A theoretical study of the flow of slightly compressible non-Newtonian fluids in eccentric annuli with entrance effects.

摘要

The steady, laminar flow of a cement slurry in the entrance region of an eccentric annulus is studied theoretically. Both concentric and eccentric annuli are discussed. The compressible cement slurry is modeled as a non-Newtonian power law fluid. The flow is axial with stationary boundaries.;The governing equations (continuity equation, momentum equation, and thermodynamic equation of state) are mapped into bipolar coordinates for numerical modeling using finite-difference techniques. The entrance length is determined using a 98% velocity profile development criterion. Picard iterations are performed for the velocity dependent viscosity values. Pressure iterations are performed at each forward slice using an interpolating technique until a mass balance convergence criterion is met. Mass flow rate is determined by numerically integrating the calculated velocity profile using Simpson's 1/3 rule. The definition of the generalized Reynolds number is utilized to approximate the viscosity at the annular inlet.;Model validation is established using laminar steady flow of Newtonian and non-Newtonian fluids in concentric and eccentric annuli. Flows with no entrance effects are validated using Snyder and Goldstein (1965), Tosun (1984), and Hanks and Larsen (1974). The model is then extended to consider entrance effects and validated using results from Tiu and Bhattacharyya (1973, 1974).;The significance of this work lies in the planning of an effective primary cementing program. A sensitivity analysis is performed to determine the relative sensitivity of the modeled system, including entrance length, to various input parameters. Rheological parameters (power law index, consistency index, and compressibility) consistent with oil well cement slurries are varied as input parameters. Annular geometry, annular inclination, hydraulic diameter, fluid velocity, and fluid pressure at the inlet are also varied. The effect of these parameters on the developing velocity, pressure gradient, and viscosity profiles, as well as entrance length, is discussed.