A new empirical method based on log-transformation regressions for the estimation of static formation temperatures of geothermal, petroleum and permafrost boreholes

A new practical method based on logarithmic transformation regressions was developed for the determination of static formation temperatures (SFTs) in geothermal, petroleum and permafrost bottomhole temperature (BHT) data sets. The new method involves the application of multiple linear and polynomial (from quadratic to eight-order) regression models to BHT and log-transformation (Tln) shut-in times. Selection of the best regression models was carried out by using four statistical criteria: (i) the coefficient of determination as a fitting quality parameter; (ii) the sum of the normalized squared residuals; (iii) the absolute extrapolation, as a dimensionless statistical parameter that enables the accuracy of each regression model to be evaluated through the extrapolation of the last temperature measured of the data set; and (iv) the deviation percentage between the measured and predicted BHT data. The best regression model was used for reproducing the thermal recovery process of the boreholes, and for the determination of the SFT. The original thermal recovery data (BHT and shut-in time) were used to demonstrate the new method's prediction efficiency. The prediction capability of the new method was additionally evaluated by using synthetic data sets where the true formation temperature (TFT) was known with accuracy. With these purposes, a comprehensive statistical analysis was carried out through the application of the well-known F-test and Student's t-test and the error percentage or statistical differences computed between the SFT estimates and the reported TFT data. After applying the new log-transformation regression method to a wide variety of geothermal, petroleum, and permafrost boreholes, it was found that the polynomial models were generally the best regression models that describe their thermal recovery processes. These fitting results suggested the use of this new method for the reliable estimation of SFT. Finally, the practical use of the new method was highlighted because it only requires the use of BHT and shut-in time measurements as the main input data, which represents an enormous advantage over most of the analytical methods reported in the literature that require a large number of measurements (e.g. circulation time, the thermophysical and transport properties of the formation or drilling fluid, among others).