Mathematical Modelling of the Flow Rate in a Marsh Funnel
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.
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