The friction loss correlations for the Non-Newtonian fluids in a circular pipe were developed based on the experimental data collected in the small size pipe (less than 2.5” I.D.). A common horizontal well is completed with a 4.5” (ID=4”) casing or 5.5” (ID=5”) casing. During the fracturing job, up to 50 to 75 barrel/min fracturing slurry fluids (gel or surfactant fluid) would be pumped down to the hole. Based on these operation conditions, the generalized Reynolds number (based on the power law fluid) could be in an order of 1.5x106. It is a turbulent flow. The friction loss for the Non-Newtonian fluids depends on the multiple variables (fluid type, surfactant/gel load, sand load, temperature, salinity, and pipe diameter/roughness, and shear history).
My questions for the industry experts and fellows are:
1. Can we use the correlations for the Non-Newtonian fluid in the published papers to estimate the friction loss in a 5” pipe for the fracturing application? How much error would itbe?
2. If not, how can we scale-up to predict the friction loss in a large pipe?
3. Is there any database which contains the friction loss data of the Non-Newtonian fluid for the pipe flow?
Thanks for the help.
Jeff Li
I suggest you develop a mechanistic model similar to the two layer model for slurry flows through a pipeline (Shook and Wilson, 1992). In such models you can include experimental measurements (viscosity etc) and these models scale up reasonably well..
Thanks all of your comments and replies regarding to my questions!
There are a few scale-up methods which can be used to predict the friction loss for a Non-Newtonian fluid in a large pipe based on the correlation which is developed based on the data collected in the small scale pipes. There is no universal correlation to cover all key parameters' effect on the friction coefficient for Non-Newtonian fluid. Therefore, we need to conduct the experiment to collect the friction loss data under various conditions (fluid type, surfactant/gel load, sand load, temperature, salinity, and pipe diameter/roughness, and shear history). However, we need put effort to collect the data in a wisely way.
In the following paper you may find a correlation for the friction factor for Model of Ostwald-de Waele: \sigma = A \dot{\varepsilon}^\alpha
A = consistency factor
\dot\varepsilon = rate of strain
\sigma = shear stress
\alpha = behavior index alpha>1 dilatant \alpha
Don't hesitate to contact me directly to my e-mail if you need more help. If you look for me in Google you will find me. By the way, the code is in FORTRAN and is a part of a program developed by me.
Here is a calculation worksheet I made about a year ago, for a leading oil-field service Company, for pumping of a cross-linking gell stuff, a typical non-newtonian fluid.
You can play with it. Just enter the Three input parameters (viscosity, density, and flow rate), plus assigning the pipe lengths for each session of various pipe size, you will then reach an estimated total friction loss as you find as the "Sum.Friction. in bar" in the sheet.
Not sure if this tailored Version for gell pumping will also give realistic results for you, but since all the Equations are incorporated, you can simply modify anywhere until it suits Your style and need. Hope it can help a little.
If you need background material based on which I made this calculation sheet, feel free to contact me:)
If the worksheet use the power law for non-newtonian fluids let me ask you something.
What is the meaning of viscosity in the input and what is the shear rate for it?
Maybe it is the consistency factor or not.
You must review the book:
Fluid Mechanics for Petroleum Engineers_-_E. Bobok
Review the section IX.1.4.4. pag.197 of
https://www.academia.edu/11942882/Mec%C3%A1nica_y_Termodin%C3%A1mica_de_Sistemas_Materiales_Continuos
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