11 replies to this topic

[Kunal_DNV]

Hi,

I am doing momentum calculations ( rhoV2) for the PSV tail pipe. Company standard requires it to be below 150,000 Pa@ 0 backpressure condition.

Details:

Rated mass flowrate - 4666 Kg/hr
Density @ 0 back pressure - 0.6408 Kg/m3
Tail pipe ID - 42.845 mm ( cxs area - 1.44E-3 m2)

Using above inputs i get vol. floware = 2.022 M2/sec and velocity=1404 M/sec ( 2.022/1.44E-3 m2)

Case - 1
Momentum = rhoXV2
= 0.6408X1404X1404
=1,263,155 ( This is much much higher than the 150,000pa)

But can the velocity be higher than the sonic velocity?
Case - 2
Sonic velocity for this case is 460.31 M/sec @ critical pressure( please see the formula i used for sonic velocity calculation ). And rhoV2 ( V= sonic velocity) would be 135,776.

Please advise which case is correct.  Untitled.jpg   69.31KB   54 downloads

[ankur2061]

Following is the methodology:

Q = W / rho ---------------(1)

where:

Q = Volume flow rate, m³/h

W = mass flow rate, kg/h

rho = density at the flowing conditions (temp, pressure), kg/m³

v = Q / A --------------(2)

where:

v = velocity in the tail-pipe, m/s

Q = volume flow rate, m³/h

A = cross-sectional area of tail-pipe (pi x D² / 4), m²(where D = ID of the tail pipe, m)

Momentum = rho x v²--------------------(3)

where mometum is in kg / m-s² (=Pa)

This should give you the desired result.

Regards,
Ankur.

[breizh]

Additional info :

Norsok standard : page 16

Hope this helps

Breizh

[paulhorth]

Kunal,

You are right - you cannot have velocity greater than sonic velocity in a straight pipe.

What your calculation shows is that your tailpipe size (2 inch NB) is too small. You need to increase the size of the tailpipe until the velocity at the outlet end (where the pressure is about 0 barg) is less than sonic velocity. A typical velocity limit for PSV tailpipes is velocity less than 0.7 Mach.
To achieve this limit, your tailpipe needs to be 6 inch - it seems that 4 inch is too small, but for you to check. If the PSV outlet flange is 2 inch, you have to fit piping expanders to get up to 6 inch.

You should then check the back pressure at the PSV for this pipe size. If it is more than 10% of the set pressure, you need to use a balanced bellows PSV.

If you use a 2 inch tailpipe, then what will happen is that the back pressure at the end of the line will be higher than 0 barg, so that the velocity at the outlet is sonic. There will be a shock wave as the gas suddenly expands to atmos pressure at the outlet end of the line. This situation is not acceptable design practice.

Paul

Edited by paulhorth, 16 September 2011 - 05:19 AM.

[Kunal_DNV]

Hi,

Thanks for the reply.

I used the same calculation steps as described by Ankur and i get vey high gas velocity.

But the question is, can the gas velocity be higher than the sonic velocity?

Regards
Kunal

[paulhorth]

Kunal,

No, the gas velocity cannot be higher than sonic velocity.
Please read my earlier post for the explanation.

The situation that you have calculated, with a 2 inch line and 0 barg exit pressure, leads to a physically impossible result. So one of these parameters has to be changed. Either (a) with a 2 inch line, the outlet pressure will be higher than 0 barg, with sonic velocity, or ( a larger line size is used, to get a velocity less than sonic with 0 barg at the outlet.

If you design the line size for an outlet velocity of 0.7 Mach, you will probably find that the rho v2 criterion is also achieved.

Paul

[fallah]

Kunal_DNV, on 15 Sept 2011 - 1:06 PM, said:

I am doing momentum calculations ( rhoV2) for the PSV tail pipe. Company standard requires it to be below 150,000 Pa@ 0 backpressure condition.

Kunal,

As far as i know, calculating rho*V2 (especially regarding rho for checking fluid flow condition or line sizing) has usually been done based on corresponding build-up back pressure. But as you mentioned seems your company standard (with 0 (gauge?) back pressure) is based on no build-up back pressure or PSV closed condition! Please clarify.

Fallah

Edited by fallah, 17 September 2011 - 01:29 AM.

[Kunal_DNV]

Fallah,

Yes the company standard specifies rhoV2 to be calculated @ no backpresure ( 0barg) condition.

You will have the highest gas velocity in tail pipe@ no bckpressure.Isn't it?

Regards
Kunal

[fallah]

Kunal_DNV, on 21 Sept 2011 - 10:23 AM, said:

You will have the highest gas velocity in tail pipe@ no bckpressure.Isn't it?

Kunal,

Even it is supposed superimposed back pressure to be 0 barg, highest gas velocity would be accompany with highest build up back pressure at PSV outlet!

Fallah

Edited by fallah, 21 September 2011 - 06:39 AM.

[paulhorth]

Kunal,

You don't seem to understand the important point here, which I have made twice now.
With your 2 inch tailpipe you will not have 0 barg anywhere in the line. You will have sonic velocity at the end of the line, and the pressure there will be whatever is required to give sonic velocity (460 m/s) in the 2 inch line with the given flowrate.

This velocity is excessive, and will risk excessive acoustic vibration leading to rupture where the 2 inch line joins a larger flare header.

YOU MUST INCREASE THE SIZE OF THIS LINE.

Using your data in the first post it is easy to make an estimate of the pressure at the end of the line:

Sonic velocity = 460 m/s, cross sectional area = 0.0015 m2, so volume flowrate = 0.709 m3/s

Mass flowrate = 4666 kg/h = 1.3 kg/s
Hence, density at the point of sonic velocity = 1.3/0.709 = 1.83 kg/m3

Density at 1 bara = 0.641 kg/m3

So, neglecting the change in temperature, the pressure corresponding to density of 1.83 kg/m3 = 1.83/0.641 x 1 = approx 2.85 bara = 1.84 barg

The value of rho.v2 at this point is 1.83 x (460)^2 = 387230 Pa. which is more than double the allowed limit.

Please try to understand what I have written above and in two previous posts.
Paul

[Kunal_DNV]

Hi Paul,

Thanks for the explanation.

I hv one more question regarding latent heat of vaporization for methane...

Please advise the effect of T&P variation on the latent heat of vaporization..When we size PSV, the LHOV used should be at what T&P?? Can we use the LHOV at standard boiliing point


Regards
Kunal

[paulhorth]

Kunal,
The latent heat to be used should be, obviously, the value at the relieving pressure.

This question makes me wonder what exactly you are trying to do.
For pure liquid methane, the latent heat at relieving pressure will allow you to calculate the relief rate for a heat input. But you have already given us a relief rate in the first post, so have you already done this?
If your vessel does not contain pure liquid methane, but in fact a typical hydrocarbon mixture with DISSOLVED methane, then the latent heat is not going to be of much use to you. You will find the latent heat becomes very small, going to zero, as the pressure increases. Then you will have an infinitely large relief rate!
So you can't use latent heat for a typical fire relief rate on a medium to high pressure separator. You have to run a simulation which is quite complicated to describe. Beyond the scope of this forum.

Paul