Permeation of gases in polymers: parameter identification and nonlinear regression analysis

Using experimental data from permeation experiments on particularly developed experimental devices at the Institut Français du Pétrole (IFP) we are able to study this dependency and have produced a method which allows to identify the parameters in the model from this data. Mathematically, this leads to a nonlinear least-squares optimisation problem with constraints in the form of partial differential equations (PDEs), which we will concentrate on in this paper. In particular, we will focus on the statistical analysis of the results and give confidence intervals for the estimated parameters. We will also present tests to check whether the assumptions on our model are appropriate and to identify whether the introduction of a concentration-dependent diffusion coefficient is necessary for particular pairs of gas and polymer and at certain temperatures and pressures. We will demonstrate the performance of our method and the statistical analysis of the results on some data obtained with the experimental devices at the IFP.