Mathematical Modelling of the Flow Rate in a Marsh Funnel

  • Ahmad Sedaghat
  • Mohamed Abdulsalam Ali Omar
  • Sadeq Damrah
  • Mohamed Gaith


Marsh Funnel is the practical method to measure viscosity of drilling fluids. Nanoparticles may be added to drilling fluids to reduce skin friction, reduce energy consumption, and increase life cycle of drilling equipment for an energy efficient environment in oil and gas industry. The discharge time is the only measured parameter during operation. However, it is possible to measure the funnel volume discharge rate and the corresponding time from which it may be possible to determine some additional rheological parameters such as yield point, apparent viscosity and plastic viscosity of drilling lubricants. In this study, a new approach is introduced for mathematical modelling of the discharge flow rate in the Marsh Funnel using a deformable control volume representation of continuity equation. Accurate calculation of discharge rate is the fundamental parameter for determining other rheological properties of complex non-Newtonian fluids particularly when nanoparticles are added for enhancing lubrication or for protecting shale against instabilities. Results of the present mathematical modelling is compared with some experimental available measurements of Newtonian fluid in the Marsh Funnel and explained.


1. Meng, X.; Zhang, Y.; Zhou, F.; Chu, P. Effects of carbon ash on rheological properties of water-based drilling fluids, J. of Pet. Sci. and Eng. 2012, 100, 1–8. 
2. Guria, C.; Kumar, R.; Mishra, P. Rheological analysis of drilling fluid using Marsh Funnel, J. of Pet. Sci. and Eng. 2013, 105, 62–69. 
3. Sönmez, A.; Verşan Kök, M.; Özel, R. Performance analysis of drilling fluid liquid lubricants, J. of Pet. Sci. and Eng. 2013, 108, 64–73. 
4. Almahdawi, F.H.M.; Al-Yaseri, A.Z.; Jasim, N. Apparent Viscosity Direct from Marsh Funnel Test, Iraqi J. of Chem. and Pet. Eng. 2014, 15(1), 51- 57. 
5. Balhoff, M.T.; Lake, L.W.; Bommer, P.M.; Lewis, R.E.; Weber, M.J.; Calderin, J.M. Rheological and yield stress measurements of non-Newtonian fluids using a Marsh Funnel, J. of Pet. Sci. and Eng. 2011, 77, 393–40. 
6. Schoesser, B.; Thewes, M.; Marsh Funnel testing for rheology analysis of bentonite slurries for Slurry Shields, ITA WTC 2015 Congress and 41st General Assembly, May 22-28, 2015, Lacroma Valamar Congress Center, Dubrovnik, Croatia. 
7. Cremonesi, M.; Ferrara, L.; Frangi, A.; Perego, U. Simulation of the flow of fresh cement suspensions by a Lagrangian finite element approach, J. Non-Newtonian Fluid Mech. 2010, 165, 1555–1563. 
8. Mohammed, M.H.; Pusch, R.; Knutsson, S.; Hellström, G. Rheological Properties of Cement-Based Grouts Determined by Different Techniques, Engineering, 2014, 6, 217-229. 
9. Abdulrahman, H.A. et al., Calculation Rheological Properties of Water Base Mud Using Marsh Funnel, B.Sc. Dissertation, Sudan University of Science and Technology, 2015. 
10. Munson, B.R.; Huebsch, W.W.; Rothmayer, A.P. Fundamentals of Fluid Mechanics, 7th ed., Wiley, 2012.

Mathematical Modelling of the Flow Rate in a Marsh Funnel
How to Cite
SEDAGHAT, Ahmad et al. Mathematical Modelling of the Flow Rate in a Marsh Funnel. Journal of Energy Technology Research, [S.l.], v. 1, n. 1, p. 1-12, feb. 2017. ISSN 2514-4715. Available at: <>. Date accessed: 01 may 2017. doi: