A Closed-Form Hydraulics Equation for Aerated-Mud Drilling in Inclined Wells

Abstract

Summary Accurate prediction of shut-in and flowing bottomhole pressures (BHPs) in inclined holes presents a challenge in aerated-mud drilling. It is highly desirable to develop a simple and accurate hydraulics equation for this purpose. This paper fills the gap. A closed-form hydraulics equation was developed in this study on the basis of recent experiments on multiphase flow in an inclined-well model. The newly developed hydraulics equation is a four-phase model that considers injected liquid, injected gas, formation-fluid influx, and cuttings entrained at the bottom of the hole during drilling. It degenerates to the Poettman and Bergman equation when terms for friction loss, cuttings weight, gas weight, and temperature variation are neglected. The equation was first calibrated with the data measured from a full-scale research borehole. It was then tested with two field cases covering a deep (7,403 ft vertical depth) and a shallow (697 ft vertical depth) horizontal well drilled with aerated muds. The results show 3.42 and 0.8% error of the equation in BHP prediction for the deep and shallow wells, respectively. The equation was also compared with two commercial software packages (S1 and S2) using the measured BHP from another well. It indicates that the flowing BHP calculated by the equation is comparable to that from S1 and much more accurate than S2. Sensitivity analyses with Eq. 7 show that the gas-injection rate affects "static" pressure more than flowing pressure in the annular space for the tested data range. The sensitivity analyses also indicate very high equivalent circulating density (ECD) and low equivalent mud weight (EMW) in shallow depths near the surface.