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

Boyun Guo,Jun Li,Jinze Song,Gao Li

doi:10.1007/s12182-017-0164-3

Abstract

The performance of gas-drilling (drilling oil and gas wells with air, nitrogen, or natural gas) is very unpredictable in many areas due to lack of proper design of drilling parameters because of limited understanding of gas–rock interaction which requires knowledge of heat transfer in the well system. Complete analysis of rock failure requires an accurate mathematical model to predict gas temperature at the bottom hole. The currently available mathematical models are unsuitable for use for the purpose because they do not consider the effects of formation fluid influx, Joule–Thomson cooling, and entrained drill cuttings. A new analytical solution for predicting gas temperature profiles inside the drill string and in the annulus was derived in this study for gas-drilling, considering all these three effects. Results of sensitivity analyses show that formation fluid influx can significantly increase the temperature profiles in both the drill string and the annulus. The Joule–Thomson cooling effect lowers the temperature in the annulus only in a short interval near the bottom hole. The drill cuttings entrained at the bottom hole can slightly increase the temperature profile in the annulus.

Highlights

Gas has been widely used as the working fluid in drilling injection wells, geothermal fluid wells, and oil and gas production wells (Lyons et al 2009)
A new analytical solution for predicting gas temperature profiles inside the drill string and in the annulus was derived in this study for gas-drilling, considering all these three effects
The drill cuttings entrained at the bottom hole can slightly increase the temperature profile in the annulus

Summary

Introduction

Gas (air, nitrogen, or natural gas) has been widely used as the working fluid in drilling injection wells, geothermal fluid wells, and oil and gas production wells (Lyons et al 2009). The proportion of largesize cuttings drops and that of small cuttings increases This trend of cuttings size change may be explained by three principles: (1) rock drillability drops with depth, (2) more cuttings collision in deep holes, and (3) more thermal failure of rock in friction-heated deep/hard formations. The latter model treats the annular fluid as a non-flowing layer of insulation and uses equivalent thermal conductivity of the flowing fluid in the annulus It does not consider the effects of formation fluid influx and drill cuttings, and it does not predict the annular temperature profile. A new analytical solution was derived in this study for temperature prediction, considering the flowing gas, formation fluid influx, Joule–Thomson cooling, and entrained cuttings in the annular space It corrects the result given by Li et al.’s (2015) model by 14%

Mathematical model

Model comparison

Sensitivity analysis

Findings

Conclusions