Annular Pressure Gradients of Elliptical Wellbore: Prediction and Influential Factor Analysis

Th establishment of conventional pressure gradient models is based on the idea that the cross section of a wellbore is round, however, in practical situation, the cross section of a wellbore is elliptical under the influence of non-uniform in-situ stresses. The flow pattern in annular space of an elliptical cross-section wellbore is obviously different to the flow pattern in annular space of a round cross-section wellbore. Based on the basic equations of fluid mechanics, a concept of "effective hydraulic diameter" has been introduced in establishing a pressure loss model of annulus flow in elliptical wellbore. Studies showed that with an increase in the ratio of long radius over short radius of an elliptical wellbore, the average flowrate in the annular space decreases, and the annular pressure gradient decreases with it. The greater the ratio of the long radius over the short radius of an elliptical wellbore, the more obvious the grading of the high and low flowrate areas along the helix direction of the annular space. Furthermore, compared with simulation results (using the CFD software), this model has calculation errors that are in a range of less than ±10%. Analyses of affecting factors indicated that when other conditions remain constant, the annular pressure gradient of a elliptical wellbore increases somewhat linearly with increases in annular flowrate and yield point and consistency index of the fluid, and somewhat exponentially with increases in flow index. The model established based on the studies can be used to calculate the wellbore pressure of an elliptical wellbore.