Study on Distribution of Wellbore Temperature in Gas Drilling with Gradient Equations

Abstract

Precise calculation of gas temperature profile is the key to gas drilling design. It is traditionally assumed that the gas temperature distribution in the wellbore is equal to the formation temperature, without considering the influence of fluid flow and Joule-Thomson cooling effect. This paper puts forward a gradient equation method for gas temperature distribution in wellbore considering gas flow and Joule-Thomson local cooling of the bit. The method applies pressure, temperature, density, and velocity equations to gas flow in drillstrings and annulus. The solution of the gradient equation is in the form of the fourth-order Runge-Kutta equation. Bottom wellbore temperatures measured at depths of 700 to 2000 m in an actual well are consistent with those predicted by the gradient method. Due to the Joule-Thomson cooling effect at the bit nozzle, the temperature drops by about 30°C. The sensitivity analysis is carried out by gradient method, and the results show that the temperature drop range of different nozzle sizes can reach 60°C due to the Joule-Thomson cooling effect. Stable temperature curves can be established within a few minutes of the gas cycle. Due to the influence of gas flow and Joule-Thomson cooling, the gas temperature in the wellbore deviates significantly from the geothermal temperature in the formation under the flow condition. The temperature of the gas in drillstrings increases as the drill depth increases and then decreases rapidly near the bottom of the hole. As the gas flows upward along the annulus, the gas temperature rises first, surpasses the formation temperature, and then decreases gradually along the geothermal gradient trend.