Annular Frictional Pressure Losses

The most common viscosity models used in the drilling industry are the Bingham, the Power-Law and the Herschel-Bulkley models. In addition, it is common to refer to the low-shear yield-point. The scope of the present paper is to discuss viscosity models and pressure drop model for calculating hydraulic properties for field applied drilling fluids. The commonly used Herschel-Bulkley consistency parameter k is found inadequate in describing fluid properties properly for field applications, as it has a unit dimension dependent on n. Hence, the model is not optimal for intuitive understanding or digital applications. Therefore, the Herschel-Bulkley model is re-written, based on Nelson and Ewoldt (2017), and base its parameters directly on the yield stress and the additional or surplus shear stress at a pre-determined shear rate relevant for the actual flow situation (Saasen and Ytrehus, 2018). The Herschel-Bulkley model includes the Bingham and power-law models by selection of their parameters. The appearance of a non-zero yield stress makes all annular calculations complicated. Two yield stress boundaries with constant velocity will be introduced, leading to a complex set of equations. Often, an iterative procedure is selected to be able to calculate the flow equations. Therefore, to simplify the calculations, it is common to use the power-law model for the fluid flow calculations. None of the common couple models with the selection of viscosity data from measurements conducted at relevant shear rates. In the presented approach the parameters are selected from a realistic range of shear rates. In the presentation examples will be given showing how the Herschel-Bulkley fluid can be transferred to simple models for axial flow in an annulus where the inner cylinder does not rotate. It is common to use the narrow slot approximation. This method was used by Founargiotakis et al. (2008). In the presentatuin both the modified Herschel-Bulkley model with dimensionless shear rates and the traditional model where the consistency depends on the shear rate will be presented. The dimensionless shear rate model can easily be translated back to the traditional form and visa-versa. Mathematical models will be presented. Hence a framework is given that is easier to use in correlations including pressure, temperature and composition.