Flow modelling of chemical species through a chromatographic column

We study a mathematical model describing the flow of a gas through a chromatographic column, which consists of three different levels: the zeolite crystals, the pellets (assembling some zeolite crystals), and the column. We prove an existence and uniqueness result and compute an approximate value of the diffusion coefficient inside the crystals comparing the solution and an experimental observation of the outgoing signal, using the Laplace transform and a numerical inversion of the Laplace transform.