choked flow

[rustin03]

Hi everyone,

I am helping analyze a ruptured 16" diameter pipe that was carrying gasoline. There is a roughly 10" diameter hole in the side of the pipe. The internal operating pressure was around 1400 psi, and the pressure outside the pipe was standard atmospheric pressure, 14.7 psi.

Someone asked me whether the flow could be choked as it exits the pipe. However, choking is only a phenomena that i've seen with respect to the compressible flow of gases.

So here we have a pipe carrying gasoline. Can the flow be choked? And if so, what is the criteria for determining whether the flow is choked or not?

Thanks!

 

[Montemayor]

rustin03:

Be careful when dealing or communicating with someone that has training or dealings with the oil patch industry. Petroleum engineers and associates delight in calling the throttling of a liquid or gas production line, or any other pipe with a valve, "choking". To them, a "choke" valve is a throttling valve.

Now lets agree on the principle of "choked flow": it is the maximum flow that a gas or vapor can achieve and is related to sonic flow. This is a term accepted in all fluid mechanics circles in all the countries I've been in. So, if you are talking about liquid gasoline going through the phenomena of "choked flow" the argument doesn't hold water. If the gasoline is in the vapor state, yes you can have Choked flow; however, at 1,400 psig I doubt that is the case. You could not have had choked flow with liquid gasoline going through the hole.

By the way, are you sure you got a hole in the P/L that is 10/16 = 62.5% of the pipe diameter? That is a hell of a hole! Could you tell us what generated this type of failure and the amount of gasoline spilled?

Art Montemayor
Spring, TX

 

[rustin03]

Thanks so much for the reply!

You're right, that is a huge hole! I actually just made up that number to approximate the area of the actual hole, which is quite asymmetric.

The actual hole is long and thin, and oriented in the axial direction. It appears to have been caused by immediate overstress failure when some idiot sliced along the side of the pipe with a backhoe.

I'm not sure about the amount of gas spilled, although I am going to try to find out.

Thanks again,
Rustin

 

[Tremolo]

Rustin,

Choked flow limitations are often considered for liquids at high pressure discharging to atmospheric conditions.

Typically, choking for a liquid held at high pressure occurs when the fluid depressurizes to its vapor pressure as is moves through the break site. In this case, you would calculate the break flow based on the difference between the stagnation pressure and the vapor pressure.

A simple example is the discharge of slightly subcooled water. Suppose you have 500 F liquid water in a pipe at 1400 psia. The saturation pressure for 500 F water is 680 psia. So, if the pipe ruptures and discharges to atmospheric pressure, the break flow will actually be based on the pressure drop from 1400 psia to 680 psia. If, on the other hand the water temperature is only 100 F, for which the saturation pressure is 1 psi, then there would be no choking and the full pressure drop to atmospheric pressure would be used to calculate the break flow.

For your case, if you know the vapor pressure of the gasoline, you can use that as a criterion for choking. If the vapor pressure is greater than atmospheric pressure, then you could expect choked flow.

Finally, for liquid discharge through long nozzles (as opposed to the discharge through the thickness of a pipe wall), the liquid may flash prior to reaching the nozzle exit. In this case you would have to consider two-phase critical flow. The choking limits for two-phase flow are slightly more complicated.

TREMOLO.

 

[hacksaw]

choked or not, the critical issue is the density flowing through the exit area and the thoughest to estimate(two phase flow is likely). you may be restricted to comparing several scenarios so as to bracket the actual flow. hopefully you have enough metering on the line and can estimate the loss independently.

good luck,

 

[zdas04]

Having been asked to estimate (for immediate Federal Reporting requirements) the flow from several pipe failures. I've always used single-phase liquid arithmetic and every time that has been within 10% of the amount we could account for in the calm light of day.

The amount of phase change, the timing of the phase change, and the impact of the vapor on the flow calculations will seldom point you towards adding the complexity of choked flow or (god forbid) multi-phase flow. I've seen video of a liquid propane leak that looked very much like the phase change happened after the fluid left the tank. The cloud was far enough away from the hole that I would have used single-phase liquid arithmetic on that one as well. I'm sure the last chunk of the propane went through the hole as gas (possibly in choked flow, but probably not), but I couldn't tell that the compressible-flow portion of the total flow was within the accuracy of the calculation.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[katmar]

Hi rustin03,

Your question as to whether you could have choked flow with a liquid is an interesting one. I believe that it is theoretically possible, but EXTREMELY unlikely to ever happen in a natural or industrial environment.

With gas supplied at P1, and flowing through a fitting and dropping to P2, the flow increases as P2 decreases from an initial value equal to P1 until P2 reaches the point where the gas velocity is equal to the sonic velocity. The way I have always understood this maximum flow is that if P2 decreases below this critical value, there is no way that the information that the pressure has decreased further, can get to the upstream location because the information can only travel back through the gas at the speed of sound. In other words the upstream location can never "know" that the pressure has decreased below the critical value.

I cannot see why the (theoretical) situation with a liquid should be any different, and therefore choked flow should be possible with a liquid???

However, there are some very real practical reasons why we never see it happen. Firstly, the velocity of sound is very much higher in a liquid than in a gas. Typically 5000 ft/s in water. It would take a lot of energy to get the liquid to this velocity. Secondly, you cannot store pressure energy in a liquid as easily as you can in a gas. When your backhoe operator ripped the pipe open, the pressure just inside the hole would have instantaneously dropped way down because the increased flow (due to the gasoline lost through the hole) would have increased the friction pressure drop down the pipe.

Personally, I would go with the simple method proposed by David Simpson. This would give you a "worst-case" scenario, but is probably as close to the truth as you are likely to get.

 

[Tremolo]

I have checked a few references and found that gasoline vapor pressure is typically less than 15 psia. Therefore, your pipe break discharging gasoline to atmospheric pressure will probably not be choked.

As to the more general issue of choked flow in all-liquid systems, there are many process fluids that are stored as liquids at high pressure for which choked flow discharge must be considered. Although the liquid itself will not exhibit choked flow, if the system pressure ever decreases significantly, such as due to a pipe rupture or opening of a safety valve, the liquid will often begin to vaporize. It is the resulting two-phase flow that must be analyzed for choked flow. In the case of safety valve discharge, use of an all-liquid (or all vapor) calculation would overestimate the valve relief capacity.

Here’s a specific example of choked flow occurring in an “all liquid” system that is regularly encountered. Process facilities typically use a pumped cold water system for heat exchangers. Often times, the cold water passes through the heat exchanger, is heated, and then flows through a flow control valve. The pressure drop across the control valve is sometimes large enough to cause flashing of the liquid water, in which case choked flow occurs through or slightly downstream of the control valve.

So, simply because a system is designed to contain a liquid at high pressure, it does not preclude the occurence of a choked flow condition.

TREMOLO.

 

[Montemayor]

Tremolo:

The reason I said that at 1,400 psig I doubt that you could have choked flow with liquid gasoline in a P/L is because I thought it natural to expect the fluid to be supercooled due to the U/G temperature being 50 oF (max.).

The flashing of a saturated fluid (such as steam condensate) at an elevated pressure throttled down to a lower pressure and causing choked flow is something we deal with on a normal basis. Under these conditions, you have choked, limited flow. However this, as I said, is not what I would expect in the case described since the gasoline would be subcooled and additionally it is a mixture of various boiling point constituents - it doesn't have just one vapor pressure! Gasoline, like many other organic and hydrocarbon compounds, has a Reid Vapor Pressure. However, the True Vapor Pressure is varying in a decreasing manner as the lighter components vaporize first -followed by the heavier. This is so because it is not a pure component, but a mixture. In writing my post, I failed to mention these supporting assumptions and data. I also would expect the escaped gasoline, upon expansion, to cool down considerably due to evaporation effects - very much like the effect you see in a natural draft cooling water tower.

I hope the above explains my comments better.

Art Montemayor
Spring, TX