Initial Formation Temperatures by Inversion of Logged Temperatures in Geothermal Wells

A method was implemented to compute the unknown initial condition for combined cycles of cooling (mud circulation) and heating (shut-in) heat transfer processes during drilling of geothermal wells with lost circulation effects. This initial condition is the unperturbed formation temperature of a geothermal reservoir. An objective function is constructed based on nonlinear least-squares and the difference between computed and measured temperatures during well shut-in as a function of time and position. The function is minimized subject to three independent variables. Well temperatures were computed from the corresponding direct problem with an assumed initial condition which is later modified using the Levenberg – Marquardt optimization algorithm (Marquardt, 1963). Solution of the heat transfer problem involves various physical of the well: the drilling pipe, the annular space and the surrounding formation. Implicit finite differences are used for the well regions and the 2-D conduction – convection formation problem is solved using the ADI scheme. Results of application are presented for one Mexican geothermal wells, which show reasonable matching of logged temperatures.