Self-ignition of coal dust deposits poses a higher risk of fires in oxygen-enriched oxy-fuel combustion systems. In this work, we develop a numerical method, using the commercial software COMSOL Multiphysics, to investigate self-ignition behaviour of coal dust accumulations with a main emphasis on the roles of oxygen, diluent gas and dust volume. A one-step 2nd-order reaction kinetic model considering both coal density and oxygen density is used to estimate reaction rate using the kinetic parameters from previously conducted hot-oven tests. This model is validated to predict the transient temperature and concentration profiles of South African coal dusts until ignition. The computed self-ignition temperatures of dust volumes show a good agreement with experimental results. In addition, it is found that the inhibiting effect of carbon dioxide is comparatively small and oxygen consumption increases dramatically after ignition. Parameter analysis shows that the heating value and kinetic parameters have a comparatively pronounced effect on self-ignition temperature. The model provides a satisfactory explanation for the dependence of self-ignition behaviour on gas atmospheres, thus helping to further understand the fire risk of self-ignition in oxy-fuel combustion systems. (C) 2016 Elsevier Ltd. All rights reserved.