8 replies to this topic

[kruegsw]

All,

I accidently posted this in the process simulation forum first - Sorry for the re-post in this forum.

Issue:

I need to pump a viscous, shear-thinning fluid a distance of 80 feet from the storage vessel to a receiving vessel in batches of 400 gallons each (3 or 4 batch transfers per day). Thank you in advance for your time.

 schematic for ChE Resources.bmp   327.56KB   73 downloads

I have two concerns:

1) Design Flow Rate
20 gpm forward is desired. You will see below that this does not appear to be an issue.

2) Pump Start-up
Due to the shear-thinning nature of this fluid, the highest apparent viscosity of the fluid occurs at stagnation (no shear applied). Mathematically, if you assume a very small flow rate (say, 0.001 gpm) your pressure drop through the line is enormous due to the power-law correlation (see background below). Yet, somehow I need to get this fluid moving (after which shear will thin the fluid out and allow me to increase flow even more).

Potential Solution:

Use a gear pump with variable frequency drive (VFD) as my forwarding pump. Start the pump slowly using the VFD, pumping through the recirc loop and back to the storage vessel. Ramp up flowrate slowly and fluid is sheared. When ready to forward, open valve in forwarding line and slowly pinch back control valve (CV) in recirc loop. As pressure in recirc loop rises we will begin to see flow at flow meters in forwarding line (I hope!). A pressure transmitter (PT) at the pump outlet will modulate the CV position to avoid overpressure of the pipe line. As flow proceeds forward the fluid will become less viscous due to shearing, eventually (the reduced pressure drop seen in the forwarding line will allow us to) close the CV completely. At which point we are pumping forward at the target flow rate of 20 gpm.

Background:

I have collected viscosity data, which varies with shear rate according to the following correlation:

Apparent Viscosity [cP] = 42000*(Shear Rate [1/s])^(-0.7)

Using this power law and an excel-based pressure drop spreadsheet, I have calculated the following matrix for pressure drop (in psi) at various flow rates and line size combinations:

1" Dia. 2" Dia. 3" Dia. 4" Dia. 5" Dia.
0.1 gpm 30 60 97 140 195
0.5 gpm 15 25 37 121 69
1 gpm 13 19 26 35 46
5 gpm 10 18 14 17 -
10 gpm 11 11 12 14 -
20 gpm 16 10 11 2 -
30 gpm 23 10 10 11 -
40 gpm 147 24 10 10 -
50 gpm 105 11 10 10 -
100 gpm 68 16 10 10 -
*Apologies - I had difficulty setting up this matrix, note that the top row shows different line sizes and the far left column shows varying flow rate, the numbers therein describe the pressure drop (in psi) for that combination of line size and flow rate
*NOTE that the above table assumes L=80 feet, dz=+20 ft, 4 Gate Valves, 1 Exit, and 1 misc velocity head

It appears I should be ok with 150# flanges for now, but using 300# flanges is an option for the pump start-up issue.

[Ollie]

Kruegsw,

here are a couple of remarks based on my experience with polymers. What is the nature of the fluid you intend to pump ?

- a pump with a variable frequency drive should work (at least with a volumetric pump such as a gear pump). In this case the good new is you most probably do not even need a recirculation loop (plenty of advantages ! Everybody will be happy : operation, maintenance, controls...).

- There might be a twist in the pressure drop calculation. At very low throughput hence very low shear rate is your power law validated ? Does it take into account some kind of "plateau" common for pseudoplastic fluid ? Quite often below a certain shear rate the viscosity stays constant. This will generally be the case if you handle a molten polymer or a polymer solution.
The consequence would be that at very low throughput the pressure drop would be much lower than what the current calc is showing.

- On the other hand one aspect you really need to refine in your design is the suction size of the pump : what occurs on the discharge also occurs at the suction and it is very common to see pumps starved because of the very high pressure drop on the suction size. Generally the connection from the tank to the pump should be as short and straight as possible, with a very thorough and complete heating / heat insulation if the fluid is thermoplastic.

[ankur2061]

Ollie,

Molten polymers like PET (Polyethylene Terephthalate) do not exhibit appreciable shear thinning properties & pressure drop calculations are not done on a power law basis (non-newtonian behaviour). Instead molten PET is treated as a Newtonian fluid & pressure drop calculations are done using a modified form of the Hagen-Poiseuille equation considering laminar flow characteristics. The modified form of the H-P equation used for polymer pipe pressure drop is as follows:

DP = (128*M*n*l) / pi*rho*d⁴*3600*10⁵

where:

DP = pressure drop in pipe, bar
M = Mass flow rate of polymer, kg/h
n = Dynamic Viscosity, Pa-s
l = length of pipe, m
rho = density of polymer, kg/m³
d = inside diameter of pipe, m

This above equation is applicable to flow in pipes of industrial molten polymers like PET, PBT, PTT, Nylon-6, Nylon 6,6.

However, it is imortant to note that due to the high pressure drops encountered even in short polymer pipes, appreciable temperature rise is seen which in turn reduces the viscosity of the polymer by thermal degradation. Viscosity corrections need to be done for every short segment of pipe for arriving at accurate pressure drop values for a given length of pipe.

Regards,
Ankur.

[latexman]

Stuart,

Is the viscosity of your shear-thinning fluid dependent or independent of time? Most are independent of time and since you are using a power law, I assume your fluid is time independent. If that is the case, I would not worry about the start-up issue you mentioned very much. The viscosity of the fluid will change instantaneously with the flow/shear rate imparted by the pump. My experience in this case is that no special ramping up is needed; just turn on the pump. Also, the 150 # flanges should be more than adequate. I'd start-up just recirculating; then, when that is stable, open the ABV.

Now if your shear-thinning fluid is dependent on time, then you have to worry about this issue.

Ollie's advice on extrapolating a power-law equation past the data to fit the equation is very good, and is often over looked. You need to know your rheology at all shear rates the fluid will see.

Most rheometers ramp the speed of the viscometer up and then ramp it back down. If the two curves overlap (or mostly overlap) the fluid is time independent. If it draws an oval-like shaped curve (the up and down curves do not overlap), it's time dependent.

[kruegsw]

Thank you Ollie, Ankur, and Latexman for your input.

Ollie

Fluid Description:
The fluid of interest is 6% solids in water, and the solids are known viscosity modifiers. I don't have experience with such fluids, but I don't expect it to behave as a molten polymer such as Ankur describes. The best way to describe it is “snotty”. I have a gallon container in my office…

If (somewhat gently) shaken, the fluid wobbles about but the shape is kept intact. If the container is turned on its side, the fluid will flow. If first shaken vigorously, the fluid flows much easier and remains somewhat less viscous for a short period of time. If poured into a jar, the fluid is thick enough that it falls in 'folds' of material which may result in air being trapped in portions of the jar. If I then shake that jar (with the cap on), the bubbles will coalesce near the top of the jar.

As you can see from above, this fluid is certainly pseudoplastic (shear-thinning) and potentially thixotropic (apparent viscosity decreasing with duration of stress). I am arranging for testing to see if the fluid is indeed thixotropic.

VFD and pump priming:
We thought the VFD would be needed during pump start-up to avoid priming issues when ramping up to the target flow rate too quickly (20 gpm).

This is a retrofit project so we have to live with the storage vessel in place. However, we are moving the pump as close as possible to the sunction flange and making the pipe size as big as possible (the suction nozzle to the pump is 4” dia). The suction nozzle is vertical, so we will need a 90 degree bend before the pump. Do you think it is over-kill to specify a long radius 90 degree bend?

More Viscosity Data:
I have provided an image of my viscosity vs shear rate curve below, I’ve updated my data with a second round of testing. As you can see – the fluid doesn’t appear to have an obvious plateau in the viscosity at low shear rate.

 Viscosity Curve for ChE Resources.bmp   976.59KB   62 downloads

Latexman

I do not know for certain whether the shear-thinning properties of the fluid are time dependent or not. From my description (to Ollie) above I think so, but your question has prompted me to get this tested – I will let you know.

When we pump this fluid through the pipeline for the first time, I am not worried about pump start-up. I am mostly worried about attempting to transfer it forward through an 80 foot line, full of stagnant fluid. I am not sure how to calculate the expected pressure drop at this boundary condition.

[kruegsw]

It appears the fluid I have is not a bingham fluid either, see the shear stress vs shear rate graph (calculated from the same data as in my previous post, using the relationship tau = viscosity*shear rate).

http://en.wikipedia....onian_fluid.PNG
 shear stress vs shear rate.bmp   803.3KB   30 downloads

Note that this data corresponds to "steady-state" data points (when taking data with instrument, hold shear rate constant until the apparent viscosity value hits steady state). Tomorrow I will have the data Latexman refences to test for whether the fluid's apparent viscosity is time depedent or not.

[agorag]

In the order of reducing shear, gear pumps are followed by double screw and then diaphragm and in-line-single-screw pumps.
I've seen in a food industry where the pipelines were gradually sloping upward, downstream of a single screw in-line pump, to minimise shear in the pipeline & bends.
Your scheme appears to be Ok.

[Ollie]

Agorag, I did not understand that for the fluid in question high shear rate was to be avoided ? This is why I was advising gear pump, to minimize pressure drop thanks to high shear.

Kruegsw, I do not have any clue regarding the impact of the long radius elbow. It helps in term of pressure drop in case of a Newtonian fluid, but I am not sure of the interest of it for a non newtonian fluid.

Regarding your viscosity / shear rate curve it usually is displayed under (logarithm viscosity) / (shear rate) form. you might want to display it under this form and talk with gear pump suppliers based on it. They should be able to give you sound advice by comparing your curve with their past experiences.

Good luck,

Ollie

[kruegsw]

I have procured shear stress vs shear rate data, with shear ranging 6 orders of magnitude (0.001 to 1000 reciprocal seconds). The fluid behaves according to a power law for that entire range, deviating only at very low shear rates (less than 0.01 1/s). With this new correlation I expect far less pressure drop than I had originally feared. The shear stress vs shear rate curve for this fluid approaches the origin, so there does not appear to be a significant yield stress - this resolves much of my pump-startup concerns.

If anybody is interested, I can provide a (sufficiently sterlized) shear stress vs shear rate graph, viscosity vs shear rate graph, shear rates for expected flow rates and pipe size combinations, and pressure drop vs flow graph. The numbers aren't so much important as understanding how these parameters affect one another.

Thank you all for your help.

Edited by kruegsw, 17 June 2010 - 05:24 PM.