Back-pressure

[Drexl]

Hi,

I have a safety valve including inlet and outlet piping and can say that the system is ok (<3% inlet loss, <10% outlet loss) with a superimposed back-pressure equal to atmosphere.

If I lower the superimposed backpressure, e.g. the pressure in the tank in which the safety valve outlet pipe ends - is it possible that the total back-pressure at the outlet of the valve could increase?

Is there any easy way to prove this by using appropriate reference litterature?

More specifically I'm wondering about this because of flashing water which reach choked flow in outlet piping at lower back-pressures.

Drex

 

[Latexman]

There are several things going on - mass flow, densities, pressures, dPs, and temperatures. My gut is saying "no". I'd run the calcs at atmospheric and sub-atmospheric and see. That seems to be the easist way to have your proof.

Good luck,
Latexman

 

[Drexl]

Problem is that the easy way to do the pressure drop calculation at the lower pressure (0.1 bara in tank) is to be conservative, and assume that all flow is at constant pressure, e.g 0.1 bara. Then you get a lot of flashing, very high velocity and very unacceptable pressure drop.

To correct the model you can divide it in smaller parts. Start iterating from the tank using two-phase at sonic velocities. At this point I stop trusting my excel/fluid dynamics skills. That's why I would rather be able to simplify.

 

[Latexman]

With the complexities being imposed on the problem by lowering the outlet pressure so low, I doubt the answers you get by simpifing will be much use. With compressible, two-phase flow you will not find a single analytical equation where P₁, the pressure at the PSV outlet, can be separated and you can look at the other side of the equation and say, "ah ha!" It's not that simple, and it just doesn't exist.

With the tailpipe going to atmospheric, is it liquid flow or two phase?

Good luck,
Latexman

 

[Drexl]

To atmospheric pressure it is still liquid, temperature is below 100 degC.

 

[zdas04]

Latexman has it right. This is an amazingly complex flow. At the PSV, the velocity is sonic. Some small distance downstream, the velocity resolves to transonic which is compressible and has no analytic solutions (and simulations are of very minor value).

Some distance downstream of the start of the transonic region you'll start to see flow that kind of lends itself to incompressible flow analysis (but you need to be really careful choosing the closed-form equation that you use, most have problems with the transition to vacuum). Finding that point analytically is nearly impossible.

I would assume that the end of transonic is an insignificant distance downstream and use the Spitzglass formula (see GPSA Engineering Field Data book), restructured to calculate upstream pressure. Since you know your flow rate and downstream pressure this should give you a direct answer to your question.

Just for assurance, I'd then assume that the end of transonic flow is in the middle of the length of pipe. That should give you some confidence in the answer to your original question "can lowering the downstream pressure raise upstream pressure?".

David

 

[Latexman]

There may be some "frozen equilibrium" or "non-equilibrium" flow going on right at and near the PSV outlet in your case too. Luckily, ignoring it is probably conservative. I saw this phenomenom via calculation at an orifice with liquid/two-phase anhydrous ammonia at a unit I used to run.

Good luck,
Latexman

 

[zdas04]

"Frozen equilibrium" is a new term to me. Not to drag Drexl's thread into the weeds, but could you describe it?

David

 

[Latexman]

Most engineering calculations (fluid flow, mass transport, thermodynamics, etc.) assume the fluid attains equilibrium instantaneously (time independent). In thermo class the concept of a "state function" that was dependent on T, P, concentration, etc., BUT NOT TIME was beat into us. Unfortunately, there are situations where the time required for a fluid to reach equilibrium is significant enough to mess up the math, i.e. a bad assumption was made. An area where frozen equilibrium is sometimes not a good assumption is high speed fluid flow where there is a phase change involved, i.e. a PSV with phase change like this OP. I've seen it once in my career, so it's been rare for me. There may have been more times, but there may not have been a problem or a need to explain a difference from the design basis, so who cares, right?

Good luck,
Latexman

 

[zdas04]

That makes sense, thanks.

David