Simplified modeling of YPL fluid flow through a concentric elliptical annular pipe

Accurate prediction of the pressure gradient is the prerequisite for precise control of downhole pressure; such control can effectively avoid the complicated underground situations caused by improper downhole pressure control, such as well leakage, overflow and wall instability. The existing model of the annular pressure gradient in drilling process only considers a perfectly cylindrical wellbore; however, the real drilling hole easily becomes an elliptical wellbore under non-uniform in situ stress, leading to the relatively large error of the conventional model. Based on the theories of fluid mechanics, the analytical and simplified models of steady-state laminar flow in the concentric elliptical annular (elliptical wellbore) pipe are established. The analytical model is validated by the computational fluid dynamics (CFD) simulations of Fluent software. In addition, the simplified model was validated by analytical solutions. The primary conclusions are as follows. (1) When the flow rate is constant, the axial average and maximum velocities increases linearly and exponentially, respectively, with the increase of ε. The velocity profile of the analytical model is in good agreement with the velocity profile of the CFD simulations. (2) The CFD simulations are in perfect agreement with the analytical results, and the error of the pressure gradient is within ±10% error bands for pressure gradient. (3) The simplified model predictions are in good agreement with the analytical model results, and the error of most of the results is within ±5% bars. The model is convenient for use in predicting the pressure gradient accurately for yield power law (YPL) fluid flowing in an elliptical wellhole.