Viscosity Models for Drilling Fluids: Viscosity Parameters and Their Use

The most common viscosity models used in the drilling industry are the Bingham, the Power-Law and the Herschel-Bulkley models. The scope of the present paper is to outline how to select the individual models, and how the models need to be re-formulated to be able to have parameters with a physical meaning. In principle, the Bingham model itself have physical parameters being the yield point and the plastic viscosity. However, the Bingham model very often only very poorly describe the viscosity in complex fluids. This yield stress can be described within a reasonable accuracy by application of the low-shear yield point. A similar problem exists with the Power-Law model resulting from the model’s absence of a yield stress. The compromise model is the Herschel-Bulkley model which contains a yield stress and a power-law term. This model describes the drilling fluid viscosity with reasonable accuracy and includes both the Bingham and Power-Law models as limit formulations. It is not possible to select fluids based on the Herschel-Bulkley traditional parameters alone. The reason is that the Herschel-Bulkley power-law term’s viscosity parameter has a unit dependent on its power-law exponent. In the present approach the fluid is described using a yield stress, a surplus stress at a characteristic shear rate of the fluid flow and finally a power-law exponent making the fluid applicable in the practical shear rate ranges. The surplus stress is no-longer dependent on other parameters. Hence, we have re-arranged the viscosity model to have independent measurable quantities.