Statistical evaluation of methods for the calculation of static formation temperatures in geothermal and oil wells using an extension of the error propagation theory

The feasibility of using the more sophisticated weighted least-squares (WLS) model, as opposed to the traditional ordinary least-squares (OLS), in linear regressions of BHT data to estimate the static formation temperatures (SFT) was investigated. The most commonly used analytical methods (line-source; spherical and radial heat flow; and cylindrical heat source) were applied. Error propagation equations were derived to calculate errors in the time function of each method. These errors were combined with the BHT measurement errors to compute weighting factors for applying the WLS. Intercept uncertainties were estimated for all regressions using sets of synthetic and actual borehole logs taken from geothermal and oil applications. SFT computed with the spherical and radial heat flow method were generally greater than those from the other two methods.