fluid falling in vertical pipe 3

[michaelmauser]

We want to fill an underground fuel tank with an existing 1-inch pipe which drops 1400 feet vertical before running 800 feet horizontal to the tank. We are considering using a same size batch tank on the surface with a valve there and no where else. How can we determine if we need to throttle to avoid too high a pressure?

 

[mbeychok]

.
michaelmauser:

Is the underground tank vented to the atmosphere? If not, you should consider the fact that the 1400 feet of liquid head will impose a pressure of approx. 485 psig on the underground piping and on the underground tank (assuming a fuel specific gravity of 0.8 and neglecting the additional head imposed by the height of liquid fuel in the feed tank located on the ground surface).

Milton Beychok
(Contact me at www.air-dispersion.com)
.

 

[JStephen]

At partial valve openings, you should get cavitation in the line downstream of the valve, which I suppose would be undesirable?

 

[michaelmauser]

The underground tank is vented to the atmosphere.

 

[michaelmauser]

We didn't think about cavitation as a problem, we just were more concerned with excessive pressures and hammer. We would fill as fast as we could with the valve full open if that would work.

 

[CRG]

I can think of several scenarios for unintended consequence giving advice about this type of problem with limited information. Most result in fuel spills with unknown consequences.

What type and size of tank is at the underground level?
Are there any isolation valves on the tank inlet? (no)
Is there any overflow prevention devices?
Is there a diffuser on the fuel inlet?
Are there any flow restricting devices at the tank?
Is it possible for any contamination getting into the fuel system that may change the flow characteristics of the system?
What atmosphere is the underground tank vented to? (below grade by tank or surface)
Is it possible for the vent to become blocked?
What is the design pressure for the piping system connecting the below grade tank to the surface?
What procedure will be followed if the tank is overfilled?
How long will the system be in service?

So to answer michaelmauser question, How can we determine if we need to throttle to avoid too high a pressure? I recommend that:
1. You should consider every possible scenario that could develop during the tank fill process.
2. Consider that the end operator for the tank fill may have no idea of what they are doing and the resulting consequences of their actions.
3. You have to have a complete understanding of the physics of the problem for all possible scenarios.
4. Decide what the acceptable risks are and design the system.

 

[Cockroach]

The Torricelli Principle, water falls like any other solid object under the influence of gravity. Therefore you can look at water like a series of small spheres falling under the their own weight in a uniform gravitational field.

Essentially then, v=sqrt(2gh) for h=total vertical height or 1400 ft. Since the water falls from rest, you can work out all the necessary information required to come up with pressure(s). This may be important as the vertical drop starts to go into the horizontal leg of the pipe network. The change in direction would cause an acceleration, hence an increase in force experienced by the pipe. I would be looking at this for potential problems.

Sounds like a pretty straight forward problem. I would have no or at least little concern for "unintended consequences". My understanding in usage of this forum is to generate brainstorming discussion rather than post solutions to various problems.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[JStephen]

The "water falling down a pipe" problem has some pitfalls (whether water or fuel).

If the pressure in the pipe right below the upper tank is essentially atmospheric, then flow will be limited by orifice flow, and flow rate will not increase as the pipe drop changes, etc.

If you assume that the entire pipe is full of fluid, you can calculate some enormous flow rates using Bernouli's equation. Be sure to check pressures back up the pipe, in particular to make sure they don't calculate out to negative (either gauge or absolute). Bernouli's equation is an energy equation based on the beginning and ending points in the pipe, and all the in-between points are neglected. This can give some very unrealistic effects. The pipe friction may be enough to prevent this effect, or may not.

The catch is, you typically don't know what the presure is at the top of the pipe, so you don't know which of the two cases above applies.

I would be very hesitant to use droplet size, drag coefficients, etc., in an effort to calculate flow down the pipe, without experimental backup. I can't imagine that a drop goes very far without contacting a pipe wall or another pipe.

Several points I can think of that may become important. You should have considerable thrust at the elbow and considerable drag on the lengths of pipe. You may get pipe movement there that you wouldn't normally expect. (IE, how much does that pipe stretch just due to friction force?) The stream at the outlet could be like a firehose several times over.

If the bottom tank is 3/4 empty, and person topside thinks it IS empty, you have problems in a big way.

 

[katmar]

There was a lively discussion of exactly this problem in thread378-81608

If your system was ever in a static situation with the pipes full, you would get a pressure of about 520 psi at the bottom of the vertical section. I suggest you avoid this ever happening.

The way I see it, you have two choices. The one I favor is to fill the top tank with its outlet valve closed, and then to open this valve fully and let all the fuel run down in a batch. There should be no other valves in the line between the two tanks (unless thay are locked open and only available for maintenance purposes). You should check the regulations on whether valves are permissable. With this mode of operation you would get a flowrate of about 30 USgpm and a maximum pressure at the bottom of the vertical section of about 200 PSI. The valve should not be closed before all the fuel has drained out. See my comments in the referenced thread.

The second option is to allow the fuel to drain from the top tank under carefully controlled conditions, such that the vertical pipe remains in the self-venting regime at all times. See the comments and references by Art Montemayor in the above thread. The flowrate would be much less than the 30 USpgm mentioned above, but this is the safe and cautious way to do it.

Seeing that you have an existing line, your choice will probably be governed by the pressure rating of the line.

 

[michaelmauser]

Thanks for the reference to the other thread. If I fill the tank at the top, then open the valve, I think that the maximum pressure differential we can possibly see in the piping from the tank to the beginning of the vertical drop will be atmospheric (12 psia at our elevation) minus the vapor pressure of diesel (close to 0 psia). We can estimate the maximum flow and then calculate the height of the column at the bottom of the vertical pipe that will result in that maximum flow being conveyed through the filled base of the vertical section and the remaining horizontal section. I'm assuming the rate of falling flow will not be the limiting factor. Is this how you estimated 30 gpm and 200 psi?

 

[katmar]

The maximum pressure differential you can possibly see in the piping from the top tank to the beginning of the vertical drop is simply the static height difference between the surface of the fuel in the tank and the top of the vertical leg. It has nothing to do with atmospheric pressure (unless you really want to split hairs!). That is why I recommended in the other thread that this section of pipe should be of a larger diameter than the vertical section - this applies whether you are running the pipe full or in self-venting mode because two phase flow is even more troublesome in horizontal piping than in vertical piping.

I calculated the flow rate by taking the pressure driving force as the 1400 ft vertical height difference times the fuel SG, which I assumed to be 0.84. This gave a driving force of 520 psi. I then used a simple program to work out what flowrate this pressure would push through 2200 ft of 1" pipe. This gave me the 30 gpm.

The purists will tell you this is wrong way to look at it. You should think in terms of the Bernoulli equation with a pressure differential of zero and a height difference giving a potential energy difference. It comes to the same thing in the end, but if you are ever struggling to sort out what the true picture is, it is always better to formulate the problem in the classic Bernoulli format.

You need to recognize that if the receiving tank were directly at the bottom of the vertical section, a pressure gage at the bottom of the pipe (just before it enters the receiving tank) would show a pressure of zero gage while the fuel was flowing (provided the pipe runs full). This is because the falling fuel will accelerate until the friction head loss exactly matches the potential energy available due to the height difference. This is per Bernoulli.

In your case the fuel reaching the bottom of the vertical drop needs sufficient pressure to drive it through the 800 ft of horizontal piping. Any piping pressure drop program will tell you that 30 gpm flowing through 800 ft of 1" line will result in a friction head of about 200 psi. The flow down the vertical leg will equilibrate until it uses up sufficiently less than the full amount of static head available to leave enough head to overcome the friction in the horizontal section.

One thing to be careful of (and I have not checked it myself) is to see what linear velocity in the pipe this will result in. With flammable fluids that are subject to static electric sparking there are maximum velocities specified in the codes. They are there for good reasons and they should be observed.

I hope this is all clear? Just ask if there are any areas where you need more detail because this sort of problem is not intuitively obvious if you have not faced them before.

 

[michaelmauser]

Thank you. I understand your logic now. I was thinking of the process of filling the pipe. Assume the tank has 10 feet of head and a horizontal run before it drops vertically. You open the valve and there would be 10 feet of differential head (3.6 psid) accelerating the fuel through the pipe. As the fuel drops down the pipe, if it flows as a plug, it should reach a distance where the weight of the column minus the sum of the friction head in the column and the opposing air pressure will be the vapor pressure of the diesel and we would have 0 psia at that point and the column breaks. Assuming this happens at the point the pipe goes vertical, we would have 12 psid (given 12 psia atmospheric pressure at out location) acting on the horizontal section of pipe. That would give the maximum flow rate from the tank. Anyway, that was my reasoning. I agree with your reasoning for a pipe that is filled, I just haven't resolved how it gets there, if ever. One concern in the earlier post was not exceeding 7 m/s because of static electricity. 30 pgm in 1-inch pipe is 3.4 m/s but wouldn't the initial fuel falling in the pipe travel faster?

 

[JStephen]

katmar, did you actually calculate the pressure differential at the inlet to the 1" pipe, assuming 1" pipe runs all the way to the upper tanks? That is the issue I have run into, where the calculations seem fine, but you can then show a negative absolute pressure at this point.

Michael, you mention the vapor pressure of the diesel a couple of times. So far as I understand it, this would have nothing to do with the flow. The vapor pressure is the partial pressure of the fluid in the fluid/air mixture in the tank, but only the total pressure at that point would affect flow. Assuming, that is, that the upper tank is vented to the atmosphere (which it should be).

 

[katmar]

Michael,

The question of droplets falling off the face of the intial fuel going down the vertical leg is a difficult one. A droplet having a diameter of about 1 mm would fall in free air at the 3.4 m/s the fuel wants to travel at, so anything bigger would fall away from the face. But here we do not have static air - it is also flowing downwards at 3.4 m/s. I'm afraid this analysis is beyond me and I would turn to the codes and installation guides issued by the fuel suppliers.

It has just occurred to me that the initial flowrate (before the vertical section is full) would be higher - about 40 gpm with a velocity of 4.5 m/s (sorry about the mixed units). It is only once the bottom horizontal section is full and the head in the vertical section has to overcome the combined friction of the horizontal and vertical sections that the flowrate drops back to 30 gpm.

JStephen,
You are correct to be concerned about negative pressures, and Michael also expressed concerns about the column breaking. Note that you may find negative GAGE pressures but never negative ABSOLUTE pressures. The software may predict negative absolute pressures but that is just a programming error.

In the previous thread (See thread378-81608 ) it was mentioned by people who had hands-on experience with these things that they found gurgling, bubbling and vibration, all of which indicate exactly this. That was why I said that the most important section of the piping is the bit between the top supply tank and the top of the vertical leg. It is essential that the vertical leg be fed with as much fuel as it can cope with. If this condition is met you will have a zero pressure gradient down the vertical section - static head exactly matches friction head. In your particular case you will not have a zero pressure gradient because head must be "retained" to overcome the friction in the horizontal section at the bottom.

If insufficient feed is available you will generate negative gage pressures and the column may break. This is the only area where the vapor pressure of the fuel is important. But this situation should be avoided and designed out of the system.

A typical example of this is a barometric leg under a vacuum condenser where the superficial velocity down the pipe may be as low as 0.1 m/s - but in this case you want the column to break and maintain the vacuum (i.e. negative gage pressure).

I think this is a case where considering the opposite extremes helps to get it in perspective. Imagine a pump between the top tank and the top of the vertical leg. If this pump could deliver 2000 psi you would never get the column breaking. On the other hand if you had no pump and you just cracked the drain valve you would get the column breaking. Somewhere in between these extremes is the safe and economic point where you want to operate. And that the point where the vertical leg is fed just exactly what it wants to be in equilibrium. Obviously you cannot size the top horizontal section to match this exactly, so you would end up oversizing the top horizontal pipe slightly.

 

[JStephen]

"Note that you may find negative GAGE pressures but never negative ABSOLUTE pressures. The software may predict negative absolute pressures but that is just a programming error."

In real life, you don't expect to find negative absolute pressures. Using energy-type equations, you CAN calculate negative absolute pressures. It simply indicates that your model no longer matches up to reality. It isn't a programming error, but an error in the model used.

 

[CRG]

One concern in the earlier post was not exceeding 7 m/s because of static electricity.

michaelmauser ,in addition to your concerns regarding the velocity of fuel in the one inch pipe you should also consider what takes place in tank. API RP 2003, 4.5.2 Control of Electrostatic Charge Generation discusses some of the problems. Also, note that 7 m/sec is only valid for small diameter pipes to reduce the problems associated with static charge. Larger diameter pipes should have much lower flow rates to minimize the static charge (V*d < 0.5m^2/sec).