During the thermogravimetric measurement of carbon oxidation reactivity, the sample is contained in a crucible, and oxygen has access only through the top surface of the particle bed. Condensed carbons such as soot and carbon black have such large surface areas that oxygen mass transfer limitations control their combustion in such situations. A technique to describe the mass transfer processes has been developed, in which the gas phase and in-bed transfer processes have been decoupled. The gas phase is modelled by the CFD package FLUENT and diffusion within the bed is described by a mono-dimensional model. The procedure has been used to examine the accessibility of oxygen to samples contained in deep and shallow crucibles, and also the orientation of the flow with regard to the crucible mouth. In all cases, the transport of oxygen to the bed surface was dominated by molecular diffusion. Some existing experimental data for carbon black combustion were re-analysed to extract the true reactivities.