In order to reduce overall fuel consumption, or to partially substitute a "valuable" fuel with a poor one, in industrial heating, oxygen enrichment of combustion air can be very effective. For the second option, a general criterion is stated in this paper for examining the suitability of oxygen enrichment in single cases. The topic is particularly interesting, as for the first time, it is now feasible to produce oxygen enriched air using permeable membranes on a commercial scale and with costs that are remarkably lower than those of other existing techniques. In this paper, the subject is investigated after some remarks about the definition of the "usable exergy" parameter, which was already proposed in previous papers by one of the authors and is here utilized for the above criterion.