CFD simulations are valuable tools in evaluating and deploying oxy-fuel and other carbon capture technologies either as retrofit technologies or for new construction. However, accurate predictive simulations require physically realistic submodels with low computational requirements. In particular, comprehensive char oxidation and gasification models have been developed that describe multiple reaction and diffusion processes. This work extends a comprehensive char conversion code (the Carbon Conversion Kinetics or CCK model), which treats surface oxidation and gasification reactions as well as processes such as film diffusion, pore diffusion, ash encapsulation, and annealing. In this work, the CCK model was thoroughly investigated with a global sensitivity analysis. The sensitivity analysis highlighted several submodels in the CCK code, which were updated with more realistic physics or otherwise extended to function in oxy-coal conditions. Improved submodels include a greatly extended annealing model, the swelling model, the mode of burning parameter, and the kinetic model, as well as the addition of the Chemical Percolation Devolatilization (CPD) model. The resultant Carbon Conversion Kinetics for oxy-coal combustion (CCK/oxy) model predictions were compared to oxy-coal data, and further compared to parallel data sets obtained at near conventional conditions.