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In this work, a hybrid analytical and numerical solution for transient heat conduction across a composite cylindrical sector is presented. A two-dimensional domain consisting of a multi-layer circular sector of angle φ was investigated (φ < 2 π). The Separation of Variables Method (SVM) was applied to solve the partial differential equation with non-homogeneous boundary conditions of the first, second and third kinds prescribed in the radial direction. Homogeneous boundary conditions of first and second kinds were arbitrated in the angular direction. A spatial time-independent source term g i (r , θ) was considered. The radial eigenvalues problem for the (r , θ) domain returns only real quantities and depends implicitly on the angular eigenvalues. Results for time dependent temperatures using the Separation of Variables Method were compared with numerical results, showing good accuracy. A second set of results was developed to investigate boundary conditions, material properties and the thermal source power required to rise temperature levels (mainly around the mid-angle φ /2) high enough to promote melting of certain layers of materials. These results might be useful for investigating a novel technology for the decommissioning of oil wells using thermal sources, often referred to in the literature as Thermal Plug and Abandonment (TP&A). [ABSTRACT FROM AUTHOR]

This work presents a hybrid analytical/numerical approach for transient heat conduction through composite hollow cylinder structures applied for Plug and Abandonment (P&A). The Distribution Transfer Function Method (DTFM) is a mathematical framework able to solve both nonhomogeneous boundary conditions and a nonlinear partial differential equation with spatial-temporal source term, presenting good agreement with Finite Element Method (FEM) and other analytical approaches. A new technology of Thermal Plug and Abandonment (TP&A) devoted for P&A operation is studied in this work, where a heat generator is used to melt the first layer of the well structure. The heat source will be modeled using thermite within the oil well manifold structure, which must be descended to desirable depths along the borehole through a cylindrical container. After an exothermic reaction the temperature fields will be determined by means of DTFM method. A novel adaptative step-wise procedure applied for DTFM allows one to solve non-differentiable heat flux, thermal and volumetric heat source profiles which exact quadrature regression are not able to solve. This method provides simple replicability, which can be reproduced for many emerging fields where transient heat conduction is an important parameter to be accounted for. Using experimental data as input in DTFM provides insight that the temperature response overcame the design melting point of the production tube, being capable of melting down the production tubing wall, which is a valuable achievement for oil industries since not removing the production tubing can save a great amount of time, and hence save costs for oil industries. [ABSTRACT FROM AUTHOR]