The Effect of Thixotropy on Pressure Losses in a Pipe

Drilling fluids are designed to be shear-thinning for limiting pressure losses when subjected to high bulk velocities and yet be sufficiently viscous to transport solid material under low bulk velocity conditions. They also form a gel when left at rest, to keep weighting materials and drill-cuttings in suspension. Because of this design, they also have a thixotropic behavior. As the shear history influences the shear properties of thixotropic fluids, the pressure losses experienced in a tube, after a change in diameter, are influenced over a much longer distance than just what would be expected from solely entrance effects. In this paper, we consider several rheological behaviors that are relevant for characterizing drilling fluids: Collins–Graves, Herschel–Bulkley, Robertson–Stiff, Heinz–Casson, Carreau and Quemada. We develop a generic solution for modelling the viscous pressure gradient in a circular pipe under the influence of thixotropic effects and we apply this model to configurations with change in diameters. It is found that the choice of a rheological behavior should be guided by the actual response of the fluid, especially in a turbulent flow regime, and not chosen a priori. Furthermore, thixotropy may influence pressure gradients over long distances when there are changes of diameter in a hydraulic circuit. This fact is important to consider when designing pipe rheometers.