Tank Filling/Overflow of tank investigation 1

[DaEarl]

Greetings,
I am currently part of an investigation involving the overflow of a tank. The system is as follows: two tanks, each the same diameter and height, each containing water, are both connected by a 16" CS pipe (300ft.). Water is pumped into both tanks at a constant rate. Tank 1 at 7500gpm and tank 2 at 1100 gpm. Tank 1 has a water level of 27 ft. and tank 2 has a 24 ft. level. My task is to develop a timeline for the overflow of tank 1 to corroborate the story of the operator in charge of the tanks.

MY METHOD: 1)I developed an equation for the flow of water through the 16" pipe. I derived the equation by Bernoulli's equation. I wrote the flowrate of the water as a function of the difference in height b/w the tanks taking into account the friction factor (f), equivalent length of pipe (L), and the diameter (D). 2)I used the continuity equation to describe the net flow rate of each tank (Q1net=Q1in-Qpipe; Q2net=Q2in+Qpipe). 3)I divided each net flow rate for each pipe and then divided by the area of the tanks (Q1net/A). This value is then multiplied by a time interval (30s) which in turn returns a height change. I continued iterating for 30s intervals until tank 1 reaches the 40ft. level (overflow level).

QUESTION: Is this a reasonable solution to the problem?

Thanks,
Kyle

 

[BigInch]

Yes, and you should get a very reasonable answer, as long as you adjust a little bit and use the average flowrate in the 16" between the value of the last step and what you calculate as the current step's flowrate. Since you probably don't consider the time to accelerate the flow in the 16" between steps, you may have some error there. That flowrate may change somewhat gradually, since there is not a whole lot of head driving it. See how long it takes to accelerate the mass of water in the 16" from the previously calculated velocity and the new velocity. You could try reducing the time interval of the steps to see if there is any significant change in the answer. If there is no significant change in the time to overflow, you're good.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[jmw]

The reasonable answer is that it is easier and cheaper to fit high level alarms to shut-off the flow and not rely on operators for too much; there will always be incidents because the operator watched the wrong tank, went for coffee, died, end of shift etc.

All you will really prove in the end is that it isn't reasonable to expect operators not to foul up some time.

By the way, this sounds like one of those home work style questions....

JMW

http://www.ViscoAnalyser.com

 

[DaEarl]

jmw,

This is in fact a safety investigation of a stormwater tank at a refinery that overflowed. Not a homework problem. If there were high level alarms on the tank in question I would not be a part of the investigation. The only level gauge available was on the tank that did not overflow. And I also do not think it is unreasonable for operators to have to pay attention to the levels of a tank when they are pumping a large amount of water into them. Do you turn on your bathwater and then leave to go get coffee, take a nap, etc.

Kyle

 

[BigInch]

The strange variable in this equation is the open connecting piping between the two tanks. That doesn't seem to add up. Why have them connected? If a connection is required for some reason, I really see no reason why the connection should have been left open under the circumstances.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[DaEarl]

BigInch,

I agree. This also seems strange to me. This equalization line is also connected to a third tank. However, this third tank is out of service for repairs so the flow was blocked to Tank 2. If the other tank would have been used they would have never overfilled Tank 1.

Kyle

 

[BigInch]

The skeleton lies under the valve wheel to tank 2.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[DaEarl]

BigInch,

This is the very question I was asking the operators yesterday. I told them that if the gate valve on Tank 2 was partially closed, this was a huge problem and that the other information they gave to me like flow rates in and out are useless if they don't know what position the valves are in.

Thanks BigInch

Kyle

 

[BigInch]

Oops. If you don't know the position of the valves, everything is useless, including them.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[JStephen]

Your approach sounds reasonable to me, if I understand it correctly.

I would like to point out that if the pipe has been there a while, then your estimation of the friction in the pipe could be considerably off. Of course, any valves being partially closed would worsen the situation.

You should have some start-up time where the relative heights are adjusting, but after a while, one tank should lag the other by a constant height. You're adding 8600 GPM to both tanks, works out to 4300 gpm each, so you need to have 3200 gpm flowing through the interconnect. The head loss in the interconnect at that flow rate would be the steady-state difference in heights between the two tanks.

You might also check into those flow rates. If they're pumping water up over the tops of each tank, then it might be constant the whole while. But if they're just pumping into shell nozzles, then the flow rate should change as the tanks get fuller.

 

[DaEarl]

Thanks JStephen,

I want to add that the 7500 GPM flow rate is based on the stormwater pumps' curves. I was told by operators that the discharge pressure for the pumps operating in parallel was around 60 psig and this corresponds to 7500gpm. However, I was given some more info just yesterday that shows a timeline of sorts. What I know is that Tank 1 definitely overflowed after 3 1/2 hours. This contradicts my flowrate of 7500 GPM which contradicts the reported discharge pressure of 60 psig and the pump curves. So I am at a crossroads. It is difficult to develop a timeline based on hydraulic calculations when I am limited by the accuracy of the information given to me by the operators.

Kyle

 

[BigInch]

You might try calculating the range of possible results from both the info you received and what you think might have happened. Ie., What would have been the flowrate, given overflow at 3.5 hours? What does the pump curve say about what should have been the discharge pressure at the flowrate that gives you a 3.5 hour timeline?

Curious, what are the diameters and overflow heights of the tanks?

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[DaEarl]

BigInch,

I started working on this very approach today. The diameter of tank 1 and tank 2 are both 120ft. Both have a height of 40ft. The best timeline that I have is that after 2 hours 20 minutes, a high level alarm on tank 2 went off, which is set at 75%. This is what told the operators that if tank 2 is at a high level of 75%, tank 1 has surely overflowed. So at 3 hours, the pumps were shut down and at 3 and 1/2 hours the operators notified authorities. Also, the max height of tank 2 went to 38 feet at about 3hours and 20 minutes.

Kyle

 

[BigInch]

With the same tank diameters and heights, (are the bases at the same elevation?) I can now say,
If I close the 16" valve,
TK1 reaches 40ft in 2 hr 26 min.
TK2 reaches 40ft in 20h 30m. Just looking at that, one can see that the flowrate of TK2 must be 10 X higher (say 10000 gpm) for both tanks to overflow at anywhere near the same time.
If I take half of that 10000 from tank 1 through the 16" line, its up to 1100+5000 = 6100 now, and I notice now also that the input to tank 1 must go to 12000 in order for it to keep on rising at the same rate it was and TK2 is still only rising at 60% of the needed rate.

************************************************
With the same tank diameters and starting with 24-27, TK2 flowrate must be higher than TK1 flowrate for at least some time.

For example, to get them both overflowing at somewhere around 2h 30m, I need 7000 gpm in TK1 and 8500 in TK2.

It doesn't seem like constant flowrates being pumped into the tanks can be assumed,

If TK 2 was to reach 75% hi (30 ft level) in 2h 20m, the min flowrate from the 24 ft level was 3600 gpm,
to reach 75% (30') in 2h 20m, flowrate from the 24 ft level was 5922 gpm
to reach 40' in another hour(from the 30' level), the flowrate in was 11280 gpm
**************************************************
Both tanks have the same base elevation, right?

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[DaEarl]

BigInch,

Yes, both tanks have the same base elevation. However, that is what I see on paper. In the field, I know my eyes could be deceiving me, it looks as if tank1 is slightly below grade. Maybe 1 to 2 ft. lower than tank2.

Also I believe you are right about the rate of water being pumped. Constant flowrates from the pumps doesnt seem to check out.

I think I am just going to evaluate several cases at different flowrates, taking into account the loose timeline I was given. There is only so much the hydraulic calcs. can tell one if there isn't enough information.

The way I developed the flowrate b/w the tanks as follows: Q=((delH)^.5)/((1/2g)+(fL/D2g)^.5); where f=.018 (higher than the value reported in Cameron of .013), L=533ft. (equivalent length;all straight runs & fittings), and D=diameter of 16" pipe.

If tank 1 has a higher flowrate, as it should because tank 2 did not overflow, the flow b/w the tanks will increase as a function of the height difference b/w the tanks. In one of analyses I will assume that tank 1 has overflowed when tank2 reaches 75%

Kyle (Murphy Oil USA)

 

[BigInch]

No 1 or 2 foot difference in elevation won't do it. I was thinking maybe 50 foot or so might skew the flow enough between tanks. There really is not a lot of flow between the two tanks if there is equal elevation relative to the input flows ie, couple of hundred gpm, vs 5-7k gpm.

Rather than solve a Darcy-Weisbach or Colebrook flow equation for the 16" each timestep, I figured the system curve for the 16" based on a (Churchill) calculation of 5 cases of assumed differential heads on a 16" diam flat elevation 300 ft long pipe, plotted it in Exl, got the trendline coefficients, then in each timestep, just solve for Q (cfs) given the just previously calculated differential level, h (ft). It isn't totally accurate, but should give good enough results for this work, the 16" system equation I used was,

Q_cfs = 0.0283 * dH^2 + 0.0363 * dH, where dH in feet.

One other thing to verify, there isn't a 16" riser up to the top of a tank or anything like that is there? In other words, the 16" is connecting more or less tank bottom to tank bottom, right?

Well, it does seem there is some major discrepancies in the reported inlet flowrates. Get the ops to explain that away. What's the pump curves look like? Could the pumps be the source of the variation in inlet flowrates? Their flowrates may decrease pumping into increasing tank levels. Just another thought.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[DaEarl]

BigInch,

Yes the 16" connector does run from tank bottom to tank bottom.

By the way, what is the form of the Churchill equation?
Does it work equally well for all flow regimes or is it limited to fully developed turbulent flow? What are its advantages and disadvantages?

I am going to see who in Ops might have extensive experience with the stormwater pumps and their operation. I have a feeling that these pumps may be at the root of my problems.

Kyle (MOUSA)

 

[BigInch]

Advantages,
Noniterative solution for f,
f is valid for laminar or turbulent flow,

No disadvantages that I know of. No flow equation gives the same exact solution as Mother Nature does in the field, and even she changes her answer from time to time inexplicably over the known variables, so its certainly within the accuracy of all other equations, if not better.

[COLOR=white red]No iteration for f makes it a hands down winner in my book.[/color]

from the webpage,

http://www.mechengcalculations.com/jmm/pipe002.html

Absolutely something funny going on with the pumps. Neither of the tanks were draining anything, right? The TK2 pump (maybe both) definately were not running at constant flowrates and there is no way that the open 16" could make up the difference from TK1 with those low differential heads between the tanks so that it could add 4000-6000 gpm to the 1100 reported pump input rate and fill TK 2 fast enough to overflow at anywhere near the same time as TK1. That much I can be sure about (given present info).

Keep us posted here, or drop me a line at my e-mail (find on on my webpage). I'm really interested to know how it resolves.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[DaEarl]

BigInch,

Thanks for all of your help and interest. I am going to experiment with the Churchill equation and do my best to get to the bottom of this problem at work this week.

Once again, thanks for all the help and suggestions!

Kyle (MOUSA)

 

[tbedford]

As I read through these threads, there is much info that is either questionable or incorrect as supplied by the operators. So I have to ask, how certain are you of the original tank levels?

TAB