Humidification dehumidification (HDH) is a desalination technology that has shown promise in small scale, decentralized applications. Previous studies on the multi-staging of HDH have used fixed-effectiveness models which do not explicitly account for transport processes in the components. However, to fully understand the effect of the variation of the mass flow rate ratio, it is necessary to implement heat and mass transfer models of the HDH system. In this paper, we model an HDH system consisting of a packed-bed humidifier and a multi-tray bubble column dehumidifier. We study the effect of the mass flow rate ratio on the performance of a fixed-size system, and we consider its effect on the entropy generation and the driving forces for heat and mass transfer. In addition, we define a generalized energy effectiveness for heat and mass exchangers. We also implement an air extraction/injection and simulate a wide range of operating conditions. We define criteria for the best system performance, and we study the effect of the distribution of available area between separate stages. We also present a thorough explanation of why the direction of extraction should always be from the humidifier to the dehumidifier. (C) 2015 Elsevier B.V. All rights reserved.