Numerical modeling of helical flow of viscoplastic fluids in eccentric annuli

Helical flow of viscoplastic Herschel‐Bulkley fluids in concentric and eccentric annuli with rotating inner cylinder was investigated numerically. Similar flows occur in drilling operations of oil and gas wells. A finite volume algorithm with a nonstaggered grid system and a nonorthogonal curvilinear coordinate system to handle irregular geometry of an eccentric annulus was used to analyze the problem. Papanastasiou's modification of the Herschel‐Bulkley (Yield‐Power‐Law) constitutive equation was used to model the shear rate‐dependent viscosity of a viscoplastic fluid. For a fixed axial pressure gradient, the axial flow rate increased with increasing rotational speed of the inner cylinder. The discharge, as well as torque required to rotate the inner pipe, increased with increasing eccentricity for a fixed axial pressure gradient and inner cylinder rotational speed. Discharge also increased with increasing axial pressure gradient at a fixed eccentricity and rotational speed of the inner pipe. The flow field in an eccentric annulus is complex because vigorous secondary flow is produced in addition to the primary axial helical flow. Blockage at the narrow part of the eccentric annulus, when present, intensifies this secondary flow, with the discharge decreasing initially, then increasing, and decreasing again with increasing height of the blockage.