Estimating the Initial-Formation Temperature and Flowing-Temperature Gradient with Transient-Temperature Analysis: Applications in Gas Reservoirs

The formation temperature constitutes one of the essential factors that affect the wellbore fluid temperature behavior in production mode. The amount and direction of the radial heat transfer between the surrounding formation and the wellbore depend on the temperature differential and thermal properties of the media. Traditional studies probing geothermal gradients depended principally on extrapolating the transient bottomhole temperature to infinite shut-in time for obtaining the undisturbed formation temperature. After that, a straight line from the surface to the bottomhole condition constituted the geothermal gradient. Of course, the implicit assumption in this approach is that a linear geothermal gradient exists in light of unavailability of depth-wise temperature measurements. This study presents a new transient-temperature analysis approach to determine the undisturbed formation temperature. Specifically, we show the application of the line-source solution that has roots in the temperature-diffusivity equation. Secondly, using the distributed temperature measurements associated with transient-pressure testing, we proved that the bottomhole or static temperature is time-dependent, leading to alteration of the geothermal gradient in a well's proximity. Finally, the lowering of the temperature-derivative plateau with increasing depth during well shut-in periods indicated an increase in thermal conductivity, resulting in a nonlinear geothermal gradient.