Finite integral transform with homogenized boundary conditions solution of transient heat conduction applied to thermal plug and abandonment of oil wells

Abstract

After the end of productive life of a geological oil reservoir, a set of operations for well Plug and Abandonment (P&A) is performed to recover the soil layers to its natural state. As traditional P&A techniques are expensive activities, alternative technologies are gaining renewed interest for capital expenditure reduction and leak risks mitigation. Hence, the Thermal Plug and Abandonment (TP&A) procedure is here investigated by focusing on the fulfillment of two intermediate milestones, combining new technology with conventional P&A practices. The first milestone consists in applying a thermite exothermic reaction to generate enough heat for melting the entire thickness of the production tube. The second milestone aims to determine if the resulting molten section has sufficient dimensions to allow for the passage of the cement pumped downhole, thus ensuring the complete sealing of the oil well's cross-section. The thermal investigation was conducted by applying a homogenized form of the Finite Integral Transform (FIT) analytical framework to solve the transient heat conduction equation in 2-D polar coordinates. The well assembly was geometrically discretized as a multilayered circular domain. The thermite reaction was modeled as a theoretical volumetric heat source profile dependent on both time and space, placed in the innermost layer. While a pure FIT approach may only be used to solve Neumann boundary conditions, the combined scheme applied here copes with any type of boundary condition. Hence, the integration of FIT with homogenization satisfies the Dirichlet condition requirement of the TP&A procedure. The methodology was verified through an equivalent Finite Volume Method (FVM) solution obtained using a commercial code. The results evidenced that within the 5 min duration of thermite reaction, the entire circumferential section of the production tube exceeds the steel melting temperature by at least 227 °C, thus fulfilling both milestones set. The research outcomes are part of a series of investigation steps to thoroughly analyze the new TP&A technology with regard to its compliance with the regulatory norms established to P&A operations.