Identification of mathematical model and parameter estimation of erythromycin migration in two different porous media, based on column tests

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Monika Okonska
Katarzyna Pietrewicz


The amount of pharmaceuticals found in groundwater has risen over the last few years. Erythromycin is an example of an antibiotic widely used in human health care and veterinary practice that can be transported into the subsurface. The aim of the presented research was to 1) determine the mathematical model of erythromycin migration in two different porous media, 2) estimate the model parameters and 3) compare the migration of the antibiotic in the investigated media. The research was conducted in a specially prepared laboratory stand where column tests were performed. One column was filled with glass granules (70% SiO2, 600–800 μm in diameter) and the second column was filled with a natural sediment (sandur sand). The migration of a conservative tracer and erythromycin was examined in both columns. The experiments were performed in two separate steps. In the first step, a conservative tracer, subject to advection and dispersion processes, was injected into the column and its transport was investigated. The second step involved investigating the migration of erythromycin. A conductivity meter was installed at the output of the column in order to determine tracer concentrations based on calibration curves. Short-time pulse injections and continuous injection were applied during the experiments. An interpretation of the experiments results was conducted in the MATLAB environment. A mathematical model of erythromycin migration was determined from the shape of pulse breakthrough curves, which were characterized by a set of descriptors: the time of maximum tracer concentration at the output tmax, the spread of the breakthrough curve s, and relative tracer recovery e. This procedure involved implementing an identification algorithm developed by the authors. It was proved that the migration of erythromycin is best described by a hybrid model that assumes the coexistence of equilibrium and non-equilibrium sorption. In the next stage of the research, the transport and sorption parameters were estimated through numerical optimization procedures. The convergence between theoretical and experimental breakthrough curves was analysed qualitatively by calculating the root mean square error RMSE and correlation coefficient r.


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