalues
1E-12
<----- Jacobi Sweep Tolerance
1E10
<----- Decomposition Singularity Tolerance
0
<----- Subspace Size (0 - Not Used)
2
<----- No. to Converge Before Shift Allowed (0 - Not Used)
0
<----- No. of Iterations per Shift (0 - Pgm Computed)
0
<----- % of Iterations per Shift Before Orthogonalization
N
<----- Force Orthogonalization After Convergence (Y/N)
N
<----- Use Out-of-Core Eigensolver (Y/N)
100
<----- Frequency Array Spaces
LUMPED MASSES
SNUBBERS
32
Pipe Forces due to Relief Valve Discharge
EXCITATION FREQUENCIES FOR HARMONIC ANALYSIS
HARMONIC FORCES
HARMONIC DISPLACEMENTS
FORCE SPECTRUM EDITING
34327 , X , 260 , 1
-16868 , Y , 410 , 2
34327 , X , 150 , 3
-16868 , Y , 720 , 4
DYNAMIC LOAD CASE DATA
DYNAMIC LOAD CASE # 1
FPSV , 1 , X , 1
FINT , 1 , Y , 2
STRESSTYPE(OCC)
DYNAMIC LOAD CASE # 2
FPSV , 1 , X , 3
FINT , 1 , Y , 4
STRESSTYPE(OCC)
DYNAMIC LOAD CASE # 3
FPSV , 1 , X , 1
FINT , 1 , Y , 2
STRESSTYPE(OCC)
FPSV , 1 , X , 3
FINT , 1 , Y , 4
STATIC/DYNAMIC COMBINATION CASES
COMBINATION CASE # 1
S13(L13:W+P3+H+F1(SUS)) , 1
D1 , 1
STRESSTYPE(OCC)
COMBINATION CASE # 2
S14(W+P4+H+F1(SUS)) , 1
D2 , 1
STRESSTYPE(OCC)
COMBINATION CASE # 3
S16(W+P6+H+F1(SUS)) , 1
D3 , 1
STRESSTYPE(OCC)
COMBINATION CASE # 4
S6(W+D3+T3+P3+H+F1(OPE)) , 1
D1 , 1
STRESSTYPE(OPE)
COMBINATION CASE # 5
S7(W+D4+T4+P4+H+F1(OPE)) , 1
D2 , 1
STRESSTYPE(OPE)
COMBINATION CASE # 6
S9(W+D6+T6+P6+H+F1(OPE)) , 1
D3 , 1
STRESSTYPE(OPE)
SPECTRUM DEFINITIONS
FPSV ,
* USER ENTERED TIME HISTORY PULSE
*
TIME(milliseconds)
FORCE( N.)
*
0.00000
0.00
*
8.00000
34327.00
*
16.00000
34327.00
*
24.00000
0.00
FPSV , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
0.0002 , 0.0044
0.0033 , 0.0220
0.0167 , 0.1082
0.0528 , 0.3405
33
Pipe Forces due to Relief Valve Discharge
0.1289 , 0.8113
0.2673 , 1.5234
0.4952 , 1.9988
0.8448 , 1.9965
1.3532 , 1.9910
2.0625 , 1.9791
3.0197 , 1.9556
4.2768 , 1.9121
5.8907 , 1.8372
7.9233 , 1.7175
10.4414 , 1.5421
13.5168 , 1.3126
17.2262 , 1.0590
21.6513 , 1.1483
26.8787 , 1.2153
33.0000 , 1.0997
FINT ,
* USER ENTERED TIME HISTORY PULSE
*
TIME(milliseconds)
FORCE( N.)
*
0.00000
0.00
*
8.00000
0.00
*
62.80000
16868.00
*
1062.8000
16868.00
*
1070.8000
0.00
FINT , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
0.0002 , 0.0044
0.0033 , 0.0220
0.0167 , 0.1082
0.0528 , 0.3405
0.1289 , 0.8113
0.2673 , 1.5234
0.4952 , 1.9988
0.8448 , 1.9965
1.3532 , 1.9910
2.0625 , 1.9791
3.0197 , 1.9556
4.2768 , 1.9121
5.8907 , 1.8372
7.9233 , 1.7175
10.4414 , 1.5421
13.5168 , 1.3126
17.2262 , 1.0590
21.6513 , 1.1483
26.8787 , 1.2153
33.0000 , 1.0997
NATURAL FREQUENCY REPORT
(Hz)
(Radians/Sec)
MODE
FREQUENCY
FREQUENCY
1
2
3
4
5
6
7
8
9
10
11
2.640
2.880
4.144
4.413
4.923
5.320
6.764
7.977
9.502
10.549
11.781
16.587
18.093
26.038
27.727
30.931
33.425
42.500
50.120
59.705
66.281
74.025
(Sec)
PERIOD
0.379
0.347
0.241
0.227
0.203
0.188
0.148
0.125
0.105
0.095
0.085
34
Pipe Forces due to Relief Valve Discharge
12
13
14
15
16
17
18
19
20
13.581
13.802
14.665
15.834
17.308
22.220
25.531
30.771
33.894
85.331
86.721
92.145
99.488
108.746
139.610
160.414
193.342
212.965
0.074
0.072
0.068
0.063
0.058
0.045
0.039
0.032
0.030
14.12 – Calculated Maximum Stresses – Static and Dynamic
Static – Permanent Loads
Highest Stresses: (
KPa
) LOADCASE 14 (SUS) W+P4+H+F1
CodeStress Ratio (%):
50.6 @Node
240
Code Stress:
65873.8 Allowable:
130112.3
Axial Stress:
17649.5 @Node
120
Bending Stress:
49838.6 @Node
240
Torsion Stress:
2165.9 @Node
360
Hoop Stress:
37004.3 @Node
50
3D Max Intensity:
65104.0 @Node
240
Static – Thermal Effects
Highest Stresses: (
KPa
) LOADCASE 20
CodeStress Ratio (%):
68.1 @Node
Code Stress:
183173 Allowable:
Axial Stress:
2415.1 @Node
Bending Stress:
146775.1 @Node
Torsion Stress:
53789.8 @Node
Hoop Stress:
0.0 @Node
3D Max Intensity:
215901.7 @Node
(EXP) L20=L6-L13
240
269135.5
280
240
240
20
240
Dynamic – PSV A open – Combination 1 (Sus 13+D1)
****
****
B31.3 -2008, December 31, 2008
CODE STRESS CHECK PASSED
HIGHEST STRESSES: (
KPa
)
CODE STRESS %:
60.8 @NODE 240
STRESS:
105246.9 ALLOWABLE:
BENDING STRESS:
87990.1 @NODE 240
TORSIONAL STRESS:
4294.1 @NODE 280
AXIAL STRESS:
21748.6 @NODE 290
3D MAX INTENSITY:
105240.9 @NODE 240
173049.
Dynamic – PSV B open – Combination 2 (Sus 14+D2)
****
****
B31.3 -2008, December 31, 2008
CODE STRESS CHECK PASSED
HIGHEST STRESSES: (
KPa
)
CODE STRESS %:
55.6 @NODE 130
STRESS:
96219.9 ALLOWABLE:
173049.
BENDING STRESS:
79229.1 @NODE 130
TORSIONAL STRESS:
3184.3 @NODE 240
AXIAL STRESS:
21653.4 @NODE 590
3D MAX INTENSITY:
96595.2 @NODE 130
Dynamic – PSVs A&B open – Combination 3 (Sus 16+D3)
****
****
B31.3 -2008, December 31, 2008
CODE STRESS CHECK PASSED
HIGHEST STRESSES: (
KPa
)
CODE STRESS %:
72.0 @NODE 240
STRESS:
124651.4 ALLOWABLE:
173049.
BENDING STRESS:
106552.0 @NODE 2400
TORSIONAL STRESS:
6636.6 @NODE 240
AXIAL STRESS:
21769.1 @NODE 290
3D MAX INTENSITY:
124639.4 @NODE 240
35
Pipe Forces due to Relief Valve Discharge
15 – Calculation Example in a Closed System – Fluid Collected into a Blowdown
Vessel
The determination of the forces acting on piping in closed systems, which are collected in a blowdown vessel,
can be performed by two different methods: an approximate method and an accurate method. In this example,
the evaluation that is highlighted aims to elucidate the method of defining forces through the approximate
method.
This example studied here is interesting because the upstream drains of the valves were breaking. We did a
liquid hammer analysis on the inlet pipes and a fluid blow analysis on the discharge pipes.
Originally, the report that was drawn up aimed to analyze the inlet and outlet lines of the PSVs 29615 & 29616
from the natural gas condensate processing unit due to cracks detected in the inlet drains of the PSVs.
This analysis’ main goal is to propose changes in the support of the lines so that integrity is guaranteed,
according to the codes adopted as reference in the evaluation. Therefore, we were proposing to change the line
supports so that the operation would be safe.
15.1 – Caesar Coded Model and Isometric Line Calculation.
Mathematical model taken from Caesar II
36
Pipe Forces due to Relief Valve Discharge
Detailed calculation Isometrics
Sheet 1
37
Pipe Forces due to Relief Valve Discharge
Sheet 2
15.2 – Process Data
SII
SII
SII
SII
3"
3"
3"/4"/6"
3"/4"/6"
14"
HC
HC
HC
HC
HC
296
296
296
296
650
010
009
155
156
10
Ba
Ba
Bg
Bg
Bg
-
IQ
IQ
IQ
IQ
IQ
25
25
25
25
51
GNLP
GNLP
GNLP
GNLP
GNLP
L
L
L
L
L
10-HC-296-017-Ba
10-HC-296-016-Ba
PSV-29615
PSV-29616
6"-HC-296-155/156
PSV-29616
PSV-29615
14"-HC-650-010
14"-HC-650-010
14"-HC-650-025
Tope Pope Massa Espe
ºC kgf/cm2 kg/m3
73 11,80 529,0
73 11,80 529,0
73 3,50 529,0
73 3,50 529,0
73 3,50 529,0
15.3 – Line Geometry Data – Diameter, Schedule, Insulation, and Materials
Tproj P Proj
ºC kgf/cm2
107 16,6
107 16,6
200 5,0
200 5,0
200 5,0
Pteste
kgf/cm2
24,9
24,9
7,5
7,5
7,5
38
Pipe Forces due to Relief Valve Discharge
15.4 – Datasheet of the PSV-29615 & PSV-29616
39
Pipe Forces due to Relief Valve Discharge
15.5 – Assumptions Adopted in Determining Dynamic Forces
Simulated Scenario
Two PSVs opening. Due to the distance from the Header to the PSV, a hammer will occur in the
upstream section and a fluid shock will occur in the downstream section of the PSVs
to the discharge pickup manifold.
We simulated the opening three times, starting the opening at 1 ms after normal flow and the opening of
the PSV at 2 ms, with three consecutive events.
Basic Project Data
Unit type
Gas Condensate Processing Unit
System
U-296 (GLP)
Pressure (Opening)
Relief Temperature
Maximum Flow
Piping Material ; J/M
ASTM A-333 Gr. 6
Upstream of the PSV
Dow nstream of the PSV
Relief Header (10")
Receiving Manifold (14")
Piping diameters
PSV - 29615
Flow
rate
PSV - 29616
1696,5700 kPa (g)
106,0 ºC
32180,0 kgs/h
API-5L Gr.B
ID
77,92 mm
154,08 mm
254,46 mm
333,34 mm
mm
mm
mm
mm
mm
6"-HC-296-155-Bg
3"-HC-296-009-Ba
6"-HC-296-156-Bg
3"-HC-296-010-Ba
32180,0
32180,0
32180,0
32180,0
kg/
kg/
kg/
kg/
OD
88,90 mm
168,30 mm
273,10 mm
355,60 mm
mm
mm
mm
mm
mm
h
h
h
h
Sketch for calculation
Spreadsheet Interconnection
Header = 10"-HC-295-017-Ba
Header = 10"-HC-295-016-Ba
Entry = Hammer
PSV-29615
PSV-29616
Discharge = Shock
Manifold = 14"-HC-650-010-Bg
Calculation Assumptions
1 - Three scenarios will be evaluated. PSV 15 opening, PSV 16 opening, and both simultaneous.
2 - The reflections were disregarded.
3 - The overpressure calculation was calculated considering the flow conditions of the PSVs.
40
Pipe Forces due to Relief Valve Discharge
15.6 – Calculation of the Dynamic Forces in the Inlet Pipes Due To a Liquid Hammer from the PSV29615 & PSV-29616
Basic data for the calculation = PSV-29615/16
Calculation of forces at the entrance section of the PSV-29615/16
Considered as a Liquid Hammer
Pipe of Ø3" x Sch. 40 with length of 18,653 m PSV-29615 & 18,959 m for PSV-29616
Process data for the calculation (PSV-29615/16)
Required Mass Flow
kg ==> Mass
=
32.180,00
379,2º K
=
106,0
O
=
425,6
N.m / kg . OK
=
0,07792
Gas constant k
=
1,27
Absolute Opening Pressure
=
1.697,00
Opening temperature
Gas constant Rg
Inner diameter of tube
3"xSch40
Calculation of the velocity of sound in the liquid through the pipe (C = m/s) ( PSV-29615/16)
 = 529,0 kg/m3
Liquid Density (in Mass)
Modulus of elasticity of the fluid
Ef = 372,658 MPa
Modulus of elasticity of the pipe
E = 206.910,0 MPa
Ratio between modules
Ef/E = 0,001801063
Wall diameter/thickness ratio
d/t=22,7


Ef
C 
    Ef
     * 
   E



  d   
 *    
  t   
Sound Speed in liquid
C=822,7 m/s
Calculation of flow rate variation (V) for the PSV-29615/16
Internal cross-sectional area
V 
Ai = 0,0048 m2
Q
Ai * 
Speed variation
V = 3,50 m/s
Calculation of P and wavelength L as defined by the PSV-29615/16
P  1,00 *  * C * V
L  C * t abertura
kg/h
C
m
kPa
41
Pipe Forces due to Relief Valve Discharge
Valve open time assumed
tabertura = 2 ms
Section pressure variation
P = 1.619.294,21Pa = 16,507 kgf/cm2
Wave-length
L = 1,65 m
Calculation of maximum unbalanced force (F) for the PSV-29615 & 29616
F  P * Ai
Maximum unbalanced force
F = -7.721,73 N = -787,13 kgf
Determination of values for each pipe section for the PSV-29615
Section
Pipe 11
Pipe 12
Pipe 13
Pipe 14
Pipe 15
Pipe 16
Pipe 17
Pipe 18
Pipe 19
Pipe 20
L (Length)
mm
1872,0
508,0
710,0
1477,0
5680,0
610,0
4010,0
610,0
1010,0
2166,0
tr
ms
2,0
0,6
0,9
1,8
2,0
0,8
2,0
0,8
1,2
2,0
Force
kN
-7,72
-2,38
-3,33
-6,93
-7,72
-2,86
-7,72
-2,86
-4,74
-7,72
td
ms
0,28
0,00
0,00
0,00
4,90
0,00
2,87
0,00
0,00
0,63
t
ms
4,3
1,2
1,7
3,6
8,9
1,5
6,9
1,5
2,5
4,6
Determination of values for each pipe section for the PSV-29616
Section
Pipe 1
Pipe 2
Pipe 3
Pipe 4
Pipe 5
Pipe 6
Pipe 7
Pipe 8
Pipe 9
Pipe 10
L (Length)
mm
1872,0
508,0
2790,0
1477,0
5430,0
610,0
2735,0
610,0
760,0
2167,0
tr
ms
2,0
0,6
2,0
1,8
2,0
0,8
2,0
0,8
0,9
2,0
Force
kN
-7,72
-2,38
-7,72
-6,93
-7,72
-2,86
-7,72
-2,86
-3,57
-7,72
td
ms
0,28
0,00
1,39
0,00
4,60
0,00
1,32
0,00
0,00
0,63
t
ms
4,3
1,2
5,4
3,6
8,7
1,5
5,3
1,5
1,8
4,6
Caesar II inputted force x time graphics in the PSVs entry sections
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
2,0
4,0
0
-0,5 0,0
-1
-1,5
-2
-2,5
-3
6,0
2,0
4,0
6,0
Force (kN)
Force (kN)
Since the pipe runs are approximately equal, the graphics for the two valves are similar, so we will show only
one set of graphics that will be applied to both valves. The pipe numbering refers to the PSV-29616, but please
understand that they are the same as pipes 11 - 20 of the PSV-29615.
Time (ms)
Tubo 1
Time (ms)
Tubo 2
.
42
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
5,0
10,0
Force (kN)
Force (kN)
Pipe Forces due to Relief Valve Discharge
10,0
15,0
10,0
20,0
0
-0,520,0
-1
-1,5
-2
-2,5
-3
-3,5
20,5
17,0
21,0
Tubo 7
22,0
23,0
18,0
Tubo 6
21,5
22,0
Force (kN)
4,0
Time (ms)
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
10,0
Tubo 9
6,0
Tubo 11
20,0
30,0
Time (ms)
Force (kN)
2,0
Tubo 8
Time (ms)
24,0
Force (kN)
Force (kN)
16,0
Time (ms)
30,0
Time (ms)
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
-9
Tubo 4
Force (kN)
Force (kN)
0
-0,515,0
-1
-1,5
-2
-2,5
-3
-3,5
Tub…
Time (ms)
0
-0,521,0
-1
-1,5
-2
-2,5
-3
-3,5
-4
15,0
Time (ms)
20,0
Time (ms)
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
10,0
Force (kN)
Force (kN)
5,0
5,0
Tubo 3
Time (ms)
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
0
-0,5 0,0
-1
-1,5
-2
-2,5
-3
2,0
Time (ms)
4,0
Tubo 10
6,0
Tubo 12
43
Pipe Forces due to Relief Valve Discharge
4,0
10,0
15,0
Tub…
Time (ms)
22,0
22,5
23,0
10,0
15,0
20,0
Force (kN)
10,0
25,0
Time (ms)
Tubo 16
20,0
30,0
Tubo 17
Time (ms)
26,0
Force (kN)
24,0
Force (kN)
23,0
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
-9
Tubo 18
Time (ms)
0
-0,5 22,0
-1
-1,5
-2
-2,5
-3
-3,5
-4
-4,5
-5
5,0
Time (ms)
23,5
Force (kN)
0
-0,521,5
-1
-1,5
-2
-2,5
-3
-3,5
Tubo 14
Time (ms)
0
-0,5 0,0
-1
-1,5
-2
-2,5
-3
-3,5
20,0
10,0
Force (kN)
Force (kN)
5,0
5,0
Tubo 13
Time (ms)
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
-9
0
-1 0,0
-2
-3
-4
-5
-6
-7
-8
6,0
Force (kN)
2,0
Force (kN)
0
-0,5 0,0
-1
-1,5
-2
-2,5
-3
-3,5
Tubo 19
0
-1 22,0
-2
-3
-4
-5
-6
-7
-8
-9
24,0
26,0
Time (ms)
28,0
30,0
Tubo 20
15.7 - Calculation of the Dynamic Forces in the Discharge Pipes Due To the Shock of “Flashing”
Liquid from the PSV-29615 & PSV-29616 by the Approximate Method
Observation: At this point, it is worth observing that the calculation of the forces due to the flash fluid stroke, in
a more precise approach, is solved with equations of thermodynamics and fluid mechanics. However, the
methodology used below characterizes an approximate method for determining the forces. The article
PSV=Comparison=Theoretical x Simplified, explains the methodology in more detail and compares the different
methods.
Basic data for the calculation of the PSV-29615/16 forces
Calculation of forces in the output section of PSV-29615/16
Considered as a “blow” of flashing liquid
44
Pipe Forces due to Relief Valve Discharge
Pipe of Ø3" x Ø6” (Sch. 40) with length of 4,324 m PSV-29615 & 4,324 m for PSV-29616
Process data for the calculation = PSV-29615/16
60,8 m3/h
Required Flow
Q
=
Opening temperature
T
=
Modulus of elasticity of the fluid (Bulks)
Ef
Modulus of elasticity of the pipe adopted
E
=
206.910,0 MPa
Inner diameter of pipe
Di
=
0,1541 m
t
=
7,11E-03 m
Pa
=
Dens
=
Pipe wall thickness
Absolute opening pressure
Fluid Density
106,0
 = 529,0 kg/m3
Modulus of elasticity of the fluid
Ef = 372,658 MPa
Modulus of elasticity of the pipe
E = 206.910,0 MPa
Ratio between modules
Ef/E = 0,001801047
Wall diameter/thickness ratio
d/t=22,7
C




Ef




 Ef   d    



*


 *    

E

  t   


Speed of sound in the liquid
C=822,7 m/s
Time the wave goes from one curve to the adjacent one (ts)
Speed of sound in the fluid in the pipe
C = 822,7 m/s
Worst distance between two adjacent curves
L = 1,838 m
ts 
L
C
Time
ts = 0,002234 s
Calculation of specific fluid weight ()

Dens * 1000 * 9,81
1
Specific weight
= 5.189,49 N/m3
C
372,658 MPa
1697,00 kPa
0,529 adm
Calculation of the speed of sound in the liquid through the pipe (C = m/s) = PSV-29615/16
Liquid Density (in Mass)
O
45
Pipe Forces due to Relief Valve Discharge
Calculation of flow rate variation (V) for PSV-29615/16
Internal cross-sectional area
V 
Ai = 0,0186 m2
Q
Ai
V = 0,90628 m/s
Speed variation
Calculation of P and wavelength L as defined by PSV-29615/16
P  1,00 *  * C * V
P = 394.000,0 Pa = 4,021 kgf/cm2
Section pressure variation
Calculation of maximum unbalanced force (F) for the PSV-29615 & 29616
F  P * Ai
Maximum unbalanced force
F = -7.350 N = -750,0 kgf
Determination of values for each pipe run for the PSV-29615&PSV-29616
In this type of calculation (fluid shock), the force in each pipe is independent of the length of the section of each
pipe. Consequently, the total force developed in the blow acts in both a pipe of only a few mm and a long one.
Naturally, the difference is the time that this force acts on each pipe section.
Section
Length
mm
995
1839
1487
21
22
23
Time (ti)
ms
1,21
2,24
1,81
Time
ms
1,21
3,44
5,25
Caesar II encoded graphics in the PSVs’ outputs
Since the pipe runs are equal, the graphics for the two valves are the same. The numbering of the pipes refers to
the PSV-29616, but understand that they are the same as the PSV-29615 pipes. We have inserted the repetition
of the force three times in the model in order to obtain the maximum effects because the pipe sections are
short.
10
Force in kN
8
6
4
2
21
0
-2
0
5
10
15
-4
-6
Time in ms
20
25
30
35
46
Pipe Forces due to Relief Valve Discharge
Force
22
9
8
7
6
5
4
3
2
1
0
22
0
5
10
15
20
25
30
Time
Force
23
9
8
7
6
5
4
3
2
1
0
23
0
5
10
15
20
25
30
Time
15.8 – Inputted Static and Dynamic Cases
15.8.1– Static Cases
Case 1 – Lines upstream of the PSVs under Project conditions. PSV-29616 open with discharge piping under
project conditions and downstream piping from PSV-29615 under ambient conditions.
Case 2 – Lines upstream of the PSVs under project conditions. PSV-29615 open with discharge piping under
project conditions and downstream piping from the PSV-29616 under ambient conditions.
Case 3 – Lines upstream of the PSVs under project conditions. PSV-29615 and 29616 open with the discharge
pipes under project conditions.
Case 4 – Lines upstream of the PSVs under operating conditions. PSV-29615 and 29616 closed with discharge
piping under ambient conditions.
15.8.2– Dynamic Cases
Case 1 – PSV-29616 discharging with suction and discharge pipes with applied dynamic forces.
Case 2 – PSV-29615 discharging with suction and discharge pipes with applied dynamic forces.
Case 3 – PSV-29615 e 29616 discharging with suction and discharge pipes with applied dynamic forces.
15.9 – Dynamic Input
S2
6
0.0
50
33
0.1
<----<----<----<----<----<-----
Analysis Type (HARMONIC/SPECTRUM/MODES/TIMEHISTORY)
Static Load Case for Nonlinear Restraint Status
Stiffness Factor for Friction (0.0-Not Used)
Max. No. of Eigenvalues Calculated (0 - Not Used)
Frequency Cutoff (Hz)
Closely Spaced Mode Criteria
47
Pipe Forces due to Relief Valve Discharge
N
<----- Re-use Last Eigensolution (Frequencies and Mode Shapes)
MODAL
<----- Spatial or Modal Combination First
SRSS
<----- Spatial Combination Method (SRSS/ABS)
GROUP
<----- Modal Combination Method (Group/10%/DSRSS/ABS/SRSS)
Y
<----- Include Missing Mass Components (Y/N)
SRSS
<----- Missing Mass Combination Method (SRSS/ABS)
ABS
<----- Directional Combination Method (SRSS/ABS)
LUMPED
<----- Mass Model (LUMPED/CONSISTENT)
Y
<----- Sturm Sequence Check on Computed Eigenvalues (Y/N)
6
<----- Estimated No. of Significant Figures in Eigenvalues
1E-12
<----- Jacobi Sweep Tolerance
1E10
<----- Decomposition Singularity Tolerance
0
<----- Subspace Size (0 - Not Used)
2
<----- No. to Converge Before Shift Allowed (0 - Not Used)
0
<----- No. of Iterations per Shift (0 - Pgm Computed)
0
<----- % of Iterations per Shift Before Orthogonalization
N
<----- Force Orthogonalization After Convergence (Y/N)
N
<----- Use Out-of-Core Eigensolver (Y/N)
100
<----- Frequency Array Spaces
LUMPED MASSES
SNUBBERS
EXCITATION FREQUENCIES FOR HARMONIC ANALYSIS
HARMONIC FORCES
HARMONIC DISPLACEMENTS
FORCE SPECTRUM EDITING
7720 , Z , 15 , 1
-2380 , Y , 28 , 2
7720 , X , 36 , 3
-6930 , Y , 45 , 4
7720 , Z , 56 , 5
-2860 , Y , 208 , 6
7720 , X , 315 , 7
-2860 , Y , 328 , 8
-3570 , Z , 340 , 9
-7720 , Y , 360 , 10
7720 , Z , 705 , 11
-2380 , Y , 718 , 12
3330 , X , 723 , 13
-6930 , Y , 735 , 14
7720 , Z , 746 , 15
-2860 , Y , 898 , 16
7720 , X , 1005 , 17
-2860 , Y , 1018 , 18
-4740 , Z , 1030 , 19
-7720 , Y , 1050 , 20
7350 , X , 460 , 21
7350 , (0.707,0,-0.707) , 608 , 22
-7350 , Y , 620 , 23
7350 , X , 1150 , 24
7350 , (0.707,0,-0.707) , 1298 , 25
-7350 , Y , 1310 , 26
DYNAMIC LOAD CASE DATA
DYNAMIC LOAD CASE # 1
HT1 , 1 , Z , 1
STRESSTYPE(OCC)
HT2 , 1 , Y , 2
HT3 , 1 , X , 3
HT4 , 1 , Y , 4
HT5 , 1 , Z , 5
HT6 , 1 , Y , 6
HT7 , 1 , X , 7
HT8 , 1 , Y , 8
48
Pipe Forces due to Relief Valve Discharge
HT9 , 1 , Z , 9
HT10 , 1 , Y , 10
ST21 , 1 , X , 21
ST22 , 1 , (0.707,0,-0.707) , 22
ST23 , 1 , Y , 23
DYNAMIC LOAD CASE # 2
HT11 , 1 , Z , 11
STRESSTYPE(OCC)
HT12 , 1 , Y , 12
HT13 , 1 , X , 13
HT14 , 1 , Y , 14
HT15 , 1 , Z , 15
HT16 , 1 , Y , 16
HT17 , 1 , X , 17
HT18 , 1 , Y , 18
HT19 , 1 , Z , 19
HT20 , 1 , Y , 20
ST21 , 1 , X , 24
ST22 , 1 , (0.707,0,-0.707) , 25
ST23 , 1 , Y , 26
DYNAMIC LOAD CASE # 3
HT1 , 1.000000 , Z , 1
HT2 , 1.000000 , Y , 2
HT3 , 1.000000 , X , 3
HT4 , 1.000000 , Y , 4
HT5 , 1.000000 , Z , 5
HT6 , 1.000000 , Y , 6
HT7 , 1.000000 , X , 7
HT8 , 1.000000 , Y , 8
HT9 , 1.000000 , Z , 9
HT10 , 1.000000 , Y , 10
HT11 , 1.000000 , Z , 11
HT12 , 1.000000 , Y , 12
HT13 , 1.000000 , X , 13
HT14 , 1.000000 , Y , 14
HT15 , 1.000000 , Z , 15
HT16 , 1.000000 , Y , 16
HT17 , 1.000000 , X , 17
STRESSTYPE(OCC)
HT18 , 1.000000 , Y , 18
HT19 , 1.000000 , Z , 19
HT20 , 1.000000 , Y , 20
ST21 , 1.000000 , X , 21
ST22 , 1.000000 , (0.707,0,-0.707) , 22
ST23 , 1.000000 , Y , 23
ST21 , 1.000000 , X , 24
ST22 , 1.000000 , (0.707,0,0.707) , 25
ST23 , 1.000000 , Y , 26
STATIC/DYNAMIC COMBINATION CASES
COMBINATION CASE # 1
S6(L6:W+P1(SUS)) , 1
STRESSTYPE(OCC)
D1 , 1
COMBINATION CASE # 2
S2(W+D1+T1+P1(OPE)) , 1
D1 , 1
STRESSTYPE(OPE)
COMBINATION CASE # 3
S7(W+P2(SUS)) , 1
D2 , 1
STRESSTYPE(OCC)
COMBINATION CASE # 4
49
Pipe Forces due to Relief Valve Discharge
S3(W+D2+T2+P2(OPE)) , 1
D2 , 1
STRESSTYPE(OPE)
COMBINATION CASE # 5
S8(W+P3(SUS)) , 1
D3 , 1
STRESSTYPE(OCC)
COMBINATION CASE # 6
S4(W+D3+T3+P3(OPE)) , 1
D3 , 1
STRESSTYPE(OPE)
SPECTRUM DEFINITIONS
HT1 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
* FORCE Spectrum Data File
*
Horizontal
*
TIME(milliseconds)
FORCE( N.)
*
1.00000
0.00
*
3.00000
7720.00
*
3.30000
7720.00
*
5.30000
0.00
*
FREQ (HZ)
MULTIPLIER
0.0002063
0.0037054
0.0033000
0.0005217
0.0167063
0.0000469
0.0528000
0.0007537
0.1289062
0.0019080
0.2673000
0.0038475
0.4952062
0.0071629
0.8448001
0.0122005
1.3532062
0.0195520
2.0625000
0.0298028
3.0197065
0.0436342
4.2768006
0.0617876
5.8907051
0.0850831
7.9232974
0.1143919
10.4413996
0.1506408
13.5167885
0.1947903
17.2261925
0.2478146
21.6512794
0.3106548
26.8786774
0.3841630
32.9999619
0.4690095
HT2 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
* FORCE Spectrum Data File
*
Horizontal
* USER ENTERED TIME HISTORY PULSE
*
TIME(milliseconds)
FORCE( N.)
*
3.30000
0.00
*
3.90000
2380.00
*
3.90000
2380.00
*
4.50000
0.00
*
FREQ (HZ)
MULTIPLIER
0.0002063
0.0447030
0.0033000
0.0020969
0.0167063
0.0000524
0.0528000
0.0001927
0.1289062
0.0005840
0.2673000
0.0010265
0.4952062
0.0018758
0.8448001
0.0031735
1.3532062
0.0051074
2.0625000
0.0077849
3.0197065
0.0113862
50
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
4.2768006
0.0161232
5.8907051
0.0222053
7.9232974
0.0298702
10.4413996
0.0393578
13.5167885
0.0509453
17.2261925
0.0649179
21.6512794
0.0815780
26.8786774
0.1012435
32.9999619
0.1242467
HT3 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
3.90000
0.00
5.90000
7720.00
7.30000
7720.00
9.30000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0058713
0.0033000
0.0005262
0.0167063
0.0000870
0.0528000
0.0010868
0.1289062
0.0028098
0.2673000
0.0057202
0.4952062
0.0105571
0.8448001
0.0180478
1.3532062
0.0289049
2.0625000
0.0440558
3.0197065
0.0644951
4.2768006
0.0913214
5.8907051
0.1257311
7.9232974
0.1689925
10.4413996
0.2224369
13.5167885
0.2874086
17.2261925
0.3652132
21.6512794
0.4570083
26.8786774
0.5636601
32.9999619
0.6855278
HT4 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
7.3000
0.00
9.1000
30826.18
9.1000
30826.18
10.9000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0054855
0.0033000
0.0008614
0.0167063
0.0002487
0.0528000
0.0006689
0.1289062
0.0014984
0.2673000
0.0030169
0.4952062
0.0056022
0.8448001
0.0095590
1.3532062
0.0152999
2.0625000
0.0233224
3.0197065
0.0341474
4.2768006
0.0483602
5.8907051
0.0665990
51
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
7.9232974
0.0895501
10.4413996
0.1179521
13.5167885
0.1525737
17.2261925
0.1942082
21.6512794
0.2436491
26.8786774
0.3016565
32.9999619
0.3689086
HT5 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
9.10000
0.00
11.10000
7720.00
15.70000
7720.00
17.70000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0332612
0.0033000
0.0007328
0.0167063
0.0005697
0.0528000
0.0022225
0.1289062
0.0053670
0.2673000
0.0110735
0.4952062
0.0205292
0.8448001
0.0350336
1.3532062
0.0561079
2.0625000
0.0855018
3.0197065
0.1251367
4.2768006
0.1771006
5.8907051
0.2436195
7.9232974
0.3269595
10.4413996
0.4293124
13.5167885
0.5525536
17.2261925
0.6978961
21.6512794
0.8653263
26.8786774
1.0527998
32.9999619
1.2551268
HT6 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
15.70000
0.00
16.40000
2860.00
17.00000
2860.00
17.70000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0412323
0.0033000
0.0025600
0.0167063
0.0000278
0.0528000
0.0006488
0.1289062
0.0009161
0.2673000
0.0022562
0.4952062
0.0040483
0.8448001
0.0068901
1.3532062
0.0110494
2.0625000
0.0168588
3.0197065
0.0246692
4.2768006
0.0349327
5.8907051
0.0481117
7.9232974
0.0647050
10.4413996
0.0852538
52
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
13.5167885
0.1103359
17.2261925
0.1405569
21.6512794
0.1765535
26.8786774
0.2189810
32.9999619
0.2684968
HT7 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
17.00000
0.00
19.00000
7720.00
20.30000
7720.00
22.30000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0040095
0.0033000
0.0020982
0.0167063
0.0003640
0.0528000
0.0010796
0.1289062
0.0026659
0.2673000
0.0055501
0.4952062
0.0102574
0.8448001
0.0175054
1.3532062
0.0280538
2.0625000
0.0427618
3.0197065
0.0625967
4.2768006
0.0886372
5.8907051
0.1220365
7.9232974
0.1640333
10.4413996
0.2159200
13.5167885
0.2790122
17.2261925
0.3545878
21.6512794
0.4437965
26.8786774
0.5475203
32.9999619
0.6661704
HT8 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
20.30000
0.00
21.10000
2860.00
21.10000
2860.00
21.80000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0796941
0.0033000
0.0008278
0.0167063
0.0009138
0.0528000
0.0002562
0.1289062
0.0007058
0.2673000
0.0012536
0.4952062
0.0023293
0.8448001
0.0039885
1.3532062
0.0063726
2.0625000
0.0097231
3.0197065
0.0142289
4.2768006
0.0201543
5.8907051
0.0277587
7.9232974
0.0373342
10.4413996
0.0491935
13.5167885
0.0636754
17.2261925
0.0811315
53
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
21.6512794
0.1019404
26.8786774
0.1264929
32.9999619
0.1551952
HT9 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
21.10000
0.00
22.00000
3570.00
22.00000
3570.00
22.90000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0344375
0.0033000
0.0021694
0.0167063
0.0004840
0.0528000
0.0002498
0.1289062
0.0005685
0.2673000
0.0014964
0.4952062
0.0028029
0.8448001
0.0047942
1.3532062
0.0076470
2.0625000
0.0116628
3.0197065
0.0170744
4.2768006
0.0241833
5.8907051
0.0333084
7.9232974
0.0447971
10.4413996
0.0590286
13.5167885
0.0763982
17.2261925
0.0973348
21.6512794
0.1222821
26.8786774
0.1517030
32.9999619
0.1860691
HT10 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
22.00000
0.00
24.00000
7720.00
24.60000
7720.00
26.60000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0116512
0.0033000
0.0014182
0.0167063
0.0003931
0.0528000
0.0008418
0.1289062
0.0021320
0.2673000
0.0043672
0.4952062
0.0080921
0.8448001
0.0138025
1.3532062
0.0221050
2.0625000
0.0336928
3.0197065
0.0493223
4.2768006
0.0698441
5.8907051
0.0961719
7.9232974
0.1292925
10.4413996
0.1702451
13.5167885
0.2201011
17.2261925
0.2799369
21.6512794
0.3507762
26.8786774
0.4335108
54
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
32.9999619
0.5287840
HT11 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
1.00000
0.00
3.00000
7720.00
3.30000
7720.00
5.30000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0037054
0.0033000
0.0005217
0.0167063
0.0000469
0.0528000
0.0007537
0.1289062
0.0019080
0.2673000
0.0038475
0.4952062
0.0071629
0.8448001
0.0122005
1.3532062
0.0195520
2.0625000
0.0298028
3.0197065
0.0436342
4.2768006
0.0617876
5.8907051
0.0850831
7.9232974
0.1143919
10.4413996
0.1506408
13.5167885
0.1947903
17.2261925
0.2478146
21.6512794
0.3106548
26.8786774
0.3841630
32.9999619
0.4690095
HT12 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
3.30000
0.00
3.90000
2380.00
3.90000
2380.00
4.50000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0447030
0.0033000
0.0020969
0.0167063
0.0000524
0.0528000
0.0001927
0.1289062
0.0005840
0.2673000
0.0010265
0.4952062
0.0018758
0.8448001
0.0031735
1.3532062
0.0051074
2.0625000
0.0077849
3.0197065
0.0113862
4.2768006
0.0161232
5.8907051
0.0222053
7.9232974
0.0298702
10.4413996
0.0393578
13.5167885
0.0509453
17.2261925
0.0649179
21.6512794
0.0815780
26.8786774
0.1012435
32.9999619
0.1242467
HT13 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
55
Pipe Forces due to Relief Valve Discharge
* FORCE Spectrum Data File
*
Horizontal
* USER ENTERED TIME HISTORY PULSE
*
TIME(milliseconds)
FORCE( N.)
*
3.90000
0.00
*
4.80000
3330.00
*
4.80000
3330.00
*
5.60000
0.00
*
FREQ (HZ)
MULTIPLIER
0.0002063
0.0641523
0.0033000
0.0031999
0.0167063
0.0003098
0.0528000
0.0002299
0.1289062
0.0007280
0.2673000
0.0013844
0.4952062
0.0026451
0.8448001
0.0045252
1.3532062
0.0072219
2.0625000
0.0110182
3.0197065
0.0161253
4.2768006
0.0228423
5.8907051
0.0314570
7.9232974
0.0423101
10.4413996
0.0557497
13.5167885
0.0721570
17.2261925
0.0919351
21.6512794
0.1155048
26.8786774
0.1433042
32.9999619
0.1757868
HT14 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
* FORCE Spectrum Data File
*
Horizontal
* USER ENTERED TIME HISTORY PULSE
*
TIME(milliseconds)
FORCE( N.)
*
4.80000
0.00
*
6.60000
6930.00
*
6.60000
6930.00
*
8.30000
0.00
*
FREQ (HZ)
MULTIPLIER
0.0002063
0.0051030
0.0033000
0.0005180
0.0167063
0.0003371
0.0528000
0.0005619
0.1289062
0.0013907
0.2673000
0.0029397
0.4952062
0.0054503
0.8448001
0.0092868
1.3532062
0.0148780
2.0625000
0.0226748
3.0197065
0.0332011
4.2768006
0.0470171
5.8907051
0.0647497
7.9232974
0.0870661
10.4413996
0.1146836
13.5167885
0.1483514
17.2261925
0.1888463
21.6512794
0.2369452
26.8786774
0.2934008
32.9999619
0.3588887
HT15 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
* FORCE Spectrum Data File
*
Horizontal
56
Pipe Forces due to Relief Valve Discharge
* USER ENTERED TIME HISTORY PULSE
*
TIME(milliseconds)
FORCE( N.)
*
6.60000
0.00
*
8.60000
7720.00
*
13.50000
7720.00
*
15.50000
0.00
*
FREQ (HZ)
MULTIPLIER
0.0002063
0.0214902
0.0033000
0.0000820
0.0167063
0.0008481
0.0528000
0.0022741
0.1289062
0.0055812
0.2673000
0.0116019
0.4952062
0.0214568
0.8448001
0.0366209
1.3532062
0.0586539
2.0625000
0.0893807
3.0197065
0.1308146
4.2768006
0.1851269
5.8907051
0.2546325
7.9232974
0.3416793
10.4413996
0.4484993
13.5167885
0.5769636
17.2261925
0.7281651
21.6512794
0.9017984
26.8786774
1.0952513
32.9999619
1.3023694
HT16 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
* FORCE Spectrum Data File
*
Horizontal
* USER ENTERED TIME HISTORY PULSE
*
TIME(milliseconds)
FORCE( N.)
*
13.50000
0.00
*
14.20000
2860.00
*
17.00000
2860.00
*
17.70000
0.00
*
FREQ (HZ)
MULTIPLIER
0.0002063
0.0583083
0.0033000
0.0025600
0.0167063
0.0000278
0.0528000
0.0010377
0.1289062
0.0030548
0.2673000
0.0058541
0.4952062
0.0108604
0.8448001
0.0185915
1.3532062
0.0297542
2.0625000
0.0453605
3.0197065
0.0663961
4.2768006
0.0940186
5.8907051
0.1294472
7.9232974
0.1740123
10.4413996
0.2290930
13.5167885
0.2961123
17.2261925
0.3764724
21.6512794
0.4714734
26.8786774
0.5821866
32.9999619
0.7092647
HT17 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
* FORCE Spectrum Data File
*
Horizontal
* USER ENTERED TIME HISTORY PULSE
*
TIME(milliseconds)
FORCE( N.)
57
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
17.00000
0.00
19.00000
7720.00
21.90000
7720.00
23.90000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0040573
0.0033000
0.0013319
0.0167063
0.0005276
0.0528000
0.0016145
0.1289062
0.0039394
0.2673000
0.0082333
0.4952062
0.0152322
0.8448001
0.0260024
1.3532062
0.0416595
2.0625000
0.0634868
3.0197065
0.0929314
4.2768006
0.1315596
5.8907051
0.1810705
7.9232974
0.2432339
10.4413996
0.3198539
13.5167885
0.4126575
17.2261925
0.5231363
21.6512794
0.6523015
26.8786774
0.8003021
32.9999619
0.9658965
HT18 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
21.90000
0.00
22.60000
2860.00
22.60000
2860.00
23.40000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0329916
0.0033000
0.0034309
0.0167063
0.0001497
0.0528000
0.0000151
0.1289062
0.0006071
0.2673000
0.0012157
0.4952062
0.0023225
0.8448001
0.0039749
1.3532062
0.0063700
2.0625000
0.0097170
3.0197065
0.0142252
4.2768006
0.0201563
5.8907051
0.0277602
7.9232974
0.0373318
10.4413996
0.0491932
13.5167885
0.0636741
17.2261925
0.0811320
21.6512794
0.1019405
26.8786774
0.1264935
32.9999619
0.1551948
HT19 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
22.60000
0.00
23.80000
4740.00
58
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
23.80000
4740.00
25.10000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0225185
0.0033000
0.0005135
0.0167063
0.0002969
0.0528000
0.0004219
0.1289062
0.0010098
0.2673000
0.0020863
0.4952062
0.0038874
0.8448001
0.0066370
1.3532062
0.0106326
2.0625000
0.0162029
3.0197065
0.0237161
4.2768006
0.0335850
5.8907051
0.0462595
7.9232974
0.0622099
10.4413996
0.0819605
13.5167885
0.1060608
17.2261925
0.1350876
21.6512794
0.1696390
26.8786774
0.2103213
32.9999619
0.2577326
HT20 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
23.80000
0.00
25.80000
7720.00
26.50000
7720.00
28.50000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0042135
0.0033000
0.0002703
0.0167063
0.0003060
0.0528000
0.0009651
0.1289062
0.0022293
0.2673000
0.0045135
0.4952062
0.0083992
0.8448001
0.0143375
1.3532062
0.0229522
2.0625000
0.0349865
3.0197065
0.0512188
4.2768006
0.0725305
5.8907051
0.0998690
7.9232974
0.1342588
10.4413996
0.1767761
13.5167885
0.2285302
17.2261925
0.2906286
21.6512794
0.3641185
26.8786774
0.4499003
32.9999619
0.5485986
ST21 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
1.00000
0.00
3.00000
7350.00
4.00000
7350.00
6.00000
0.00
59
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
12.00000
0.00
14.00000
7350.00
16.00000
7350.00
18.00000
0.00
24.00000
0.00
26.00000
7350.00
27.00000
7350.00
29.00000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0230917
0.0033000
0.0019120
0.0167063
0.0010325
0.0528000
0.0034286
0.1289062
0.0081506
0.2673000
0.0167926
0.4952062
0.0310885
0.8448001
0.0530219
1.3532062
0.0847719
2.0625000
0.1287137
3.0197065
0.1869880
4.2768006
0.2609548
5.8907051
0.3499873
7.9232974
0.4494577
10.4413996
0.5476286
13.5167885
0.6218094
17.2261925
0.6354471
21.6512794
0.6731203
26.8786774
0.6671876
32.9999619
0.6076787
ST22 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
4.00000
0.00
6.00000
7350.00
8.00000
7350.00
10.00000
0.00
12.00000
0.00
14.00000
7350.00
16.00000
7350.00
18.00000
0.00
20.00000
0.00
22.00000
7350.00
24.00000
7350.00
26.00000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0076509
0.0033000
0.0021636
0.0167063
0.0013159
0.0528000
0.0042080
0.1289062
0.0096607
0.2673000
0.0201944
0.4952062
0.0372776
0.8448001
0.0636591
1.3532062
0.1018573
2.0625000
0.1549248
3.0197065
0.2258680
4.2768006
0.3173223
5.8907051
0.4307719
7.9232974
0.5650629
10.4413996
0.7140545
60
Pipe Forces due to Relief Valve Discharge
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
13.5167885
0.8630556
17.2261925
0.9843357
21.6512794
1.0330235
26.8786774
1.0295671
32.9999619
1.0806023
ST23 , FREQUENCY , FORCE-MULTIPLIER , LINEAR , LINEAR
FORCE Spectrum Data File
Horizontal
USER ENTERED TIME HISTORY PULSE
TIME(milliseconds)
FORCE( N.)
8.00000
0.00
10.00000
7350.00
12.00000
7350.00
14.00000
0.00
14.00000
0.00
16.00000
7350.00
18.00000
7350.00
20.00000
0.00
20.00000
0.00
22.00000
7350.00
24.00000
7350.00
26.00000
0.00
FREQ (HZ)
MULTIPLIER
0.0002063
0.0310819
0.0033000
0.0002572
0.0167063
0.0013159
0.0528000
0.0037541
0.1289062
0.0096609
0.2673000
0.0201395
0.4952062
0.0373461
0.8448001
0.0636691
1.3532062
0.1019321
2.0625000
0.1551712
3.0197065
0.2266318
4.2768006
0.3194819
5.8907051
0.4363799
7.9232974
0.5785705
10.4413996
0.7444481
13.5167885
0.9272288
17.2261925
1.1116440
21.6512794
1.2698396
26.8786774
1.3575718
32.9999619
1.3360974
15.10 – Calculated Maximum Stresses
15.10.1 – Greater relationships of static stresses
Static Stresses – Permanent Loads - SUS
CODE STRESS CHECK PASSED
: LOADCASE 6 (SUS) W+P1
Highest Stresses: (
KPa
) LOADCASE 6 (SUS) W+P1
CodeStress Ratio (%):
17.0 @Node
10
Code Stress:
23438.9 Allowable:
137895.1
Axial Stress:
8914.8 @Node
1410
Bending Stress:
22266.6 @Node
1060
Torsion Stress:
1309.6 @Node
720
Hoop Stress:
17851.5 @Node
620
3D Max Intensity:
33156.5 @Node
1060
61
Pipe Forces due to Relief Valve Discharge
Static Stresses – Thermal Effects - EXP
CODE STRESS CHECK PASSED
: LOADCASE 11 (EXP) L11=L3-L7
Highest Stresses: (
KPa
) LOADCASE 11 (EXP) L11=L3-L7
CodeStress Ratio (%):
78.7 @Node
1310
Code Stress:
162612.9 Allowable:
206684.1
1130
Axial Stress:
2325.8 @Node
Bending Stress:
162456.3 @Node
1310
Torsion Stress:
11747.3 @Node
1020
15
Hoop Stress:
0.0 @Node
3D Max Intensity:
217263.8 @Node
1310
15.10.2 – Greater relationships of dynamic stresses
Dynamic Stresses - OCC – Combination 5 (Static S8+Dynamic D3)
****
CODE STRESS CHECK PASSED
HIGHEST STRESSES: (
CODE STRESS %:
STRESS:
BENDING STRESS:
TORSIONAL STRESS:
AXIAL STRESS:
3D MAX INTENSITY:
KPa
)
55.3
101330.7
122532.7
11242.1
17823.6
127013.3
@NODE 1055
ALLOWABLE:
@NODE 1310
@NODE 1130
@NODE 746
@NODE 1310
183401.
15.11 – Resulting Natural Frequencies
MODE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
FREQUENCY
12.209
12.892
13.021
13.542
15.055
16.350
18.044
20.701
24.526
24.547
27.425
28.966
30.303
30.756
33.378
Obs.: 1º Mode = 12,209 Hz > 2 Hz  ok!
FREQUENCY
76.711
81.005
81.813
85.086
94.592
102.732
113.376
130.068
154.100
154.230
172.316
181.996
190.398
193.243
209.722
PERIOD
0.082
0.078
0.077
0.074
0.066
0.061
0.055
0.048
0.041
0.041
0.036
0.035
0.033
0.033
0.030
62
Pipe Forces due to Relief Valve Discharge
15.12 – Details of Drains and Vents, and Proposed Supports
Details to be adopted in Drains and Vents
em
Hold down supports should be designed as suggested below.
HolD Down supports with horizontal guide should be designed as suggested below.
63
Pipe Forces due to Relief Valve Discharge
16 - Conclusions
1st – The mathematical model used in this type of calculation should be as accurate as possible. Note that the
supports must either be modeled as a structure or must have their respective rigidities considered.
2nd – This calculation method evaluates the forces in an approximate way, but the dynamic excitation results
produce satisfactory results.
3rd – Carefully observe the recommendations made regarding model discretization are critical. (Approaches and
considerations in a piping system).
4th – A well-structured analysis with acceptable support and response levels within admissible values does not
change process conditions, so if there is Chattering, it will continue to happen. The proposed conclusion of this
evaluation ensures the integrity of the system according to the considered scenarios and recommendations of
the adopted calculation standards.
5th – In dynamic calculations, the supporting structures that will restrict the guides and locks should be
calculated with the maximum arrow criterion = Span/1000, at least.
17 – Reference Documents
Program Manual - Caesar II – Version 5.3 – Application guide, User guide and Technical reference manual
Technical Norm – ASME B31.3 – Process Piping - 2012
Technical Norm – API RP520 – Part I - Sizing, Selection, and Installation of Pressure-Relieving Devices in
Refineries – Jan 2000.
Technical Norm – API RP520 – Part II - Sizing, Selection, and Installation of Pressure-Relieving Devices in
Refineries – Aug 2003.
Technical Norm – API RP521 – Guide for Pressure-Relieving and Depressuring Systems – Mar 1997.
Technical Norm – ASME B31.1 – Power Piping – 2012
BOS B31 Manual – B31.3 Hydraulic Load consideration per Para. 301.5 – 2010
Biography
18– Biography
José Francisco Vianna Pereira is a Pipe Stress Analysis Consultant with degrees in Mechanical
Operational Engineering and Civil Engineering. He has worked for large project companies in Rio
de Janeiro and São Paulo in the mining and metallurgy, industrial, offshore, and nuclear areas.
He worked on the Angra 2 plant project for 10 years, and after taking a course on Structural
Dynamics, had the opportunity to work with calculations of lines and special supports
submitted to earthquakes. He worked at FPSO at a Kellog partner company.
For 15 years, he was hired as a consultant at Petrobras, where he had the opportunity to solve problems related
to vibration and hydraulic transients from refineries. In recent years, he has accepted the challenge of working
on Ø84 ”, Ø50” and Ø30” in the Comperj Flare Lines project, with the assistance of programs such as SAP2000,
NozzlePro, FEbend, FETee of PRG, and has established calculation methods by finite elements with shells.
Vianna has been a Caesar II user since version 2.2. He also worked as a professor of the postgraduate course in
Mechanical Engineering of PROMINP in the PUC x Petrobras x Federal Government agreement, having had the
opportunity of teaching and assisting in the formation of 8 classes with approximately 30 students in each class.
64
Pipe Forces due to Relief Valve Discharge
Some alumni are now colleagues in his recent work. Teaching and being in contact with alumni defined the need
to clarify some points in Pipe Stress Analysis, generating articles for this purpose.
CVA Engenharia Ltda is his own company that has operated in the market since 1998.
vianna@jfvp.com.br
Cell phone +55 – 21 -97320-9059.
65