Spiral laminar flow of yield-power-law fluids in partially blocked annulus

Abstract

During drilling of directional and horizontal wells, cutting beds inevitably form in highly deviated and horizontal sections. Because of the centralizer, both concentric and eccentric annuli can exist in both highly deviated and horizontal sections. Existing studies on the helical laminar flow of a non-Newtonian fluid in partially blocked concentric and eccentric annuli are mainly based on numerical models, laboratory experiments, and computational fluid dynamic (CFD) simulations. Directly applying the research results to drilling engineering is difficult. To accurately and conveniently predict the pressure gradient of helical laminar flow with a fixed horizontal cutting bed, this work first presents a new model based on fluid mechanics to compute the pressure loss of a yield-power-law (YPL) flow in partially blocked concentric and eccentric annuli in a laminar helical-flow state. Second, the Fluent software is used to simulate the helical laminar flow of the YPL fluid with a fixed horizontal cutting bed. The existing experimental measurements, mathematical model calculation, and Fluent software simulation results are used to verify the proposed simplified model. The results show that the predicted results of the simplified model agree well with the existing numerical results, existing experimental data, and CFD simulation results; the error is only ±5%. The new simplified model can achieve accurate and convenient prediction of the pressure gradient of a spiral laminar flow in an annulus with a fixed horizontal cutting bed.