Using the vronskian to analyse the thermogram of a producing well

Abstract

The functional dependence of thermograms in producing wells has been studied in order to determine the initial temperature distribution along the wellbore. Information about the initial thermal field makes it possible to ensure the reliability of solving the problem of determining the operating intervals in production wells. In this paper, we propose a method for isolating the linear dependence on the thermogram profile in the intervals of the absence of fluid movement (in the sump of a working and along the trunk of an idle well) by constructing a special function – the vronskian. In this paper, it is established that the use of the vronskian can be used to restore the geothermal distribution, as well as to obtain the value of the geothermal gradient and temperature in the analysis of the thermogram. To discuss the possibilities of the proposed method, three cases were used: a model and two thermograms in a real field study. The first option considered is a synthetic thermogram with a quasi-stationary mode of operation of the well. In the second and third cases, the results of thermometric studies in the well with a short-term inflow from the reservoir with the same and different lithological structure of the intervals in the sump are presented. The obtained algorithm can be used to isolate the intervals of linear dependence during express processing of registered thermograms in order to obtain quantitative parameters of the operation of the borehole-formation system.