Dual-reflux pressure swing adsorption (DR-PSA) systems represent new options for producing two pure products from binary gas mixtures using adsorption. Within the constraint of DR-PSA, there are several options: feed to the low- or high-pressure bed and equalize, repressurize and blowdown with either the weakly or strongly adsorbed gas (opposite ends of the adsorption column). Each of these options leads to different flow sheets and results in different system performance, in particular productivity and work consumption tradeoff. In part I of this two part study we formulate method-of-characteristics models for all of the dual-reflux (DR) cases-in several cases new DR models are developed which are yet to be reported. In part II, we apply our models to show how the DR-PSA system can be assessed for a variety of gas mixtures and adsorbent type. (c) 2006 Elsevier Ltd. All rights reserved.