Frictional losses for liquid flowing out of a vessel into the discharge pipe - Conceptual question

[jari001]

Hi everyone,

Just curious if there are any credible scenarios where frictional losses would have to be accounted as a fluid drained out of a vessel. If I imagine an exaggerated case, I am thinking of a highly viscous fluid being gravity drained out of a vertically erected cylindrical storage tank; if a pump were involved I imagine the safety margins would cover such frictional contributions. I would think this scenario could be treated as flow through a pipe. Let me know if you have had some experiences with non-traditional flow situations.

Thanks!
-J

 

[BigInch]

There are two frictional losses you need to consider. One from fluid in the tank trying to "round the corner" as it moves from inside the tank through the outlet. That is called the outlet discharge coefficient. It is the energy cost paid to accelerate the liquid from a velocity of zero within the tank to the velocity that the fluid travels as it moves through the tank outlet. The second is the friction loss of fluid moving through any pipe attaching the tank outlet to the pump inlet.

Having a pump does not give "safety margins". Contrary to popular belief, pumps do not suck fluid from a tank. Pumps reduce the downstream pressure enough so that the upstream pressure (atomspheric pressure, or the pressure in the tank) minus the pressure near the pump's inlet is great enough such that the net force caused by that pressure difference can move the fluid along towards the pump. Fluid must arrive at the pump with enough pressure at the pump inlet to fill the pump vane space that will sweep it towards the pump discharge. The more viscous the fluid is, the more friction is generated by trying to move it and the more difficult that whole process becomes.

 

[bimr]

The flow out of a tank outlet connection is generally considered to be a minor friction loss. In some cases, the friction loss may be ignored.

However, if the tank outlet connection is located at the fluid surface, you may encounter difficulties with trapped air in the discharge pipe as well as variable fluid levels in the tank.

 

[EmmanuelTop]

Exit frictional losses are crucial in draw-off nozzles for side products (side draws like Kerosene, Diesel, AGO etc.) in distillation towers. These streams exit the tower horizontally and by gravity, and the only force available to push the liquid through the nozzle is static head of liquid on the draw-off tray. As the flow rate increases - i.e via flow control valve downstream of the product pump - exit losses approach the head of liquid on the draw-off tray and when they equalize the point of nozzle cavitation is reached - you can't increase the flow any further. That is why there are special design considerations for draw-off trays, piping, and valves.

Dejan IVANOVIC
Process Engineer, MSChE

 

[katmar]

A very common occurrence of this is in condensate return tanks and boiler feedwater tanks. Because the water is close to boiling it can lead to NPSHa problems. This is very similar to the example given by Dejan. The solution is to use bell mouthed outlets and large bore piping - and careful pump selection.

I am in a hair splitting mood today so let me say that there are 3 sources of pressure loss between the tank and the pump. The first is the "entrance loss" which is caused by the turbulence losses when the fluid flows around the corner. This can be cut by 90% by putting a well-rounded bell mouth exit from the tank. The second is what is usually called the "exit loss" and is the energy used to accelerate the fluid from zero to the flowing velocity. If you search the forum you will find semantic arguments that distinguish between acceleration losses and exit losses, but for calculation purposes they are one and the same. The way to minimise this is to use larger bore piping. The final loss is the pipe friction and this can also be minimised by using a larger pipe size.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[BigInch]

Another very common occurance of this problem comes when pumping hot gasoline from a tank. Gasoline over 40[°]C has a very high vapor pressure, which can exceed 10psia, or even more. It can easily cause vaporization and "vapor lock", a vapor blockage in an ignition system, or in a pump suction line, which can stall further pumping completely. Many pumps cannot move hot gasoline, as, after subtracting the high vapor pressure from static head, there remains insufficient net postitive suction head for the pump to function. A special type of "can pump" is needed that has very, very low NPSH requirements, and still pumping can be difficult. Fortunately petroleum products can get along being pumped at NPSH that are slightly higher than what pump manufacturers publish on their data sheets, as those stated requirements are normally based on pumping cold water.

 

[LittleInch]

Interesting discussion, but I think what the OP is going on about is frictional losses in the storage vessel itself.

For me if you had, say a storage vessel as described ( vertical cylindrical) and your out let area was greater than 10% of the area of the vertical cylinder, then you might need to think about friction as the liquid level decreased.

However most storage vessels X sectional area is in the region of 100 or more times the area of the outlet nozzle and hence frictional losses would be very low to the point of being negligible.

Highly viscous fluids ( polymers etc) have other issues as they attempt to flow out of a vessel which are not really friction based.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[BigInch]

Ya we know, but you also know how we all insist to go off into the weeds at every opportunity citing a bunch of irrelavent stuff.

 

[jari001]

Very interesting discussion, I'm still digesting everything! I intended this to be more of an open discussion but I will relate the problem I am working on that triggered me to ask this question.

I asked this question as I was trying to write down my model equation for gravity draining my storage tank (CIP waste, oil-water emulsion product, and animal oil) into a frac tank for waste disposal; my worst case waste profile still puts my solution to about the same density and viscosity of water. The bottom outlet nozzle of the tank (C_d=0.8 for a square mouth) is about 2 feet up from the top of the frac tank, so I wanted to calculate the degree to which the static pressure from the level in the frac tank will affect the transfer and work out if there would be any spill scenarios. My tank is 9 feet inner diameter and my outlet nozzle is 2 inches inner diameter, well withing the scenario LittleInch described! In imagining the scenario, I knew I wanted to use a psuedo-steady state approx. to make my model and I was trying to make sure my assumptions are justified so I went off thinking about some extreme cases.

Further info about the tank: outlet nozzle connects to a 1 inch 90 with a flange that is connected to a 2" CS pipe that is about 5 feet in length, which connects to 2" 90 (this brings the CS pipe through the containment basin) followed by another 3 foot run of the CS pipe and ends at a 3 inch ball valve (SS construction). I attached a sketch of the setup.

I used the psuedo-steady state approx. of 0 m/s for the velocity of the water at the surface of the higher elevation (surface in the tank). This would reduce my energy balance (Bernoulli eqn.) to change in potential energy of the stored liquid in the storage tank to the kinetic energy into the frac tank minus the losses in the flow path. I would use the C_d as part of my "losses" term along with friction factor calcs of the pipes, hoses, and valves. Once I derive a relationship for the velocity into the frac tank, I can figure out the height in the frac tank to understand if the level in the frac tank will equilibrate somewhere other than the top of the frac tank.

g*z_{water surface height in tank} = 0.5*(v_{into frac})^2-"LOSSES"+g*z_{water surface height in tank}

My comment about the pump was more so my opinion on the inherent over-sizing in may of the guidelines I read, but I don't doubt I'd be able to prime a pump if I were to use one. I will admit that my understanding of pumps is very rudimentary, which is why I frequent the pump engineering forum as much as I can.

(edited to clarify diameter, provide additional details of the tank, and attached sketch.)

 

[bimr]

You are missing the sketch.

 

[jari001]

Sketch attached here. Also included full link if I'm messing up the upload.

http://files.engineering.com/getfil...&file=MTTSPWN13001_MTTMFC5235002_1594_001.pdf

 

[bimr]

Don't believe there is any method that will accurately model the flow scenario that you are describing.

In particular, modeling low flow through hoses is difficult. Some manufacturers have data, but that will be limited at the low flows that you describe.

This flow scenario will be modeled as flow pipe flow. Unless the storage tank is very high, you have limited static head to force the fluid out.

If all you are worried about is overfilling the frac tank, install an overflow in the frac tank. The overflow level should be set so that the frac tank volume between tank top and overflow setpoint equals the volume of your storage tank.

 

[georgeverghese]

You havent shown details of what venting arrangements are like on the downstream frac tank. Also we assume the frac tank feed nozzle location is as shown on this sketch - somewhere partway up the tank but not at frac tank top. If there is no vent on the frac tank, as level builds up , the dead space trapped vapor at frac tank top will build up pressure..

 

[LittleInch]

Hmmm,

1) forget Bernoulli - what you have here is a relatively simple tank to tank via pipe flow system. There are many mays to calculate this, but the equivalent length method would seem to be the best for you.

2 "Once I derive a relationship for the velocity into the frac tank, I can figure out the height in the frac tank " Unfortunately for you, your driving force is wholly dependant on the liquid levels in the main tank ( which I think are going to fall and rise over time??) and if the liquid level in the frac tank is below the entry nozzle then at least that end level is fixed, but if the entry nozzle is below liquid level then the level in the frac tank will affect the velocity / flow. This is without complicating it any further if in fact either of the tanks ends up under a pressure different from each other ( i.e. atmospheric) which might also vary with height of liquid in the tank.

So what is the whole story here?
What, if any, items are fixed ( flow rate, levels, pressures etc)?
How does this flow operate - steady state or batch mode?
What are you actually trying to find out?
What measuring devices do you have for level and flow?
?Will you ever be able to find out if your calculation is correct?
Is any of this built at the moment?

IN something like this, even the smallest restriction at say a hose connection or even kink in the hose can affect flow by a significant amount so you need to be realistic in what it is you're trying to calculate.





Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[jari001]

The storage tank is a 5000 US gallon capacity atmospheric tank. There are multiple vent lines and overflow lines open to atmosphere on this tank. The combined diameter of all the vents is 6 inches (one 4in vent and two 1in vent lines). The outlet of the storage tank is a 3 inch ball valve. I did some calculations with API 2000 for breathing rates due to forced withdrawal for when we use a vacuum tanker to draw the tank down and found the venting is sufficient so I think these vents are okay for gravity draining. I need to use the rental frac tank because during our consistency lot campaign, we can't wait for the 5000 US gallon tank to get draw down every time we clean our equipment (3000 gallon waste output in one shot). The waste flow for the process was haphazardly put together a decade ago and I'm responsible for making sure we don't have any spills.

The frac tank is a 21,000 US gallon capacity tank that is a V-bottom with tires on the back. It has a slight slope to it and I am filling it from the higher end of the slope. The hose connection is made approximately 2 inches off the ground. I'm not allowed to leave the flow path open unattended so the frac tank is vented to atmosphere by opening the main manway at the top (22 inch ID). The frac tank has a "level gauge" on it that I don't trust so I can approximate the level in the frac tank by looking in through the manway.

Flow into the storage tank comes from a sump pit on a lead lag system and I check the storage tank level 2x a day. I am considering the waste transfer from the storage tank to the frac tank as a batch process because I throw the valve when I am confident I know the sump pit pump system has stopped running (I can hear the water flowing into the tank and stopping). The inlet nozzle of the frac tank will be submerged for the most of the usage time.

What I'm trying to do is figure out if the level in the frac tank will affect the transfer such that the level in the storage tank won't drain into the frac tank. My aim is to identify if overflowing the storage tank is possible and to minimize the number of times I call the tanker to draw down the frac tank until after the consistency campaign. The only info I have is level measurements and the knowledge that the starting and ending points at at 1 atm absolute.

I've included the engineering drawing of the storage tank and the vendor spec sheet for the frac tank:

http://files.engineering.com/getfil...4e-4015-9707-063363e7c197&file=Waste_Tank.pdf

http://files.engineering.com/getfil...798f&file=21K_gallon_frac_tank_spec_sheet.pdf

 

[bimr]

Regarding: What I'm trying to do is figure out if the level in the frac tank will affect the transfer such that the level in the storage tank won't drain into the frac tank.

Yes, the liquid level in the frac tank will affect the flow. The flow into the frac tank will slow as the frac tank level increases.

Suggest you consider adding some instrumentation.

Start with liquid level monitors on the tanks. Add automatic shutoff valves (fail close) on to the tank fill connections. The liquid level monitors will provide the signal to close the automatic valves.

Liquid level monitors will provide some knowledge over the liquid inventory.

Without some type of level monitoring and overflow protection, you are destined to have a spill because you seem to have little control over operation.

 

[LittleInch]

The key missing data which you definitely need is the absolute or relative elevation of the different components.

Unless your tanks are exactly level in the overflow / tank level then one tank or the other will have potential to overflow.

As the liquid levels equalize then the flow rate drops off exponentially.

Some simple things can be done.

1) FIX YOUR LEVEL GAUGE
2) Install another level gauge you trust, maybe even a Radar gauge on the frac tank.
3) Find a 12 foot long piece of timber and make notches a 1 foot levels
4) Obtain from Baker or calculate your self a depth to volume conversion for the frac tank
5) Make sure there is always 5000 gallon capacity in the frac tank before you open the valve from the storage tank.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[jari001]

I attached a picture of the setup now that the paving is finished. I apologize that it is from a bit far back.

@LittleInch
I've got items 3 to 5 covered and I can measure heights of different components. Since the setup is outside, I don't have any ready means to supply power to anything. The maintenance folks have 1 generator that I could have used if it wasn't busted...
I'm not quite sure what you meant by "Unless your tanks are exactly level in the overflow / tank level then one tank or the other will have potential to overflow". Do you mean that if any amount of the frac tank is above the lowest point of the storage tank, then it will only flow until those two liquid levels are at the same absolute height?


@bimr
Since this whole setup is outside I can't provide continuous power to anything (plus the portable generator is busted). For the short term, which is what this setup is for, I know very accurately the amount of waste sent to this storage tank and when it is sent. All the waste comes from cleaning a small skid and I have trends on the utilities to tell me how much water went to the skid and I know when operators are instructed to clean the skid. I also control when the transfer from the storage tank to the frac tank happens as well, so I'm not concerned about a spill happening due to unknown amount of liquid going to the tank. I proposed the auto-shutoff valves when I was moved onto the project but none of the managers want to review this change control because it would be complicated to to integrate and validate these pieces of equipment (pharma requires extensive documentation for changes to a GMP system, and the building automation system is considered GMP).

 

[LittleInch]

Err not quite, but thats one impact.

What I meant was that if the overflow level of one tank was higher than the other then it could overflow the other.

On the basis that the white tank is your "storage tank" ad the green tank is your "frac tank", then there is always the potential to overflow your frac tank as the white tanks is much higher than the green one. However it's not that much higher and so as your frac tank fills up and the storage tank decreases, your head available for flow will reduce to about 1m by the look of it. A 2" line will be dribbling along at that head loss so a pump would be a better solution providing you know you have enough ullage in the tank =- see my points 1 to 5 above.

Your protestations about no power do not ring true - if was in the middle of nowhere I could believe you, but you appear to be in the middle of an industrial park. Most instrumentation I know off works outside, you just need to buy the right stuff and connect it using the right cables and junction boxes / cable glands. I don't understand why someone is nickel and diming this when a spill in this location would appear to cost 100 x the cost of instrumentation and cabling

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[bimr]

Somewhat surprised that the site safety manager would let you operate this arrangement.

Regarding: I'm not quite sure what you meant by "Unless your tanks are exactly level in the overflow / tank level then one tank or the other will have potential to overflow". Do you mean that if any amount of the frac tank is above the lowest point of the storage tank, then it will only flow until those two liquid levels are at the same absolute height?


Everybody knows that liquid will seek its own level but few people know why. The reason has most to do with
 
    a) atmospheric pressure,
    b) water pressure depending on depth,
    c) water's density.

Liquid pressure depends on depth, so only at equal depths of liquid will the pressure be equal. Consider the U-tube. If liquid is at rest where each A and B are, the pressures must be equal -- otherwise a flow would occur from the region of higher to the region of lower pressure until the pressures equalize. For this to happen, the depths below the surfaces must be equal.
 
This is true whatever the density of liquid or whether or not there is atmospheric pressure.