The concept of an "Effective" diameter is introduced for the flow of drilling muds through annuli. This new diameter accounts for both annular geometry and the effects of a non-Newtonian fluid. It provides the link between Newtonian pipe flow and non-Newtonian flow through concentric annuli. The method is valid in any flow regime and can be used to determine whether a non-Newtonian flow is laminar, transitional, or turbulent. An analytical procedure is developed for computing frictional pressure gradients in all three flow regimes. The analysis also quantifies how flow transition is delayed by increasing the yield stress of a fluid. In addition, it is shown that transition in an annulus is delayed to higher pump rates as the ratio of inner to outer diameter increases. Furthermore, the method accounts for wall roughness and its affects on transitional and turbulent pressure gradients for non-Newtonian flow through pipes and concentric annuli. Finally, the method runs on a 386 PC in only a few seconds.

Keywords:
roughness, drilling fluid selection and formulation, reynolds number, drilling fluids and materials, shear rate, drilling fluid property, drilling fluid formulation, metzner, viscosity, pressure gradient
Subjects:
Drilling Fluids and Materials, Well & Reservoir Surveillance and Monitoring, Drilling fluid selection and formulation (chemistry, properties), Drilling fluid management & disposal
Copyright 1993, Society of Petroleum Engineers
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