Prediction of wellbore temperatures in gas production wells

In this paper we present a simple and physically transparent analytical solution for the prediction of wellbore temperatures in gas production wells. It is based on the extended Bernoulli equation and the steady-state energy balance applied to the flow of a real gas in a straight flow conduit. The solution includes three dimensionless numbers representing the effect of gravity, friction and wellbore heat losses, respectively, and two newly defined thermodynamic gas properties, called psi and omega. These properties are gas specific and can be readily evaluated as a function of pressure and temperature on the basis of existing correlations for the gas deviation factor (z-factor) of natural gases. The analytical solution is very well suited to quickly estimate temperature drops in straight homogeneous wells with uniform tubing strings. It can also be used, along with the existing analytical solution for wellbore pressures of Lingen, as a basic building block in a more general and rigorous prediction method for temperatures and pressures in wellbores, accommodating variable deviation angles, variable wellbore diameters, tapered tubing strings, and layered rock formations with different heat transmission characteristics.