It is nowadays well accepted that the steady state rheological behavior of drilling fluids must be modelled by at least three parameters. One of the most often used models is the yield power law, also referred as the Herschel-Bulkley model. Other models have been proposed like the one from Robertson-Stiff, while other industries have used other three-parameter models such as the one from Heinz-Casson.
Some studies have been made to compare the degree of agreement between different rheological models and rheometer measurements but in most cases, already published works have only used mechanical rheometers that have a limited number of speeds and precision. For this paper, we have taken measurements with a scientific rheometer in well-controlled conditions of temperature and evaporation, and for relevant shear rates that are representative to normally encountered drilling operation conditions. Care has been made to minimize the effect of thixotropy on measurements, as the shear stress response of drilling fluids depends on its shear history. Measurements have been made at different temperatures, for various drilling fluid systems (both water and oil-based), and with variable levels of solid contents.
Also, the shear rate reported by the rheometer itself, is corrected to account for the fact that the rheometer estimates the wall shear rate on the assumption that the tested fluid is Newtonian. A measure of proximity between the measurements and a rheological model is defined, thereby allowing the ranking of different rheological behavior model candidates. Based on the 469 rheograms of various drilling fluids that have been analyzed, it appears that the Heinz-Casson model describes most accurately the rheological behavior of the fluid samples, followed by the model of Carreau, Herschel-Bulkley and Robertson-Stiff, in decreasing order of fidelity.