A Fully Coupled Multi-Physics Finite Element Model for In-Situ Combustion Based on Semi-Global Reaction Kinetics: Mathematical Formulation, Numerical Implementation, and Validation

In-situ combustion (ISC), also referred to as fire flooding, represents one of the most technically viable enhanced oil recovery (EOR) strategies for unlocking heavy oil and bitumen resources, yet its field-scale deployment remains severely hindered by the extreme complexity of coupled multiphase flow, multi-component transport, chemical kinetics, non-Darcy heat/mass transfer, and thermo-mechanical rock deformation. Conventional numerical models for ISC predominantly adopt lumped reaction kinetics and oversimplified constitutive closures, which inherently lack the capability to resolve the spatiotemporal evolution of intermediate reactive species and yield inconsistent predictions across varying reservoir and operational conditions. To address this limitation, we present a fully coupled multi-physics finite element model for ISC processes, developed within the theoretical framework of modern combustion science. The model integrates five interacting physical fields and incorporates a 12-step semi-global kinetic mechanism that covers high-temperature oxidation (HTO), low-temperature oxidation (LTO), and thermal cracking pathways. A complete constitutive system consisting of five categories totaling 57 equations is constructed to ensure mathematical closure. The Galerkin finite element weak forms of the coupled system are derived, and a fully implicit Newton-Raphson solver is implemented for numerical discretization. Validation against field data from a conglomerate oil reservoir demonstrates satisfactory mesh independence, robust quadratic convergence (4.0 +/– 1.1 iterations per time step), and good agreement with field observations of produced gas composition (CO2, CO, O2) and temperature profiles. Quantitative comparison with published combustion tube experiments further confirms the predictive capability of the developed model.