Pressure drop through the pipeline 1

[rutherford703]

This is about a cross country pipeline. We have pressure transmitters at both the entrance of the piping and the end of the piping. The pressure drop is the difference between the two pressure transmitters. With each pressure drop, we can get the corresponding flow rate. All data are listed in the attached excel file.

The fluid properties are as follow:

Composition: (wt%)
Bitumen: 60%
Water: 30%
fine solid: 10%
Fluid temperature: 53C
Fluid viscosity: 50 CP
Fluid density: 1070 kg/m3

Piping Data:
Piping ID: 35 inches
piping length: 40 km
Piping material: CS

The fluid can be treated as Newtonian fluid.

Based on the pressure drop calculation formula:
Delta P=K*l/d*(ro)*u^2/2/g
I will expect that I can get a constant number by calculating u^2/(delta p). However, the plot of u^2/(delta p) vs u clearly shows a u power 2 relationship. Can someone comment why?

Thanks in advance.

 

[ione]

Well the K in your formula is the friction factor. You should go deeper with the Darcy Weisbach equation.

http://en.wikipedia.org/wiki/Darcy–Weisbach_equation

http://en.wikipedia.org/wiki/Darcy_friction_factor_formulae

 

[BigInch]

You also have too much disassociated data to find any one neat relationship. If you do find one, you will have too much variation to make it a useful predictor. I plotted just your Q,dP data in normal X,Y cartesian coordinates and those dots are all over the place. You get the same flowrate of 800 l/s through a very wide range of pressure drops varying from 1000 to 2000 kPa. Then you look again at 300 l/s and find out that it also can be had with the same range of pressure drops 1000 to 2000 kPa.

NOW I SEE WHY.
Composition: (wt%)
Bitumen: 60%
Water: 30%
fine solid: 10%

This mixture is HIGHLY NON-NEWTONIAN! Shear rate (friction factor), will vary with velocity. Flow pattern will vary with velocity, sometimes the bitumen flowing in the center, the water against the pipe wall. Friction and flow pattern will vary with the degree of emulsion present at any time. You will probably not be able to hold the same temperature over the 40 km pipeline as well, so basic viscosity will tend to increase as temperature drops. Apparent viscosity will decrease with velocity. You will start with a low flowrate and high pressure drop and after a couple of weeks you will wind up with a high flowrate and a low pressure drop. In short, you are wasting your time looking to dumb this flow relationship down to any kind of a simple relationship. It's a big job for a very good hydraulics engineer using a pipeline simulator such, as Stoner Pipeline Simulator. I have done a number of hot, heavy crude lines using diluents, not water, and they are a whole lot of work documenting all the flowrates and pressure drops possible with various inlet temperatures, outlet temperatures, soil temperatures and percent of diluents composing the mix. Good luck.

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

 

[rutherford703]

Thanks Ione for your reply.
Thanks BigInch for your opinion. I tend to agree with you that the assmption of Newtonian flow is not correct. I feel a little bit guilty to put a large file on the forum (even opening the attachment takes some time). All the data are from plant record for 5 years with 1h interval, which means that the trend shows the system real behaviour.

BigInch, As I said, this a cross country pipeline, I am trying to find a way to monitor the pipeline running to find potential leakage. I saw your previous recommendation of using pressure drop calculation to monitor the piping running status even to find the leaking point. As you said, theoretically your recommendation will work. In the real world, the situation will be more complicated.

For our plant, we use flow rates to monitor the pipeline running status. We have flow meters at the both ends; however, the flow rates from these flow meters hardly match each other, especially during transient times - downstream branches open and close. Sometimes, these transient times last a few hours instead of a few minutes based transient pressure wave theory. The flow difference frequently trigged alarm.

My intent is to modify the alarm setting based on your previous recommendation. Alarm is trigged only if there is a negative flow rate difference from the down stream flow meters. Once the alarm is trigged, I will use the formula regressioned from the past running data to calculate the exit pressure. If the pressure from the exit pressure transmitter is constantly blow the calculated value, I will treat the alarm as a real alarm.

Any thought is appreciated.

 

[BigInch]

Non-Newtonian flow has very loose relationships at times, but at others might be relatively tight. If you try to correlate simply by using Newtonian relationships it is likely that you will have far too many alarms and your operators will turn them off, or even worse, learn to randomly investigate some then learn to ignore them completely. Better off without them.

I'd try something like using neural networks to make predictions, mostly because I like neural networks, but you will need more variables than just pressure and flowrates. I would think your training data needs to be grouped pairs, inlet pressure and inlet flow, versus outlet pressure and outlet flow and all will have to incorporate time lags of outlet data to changes in inlet data. You may also get better results correlating inlet and outlet pressures, rather than pressure drops. I'd think you'd need to add temperatures too, if you have any variations that you can relate to temperatures. It's possible that you have entirely different relationships at different flowrates that will persist for long time periods for lower flowrates and shorter times at higher flowrates.

Interesting problem. My best advice is to get hold of a simulator and do leak detection by continuous comparison between actual realtime SCADA input data vs a parallel, hot running, accurate hydraulic model. I don't think you will be able to create anything else that will have a chance of being a useful tool. Otherwise I think you will be more likely to develop a tremendous source of confusion. Even if it did work with loose Newtonian relationships, you will not have any sensitivity. What good would it do to have a 200 m3/hr leak for 4 hours before you even had your first thought you might have one?

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

 

[Latexman]

More bad news I'm afraid. Those loose non-Newtonian relationships BI spoke of are almost always for laminar flow. The flow is not laminar.

Good luck,
Latexman

 

[Latexman]

The only reference I know on turbulent non-Newtonian flow is Skelland. My copy is home. I'll take a look at it this evening and chime in if I see anything useful. Maybe others know another reference.

Good luck,
Latexman

 

[rutherford703]

Thanks BigInch and Latexman!

Currently we rely on flow meters (two flow meters at the upstream one on each branch, and four flow meters at the downstream one on each branch). These flow meters are venturi type with special design for the service but not within the accuracy of +-0.5% as BigInch said. The compounded errorness makes the flow rate downstream sometimes consistently higher than the upstream flow rates while other times the downstream flow rates are consistently lower than the upstream flow rates. The piping is an underground piping with a river crossing. We are located at a remote area. Leaking to the ground may not have a big environmental impact. However, if leaking to the river, it will create a biological desaster.

 

[stanier]

You may then choose to put flow meters either side of the river where there is the highest environmental risk.

One of the difficulties is that in lower flow conditions the solids may hold up in sections of [tt][/tt]the pipeline and thus increase the apparent density. Whilst changing flow the readings may vary considerably as the line packs with solids as the fluid properties vary with density. Ie a less dense fluid flowing over settled solids.

Rather than trying t model the pipeline more instrumentation may be your solution. You then have a 12" to the foot analogue computer.

“The beautiful thing about learning is that no one can take it away from you.”
---B.B. King

http://waterhammer.hopout.com.au/

 

[BigInch]

Might try something like fiberoptic leak detection cable.

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

 

[Latexman]

Chapter 6 (54 pages and 94 equations!) in A. H. P. Skelland's Non-Newtonian Flow and Heat Transfer is on non-Newtonian turbulent flow. It might be worth getting, but at only 50 cP, I really wonder what the rheology of this stuff looks like. Any data on that? I bet it's almost Newtonian.



Good luck,
Latexman

 

[BigInch]

That's probably the apparent viscosity at 53C.
From the description above it appears that it could be similar to "Orimulsion".

"Raw bitumen has an extremely high viscosity and specific gravity between 8 to 10 API gravity, at ambient temperatures and is unsuitable for direct use in conventional power stations. Orimulsion is made by mixing the bitumen with about 30% fresh water and a small amount of surfactant. The result behaves similarly to fuel oil. An alcohol-based surfactant recently replaced the original phenol-based version; improving the transport properties of the fuel and eliminating the health concerns associated with the phenol group of surfactants.
........
It is a non-Newtonian fluid, and if it is allowed to cool below 30 °C, it will 'set'. Pumping becomes impossible, and there is no way of restarting operations or the flow through the pipeline again.

http://en.wikipedia.org/wiki/Orimulsion

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

 

[Latexman]

Agreed. It seems that to have a chance to progress the accuracy of leak detection monitoring using the existing system (no/min. investment) from a theoretical standpoint would require a much better understanding of the rheology than just an apparent viscosity at a single temperature. Yes, interesting problem.

Double containment with monitoring at the river crossing would reduce risk/liability tremendously. Does it go under or over the river?

Good luck,
Latexman

 

[rutherford703]

I am very appreciated all your opinions.

I feel terrible sorry for some wrong presenting data. I rechecked the LDT and the viscosity for the fluid (we called froth) is 25,000 CP at 50C! My god, where my memory came from! There is another number showing the viscosity is 540 CP at 80C on mass balance table. The LDT does not show pressure drop for the design flow rate. I am new to this team. I don't know if the pipeline is above or under the river water. With that high viscosity, I guess the fluid is running in laminar flow regime.

Since we have runned the pipeline for more than six years without incidents, extra investment may need to be justified.

 

[rutherford703]

If the flow is in the laminar regime and psudo-Newtonian fluid applies, the friction factor should be proportional to 1/Q based on the friction factor calculation:

f=16/Re

while the regression forumla shows the relationship is

f=aQ^2+bQ+c

so that the fluid is highly non-newtonian?

 

[BigInch]

I kinda thought that might have been a mistake.

If an emulsion, it is probably laminar. If there isn't much mixing between water and bitumen, you could have turbulent water flow and laminar bitumen flow.

I had turbulent at the beginning of the pipeline and laminar at the end. many combinations are possible, especially when changing flowrates.

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

 

[Latexman]

The fluid is highly shear thinning!

The next question is - what was the shear rate (sec[sup]-1[/sup])of the spindle when you measured 25,000 CP at 50C? Using a Brookfield? If so, get a copy of their More Solutions to Sticky Problems and study it. Also, which spindle you using? If you are lucky, the viscosity can be measured at 3 different RPMs (shear rates) and you can initially develop a crude power law model. Be sure the shear rates when measuring the apparent viscosity correspond to the range of shear rates in the pipeline! Also, there is a series of articles in Chemical Engineering magazine by M. H. Wohl. It is titled Designing for Non-Newtonian Fluids and they appeared in the Jan. 15, Feb. 12, March 25, April 8, May 6, and June 3, 1968. My advice is get/buy them! Try to track down a copy of Skelland too. It's out of print, but it pops up on the used book sites from time to time. There are other graduate level books on the subject out there too. I don't know how good they are though.

You have to understand the rheology before you can tackle the modelling! There's no way out of that.

And, you probably have to become the non-Newtonian flow expert, or else hire/contract one. (No, I don't want the job.)

Good luck,
Latexman

 

[Latexman]

N[sub]Re[/sub] ~ 35, so very laminar (overall). As mentioned, it may phase separate and change dynamically along the pipeline. Do you add surfactants to stabilize it?

Good luck,
Latexman

 

[BigInch]

I believe that 25,000 is the viscosity of the bitumen alone at ambient conditions and it's probably around 500 or less at 50C, but I'm not familiar with water emulsions, only bitumen & diluent mixtures.

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

 

[Latexman]

Is bitumen frothy? I thought he was talking about the mixture/emulsion.

Good luck,
Latexman