Interpretative Model of Radial Thermal Logging

A mathematical model of the temperature field of a fluid moving in a well is presented. It can be used as the basic one for interpreting measurements of radial temperature distributions. The initial problem has been solved on the basis of an exact "on the average" asymptotic method. The analytical solutions that describe the temperature fields of a fluid in a well shaft were obtained with the aid of the Laplace–Carson transformation. It is shown that the zero expansion coefficient describes the radius-averaged background values of the temperature field in the well. The expression for the first coefficient describes the radial temperature profiles. This means that the proposed interpretative model allows one to carry out filtration of useful temperature anomalies of the radial profile against the background of considerably large global temperature perturbations caused by the fluid flow in the shaft of an operating well and thereby to remove the problems associated with the incorrect realization of inverse problems. Based on numerical calculations, the influence of the temperature signal from the bed and of the thermophysical parameters of the filling fluid has been analyzed, and major advantages and disadvantages of the proposed interpretative model have been established.