Non-Newtonian flows in highly eccentric annuli with cuttings beds, washouts and fractures, encountered in cementing and managed pressure (and underbalanced) drilling, are solved without crude slot flow and hydraulic radius approximations. The nonlinear partial differential equations, written to customized, boundary-conforming, curvilinear coordinate grid systems providing high physical resolution in tight spaces, are solved exactly with no-slip conditions, and detailed velocity, apparent viscosity, shear rate and viscous stress fields are computed for pressure drop, hole cleaning and other applications. For fluids with yield stress, well known uncertainties related to plug zone size and shape are fully resolved using generalized Bingham plastic and Herschel-Bulkley relations applicable across transition boundaries (determined iteratively as part of the solution) reaching into and across the plug. Two-dimensional, single-phase, steady flow simulations, solved rapidly using finite difference methods, provide detailed numbers and color displays for all physical quantities within seconds, with excellent numerical stability for all fluid types with and without yield stress. Formulations for steady-state casing or drillpipe longitudinal translation and rotation are described, and extensions to model transient incompressible effects associated with starting, stopping and periodic movement, important in evaluating cement-mud displacement efficiency, axial-helical cuttings transport, swab-surge, and jarring remedies for freeing stuck pipe, are discussed. Practical problems are presented and the advantages over existing models are described. These methods extend those in the author's books Borehole Flow Modeling in Horizontal, Deviated and Vertical Wells (Gulf Publishing, 1991) and Computational Rheology for Pipeline and Annular Flow (Elsevier, 2001).

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