Flow pressure drop of laminar helical flow of power-law fluid in concentric annulus of elliptical wellbore
Accurate prediction of annular pressure drop provides the foundation for precisely controlling bottom hole pressure and ef-fectively preventing complex downhole incidents such as wellbore leakage,overflow,and even blowout.The conventional prediction method of annular pressure drop is usually based on circular wellbores,without considering the influence of irregular borehole shapes.Owing to the heterogeneity of mechanical rock parameters and in-situ stress,elliptical wellbores are easily formed.Based on fluid dynamics,a numerical model for the pressure drop of power-law fluid in laminar helical flow in elliptical wellbores was established,and was further verified by fluid mechanics simulation results and experimental data.Using the numerical model,the influencing factors of flow pressure drop were analyzed to clarify the effects of different parameters on flow pressure drop.A dimensionless pressure gradient fitting model was established by the least square method.The results show that the numerical model has an error within±5％when compared with simulation and measured results.The pressure gradient increases linearly with the increase of fluid viscosity coefficient,increases expo-nentially with the increase of flow behavior index and the ratio of inner and outer diameters,and increases logarithmically with the in-crease of average axial velocity;however,it decreases exponentially with an increase in the ratio of major and minor axes of the el-lipse and the inner tube rotational speed.The dimensionless pressure gradient shows little variation with the change of fluid viscosity coefficient.The fitting model has an error of only±5％when compared to the numerical model.The applicable parameter ranges are as follows:0.8 m/s≤vx≤1.4 m/s,40 r/min≤ω≤ 120 r/min,0.5≤Kd≤0.8,1.0≤η≤ 1.2 and 0.5≤n≤0.8.The dimensionless pressure gradient fitting model established for concentric annular laminar helical flow in elliptical wellbore enables accurate and con-venient prediction of flow pressure drop,thus laying a theoretical foundation for the fundamental study of wellbore hydraulics.
elliptical wellboreconcentric annulushelical laminar flownumerical modelfitting model
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