Several models of fluidized bed reactors are seriously limited by being based on a single bubble diameter. Solutions are presented for simple two-phase models which include a description of variation of bubble size with height. This has been achieved by dividing the bed into a number of small intervals, within each of which a mean bubble size can be used. The results of these solutions have been compared in two ways with those of models using a single bubble: by determining the single bubble size which would predict the same conversion and by calculating the conversion predicted using the single bubble size which would give the same bed expansion. Calculated results show that the single bubble size giving the same conversion exists at about 40% of the bed height and that, except for fast reactions, the conversion predicted using a single bubble size determined from bed expansion is very close to that obtained with a model incorporating bubble size variation.