Abstract
The flow of a non-Newtonian fluid in an annulus with inner cylinder rotation and eccentricity is characterized by sophisticated flow patterns that may require vast computational power or time to be resolved. The problem complexity increases for higher flow rates and rotational frequencies, having to consider the effects of axial and tangential turbulent motion, in addition to the shear-thinning and yield stress properties of many non-Newtonian fluids. Furthermore, annulus eccentricity breaks the rotational symmetry causing non-uniform axial flow. The resulting complex flow patterns affect the axial frictional pressure drop, which is often the main parameter of interest for engineering applications. Due to the added flow complexity, drilling hydraulics models are often based on purely axial flow, while the effects of rotation and eccentricity on the frictional pressure drop can be estimated and applied via empirical correlations. Models and correlations have been developed for inner cylinder rotation and eccentricity separately. However, limited work has been done on correlations that capture the combined effect, and generally accepted methods do not exist. There is thus a need for improved models for describing the combined effect of rotation and eccentricity on the frictional pressure drop. In this paper we combine experimental flow loop data, numerical simulation, and analytical calculation in an improved approach towards empirical modelling of the frictional annular pressure drop in Herschel-Bulkley type fluids with varying inner cylinder rotation and eccentricity. The need for a correlation that captures the combined effect of rotation and eccentricity has been demonstrated through numerical simulation, showing the dependence between the effects. The presented modelling is based on dimensionless quantities for generalizability and scalability across different annular flow systems.