Dear All,

there is some issue that i need to clarify in this forum since i see that many expert in Piping Stress Engineering and COde Committe are visited this forum.
The issue is about Force on PSV Closed system.
As what i know that Force that show up when PSV in closed system begin to firing is including in Impact Force so it is a dynamic event, but still we can use the quasi static method to analyze it by use the DLF factor.
As long as i know this event also not a static condition because the pressure will change rapidly when the PSV first firing.
The problem of my concern is for this PSV Closed system i usually used and consider not only the first impact/unbalanced forced in first elbow or obstruction but also in the second elbow and other downstream this PSV.
I also read in Peng book, that he mentioned that the event when PSV in closed system firing still consider as Non static condition, so from here i can take the conclusion there will be no Balanced force, it means Impact force will occurs in each elbow or obstruction but in opposite direction.
We can measure each of this Force if we know the opening time of the PSV and multiply it with the length of each pipe section to get the Max. Unbalanced force in each elbow or obstruction.
But here in my new assignement i found a different method for client method, where Force downstream of PSV (other than force on first elbow) are consider to be balanced each other.
I also found this method in one Engineering company that become a trade mark for Piping Engineering.
So for all Expert and Collegues here, i ask for your advice, amybe opinion about this Issue.
Hope that it can give another value for all of us here.
Thanks.

With Regards
Nalibsyah

As per API 520 Part 2, Cl. 4.4.2
"

Pressure-relief devices that relieve under steady-state flow conditions into a closed system usually do not transfer large forces and bending moments to the inlet system, since changes in pressure and velocity within the closed system components are small.
.....
A complex time history analysis of the piping system may be required to
obtain the reaction forces and associated moments that are transferred to the inlet piping system."


As you said in general practice, the momentum component is imposed as a reaction force at PSV.
generally divided as two cases,
Case1: When PSV pops up (Force imposed at PSV) and
Case2: When there is established flow (When the forces cancel each other)


You might find this topic interesting

http://65.57.255.42/ubbthreads/ubbthreads.php?ubb=showflat&Number=11775#Post11775
http://65.57.255.42/ubbthreads/ubbthreads.php?ubb=showflat&Number=24685#Post24685


I case of having a long run reaction forces can be imposed at the first elbow at a different case, ex: F1 at PSV and F2 at first elbow in the establised flow condition, conservatively.

The only accident with PSVs in closed systems I know it is one in which the PSV was wrong chosen and was chattering for years before piping was broken. It was a fatigue damage "assisted" by poor supports- this was the conclusion of investigations. In my opinion it would have been avoided by common sense process/piping experience but also by field operators feedback.

Reversing the point of view, you can see in field PSV arrangements that cannot be qualified by today calculations but have had a satisfactorily service for long time.

I think any calculation for PSV in closed systems is good because offers the opportunity to review the related piping and helps providing stiff supports. For this point of view the calculation must be encouraged.

In the same time, I’m in doubt that 99% of these calculations would simulate what it’s happening in field with PSV in a closed system. That's why I don't want to say one approach is wrong and another one is good.

In addition, when the Client/Company regulations are hard (and usually it is the case, because it seems to be o hot topic!) you have to comply with.

I agree with mariog and stressguy81.

I'd like to add the following.

Check should be done for pop forces and if the velocities are close to 1 mach, apply forces at elbows equal with w x v (flow times velocity)

Regards,

A further warning about Mach speed ..... it cannot in most cases be exceeded in a PSV body due to choking. Since velocity is not directly addressed in the equations given, the formulas in API RP 520 used to calculate reaction forces can give incredible results. If you check the associated velocity it may be well in excess of Mach speed and thus impossible. A reduction to a realistic mass flow rate should give better force results.

Indeed, and this is in line with Norsok P-001 limiting criteria ro x v2 less than 200 000.

However a rough formula w x v = ro x v2 x A is quite reasonable. (e.g. for a 8" line and a ro x v2= 200 000, force will be 7534 N) Not big, not small, but will lead to a lot of guides and/or stops.

Dear MoverZ

You say


Well, I cannot blame the API formulas. Maybe the people applying API formulas.

API formulas are based on "free jet" approach.
If a free jet is released in atmosphere or in a large volume, the piping system will receive a reactive force.
This is the force that API counts as:

Reactive_Force= [mass flow-rate]*[jet_velocity]+ [p_jet]*[area_jet]

where

- mass flow rate must be the actual value (it is greater than the designed flow rate, because the actual PSV orifice is larger than minimum required!)
- jet_velocity is the critical speed when the jet gas flow has Mach=1 feature (is counted in Fluid Mechanics as jet_velocity= sqrt(2*R*k*T/ ((k+1)*M)), where notations are as in API, R is the universal perfect-gas constant , in SI is R=8314.5 J/kg mol/K.
- p_jet is the gauge pressure in the released jet
- area_jet is the internal area of piping at the point where the jet is released

This is exactly the API formula, where the numerical coefficient is sqrt(2*R), in SI units sqrt(2*8314.5)=129
Obviously, the formula is based on the "choked" condition i.e. Mach=1 and this is taken into consideration by counting jet_velocity= sqrt(2*R*k*T/ ((k+1)*M)

A possible source of errors may be the term [p_jet]*[area_jet], because it seems that "p" in chocked flow is somehow out of common engineering perception and API does not give details on the subject.

I reattach a paper showing a simple way to evaluate pressure in isentropic choked flow (Mach=1). You can see the same result in some articles, but the fluid mechanics model is more complicated there.


My best regards.

Thanks for the fluid mechanics lesson Mariog, I am well aware of theory. My note was a warning since I have had occasion to check calculations where a small PSV apparently attracted a huge force, due exactly to the error I outlined. People do make mistakes and far too many 'engineers' apply equations blindly, because all too often they have found an unchecked and non-validated Excel spreadsheet solution on some dodgy company drive.

Dan,

I think your example may be written as "if there is a free-jet exiting 8" piping area with (choked) parameters complying with rho*v^2=200000 kg/(ms^2), the reaction force would be 7534 N".

For a closed system I would say it is a "better than nothing" criteria.

PS. I have a funny story with a PSV process issue in a big company that after 2 months of Olga software calculation decided to have 24" size line downstream of the 2"x4" piloted PSV. So 24" wasn't the subheader size, it was the size connection to the subheader. The model was a visual aggression and the calculation was "worse than nothing".

I think that I will not rephase as the purpose of this was more trivial.

I was talking about flow induced forces. Decent problems require decent solutions, sort of "better than nothing". For complex problems, there are other solutions and I am not one of the specialists that can solve them.

Dan,

You were talking about flow induced forces in closed systems and I was talking on the fact rho*v^2 transposed in "force criteria" would be a criteria for forces due to "free-jet" effect in open systems. I think also that rho*v^2 is a steady-state criteria and does not address to the "momentary, instantaneous forces that result when the valve first opens".

The point is I have no evidence such criteria is a decent one in closed system except the connection with subheader/header where a "free jet" may exist.

The only certitude I have is that every stress specialist and Company has the certitude that his/her/their criteria is decent. I'm not in position to say they are right or not, so I accept their approach, criteria, etc.

It is interesting (for me) to see that the process people have the certitude they don't know such decent criteria to evaluate roughly the magnitude of forces in a closed system. I accept also their position.

Best regards.

Stress guy and others, i think i need to clarify what asked. My concern is that when PSV first pop up there will be a travelling wave downstream the PSV discharge or RV discharge. This load is not balanced each other. This force will have the same history shape throught out the system but the arriving time is different in each point. This is why in API 520 as stress guy taken above mention :
A complex time history analysis of the piping system may be required to
obtain the reaction forces and associated moments that are transferred to the inlet piping system."

and in ASME B31.1 Non Mandatory App. II Para II.2.2.2 :

...."However when a safety valve discharge is connect to a relatively long run of pipe and suddenly opened, there is a period of transient flow until the steady state discharge condition is reached.

and in Para II.2.3.2 :

......"Relief Valves discharging into an enclosed piping system create a momentary unbalanced forces which act on the piping system during the first few milliseconds following relief valve lift. The pressure waves travelling through the piping system following rapid opening of the safety valve will cause bending moments in the safety valve discharge piping and the reminder of the piping system. In such a case, the designer must compute the magnitude of the loads and perform approriate evaluation of their effects."

LC Peng book page 401-403 so talk about this, where there will be a net force impact on each leg (elbow or other obstruction) downstream the RV or PSV discharge as a result of the traveling wave or transient condition.

So what i mean is that we also have to considered the effect of this transient load during pop not only at the first elbow ( i see in some company standard they apply this two condition, during steady state and pop up, but during pop up they only apply the force directly upward and horisontal at the body of the Rv or PSV.....i also have see some one post this kind of pictures in other thread about PSV too).

Apply the load at n elbow/obstruction and n+1 elbow/obstruction, but because it is quite complicated and we will not know the limit of this travelling wave unless we perform simulation (maybe with Boss fluid) or do the time history analysis for better and realistic result, then it is common to assume to apply until the third elbow/obstruction.

I have found a case where previous engineering company apply the usual method (apply upward, and horizontal at valve body), and the result the pump downstream of this RV system having a trouble. so we fix it by apply and considered the transient effect that not considered by previous company and now have been 3 years the pump still run smoothly.