Mathematical modeling of heat transfer in counter-current multiphase flow found in gas-drilling systems with formation fluid influx

The performance of gas-drilling （drilling oil andgas wells with air, nitrogen, or natural gas） is very unpre-dictable in many areas due to lack of proper design ofdrilling parameters because of limited understanding ofgas-rock interaction which requires knowledge of heattransfer in the well system. Complete analysis of rockfailure requires an accurate mathematical model to predictgas temperature at the bottom hole. The currently availablemathematical models are unsuitable for use for the purposebecause they do not consider the effects of formation fluidinflux, Joule-Thomson cooling, and entrained drill cut-Lings. A new analytical solution for predicting gas tem-perature profiles inside the drill string and in the annuluswas derived in this study for gas-drilling, considering all：hese three effects. Results of sensitivity analyses show thatFormation fluid influx can significantly increase the tem-perature profiles in both the drill string and the annulus.The Joule-Thomson cooling effect lowers the temperaturen the annulus only in a short interval near the bottom hole.The drill cuttings entrained at the bottom hole can slightlyncrease the temperature profile in the annulus.