Partially Filled Pipe Under pressure 1

[Lijantropo]

Hello Dear Colleagues,

I'm wondering if it's possible to have a partially-filled pipe but under pressure (no gravity flow).

I was thinking of a pair of tanks and a pump. The second tank is higher than the first one, and it operates at 50 psi. The pump have to overcome the static height and the pressure drop, but, what happens if the pipe is originally filled with vapor from the second tank. I believe I will have a two-phase system, but if the flow is low, is it the possibility to only have a fraction of the pipe filled with the fluid.
I have been looking for a way to explain this (using equations) but I only found for atmospheric system, under gravity flow.

Does anyone have any source (paper, book, or reference) that deals with this subject?
I really appreciate your comments.

Best regards,
Lij.

 

[BigInch]

Hard to say what's going on in your mind without a diagram of that system.

It seems like you would not have 2 phase flow, unless the pump (from tank 1) is flowing both liquid and gas, but I would imagine that, since tank 1 is lower, it is pumping liquid only. Again not 2 phase flow, you probably have two regions in the pipe each with single phase flow, one ahead with vapor flow being pushed to tank 2 by the liquid flow behind it. 2 phase flow is liquid and gas passing the same point at the same time. If the vapor is at 50 psig in the tank, then the vapor pressure is 50 -15 = 35 psia. The pressure at the surface of the liquid is 50 psig. As soon as the pump increases the pressure enough to move the liquid, the vapor in contact with the liquid is crossing the 50 psig vapor pressure level, so vapor can't exist at that point. Moving liquid = collapsing vapor space = compression of vapor in the tank as fluid moves in, tank pressure will not increase more than 50 psig, until the vapor space is all full of liquid. The pump, once reaching 50 psig, only has to increase pressure after that by the static head of the liquid as it raises to the top of the tank.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[Lijantropo]

Good afternoon,
Please find attached a sketch of this “imaginary system”. Let’s imagine that the Second tank, has a control system that keeps the pressure in 50 psig. Now, when the pump starts, the discharge pipe is filled with vapour (or pressurized air, my point is the system is not atmospheric so for me it's the same), and the liquid start displacing all this vapour (air) before it reaches the second tank. Please note that this is not a real system, and therefore the values I’m using are arbitrary, just to point out some key aspects.

The pump discharge pressure should be 50 psig and as soon as the liquid fills the pipe it will increase based on the the pressure drop and the static head. My question is (again, this is an imaginary system, so please feel free to discuss if you think we can never reach this conditions): if the flow to the second tank is low, it’s possible to have a partially filled pipe, with a constant layer of vapor (air) above, at 50 psig (or any pressure above atm)? Is there any equation that could say if in this system the flow is partially or full filled?

Dear BigInch, I can’t understand why do you say the vapour pressure is 35 psia. If it’s equilibrium at some given temperature (and in this case it's important to identify if it is vapour or air), it should be 50+14.7= 65 psia. Could you please verify your number?

Best regards,
Lij.

 

[dicksewerrat]

Looks like you are imagining a bomb waiting to blow. When the pump kicks in you will have an increase in the pressure in the tank. If the 'control' does not low the excess pressure, RUN.

Richard A. Cornelius, P.E.

http://WWW.amlinereast.com

 

[Lijantropo]

Hello Dicksewerrat,

For the sake of the argument, the control system works.

However, with regard to your comment: this issue is not only for my imaginary system. If the tank 2 is atmospheric, you still should take into account the inbreathing and out-breathing flows, and size a free vent to avoid overpressure or vacuum. The phenomena is similar: a mass of air displaced for the liquid entering, or leaving the tank.

Thanks for our comments.
Regards,
Lij.

 

[EnergyMix]

In real life you need a vent. If this is school work, you need to figure it out yourself. We don't do homework.

 

[BigInch]

You said 50 psi. You did not say 50 psia, or 50 psig. When people say 50 psi without identifying if it is atmospheric or gauge, I will always assume they mean psig, since they might not understand what absolute pressure is, being that they did not make that important distinction to begin with and probably arrived at that value by looking at a pressure gauge somewhere.

Your tank will (above the liquid level) stay at the liquid's vapor pressure until the quantity of condensed vapor, liquid volume in the tank, equals the volume of the tank. Collapse of the vapor space above by liquid filling the space in the tank will not occur as long as there is an insufficient quantity of liquid (at the system pressure and temperature) in the system to actually occupy the total volume enclosed by the system. Collapse is conditional on, I think we can explain it by saying we need the ability of the liquid to always be entering the tank to keep and maintain the vapor right at saturated conditions at all times. In the situation you describe, the tank probably has dry vapor (not saturated) in the space above.

In a small pipe cross section, where vapor space was created by liquid once filling the entire space having evacuated the region, thereby creating some lower pressure area now equal to vapor pressure of the liquid, collapse of the vapor pocket is possible only by assuming that the required volume of liquid needed to refill the localized region to keep the pressure at vapor pressure until full again is indeed as free to return as it was to evacuate in the first place. In other words, it is assumed that the vapor space remains full of saturated vapor at all times.

Maybe some chemE can help me out with that.





"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[Lijantropo]

Good morning,

Mr. EnergyMix,
I finished my university a few years ago. This is not a school work. I was evaluating new hydraulic software and among the assumptions used they include “full filled pipe”, so I start wondering, what happens if this is not the scenario. That’s why I created this imaginary system and post the question. Maybe you think this is homework because I’m asking for equation, but if this is the case, I must say that at least for me, the equations are the most adequate way to analyze and understand a system.

On the other hand, I disagree with your answer. In the real life, and talking about a pressurized system, I would install a PSV valve instead of installing a vent in the tank (to protect for overpressure), but this doesn’t answer my question (partially filled line under pressure). Thank you for your comments.

Mr. BigInch,
My mistake, I didn’t clarify if it’s 50 psig or psia. I apologize for this. Thank you for your answer. I agree with your explanation about the behavior of the liquid/vapour in the tank, but I would like you please concentrate in the pipe when the pump starts: The upper horizontal section is originally filled with vapour (or any pressurized gas) at the operating pressure of tank 2 (in this case, we supposed 50 psig). The vertical section and the lower horizontal section must be flooded. Once the pump starts, the liquid flows through the upper horizontal section and here is my question: how do we know if we have a full filled flow or if we have a biphasic flow in this upper section?

For me, if the velocity is high, the liquid will fill the entire pipe and push the vapour/air (like a plug flow). On the other hand, if the velocity is to low, we would have something similar to a biphasic flow, with liquid flowing at the bottom and a constant layer of pressurized vapour/air above. What do you think? Have you ever seen a scenario like this?

Thank you very much for your comments.
Regards,
Lij.

 

[Latexman]

Have you used Search (between Forum and FAQs) on keyword phrases like "partially filled pipe" or "open channel flow" or "Manning Equation"

Good luck,
Latexman

 

[Lijantropo]

Good morning,
Yes I have used it, but the "Manning Equation", the "Open channel flow" and the "partially filled pipe" topics discuss atmospheric gravity lines. Could I use the same equations for system under pressure?
Best Regards,
Lij.

 

[EnergyMix]

Lijantropo

My apologies for assuming that you were a student. Given that it's an imaginary system, I don't care whether you call it a vent valve, relief valve, or PSV. You understand the concept.

Presuming that in real life the pump was sized properly to allow it to actually pump from tank 1 to tank 2, it would pump single phase fluid, at least until such time the level in tank 1 was too low for it to be able to pump any more. Without a makeup source, the pump, of course, would then either shut off or destroy itself.

When the fluid reaches the horizontal level shown on the drawing, there will be mixing, but the flow coming up the pipe will be single phase and will "push" the gas back into the tank. Other than at the very beginning of flow, there will not be two-phase flow in the horizontal section of the pipe. There will definitely not be two phase flow anywhere else in the pipe. Such limited two-phase flow would probably be ignored in any actual fluid calculation.

Without a vent, the level in the tank will rise, and the free gas volume will decrease. Based on the relative dimensions in your drawing, the results will not be optimal.

Crane's Flow of Fluid's has some discussion on this type of problem. Additionally an ASME continuing education course PD-171 "Pump and Valve Selection of Optimum System Performance" discusses pumping between tanks.

The above discussion only applies to the drawing you provided. There are systems which operate with completely drained discharge piping. There are also systems which operate right at the water/steam threshold. Those tend to be more of a problem. Also, just to be clear, voids are different in piping then air or gas. The first should be avoided.

 

[Latexman]

50 psi exists at all points above the vapor/liquid interface in the pipe and tank. Back at the pump, the fluid already got enough energy to get it from 0 psi to 50 psi + elevation + friction. In the horizontal, partially-filled pipe, the only energy that will be expended is that of gradient flow overcoming friction and fittings. The pressure is a wash for this.

If you are actually going to solve this "imaginary problem" it will be much easier if you assume the pipe is sloped downward and solve for the slope assuming partially filled pipe at a constant height along the run.

Good luck,
Latexman

 

[Latexman]

To exaggerate my point, assume flow is 1 gpm and the horizontal run is 36" OD, Sch. 40 pipe.

Good luck,
Latexman

 

[BigInch]

Even if the pump is not sloped, the water as it is drawn now will flow out, since the outlet at the vessel has no dam that can stop the water from flowing on its own. If the pipe is 24" diameter, there appears to be 12" of water in there, so take a free body diagram of the last 1 in2 column of water in the pipe. On the left of the 1 in2 column at the surface you have 50 psi. On the left of the 1 in2 column down at the bottom of the pipe you have 50 psi + 1 ft high wall of water exerting pressure = 50 + 1 * 62.4 pcf / 144 in2 = 50.43 psi. On the right of the 1 in2 column where the tank opening is, you have a uniform 50 psi tank pressure on the right surface of the 1 in2 column of water. Summing horizontal forces on that 1 mm sq. column of water, there is (50 + 50.43)/2 = 50.215 average psi. On the right side you have an average 50 psi, so it's a net 50.215 psi - 50 psi = 0.215 psi x 12 inches = 2.58 lbs pushing that column of water to the right. It will go into the tank, if the pipe is sloped or not. Now take the next column of water that moved in to take the place of the first. Its almost 12" high, because the fluid level in the pipe dropped a little, so there's slightly less than 2.58 lbs pushing that one into the tank. None the less, that one goes into the tank too. etc. etc. So that's how the water flows out of the pipe, partially full, when the pipe is not sloped.

The water flow will continue on that basis indefinitely, if the pummp is turned on at low speed, so just enough water enters the inlet of the pipe to replace the water moving out of the pipe. If you speed the pump up some more than that, the "bubble" in the pipe will begin to move to the right and eventually the pipe will become full of water as a small jet into the tank begins to form. Before you reach that condition, you may see a condition where water at the entrance to the tank flows quickly, then slows, and quickly again as the bubble oscilates back and forth for awhile, but you should eventually reach a steady state condition with the pipe flow's velocity jetting into the tank.

2 phase flow in petroleum hydraulics is especially seen near the wells, where it is typical to see a combination of a certain amount of gas, some oil and gas condensates (condensed heavier petorleum gases that are liquid under pressure, but gas at atmospheric or slightly higher pressures) all flowing from the well at the same time. In that case, flow in the pipe may be nearly all gas, nearly all oil, nearly all gas and condensates, or some combination of all of them. In that condition how the flow moves in the pipe is mostly conditional on the ratio of gas to liquids that you have in the pipe at any given time. Very high gas content and little liquid will often flow as a misty gas, oil and condensates and water forming the misty droplets being carried, or blown along by the gas stream. More liquid quantities may cause other flow patterns, such as gas flowing rapidly on top of a pipe half full of liquid as you have drawn in your diagram. The liquids moving at a slower velocity than the gas. It is possible to see waves sometimes, other liquid to gas ratios create foam flow, others, especially when the viscosity of the liquid is high, may be liquid flowing along the walls of the pipe, with a center stream of gas flow in the middle of the pipe. If liquid content is high, but gas content low, you may see bubbles flowing along the pipe being carried by the liquid. If there are ups and downs along the pipeline, you may see areas where the liquid is flowing downhill, but bubbles are flowing uphill until enough gas accumulates at the top of the hill to block liquid flow for awhile until all of a sudden the bubble takes off downhill again with liquid following it. That's slug flow. If you have a very viscous product (asphalt) flowing in a cool pipe, you can get almost no flow, or very slow flow in a region near to the walls, but fast flow in the central area of the pipe that stays warm. Search for "flow regimes of 2 phase flow" and you will get hits on a number of diagrams detailing many of these combinations of flow patterns for vertical pipes and those with some variation in pipe slope

What software are you evaluating?

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[Lijantropo]

Good morning,
Mr. EnergyMix,
It’s not necessary to apologize. I only wanted to clarify that this is not homework in order to continue with the discussion. Moreover, I think of myself as a “student” since I have been working just for few years (5) and I am still learning and understanding new concepts. Thank you for extend your explanations.

Mr. Latexman,
I am particularly interested in the behavior of the fluid when it reaches the upper section in the horizontal pipe, but we can extend our analysis to a system as you propose. Let’s finish the horizontal pipe and then we can discuss about pipes going up and down.

Mr. BigInch,
Thank you very much for your explanation. I think this is the best description of what happens in the system. My drawn was not intended to represent a concrete situation (and therefore, the column of liquid inside the pipe could be higher or lower) but I believe that your analysis applies for all the situations. I have been looking at the two-phase flow equations but I was not sure if they apply here because the upper layer of vapour (air), in my opinion, is not flowing along with the liquid.

To conclude: your recommendation is to evaluate the flow regime (I believe it is stratified, due to the zero gas velocity) and try to determine all the properties of the system (pressure drop, liquid holdup, etc.) based on 2-phase equations, right?

The software I was looking at is called PSIM. I understand that it is based on Fathom (a recognized fluid software), but I have never heard about it. I believe it is possible to find a free version of this program or personal use.

Best Regards,
Lij.

 

[hydtools]

Would not density difference explain why pipe flow will be full? The less dense vapor will always remain on top of the fluid.

Ted

 

[BigInch]

In your example, given that you had a typically sized pump for the pipe, or visa versa, even if you did get some stratified flow, it would be a very temporary sisuation that would exist only until all the air was expelled and the pipe reached a full state. If the discharge into the tank was intentionally oversized, you would have simple flow in a partially filled pipe, as you say, there would be no net forward movement of the air above, it's hard to classify that as 2 phase flow. After all only one phase would be actually flowing.

Hydtools,
No the less dense fluid does not always remain above a more dense fluid. A basic 2 phase flow pattern progressing from a stratified wave flow condition is when gas flow is increased enough above the liquid such that shear between the gas and liquid tries to drive the liquid forward as fast as the gas wants to move, which slows down the gas velocity and increases local pressure. The building gas pressure builds puts extra downward pressure on the liquid near the center of the pipe under the highest gas flow, which forces the liquid at the pipe wall to climb the wall to balance the increased downward pressure in the center. Keep increasing gas flow and the liquid eventually winds up flowing in a ring adjacent to and all around the pipe wall while the gas starts flowing down the center "tube". Blow very fast through a straw at an angle close to the horizontal just above the surface of a liquid and you can see the initial trough that is created under the impinging air jet. Now get the air compressor nozzle and your cup of coffee ...

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[EnergyMix]

I agree with what BigInch is saying.

 

[Lijantropo]

Dear Colleagues,

Please see the following discussion related with sealing flow. I believe this could determine which flow makes this system partially-filled or full-filled:

http://www.eng-tips.com/viewthread.cfm?qid=177112

I think for an horizontal and vertical pipe, it is possible to use the same equations in a pressurized system, but for sloped pipe, I don’t think so (the Manning Eq. was developed based on an atmospheric constant pressure above the fluid) What do you think?

Best regards,
Lij

 

[chicopee]

In all assessment, it is an inane and probably damaging setup. Both tanks should be connected with an equalizing vapor line.