Non-Newtonian CFD Modelling of a Valve for Mud Pumps

Non-Newtonian CFD Modelling of a Valve for Mud Pumps

F. Concli C. Gorla

Free University of Bolzano/Bozen, Faculty of Science and Technology, Bolzano, Italy

Politecnico di Milano, Department of Mechanical Engineering, Milano, Italy

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| Citation



Mud pumps, like those used in the field of oil well drilling, are typically of the reciprocating type and are designed to circulate drilling fluid under high pressure down the drill string and back up the annulus. automatic valves must be applied to the fluid end in order to grant the desired pumping effect. from the engineering point of view, the design of the valve geometry must ensure that the phenomenon of cavitation does not occur and that, during the pumping action, the stiffness of the reaction coil spring is able to avoid reaching the condition of end stroke of the valve. Cavitation consists in the development of vapour cavities in the liquid phase. Inside the cavities, the pressure is relatively low. When subjected to higher pressure, the voids implode and generate an intense shock waves that promote the wear for the components (i.e. valve, valve seat, etc.). A deep understanding of the fluid behaviour is crucial for an effective design. Transient CfD simulations of the valve opening have been performed using a non-Newtonian fluid model able to describe the drilling muds. after a deep literature review, the Herschel-Bulkley model was selected as the most suitable for emulating the drilling mud. With the abovementioned approach, the reaction spring and design the valve seat to avoid premature wear phenomena were properly designed. The simulations have been also done considering a Newtonian fluid behaviour, in order to better understand the importance of considering the non-Newton behaviour for an effective designa.


cavitation, CFD, concrete, drilling mud, Herschel-Bulkley, pump, valve


[1] Shah, S.R., Jain, S.V., Patel, R.N. & Lakhera, V.J., CFD for centrifugal pumps:A review of the state-of-the-art. Procedia Engineering, 51, pp. 715–720, 2013.

[2] Ansys.

[3] OpenFOAM(R).

[4] Concli, F. & Gorla, C., Windage, churning and pocketing power losses of gears: differentmodelling approaches for different goals [Wirkungsgrad und Verluste vonZahnradgetrieben:Verschiedene Methoden für verschiedene Anwendungen]. ForschungFigure 9: Pressure contours at different equilibrium positions (a).im Ingenieurwesen/Engineering Research, 80(3–4), pp. 85–99, 2016.

[5] DualSPHysics.

[6] NanoFluidX.

[7] Bietresato, M., Friso, D. & Sartori, L., An operative approach for designing and optimisinga pipeline network for slurry collection from dairy farms across a wide geographicalarea. Biosystems Engineering, 115(3), pp. 354–368, 2013.

[8] Concli, F. & Gorla, C., Numerical modelling of the churning power losses in planetarygearboxes: An innovative partitioning-based meshing methodology for the applicationof a computational effort reduction strategy to complex gearbox configurations.LubricationScience, 29(7), pp. 455–474, 2017.

[9] Concli, F., Thermal and efficiency characterization of a low-backlash planetary gearbox:An integrated numerical-analytical prediction model and its experimental validation.Proceedings of the Institution of Mechanical Engineers, Part J: Journal of EngineeringTribology, 230(8), pp. 996–1005, 2016.

[10] Concli, F., Gorla, C., Stahl, K., Höhn, B.-R., Michaelis, K., Schultheiß, H. &Stemplinger,J.-P., Load independent power losses of ordinary gears: Numerical andexperimental analysis. 5th World Tribology Congress, WTC 2013, 2, pp. 1243–1246, 2013.

[11] Herschel, W.H. & Bulkley, R., Konsistenzmessungen von Gummi-Benzollösungen.Kolloid-Zeitschrift, 39(4), pp. 291–300, 1926.

[12] Herzhaft, B., Rousseau, L., Neau, L., Moan, M. & Bossard, F., Influence of temperatureand clays/emulsion microstructure on oil-based mud low shear rate rheology. SPEJournal,8(3), pp. 211–217, 2003.

[13] Kenny, P. & Hemphill, T., Hole-cleaning capabilities of an ester-based drilling fluid system.SPE Drilling & Completion, 11(1), pp. 3–9, 1996.

[14] Walters, K., An Introduction to Rheology, Vol. 3, Elsevier Science, 1989.

[15] Rao, M.A., Rheology of Fluid, Semisolid, and Solid Foods, Food Engineering Series,Springer Science+Business Media: New York, 2014.

[16] Abrahamsson, J., Product losses of highly viscous products in pipe systems duringdisplacement processes, Thesis for the Degree of Master of Science Division of FluidMechanics Department of Energy Sciences Faculty of Engineering Lund University, 2011.

[17] Nguyen, V.H., Rémond, S., Gallias, J.L., Bigas, J.P. & Muller, P., Flow of Herschel–Bulkley fluids through the Marsh cone. Journal of Non-Newtonian Fluid Mechanics,139(1–2), pp. 128–134, 2006.

[18] Concli, F. & Gorla, C., Analysis of an automatic valve geometry for concrete and drillingmud pumps to avoid cavitation: Non-newtonian CFD modelling. WIT TransactionsonEngineering Sciences, 120, pp. 209–217, 2018. doi: 10.2495/AFM180211

[19] Concli, F. & Gorla, C., Analysis of the oil squeezing power losses of a spur gear pairby mean of CFD simulations. ASME 2012 11th Biennial Conference on EngineeringSystems Design and Analysis, ESDA 2012, 2, pp. 177–184, 2012.

[20] Concli, F. & Gorla, C., Oil squeezing power losses in gears: A CFD analysis. WITTransactions on Engineering Sciences, 74, pp. 37–48, 2012.

[21] Concli, F., Della Torre, A., Gorla, C. & Montenegro, G., A New Integrated Approachfor the Prediction of the Load Independent Power Losses of Gears: Development of aMesh-Handling Algorithm to Reduce the CFD Simulation Time. Advances in Tribology,2016, art. no. 2957151, 2016.