An Inverse Approach for Estimation of Initial Formation Temperatures

Abstract

An inverse method for the estimation of geothermal and oil reservoir initial formation temperatures IFTs is presented. It is based on control theory whereby temperatures in the well are computed starting from an assumed reservoir temperature profile and compared with logged temperatures at different shut-in times. The comparison is performed using a control algorithm which changes the assumed reservoir temperature profile until the best fit is attained. Fluid and heat flow in the well include circulation and shut-in in the presence of lost circulation transport processes in the formation consider the reservoir as a porous medium. The first part of the algorithm included proportional control (PC) and was applied to well LV-3 from the Las Tres Virgenes Mexico, geothermal field whereby the estimated IFTs compared with measured IFT within  15ºC, an acceptable result from an engineering point of view. In the second part, the algorithm was extended to include proportional and integral control PIC. Results of application from an oil well also show that it is feasible to predict IFTs reasonably by this method. IFTs obtained with the latter method also compare well with simpler methods like the Horner and spherical-radial flow method.