Annular Fluid Forces Generated by a Non-Newtonian Fluid With Variable Flowrate and Non-Uniform Rotational Pipe Movement

In drilling operations, the precise estimation of annular fluid forces on a pipe is important to determine the drill-string movement in dynamic conditions. Yet, drilling fluids have a complex rheological behavior, and the inner pipe is usually eccentric and rotates. The pipe movement is usually non-uniform like for example when there are torsional stick-slips. Furthermore, the flow of liquid in the annulus is usually unsteady either because of pump acceleration or because of the axial pipe movement. With all these non-uniform movements of the inner pipe geometrical boundary and the accelerated flow of the fluid itself, it is unclear what is the hydraulic force applied by the fluid on the exterior of the pipe. A relationship that links the pipe movement to the total hydraulic force is derived. However, the total hydraulic force applies to both the wellbore and the pipe, and it is not evident in which proportion the total hydraulic force contributes to the hydraulic force on the pipe. To address this problem, computational fluid dynamic simulations are run to estimate the hydraulic force on a pipe subject to dynamic flow and pipe rotation conditions. It is found that even though the total hydraulic force varies substantially due to the dynamic boundary conditions, the proportion of the force that applies to the pipe varies in a much lesser extent. This proportion is compared to theoretical value corresponding to Newtonian fluids in steady-state conditions. It is found that the proportion is a linear function of the proportion for Newtonian fluids.