An Explicit and Continuously Differentiable Flow Equation for Non-Newtonian Fluids in Pipes
- Kristian Gjerstad (Teknova AS and Aker Solutions) | B. Erik Ydstie (Carnegie Mellon University) | Rune W. Time (University of Stavanger) | Knut S. Bjørkevoll (SINTEF Petroleum Research)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2014
- Document Type
- Journal Paper
- 78 - 87
- 2013. Society of Petroleum Engineers
- 1.6 Drilling Operations
- 3 in the last 30 days
- 430 since 2007
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A simple model approximates Herschel-Bulkley (HB) non-Newtonian fluids in laminar flow in pipes. It is continuously differentiable and explicit in the frictional pressure gradient. Such properties are needed for control, real-time optimization, and prediction in drilling operations. The accuracy of the new model is evaluated by comparing it with a numerical implementation of the implicit HB model and some representative approximations used in the literature. Very little loss in accuracy is experienced compared with the implicit solution.
|File Size||732 KB||Number of Pages||10|
Bailey, W. J. and Weir, I. S. 1998. Investigation of Methods for DirectRheological Model Parameter Estimation. J. Pet. Sci. Eng. 21 (1): 1-13. http://dx.doi.org/10.1016/S0920-4105(98)00040-0.
Barnes, H. A., Hutton, J. F. and Walters, K. 1989. An Introduction toRheology. Amsterdam, the Netherlands: Elsevier Science Publishers.
Beaulne, M. and Mitsoulis, E. 1997. Creeping Motion of a Sphere in TubesFilled with Herschel-Bulkley Fluids. J. Non-Newton Fluid 72(1): 55-71. http://dx.doi.org/10.1016/S0377-0257(97)00024-4.
Bird, R. B., Dai, G.C. and Yarusso, B. J. 1983. The Rheology and Flow ofViscoplastic Materials. Rev. Chem. Eng. 1: 1-70.
Bourgoyne, A. T. 1986. Applied Drilling Engineering, Vol. 2.Richardson, Texas: Textbook Series, SPE.
Davison, J. M., Clary, S., Saasen, A., et al. 1999. Rheology of VariousDrilling Fluid Systems Under Deepwater Drilling Conditions and the Importanceof Accurate Predictions of Downhole Fluid Hydraulics. Paper SPE 56632 presentedat the SPE Annual Technical Conference and Exhibition, Houston, Texas, 3-6October. http://dx.doi.org/10.2118/56632-MS.
Filip, P. and David, J. 2003. Axial Couette-Poiseuille Flow of Power LawViscoplastic Fluids in Concentric Annuli. J. Pet. Sci. Eng. 40 (3-4): 111-119. http://dx.doi.org/10.1016/S0920-4105(03)00107-4.
Fredrickson, A. and Bird, R.B. 1958. Non-Newtonian Flow in Annuli. Ind.Eng. Chem. 50 (3): 347-352. http://dx.doi.org/10.1021/ie50579a035.
Gjerstad, K., Time, R. and Bjørkevoll, K. S. 2012. Simplified Explicit FlowEquations for Bingham Plastics in Couette-Poiseuille Flow - For Dynamic Surgeand Swab Modeling. J. Non-Newton Fluid 175-176: 55-63. http://dx.doi.org/10.1016/j.jnnfm.2012.03.002.
Govier, G. W. and Aziz, K. 2008. The Flow of Complex Mixtures inPipes, second edition. Richardson, Texas: Textbook Series, SPE.
Hanks, R. W. 1979. The Axial Laminar Flow of Yield-Pseudoplastic Fluids in aConcentric Annulus. Ind. Eng. Chem. Proc. Des. Dev. 18 (3):488-493. http://dx.doi.org/10.1021/i260071a024.
Hemphill, T., Campos, W. and Pilehvari, A. 1993. Yield-Power Law Model MoreAccurately Predicts Mud Rheology. Oil Gas J. 91 (34):45-50.
Herschel, W. H. and Bulkley, R. 1926. Measurement of Consistency as Appliedto Rubber-Benzene Solutions. Proc. ASTM 26: 621-630.
Liu, Y.-Q. and Zhu, K.-Q. 2010. Axial Couette Poiseuille Flow of BinghamFluids Through Concentric Annuli. J. Non-Newton Fluid 165(21-22):1494-1504. http://dx.doi.org/10.1016/j.jnnfm.2010.07.013.
Merlo, A., Maglione, R. and Piatti, C. 1995. An Innovative Model forDrilling Fluid Hydraulics. Paper SPE 29259 presented at the Asia Pacific Oil& Gas Conference, Kuala Lumpur, Malaysia, 20-22 March. http://dx.doi.org/10.2118/29259-MS.
Mitchell, R. F. and Miska, S. Z. 2011. Fundamentals of DrillingEngineering. Richardson, Texas: Textbook Series, SPE.
Peixinho, J., Nouar, C., Desaubry, C., et al. 2005. Laminar Transitional andTurbulent Flow of Yield Stress Fluid in a Pipe. J. Non-Newton Fluid 128 (2-3): 172-184. http://dx.doi.org/10.1016/j.jnnfm.2005.03.008.
Reed, T. D. and Pilehvari, A. A. 1993. A New Model for Laminar,Transitional, and Turbulent Flow of Drilling Muds. Paper SPE 25456 presented atthe Production Operations Symposium, Oklahoma City, Oklahoma, 21-23 March. http://dx.doi.org/10.2118/25456-MS.
Skelland, A. H. P. 1967. Non-Newtonian Flow and Heat Transfer. NewYork City, New York: John Wiley and Sons.
Subramanian, R. and Azar, J.J. 2000. Experimental Study on Friction PressureDrop for Nonnewtonian Drilling Fluids in Pipe and Annular Flow. Paper SPE64647presented at International Oil and Gas Conference and Exhibition in China,Beijing, China, 7-10 November. http://dx.doi.org/10.2118/64647-MS.
Weir, I. S. and Bailey, W. J. 1996. A Statistical Study of RheologicalModels for Drilling Fluids. SPE J. 1 (4): 473-486. http://dx.doi.org/10.2118/36359-PA.
Whittaker, A. 1985. Theory and Application of Drilling FluidHydraulics. Dordrecht, the Netherlands, and Boston, Massachussetts: D.Reidel Publishing Company and International Human Resources DevelopmentCorporation.