A thermodynamic model for use in predicting heat and water transfer across a membrane in a membrane humidifier was created that could take into account fuel cell operating conditions. Experiments were conducted to obtain the necessary information to make the model complete, and also to validate its use over a range of temperatures and flow rates.

The latent effectiveness and latent number of transfer units (ε-NTU) method for mass transfer in membrane humidity exchangers was applied to PEMFC membrane humidifiers to comprise the heat and mass transfer thermodynamic model. Two limitations that cause deviations in the theoretical outlet conditions previously reported were discovered:​ 1. using a constant enthalpy of vaporization derived from the reference temperature in the Clausius-Clapeyron equation;​ and, 2. simplifying the relationship between relative humidity and absolute humidity as linear. In the model presented here, these limitations are alleviated by using an effective mass transfer coefficient Ueff. The model was created in Mathcad and the constitutive equations are solved iteratively to find the flux of water through the membrane.

The new procedure was applied to three types of membrane and compared to the curves of ε_L and NTU_L found using Zhang and Niu’s method, which is normally applied to energy recovery ventilators (ERVs). For a 70°C isothermal case, a deviation in latent effectiveness predictions was observed of 29% for Type-I membranes, 23% for lineartype membranes, and 46% for Type-III membranes, as compared to the latent effectiveness values obtained with the ERV method.

Experiments were conducted on a commercially available fuel cell humidifier to determine which parameters could be removed from a full-factorial experimental matrix. It was discovered that pressure had a lower effect on water transport than temperature over the practical operating range of fuel cell systems, so pressure effects were neglected throughout the study. The focus of the study was then on the effect of overall temperature. Furthermore, it was determined that water recovery ratio is the best performance metric because it takes into account the water supplied to the humidifier.

Two different membranes were characterized to incorporate into the thermodynamic model. The first, used as a baseline, was a porous polymer membrane with a hydrophilic additive. The second membrane was a competing novel ionic membrane. Both membranes showed similar behavior, with low water uptake profiles at relative humidities less than 80%, and a steep increase in water uptake after 80% relative humidity. The porous membrane exhibited greater maximum sorption than the ionic membrane.

Experiments were conducted with samples of the porous and ionic membrane in a single cell humidifier at isothermal conditions at temperatures of 25°C, 50°C, and 75°C. The ionic membrane showed greater water transfer over the range of laminar flows investigated. The ionic membrane’s water recovery was almost unaffected by flow rate;​ whereas the porous membrane displayed a decrease in water recovery as flow rate increased. Finally, the model was correlated with the experimental data by obtaining a corresponding diffusion coefficient for each membrane over the range of temperatures tested.