Identification of mathematical model and parameter estimation of erythromycin migration in two different porous media, based on column tests
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Published:
Jun 20, 2018
Keywords:
groundwater, erythromycin, sorption, optimization
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Abstract
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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References
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BU, Q., WANG, B., HUANG, J., DENG, S. & YU, G. (2013): Pharmaceuticals and personal care products in the aquatic environment in China: A review.– J. Hazard. Mater., 262, 189–211. doi: 10.1016/j.jhazmat.2013.08.040
CAMERON, D.R. & KLUTE, A. (1977): Convective-dispersive solute transport with a combined equilibrium and kinetic adsorption model.- Water Resour. Res., 13, 183-188. doi: 10.1029/WR013i001p00183
COLEMAN, T.F. & LI, Y. (1994): On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds.- Math. Program., 67/2, 189-224. doi: 10.1007/BF01582221
CZECH, B. (2012): Removal of pharmaceuticals from water and sewage by applying adsorption and photocatalytic methods.- In: RYCZKOWSKI, J. (ed.): Adsorbents and catalysts: the technology selected versus the environment. Nauka dla gospodarki, 2, 443-452 (in Polish).
DE VOOGT, P., JANEX-HABIBI, M.-L., SACHER, F., PUIJKER, L. & MONS, M. (2009): Development of a common priority list of pharmaceuticals relevant for the water cycle.- Water Sci. Technol., 59/1, 39–46. doi: 10.2166/wst.2009.764
FOHRMANN, G., MAŁOSZEWSKI, P. & SEILER, K.-P. (2001): Experimental determination of the copper & antimony mobility in calcareous and none-calcareous aquifer sediments in columns and 1-D reactive transport modeling.- In: SEILER, K.-P. & WOHNLICH, S. (eds.): New Approaches Characterizing Groundwater Flow. A.A.Balkema, Lisse, 315-319.
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HOLTZ, R. & KOVACS, W. (1981): An introduction to geotechnical engineering.– Prentice- Hall, New Jersey.
KÜMMERER, K. (ed.) (2008): Pharmaceuticals in the environment: sources, fate, effects and risks.– Springer-Verlag, Berlin, Heidelberg.
LEIBUNDGUT, C., MALOSZEWSKI, P. & KÜLLS, C. (2009): Tracers in hydrology.–John Wiley & Sons Ltd., Chichester.
doi: 10.1002/9780470747148
LOVMAR, M., TENSON, T. & EHRENBERG, M. (2004): Kinetics of macrolide action: the josamycin and erythromycin cases.- J. Biol. Chem., 279/51, 53506-53515. doi: 10.1074/jbc.M401625200
MA, Y., LI, M., WU, M., LI, Z. & LIU, X. (2015): Occurrences and regional distributions of 20 antibiotics in water bodies during groundwater recharge.– Sci. Total Environ., 518–519, 498–506. doi: 10.1016/j.scitotenv.2015.02.100
MALOSZEWSKI, P. (1981): Computerprogramm Field für die Berechnung der Dispersion und der effektiven Porosität in geschichteten porösen Medien.– GSF-Bericht R 269, Gesellschaft für Strahlen- und Umweltforschung, München-Neuherberg (in German).
MARCINIAK, M., KACZMAREK, M., OKOŃSKA, M. & KAZIMIERSKA-DROBNY, K. (2009): The identification of hydrogeological parameters on the basis of a numerical simulation of a breakthrough curve and optimization methods.- Bogucki Wyd. Nauk., Poznań (in Polish).
MARCINIAK, M., OKOŃSKA, M., KACZMAREK, M. & KAZIMIERSKA-DROBNY, K. (2013): The sensitivity test for a breakthrough curve recorded during tracer migration in a filtration column.- Biuletyn PIG, 456, 385-390 (in Polish).
MOMPELAT, S., LE BOT, B. & THOMAS, O. (2009): Occurrence and fate of pharmaceutical products and by-products, from resource to drinking water.– Environ. Int., 35, 803–814. doi:10.1016/j.envint.2008.10.008
OKOŃSKA, M. (2006): The identification of pollutants migration parameters in a groundwater porous medium by the method of the column experiment modelling.- Geologos 9, Bogucki Wyd. Nauk., Poznań (in Polish).
OKOŃSKA, M. (2016): Catalog of hydrogeological parameters.– www.hydrometria.
amu.edu.pl/badania-naukowe/badania-kolumnowe-migracji zanieczyszczen/, database on the website of the Department of Hydrometry, Adam Mickiewicz University in Poznań (in Polish).
PENG, X., OU, W., WANG, C., WANG, Z., HUANG, Q., JIN, J. & TAN, J. (2014): Occurrence and ecological potential of pharmaceuticals and personal care products in groundwater and reservoirs in the vicinity of municipal landfills in China.– Sci. Total Environ., 490, 889-898. doi: 10.1016/j.scitotenv.2014.05.068
SIEMENS, J., HUSCHEK, G., WALSHE, G., SIEBE, C., KASTEEL, R., WULF, S., CLEMENS, J. & KAUPENJOHANN, M. (2010): Transport of pharmaceuticals in columns of a wastewater-irrigated Mexican clay soil.- J. Environ. Qual., 39/4, 1201–1210. doi: 10.2134/jeq2009.0105
SÖDERSTRÖM, T. & STOICA, P. (1988): Systems identification.- Prentice-Hall, New Jersey.
SUN, Y., ZHU, J.-W., CHEN, K. & XU, J. (2009): Modeling erythromycin adsorption to the macroporous resin Sepabead SP825.- Chem. Eng. Comm., 196/8, 906-916. doi: 10.1080/00986440902743802
WATKINSON, A.J., MURBY, E.J. & COSTANZO, S.D. (2007): Removal of antibiotics in conventional and advanced wastewater treatment: implications for environmental discharge and wastewater recycling.- Water Res., 41/18, 4164-4176. doi: 10.1016/j.watres.2007.04.005
WATKINSON, A.J., MURBY, E.J., KOLPIN, D.W. & COSTANZO, S.D. (2009): The occurrence of antibiotics in an urban watershed: from wastewater to drinking water.- Sci. Total Environ., 407/8, 2711-2723. doi: 10.1016/j.scitotenv.2008.11.059
WEBER, W.J. JR., MCGINLEY, P.M. & KATZ, L.E. (1991): Sorption phenomena in subsurface systems: Concepts, models and effects on contaminant fate and transport. Water Res., 25, 499-528. doi:10.1016/0043-1354(91)90125-A
WITCZAK, S., KANIA, J. & KMIECIK, E. (2013): Catalog of selected physical and chemical indicators of groundwater pollution and methods of their determination.- Inspekcja Ochrony Środowiska, Warszawa (in Polish).
WU, C., HUANG, X., WITTER, J.D., SPONGBERG, A.L., WANG, K, WANG, D. & LIU, J. (2014): Occurrence of pharmaceuticals and personal care products and associated environmental risks in the central and lower Yangtze river, China.– Ecotox. Environ. Safe., 106, 19-26. doi: 10.1016/j.ecoenv.2014.04.029
XU, M. & ECKSTEIN, Y. (1997): Statistical analysis of the relationships between dispersivity and other physical properties of porous media.– Hydrogeol. J., 5/4, 4–20. doi:10.1007/s100400050254
YAO, L., WANG, Y., TONG, L., DENG, Y., LI, Y., GAN, Y., GUO, W., DONG, C., DUAN, Y. & ZHAO, K. (2017): Occurrence and risk assessment of antibiotics in surface water and groundwater from different depths of aquifers: A case study at Jianghan Plain, central China.– Ecotox. Environ. Safe., 135, 236–242. doi: 10.1016/j.ecoenv.2016.10.006
ZAJĄC, A., ZEMBRZUSKA, J., BUDNIK, I., KRUSZELNICKA, I. & GINTER-KRAMARCZYK, D. (2013): Pharmaceutical’s path in environment in the area of Wielkopolska - applications, the source of occurrence, threats.– In: Production, economy, management, marketing and environmental protection - how it is done in Wielkopolska – Gniezno, Poland, 2013, Conference materials. Hipolit Cegielski State College of Higher Education in Gniezno, Gniezno, 190–205 (in Polish).
ZUCCATO, E., CASTIGLIONI, S., BAGNATI, R., MELIS, M. & FANELLI, R. (2010): Source, occurrence and fate of antibiotics in the Italian aquatic environment.– J. Hazard. Mater., 179/1-3, 1042-1048. doi: 10.1016/j.jhazmat.2010.03.110
American Chemical Society. SciFinder.- https://scifinder.cas.org/scifinder/, 2009.
APPELO, C.A.J. & POSTMA, D. (1999): Geochemistry, groundwater and pollution.- A.A.Balkema, Rottterdam, Brookfield.
BANZHAF, S. & HEBIG, K.H. (2016): Use of column experiments to investigate the fate of organic micropollutants - a review.– Hydrol. Earth Syst. Sci., 20, 3719– 3737. doi:10.5194/hess-20-3719-2016 and doi:10.5194/hess-20-3719-2016-supplement
BOLEDA, M.A., GALCERAN, M.A. & VENTURA, F. (2011): Behaviour of pharmaceuticals and drugs of abuse in a drinking water treatment plant (DWTP) using combined conventional and ultrafiltration and reverse osmosis (UF/RO) treatments.- Environ. Pollut., 159/6, 1584-1591. doi: 10.1016/j.envpol.2011.02.051
BOROŃ, M. & PAWLAS, K. (2015): Pharmaceuticals in aquatic environment – literature review.- Probl. Hig. Epidemiol., 96/2, 357-363 (in Polish).
BU, Q., WANG, B., HUANG, J., DENG, S. & YU, G. (2013): Pharmaceuticals and personal care products in the aquatic environment in China: A review.– J. Hazard. Mater., 262, 189–211. doi: 10.1016/j.jhazmat.2013.08.040
CAMERON, D.R. & KLUTE, A. (1977): Convective-dispersive solute transport with a combined equilibrium and kinetic adsorption model.- Water Resour. Res., 13, 183-188. doi: 10.1029/WR013i001p00183
COLEMAN, T.F. & LI, Y. (1994): On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds.- Math. Program., 67/2, 189-224. doi: 10.1007/BF01582221
CZECH, B. (2012): Removal of pharmaceuticals from water and sewage by applying adsorption and photocatalytic methods.- In: RYCZKOWSKI, J. (ed.): Adsorbents and catalysts: the technology selected versus the environment. Nauka dla gospodarki, 2, 443-452 (in Polish).
DE VOOGT, P., JANEX-HABIBI, M.-L., SACHER, F., PUIJKER, L. & MONS, M. (2009): Development of a common priority list of pharmaceuticals relevant for the water cycle.- Water Sci. Technol., 59/1, 39–46. doi: 10.2166/wst.2009.764
FOHRMANN, G., MAŁOSZEWSKI, P. & SEILER, K.-P. (2001): Experimental determination of the copper & antimony mobility in calcareous and none-calcareous aquifer sediments in columns and 1-D reactive transport modeling.- In: SEILER, K.-P. & WOHNLICH, S. (eds.): New Approaches Characterizing Groundwater Flow. A.A.Balkema, Lisse, 315-319.
HENDRY, M.J., LAWRENCE, J.R. & MALOSZEWSKI, P. (1999): Effects of velocity on the transport of two bacteria through saturated sand.- Ground Water, 37/1, 103-112. doi: 10.1111/j.1745-6584.1999.tb00963.x
HOLTZ, R. & KOVACS, W. (1981): An introduction to geotechnical engineering.– Prentice- Hall, New Jersey.
KÜMMERER, K. (ed.) (2008): Pharmaceuticals in the environment: sources, fate, effects and risks.– Springer-Verlag, Berlin, Heidelberg.
LEIBUNDGUT, C., MALOSZEWSKI, P. & KÜLLS, C. (2009): Tracers in hydrology.–John Wiley & Sons Ltd., Chichester.
doi: 10.1002/9780470747148
LOVMAR, M., TENSON, T. & EHRENBERG, M. (2004): Kinetics of macrolide action: the josamycin and erythromycin cases.- J. Biol. Chem., 279/51, 53506-53515. doi: 10.1074/jbc.M401625200
MA, Y., LI, M., WU, M., LI, Z. & LIU, X. (2015): Occurrences and regional distributions of 20 antibiotics in water bodies during groundwater recharge.– Sci. Total Environ., 518–519, 498–506. doi: 10.1016/j.scitotenv.2015.02.100
MALOSZEWSKI, P. (1981): Computerprogramm Field für die Berechnung der Dispersion und der effektiven Porosität in geschichteten porösen Medien.– GSF-Bericht R 269, Gesellschaft für Strahlen- und Umweltforschung, München-Neuherberg (in German).
MARCINIAK, M., KACZMAREK, M., OKOŃSKA, M. & KAZIMIERSKA-DROBNY, K. (2009): The identification of hydrogeological parameters on the basis of a numerical simulation of a breakthrough curve and optimization methods.- Bogucki Wyd. Nauk., Poznań (in Polish).
MARCINIAK, M., OKOŃSKA, M., KACZMAREK, M. & KAZIMIERSKA-DROBNY, K. (2013): The sensitivity test for a breakthrough curve recorded during tracer migration in a filtration column.- Biuletyn PIG, 456, 385-390 (in Polish).
MOMPELAT, S., LE BOT, B. & THOMAS, O. (2009): Occurrence and fate of pharmaceutical products and by-products, from resource to drinking water.– Environ. Int., 35, 803–814. doi:10.1016/j.envint.2008.10.008
OKOŃSKA, M. (2006): The identification of pollutants migration parameters in a groundwater porous medium by the method of the column experiment modelling.- Geologos 9, Bogucki Wyd. Nauk., Poznań (in Polish).
OKOŃSKA, M. (2016): Catalog of hydrogeological parameters.– www.hydrometria.
amu.edu.pl/badania-naukowe/badania-kolumnowe-migracji zanieczyszczen/, database on the website of the Department of Hydrometry, Adam Mickiewicz University in Poznań (in Polish).
PENG, X., OU, W., WANG, C., WANG, Z., HUANG, Q., JIN, J. & TAN, J. (2014): Occurrence and ecological potential of pharmaceuticals and personal care products in groundwater and reservoirs in the vicinity of municipal landfills in China.– Sci. Total Environ., 490, 889-898. doi: 10.1016/j.scitotenv.2014.05.068
SIEMENS, J., HUSCHEK, G., WALSHE, G., SIEBE, C., KASTEEL, R., WULF, S., CLEMENS, J. & KAUPENJOHANN, M. (2010): Transport of pharmaceuticals in columns of a wastewater-irrigated Mexican clay soil.- J. Environ. Qual., 39/4, 1201–1210. doi: 10.2134/jeq2009.0105
SÖDERSTRÖM, T. & STOICA, P. (1988): Systems identification.- Prentice-Hall, New Jersey.
SUN, Y., ZHU, J.-W., CHEN, K. & XU, J. (2009): Modeling erythromycin adsorption to the macroporous resin Sepabead SP825.- Chem. Eng. Comm., 196/8, 906-916. doi: 10.1080/00986440902743802
WATKINSON, A.J., MURBY, E.J. & COSTANZO, S.D. (2007): Removal of antibiotics in conventional and advanced wastewater treatment: implications for environmental discharge and wastewater recycling.- Water Res., 41/18, 4164-4176. doi: 10.1016/j.watres.2007.04.005
WATKINSON, A.J., MURBY, E.J., KOLPIN, D.W. & COSTANZO, S.D. (2009): The occurrence of antibiotics in an urban watershed: from wastewater to drinking water.- Sci. Total Environ., 407/8, 2711-2723. doi: 10.1016/j.scitotenv.2008.11.059
WEBER, W.J. JR., MCGINLEY, P.M. & KATZ, L.E. (1991): Sorption phenomena in subsurface systems: Concepts, models and effects on contaminant fate and transport. Water Res., 25, 499-528. doi:10.1016/0043-1354(91)90125-A
WITCZAK, S., KANIA, J. & KMIECIK, E. (2013): Catalog of selected physical and chemical indicators of groundwater pollution and methods of their determination.- Inspekcja Ochrony Środowiska, Warszawa (in Polish).
WU, C., HUANG, X., WITTER, J.D., SPONGBERG, A.L., WANG, K, WANG, D. & LIU, J. (2014): Occurrence of pharmaceuticals and personal care products and associated environmental risks in the central and lower Yangtze river, China.– Ecotox. Environ. Safe., 106, 19-26. doi: 10.1016/j.ecoenv.2014.04.029
XU, M. & ECKSTEIN, Y. (1997): Statistical analysis of the relationships between dispersivity and other physical properties of porous media.– Hydrogeol. J., 5/4, 4–20. doi:10.1007/s100400050254
YAO, L., WANG, Y., TONG, L., DENG, Y., LI, Y., GAN, Y., GUO, W., DONG, C., DUAN, Y. & ZHAO, K. (2017): Occurrence and risk assessment of antibiotics in surface water and groundwater from different depths of aquifers: A case study at Jianghan Plain, central China.– Ecotox. Environ. Safe., 135, 236–242. doi: 10.1016/j.ecoenv.2016.10.006
ZAJĄC, A., ZEMBRZUSKA, J., BUDNIK, I., KRUSZELNICKA, I. & GINTER-KRAMARCZYK, D. (2013): Pharmaceutical’s path in environment in the area of Wielkopolska - applications, the source of occurrence, threats.– In: Production, economy, management, marketing and environmental protection - how it is done in Wielkopolska – Gniezno, Poland, 2013, Conference materials. Hipolit Cegielski State College of Higher Education in Gniezno, Gniezno, 190–205 (in Polish).
ZUCCATO, E., CASTIGLIONI, S., BAGNATI, R., MELIS, M. & FANELLI, R. (2010): Source, occurrence and fate of antibiotics in the Italian aquatic environment.– J. Hazard. Mater., 179/1-3, 1042-1048. doi: 10.1016/j.jhazmat.2010.03.110