Introducing a Rheology Model for Non-Newtonian Drilling Fluids

An API standard drilling fluid was investigated from laminar to turbulent flow conditions using an in-house-built viscometer at speeds from 200 to 1600 RPM. A power-based method was applied to obtain the apparent viscosity and the shear stress of the water-based drilling mud (WBM) in the annulus of the viscometer. Then, a MATLAB optimization program was developed to obtain model parameters for five rheology models integrated in a generalized Herschel-Bulkley-Extended (HBE) model and two widely used 4-parameter models in drilling industry. It is found that the Bingham, Cross, and HBE rheology models have precisely matched the WBM measurements in the viscometer. A generalized Reynolds number was applied to determine the Darcy friction factor although the PL (power law model) and the HB (Herschel-Bulkley model) exhibited a nonrealistic negative shift from the laminar friction factor.