Flow modeling and in situ viscosity monitoring for a combined rotational and pressure-driven flow of a non-Newtonian fluid through a concentric annulus

Abstract

Based on the energy dissipation rate, we proposed a systematic method for quantifying the effective viscosity, effective shear rate, and flow characteristics in a drilling flow of non-Newtonian fluids in a concentric annulus subjected to a combined pressure-driven and rotational flow. Two flow parameters, i.e., the energy dissipation rate coefficient and the effective shear rate coefficient, were introduced to quantify flow characteristics, such as the relationship between pressure drop, flow rate, torque, and rotational speed, which are nearly independent of rheological behaviors. In this work, we began with flow quantification of the individual flow problem in a concentric annulus, i.e., pressure-driven flow and rotational flow, and derived expressions of two flow parameters analytically in each case. Then, we established the flow quantification method for the combined pressure-driven and rotational flow. The proposed flow modeling scheme was derived analytically with a power-law fluid and was validated for various non-Newtonian fluids, such as Carreau and Herschel-Bulkley fluids, through extensive numerical simulations. The method can be employed for the in situ viscosity measurement of drilling muds in terms of shear rate, as well as for the estimation of torque, pressure drop, and power consumption. Maximum errors between theoretical prediction and numerical simulation results in estimating torque, pressure drop, and shear-dependent viscosity were found to be 5.5%, 7.3%, and 6%, respectively.