17th Brazilian Congress of Thermal Sciences and Engineering November 25th-28th, 2018, Águas de Lindóia, SP, Brazil ENCIT-2018 ANALYTICAL TRANSIENT HEAT CONDUCTION THROUGH AN COMPOSITE REGION OF AN INFINITE SOLID CYLINDER WITH A PERFECT THERMAL CONTACT TO A SEMI-INFINITE MEDIUM Gabriel Saavedra de Andrade Instituto Tecnológico de Aeronáutica, São José dos Campos/SP e-mail: gasaavedra.eme@gmail.com Marcelo José Santos de Lemos Instituto Tecnológico de Aeronáutica, São José dos Campos/SP e-mail: delemos@ita.br Abstract. Aiming the development of new technologies for the petrol field operations, an innovative method to tamponing oils wells is being studied due to significant advantages over the traditional cementing procedures. In a general context, a cylinder positioned at the well hole will work, initially, as a vessel for a fluid composed of chemical species capable to generate such an intense heat after an exothermic reaction, so that a strong heat source will flow by conduction throughout the composite region from the inner wall of the cylinder to the outer surface that has a perfect thermal contact with the surroundings geological formation, which will be exposed to high values of temperatures after a certain period of time. The magnitude of the temperature will be sufficient to reach the melting temperature of the cap rock, causing the vitrification and so resulting in the complete well sealing. Carrying out an unprecedent study, the present methodology will investigate which analytical approach will provide the most realistic and bests results in the existing literature by a comparison made between two mathematical techniques for the transient conduction flow through composite regions: The generalized orthogonal expansion technique utilized in deriving the solution and the Laplace transform for solving semi-infinite and infinite medium problems. Keywords: Tamponing Oil Wells, Conduction Flow, Heat Source, Composite Region, Orthogonal Expansion Technique, Laplace Transform 1. INTRODUCTION After the production oil well becomes exhausted or has no more economic potential, it is provided by the law the responsibility of the owner’s oil well to seal up the entire hole in order to prevent water contamination by some residual retained oil on the reservoir (Abshire et.al., 2012). The usual procedures for permanent abandonment wells is done by cementing the hole drilled on deep ocean. This tamponing method has relevant disadvantages when referring to the huge amount of time and money spent by doing so (Barclay et.al., 2001). Due to this concerns raised an innovative proposal of a device that will overcome those adversities, consisting by a vertical pipe containing a mixture of different chemical species placed on the production oil well that, with an exothermic reaction, will work as strong source of energy generation that will flow by conduction through the cylinder thickness, which outer surface is at perfect contact to the geological formation interface, until the heat reaches the cap rock verified at the geological formation after an amount of time, which temperature will achieve such great value of temperature that will be sufficient to reach the melting temperature of the rock. Two mathematical techniques will be used in order to develop the analytical approach, the generalized orthogonal expansion technique (Carslaw and Jaeger, 1959) utilizing a nondimensional analysis (Gu and O’Neal, 1995) in order to provide gain of generality for the case study and the Laplacian transform (Özisik, 1980). Both methods will be investigated to check if the use of one provide realistic results for the phenomena upon the other or, on the other hand, if they fit in a most interesting way when they are treated concomitantly to achieve an optimized solution. The former scheme allows a solution of multi-region problems by a direct expansion without resort to integral transformation or Green's functions and it is an extension of the method of separation of variables heretofore beyond its scope (Tittle, 1965), whereas the latter is a convenient technique for the solution of composite medium problems involving regions of semi-infinite or infinite in extent (Özisik, 1968). As a preliminary study around the subject, some assumptions would be necessary to be considered since the embryonic knowledge does not provide recommendations about optimal boundary and initial conditions. Those hypotheses will be fixed as close as possible to the existing configurations present in the literature. Then, after a tangible conclusion based on future results will allow to specify the correctness conditions that describe the phenomenon.