Uncertainty estimates of static formation temperatures in boreholes and evaluation of regression models

Abstract

Three commonly used methods for estimating static formation temperatures were evaluated: (1) the line-source or Horner method; (2) the spherical and radial heat-flow method; and (3) and the cylindrical heat-source method. Ordinary least-squares linear regression model statistical tests (sequence of signs, regression using sequential subsets of an ordered array of data, and residual sum of squares) were used to evaluate the actual relationship between the bottomhole temperature and the time functions of the methods. The statistical tests for linearity and the resulting residual sum of squares show that bottom-hole temperature versus time-function relationships are of polynomial type. Standard deviation values of the slope and intercept were calculated for the linear as well as the quadratic regression model. The quadratic regression was found to be most appropriate for this purpose and was used for the first time for calculating static formation temperatures using four data sets of actual geothermal borehole logs and two synthetic sets. The F- and Student-t tests were applied to static formation temperatures obtained from linear and quadratic regression methods. Static formation temperatures computed with the spherical and radial heat-flow method are significantly greater (at the 95 per cent confidence level) than those from the other two methods under study. The spherical and radial heat-flow method seems to overestimate 'true' values of the static formation temperatures by about 10 per cent, whereas the other two methods (Horner and cylindrical heat source) provide unbiased estimates of these temperatures. © 2005 RAS.