Abstract
This work introduces a new method to analyze the flow of fluids induced by one rotating cylinder within a substantially cylindrical space. This analysis is useful to either emulate the behavior of the flow of fluid during gravel pack or cleaning/drilling operations under the assumption of negligible effect due to a low advance-velocity or drilling-bit penetration-rate. The new method is based on the use of a non-dimensional coordinate system that enables the analysis of eccentric rotating pipes at small and large eccentricities and the Reynolds number. The eccentric annulus between two cylinders is mapped into concentric annuli by a bilinear transformation that is used to generate the coordinate system here discussed. Advantageously, the polar coordinates system is fully recovered from the discussed coordinate system once the eccentricity is set to zero.
The two- and three-dimensional linear momentum equations, mass conservation, and the particular incompressibility condition are expressed in terms of the discussed coordinate system.
To demonstrate the effectiveness of this method, the set of linear momentum equation and mass conservation for a two-dimensional steady-state flow of incompressible Newtonian fluid within an annular space at different eccentricities are asymptotically solved by using the perturbation method and compared with the analytical solution obtained by Farris (1962).
The potential applications of this method to analyze the flow in gravel pack applications, to determine the cleaning effectiveness in fully eccentrically tubulars placed in horizontal wells and the abrasive effect observed in rotational drillstrings are also proposed for future research.
