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 numerical methods applicable for calculating annular frictional pressure losses.
The topic of annular frictional pressure loss modelling has been treated in textbooks. None of these couple their models with the selection of viscosity data from measurements at the relevant shear rates.
It is earlier shown how rotation of the inner string in an annulus can complicate the flow due to establishment of Taylor vortices. There are currently no analytical methods to handle such flow. The effect of the vortices depends strongly on the fluid’s composition in addition to the flow conditions. The practical way to handle these situations are by “fingerprinting” during circulation.
In the paper examples will be presented 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. In this paper 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 vice-versa. Mathematical models will be presented. Hence a framework is given that is easier to use for digitalization and automation and in correlations including pressure, temperature and composition.