Publisher Summary This chapter focuses on the annular models conceived in Borehole Flow Modeling. General methodologies for non-Newtonian duct flows with arbitrary geometric cross-sections are also presented. Many algorithms are presented that show how duct simulation methods can be combined with solids deposition and erosion models to describe wax buildup and hydrate formation in deep subsea flowlines. The model is derived from first principle using the exact equations of continuum mechanics. These equations are written in coordinates natural to the annular geometry considered. Then second-order accurate solutions for the axial velocity field, shear rate, shear stress, apparent viscosity, Stokes product, and dissipation function are obtained. Rotational effects are important when drilling at low flow rates, or when rotating the casing during cementing. In drilling, the presence of dynamically stable fluid-dynamic obstacles in the annular mainstream means that cuttings transport will be impaired. These stationary structures may affect bed buildup both upstream and downstream. In cementing applications, their presence in the mud or the cement slurry would suggest ineffective mud displacement. It is found that the fractional blockage inferred from the presence of any closed streamlines provides a qualitative danger indicator for cuttings removal and cement displacement.