Application of a proportional-integral control for the estimation of static formation temperatures in oil wells

A strategy based on proportional-integral (PI) feedback control was applied to solve an inverse heat transfer problem for estimating static formation temperatures (SFTs) from logged temperatures in oil wells. The PI control feedbacks the error between logged and simulated temperatures during the shut-in time process, existing SFT proposal. Thus, mathematically speaking an inverse heat transfer problem was solved in this way, since SFT represents the initial conditions (which are unknown) to solve the partial differential equations governing the heat transfer process in the wellbore-formation system. The mathematical model considers transient convective heat transfer due to circulation losses to the rock surrounding a well. The methodology was tested analyzing two oil wells (MB-3007 and MB-3009) from the Gulf of Mexico and results were compared against two classic methods. The method presented in this work needs only one temperature measurement for each fixed depth to estimate the SFT.