A new model approach for an analytical calculation of a mass exchanger is presented in this work. By using three dimensionless numbers the mass transfer between two fluid flows can be calculated dependent on the flow geometry. A gas humidifier used for fuel cell application, which transfers water between two gas flows, is used as an example to illustrate the development of the operation characteristics for coflow, counterflow and crossflow. In this model approach the whole mass transfer process, governed by humidifier design and separator material properties, is described based on a single characteristic value, the effective mass transfer coefficient. The model provides a deeper understanding and prediction capability of the transfer processes which is helpful for mass exchanger designing and controlling. The coflow and counterfiow case is validated by using a water permeable membrane as separator of wet air and dry air. Measurement data of a hollow fibre separator is used to validate the cross flow operated humidifier. (C) 2016 Elsevier Ltd. All rights reserved.