A closed form mathematical model for predicting gas temperature in gas-drilling unconventional tight reservoirs

Drilling wells with gas, or gas-drilling, is a technique traditionally used to drill mining boreholes, geothermal wells, and conventional oil and gas wells. It has recently been adopted to drill shale gas wells and proven to be cost-effective in the United States. However, the performance of gas drilling is very unpredictable in many areas due to the lack of proper design of drilling parameters because of limited knowledge of gas-rock interactions. Complete analysis of gas-rock interaction requires a mathematical model to accurately predict gas temperature at bottom hole. Such a mathematical model is not available for gas-drilling. An analytical model was derived in this study to fill the gap. The analytical model is a closed form equation for predicting bottom hole gas temperature under various flow conditions. The result given by the analytical model was verified by a numerical model developed in this study. The difference between the two models was found to be less than 0.1%. A sensitivity study was carried out to identify possible sources of error when the analytical model is applied to real gas-drilling condition.