This study focuses on theories and applications of char reaction model in air and oxy atmospheres. First, a new method was derived; it can directly calculate variations in carbon diameter during char conversion. This method can replace the traditional power law and quantitatively evaluate effects of oxidation and CO2 gasification on char properties and reaction rate at different atmospheres and temperature ranges. Second, a new ash inhibition submodel was developed based on direct calculations of carbon diameter. This submodel can quantitatively explain effects of ash layer thickness and ash layer collapse on reaction rate. Third, simulations of single particle conversion were conducted using the new char reaction model. Results showed that the new method of calculating carbon diameter can result in faster reaction rate at low temperatures and vice versa compared with power law. The new ash inhibition submodel can provide slower reaction rates and increase burnout time compared with the original ash inhibition submodel. CO2 gasification in oxy-coal combustion can significantly lower apparent carbon density at high temperatures and lower particle temperature. However, combined effects of carbon gasification and decrease in apparent carbon density on reaction rate are more pronounced than effects of decreased particle temperature. Finally, utilizing the new char reaction model, computational fluid dynamics modeling was performed in drop-tube furnace and entrained-flow reactor. Predicted temperature profiles coincided with experimental values (i.e., less than 50 K temperature errors), and deviation of burnout fraction totaled less than 3%. (C) 2017 Published by Elsevier Ltd.