An Inverse Method for Estimation of Initial Temperatures in Geothermal Reservoirs: Part 2. Inverse Control Algorithm and Results of Application

Abstract

A method based on proportional control was used to solve the inverse heat transfer problem of estimating geothermal reservoir initial formation temperatures from temperatures logged in geothermal wells. The proportional control computes the error between logged and simulated well temperatures during shut-in and feeds back this information to the initial proposal of the initial formation temperature until the error is a minimum. In this sense, an inverse problem is solved since the initial formation temperature represents the initial conditions, which are unknown a priori, to solve the set of partial differential equations that govern heat transfer in the wellbore and surrounding formation during drilling. The mathematical model of the well and the formation is described in Part 1 of this article, while Part 2 described the application of the method to the estimation of the initial formation temperatures of well LV-3 from the Las Tres Virgenes, Mexico geothermal field. Estimated initial formation temperatures compare within˙15 ı C, which is an acceptable result from an engineering point of view.