Recently, a new type of bioreactor for air pollution control referred to as the foamed emulsion bioreactor (FEBR) has been developed. The process relies on the emulsion of an organic phase with a suspension of an actively growing culture of pollutant-degrading microorganisms, made into a foam with the air undergoing treatment. In the current paper, a diffusion and reaction model of the FEBR is presented and discussed. The model considers the fate of the volatile pollutant in the emulsion that constitutes the liquid films of the FEBR. Oxygen limitation as well as substrate inhibition were included in the biokinetic relationships. The removal of toluene vapors served for the validation of the model. All the model parameters were determined by independent experiments or taken from the literature. The model predictions were found to be in good agreement with the experimental data and the model provided useful insights on the phenomena occurring in the FEBR. Model parametric sensitivity studies and further discussion of the factors that limit the performance of the FEBR are presented in Part 2 of this paper.