Apparent diffusion model assessment in extraction processes by means of a Luenberger observer

In this work a clear methodology is proposed that allows the estimation of diffusion–concentration functional relationship in extraction processes, which are modelled by Fick’s second law. A criterion is proposed for deciding when the diffusivity should be considered a constant value (comparable to those obtained by the standard regression technique) and when a function depending on concentration. The methodology is based in a Luenberger observer. The diffusion–concentration relationship is refined by an optimization procedure making use of a numerical solution of the diffusion equation. The robustness of the methodology is assessed by a noise propagation analysis. The methodology is illustrated for oil extraction from tung seeds with experimental data taken from the literature.