The present invention relates to a pressure swing adsorption process, also known as PSA process, which is modified with a view to utilizing the heat from the post-adsorption stream coming from the molecular sieves to heat/vaporize the pre-adsorption stream containing the hydrated product or the mixture component(s) to be adsorbed in said sieves. The present invention provides alternative arrangements for the heat exchanger system in order to use the thermal potential of the post- adsorption stream with the elimination or minimization of the risk of a slug flow regime in the exchangers, the so-called "gush," which would be a natural result from the periodic oscillation characteristic of PSA processes. With this, the vapor consumption with the modified process according to the present invention is considerably reduced.