A new hybrid method for transient heat conduction problems is developed and applied to simulate a Plug and Abandonment (P&A) operation of oil wells. An oil well is approximated by concentric disks in a one-dimensional configuration, which allows for use of polar coordinates. The application of the Separation of Variables Method (SVM) is used as the analytical framework for the solution of the conductive heat transfer arising from a volumetric heat source located in the center of the disks. The SVM is able to solve only time-independent boundary conditions. However, using the Duhamel's theorem, the solution determined with the SVM can be used to achieve the solution when both time-dependent boundary conditions and internal heat generation are prescribed. Lastly, for verification purposes, a commercial software that solves the transient temperature field by means of numerical procedures, providing reliability to the analytical method proposed in this work.

中文翻译：

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复合圆盘瞬态热传导新分析方法应用于油井热塞废弃

开发了一种新的瞬态热传导问题混合方法，并将其应用于模拟油井的堵塞和废弃（P＆A）操作。油井近似为一维配置的同心圆盘，这允许使用极坐标。变量分离法（SVM）的应用被用作解决由位于圆盘中心的体积热源引起的传导传热的分析框架。 SVM 只能求解与时间无关的边界条件。然而，利用杜哈梅尔定理，当规定了与时间相关的边界条件和内部发热时，可以使用用SVM确定的解来获得解。最后，出于验证目的，商业软件通过数值程序求解瞬态温度场，为本文提出的分析方法提供了可靠性。