Modeling of transient hydrogen permeation process across a palladium membrane

Transient mass transfer processes of hydrogen permeating through a Pd membrane are modeled to aid in predicting the hydrogen transport behavior. The model is established in terms of the quasi-steady time and the steady permeation rate. Meanwhile, four important parameters are considered; they are the permeation lag time, the initial permeation rate, the concave up period and the concave down period. A unit step function is embedded in the model to account for the effect of the hydrogen permeation lag at a lower pressure difference. Corresponding to the lower, the moderate and the higher pressure differences (i.e. 3, 5 and 8 atm), though the hydrogen permeation undergoes a three-stage, a two-stage and a one-stage processes, respectively, these processes can be predicted well by an arc tangential function. By introducing an adjusting parameter in the arc tangential function, there exists an optimal value of the adjusting parameter when the pressure difference is lower. In regard to the moderate and higher pressure differences, the predictions agree with experiments well if the adjusting parameter is sufficiently large. Physically, the unit step function is used to account for the controlling mechanisms of hydrogen diffusion toward the membrane and the spillover of the hydrogen across the membrane. The initial jump parameter represents the rapid response of the initial hydrogen permeation. The adjusting parameter can be used to describe the relative importance of the concave up and the concave down periods.