Estimation of geothermal temperature and gradient using inversion of transient wellbore temperature measurements

This paper describes the development, validation, and application of a simulator for estimating geothermal temperature and its gradient from disturbed temperature measurements along a section of a vertical or subvertical wellbore. The simulator is based on a mathematical model including transient heat transfer during drilling, circulation, cementing, and shut-in conditions in and around a wellbore. It considers the actual schedule and parameters of the well construction stages in a layered formation. Along with a critical review of existing analogue-solutions, the paper addresses the issue of completeness of the tests for such kinds of simulators, as well as the volume and the quality of the initial data required for modeling. The developed simulator was successfully tested against several known analytical and numerical solutions and applied to real field data. Parametric studies on synthetic cases allowed us to quantitatively evaluate the impact of uncertainty in drilling schedule and formation thermal properties on the reconstructed geothermal temperature and its gradient. The uncertainty in the input time-depth curve for the wellbore when the average relative difference in day-by-day drilling depth is about 11% leads to errors up to 3% and 20% in geothermal temperature and its gradient, respectively. The typical uncertainty of +/- 30% in rock thermal properties, primarily thermal conductivity, results in errors up to 2.5% and 9.3% in geothermal temperature and its gradients, respectively. It was also shown that the noise in the recorded temperature data may result in errors in geothermal temperature gradient estimation up to several percent. Developed simulator is a useful tool for the determination of geothermal temperature and its gradient, as it is important in solving fundamental and applied problems in the geothermal and petroleum industries.