Permeation of Gases in Polymers: Parameter Identification and
Nonlinear Regression Analysis
This project resulted from two MSc thesis, by Sally Harbinson (2002)
and David Marquez (2004) in collaboration with Zakia
Benjelloun-Dabaghi (Applied Mathematics) and Marie-Helene Klopffer (Applied
Chemistry and Physical Chemistry) at ethe Institut Francais du
Petrole (IFP), Paris.
Project Description
In numerous previous studies it has been shown that the permeability
of gases in polymers depends strongly on the polymer structure, on
the gas type, as well as on the conditions of temperature and
pressure. The theoretical models that have been proposed and
developed in the literature, describe the transport mechanism of
molecular species in polymers by diffusion involving a
concentration-dependent diffusion coefficient. However, the exact
form of this dependency and exact information on the diffusion
coefficient and on the solubility coefficient are not always available in
the literature, in particular in extreme conditions like in the
case of protective polymer coatings for flexible offshore pipes
where the temperature and pressure of the diffusing gas can be
very high.
Using experimental data from permeation experiments on particularly
developed experimental devices at the Institut Francais du
Petrole (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.
The details of this work can be found in:
- R. Scheichl, M.-H. Klopffer, Z. Benjelloun-Dabaghi, B.
Flaconneche,
Permeation of Gases in Polymers: Parameter Identification and
Nonlinear Regression Analysis , Journal of Membrane Science
254, pp. 275-293, 2005.
[Home]
[Department of Mathematical Sciences]
[University of Bath]
Last updated 26/06/2006