Identification of a Moving Heat-Flux Boundary Condition in Thermite-Based Wellbore Plugging and Abandonment with Physics-Informed Neural Networks

In this work, a physics-informed neural network (PINN)-based methodology is proposed to identify a moving heat-flux boundary condition induced by a thermite reaction in thermite-based wellbore plugging and abandonment processes. The corresponding heat flux is characterized by a fixed heat-flux profile that undergoes axial translation along the inner wall of the tubular structure. The identification problem is formulated as an inverse heat conduction problem (IHCP), in which the inner-wall heat flux is inferred from temperature measurements on the outer surface of the tube. In the PINN formulation, the governing heat conduction equation is incorporated as a physical constraint to guide the training process. To facilitate stable joint identification of a fixed heat-flux profile and the associated propagation speed, the heat-flux profile is represented using a compact radial-basis-function-based (RBF-based) parameterization. The proposed approach is validated using both numerical simulations and experimental temperature data reported in the literature. In numerical simulations, the normalized root mean square error of the identified heat-flux profile remains below 0.1, while the relative error of the propagation speed is less than 0.6%. Additional tests with 5% measurement noise further confirm the stability of the identification results.