Reliable dynamic models are particularly important for applications in the automotive sector, where operating conditions change frequently. To the best of our knowledge, there is no dynamic model in the literature for this area of application that considers the relevant steps in mass transport, i.e., convective mass transfer from the gas bulk to the membrane surface, (de)sorption at the membrane surface, and diffusion through the membrane. There are two main challenges in modeling membrane humidifiers: First, the diffusion coefficient of water in the membrane shows a strong non-linear dependency on the water content. Second, reaching the sorption equilibrium is a slow process. Therefore, the relevant process steps take place on different time scales.
We propose a dynamic first-principle model that extends the capabilities of our steady-state model [1]. Both models rely on mass balances supported by equations for mass transfer and sorption behavior. The mass transfer is coupled with heat transfer; additionally, the model accounts for pressure drop within the membrane humidifier. Depending on the flow configuration, the membrane humidifier is discretized in one direction for co-current and counter-current or two directions for cross-current.
The model is validated against measurement data from our test rig [2] and from the literature. The comparison of the simulation results and experimental data shows good agreement over a wide range of operating conditions. The validated model is then used to investigate the behavior of the membrane humidifier under various load changes, i.e., changes in the amount of supply and exhaust air flow rates.
Overall, the results show that the modeling approach is valid and captures the dominant phenomena. Thus, the model might be applied in a control scheme for water management in PEM fuel cells.