You need flow rate, pipe size, temperature/viscosity curves and a lot of luck.

Wax liquid sounds like a non newtonian fluid to me so there will be shear thinning going on but also a significant gel break pressure.

2500 cP is rather high. This is more like polymer flow.

Suspect you'll need operating experience to see what sort of pressure is required.

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To add to LI’s point, you’ll need to test the rheology of the wax at operating temps. Things this high are usually shear thinning, which will greatly affect pressure drop.

Hi ,
Consider this paper to support your query (transport of non Newton fluid).
Good luck
Pierre

• https://files.engineering.com/getfile.aspx?folder=79a997ab-e740-4b17-bad2-9

Basically it's quite complex. Doing this without relevant knowledge and experience of such fluids means you can get it wrong by a factor of 10 both ways.

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Thank you LittleInch and TiCl4 for the feedback.

Thank you very much pierreick for sharing the paper. I will go through it.

So this is an established fact that waxes ("Paraffin Wax" and "Microcrystalline Wax") are considered as Non-Newtonian fluids? I was finding differing opinions when I searched online about that.

Was there any doubt.

Hi 1503-44, any simple reference to perform hydraulic pressure drop calculation for such a fluid? I am looking for a simple one as the calculation does not have to be exact.

There's no tricks. You just need good data for the wax's viscosity. For a simple analysis, you just need to assume that you have a uniform temperature and a steady flow rate everywhere.

If your wax has a uniform temperature everywhere, you can use the viscosity at that temperature to calculate the initial pressure drop. Problem will be that when the wax starts moving, the viscosity will change according to its velocity. The good news is that the viscosity will reduce and the wax will move faster and faster, if you keep the same pump discharge pressure. A VFD pump that will let you turn down the speed and reduce the discharge pressure as velocity increases will help you to keep it moving at a steady flow rate and speed, at which time a steady flow rate and velocity can be held constant, and as such bringing no further changes in viscosity.

You will need a table of viscosities of the wax at different shear rates, ie different velocities, at your flowing temperature.

You can analyse the pressure drop at any given flow rate, including zero, if you know the viscosity at your uniform temperature and flow rate. Calculate the velocity using the flow rate you want. Then select the proper viscosity to use according to the velocity of the wax and its temperature, Do that first zero flow. Zero velocity, highest viscosity, will give you the highest pump discharge pressure. To find the pressure drop at that and any other steady flow rate, calculate velocity then simply use the velocity adjusted viscosity. Assume you have steady state flow everywhere and calculate the pressure drop at that flow rate using Colebrook White equation, or Churchill, etc., or your software. Maybe there is one trick. You might have to trick your software into analysing the zero flow initial case. Most equations don't like zero as a flow rate. Just enter that as a very very low flow rate, such as 0.001 GPM.

But also be aware that if the flow stops, the wax may "gel". Then you need to add a gel break pressure to get ANY flow which can be significant.

Then you can also have cold spots where the wax goes really solid.

You sound like you really need to have an electrically traced and insulated system to keep the temperature uniform and as high as you possibly can.

Also find someone who has some level of experience. As I said before, you could be out by a factor of 10 in both directions.

If it's a gear pump then you won't need to turn it down once moving, just make sure you are at the right flow. But the pressure will fall as the flow reduces the viscosity.

Non Newtonian is weird stuff sometimes.

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Hi 1503-44 and LittleInch,

The line is steam-traced / insulated and will be maintained at a constant temperature of around 100^oC. I have the viscosity of the product at this temperature. I am trying to use FluidFlow software to do the hydraulics but cannot find a way to custom define the wax I have. I am using a simple Newtonian Flow method.

If it is a Newtonian fluid package, there may not be a way to enter variable shear rates.
So probably the only thing you can do is assume steady state flow, try to keep velocity the same everywhere by using only one pipe diameter and assume the temperature is equal at all points in the pipe.

Enter the viscosity at zero flow (0.001 GPM) to calculate your highest pressure loss and the pump discharge pressure for the startup case.

Make a new analysis case. Run the same calculation but at the steady state flow rate and this time use the viscosity at that steady state flow rate velocity to get the pressure drop and the pump discharge pressure for the steady state flow case.

Hi 1503-44, Thanks. So basically you are saying I need to know the viscosity of the product at close to 0 gpm flowrate and at the required flowrate (in my case 20 gpm). Should I contact the client to provide me that info for their product? I doubt they will have the viscosity at various flowrates. They have provided me the viscosity of their products at 100^oC temperature, which is the flowing temperature maintained in the heat traced / insulated line. Thanks again!

Isn't it a matter of viscosity at various shear rates? I suspect this is going to require a more sophisticated approach as the shear will vary the viscosity which will vary the flow profile across the pipe will then change the pressure required and that will change the viscosity distribution. In addition, the energy supplied by the shearing will increase the temperature which will lower the viscosity.

Seems like it's time to just set up a test - this will be especially needed to ensure the inlet conditions to the pump don't cause cavitation.

There are companies that specifically sell wax pumps and it is likely they have people experienced in dealing with just this sort of problem. Go to them for a quote on a suitable pump and see what they say.

They should have some graphs for their wax that look more or less like these,

Theose are plots of 3 SE Asian waxy crude oils.

What kind of wax is this?

Can't remember how you work out shear rate but I think pipe is more like 100s-1

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https://wiki.anton-paar.com/en/examples-of-the-cal...

https://en.m.wikipedia.org/wiki/Shear_rate

The problem with using the client's data is that unless you also hit the exact same flow rate, pipe diameter, and temperature, you won't replicate their viscosity. You need the data for viscosity vs shear rate at their given temperature. You can follow the following steps to get the standard parameters for shear-thinning liquids. The below steps are what I used in the past to get the viscosity parameters. This should give you what you need to ultimately determine pressure drop at a given flow, temperature, and pipe size.

Below is an example calculation I did on a shear-thinning polymer from viscosity vs shear rate data from a rheometer.



To get shear rate, you can reference the thread below and the post from Latexman:
https://www.eng-tips.com/viewthread.cfm?qid=199676