×

zbMATH — the first resource for mathematics

Mathematical modeling in chemistry. Application to water quality problems. (English) Zbl 1236.92079
Summary: This paper deals with mathematical modeling of chemical reaction systems. For the sake of simplicity the stirred tank assumption is made which allows us to remain in the framework of ordinary differential systems. The principles of chemical kinetics are recalled and the equations for the evolution of concentration of the chemical species involved in the reactions are given. The equilibrium of reversible reactions is also characterized. Then the case where low and fast reactions coexist is specifically considered by using asymptotic techniques to obtain limit models. Numerical methods are proposed and the whole methodology is applied to water quality models.
MSC:
92E20 Classical flows, reactions, etc. in chemistry
92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
65C20 Probabilistic models, generic numerical methods in probability and statistics
Software:
PhreeqcRM; PHREEQC
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alpers, C.N.; Blowes, D.W., Environmental geochemistry of sulfide oxidation, vol. 550, (1993), American Chemical Society Washington, DC
[2] Bermúdez, A., Continuum thermomechanics, (2005), Birkhäuser · Zbl 1070.74001
[3] Bermúdez, A.; Moreno, C., Duality methods for solving variational inequalities, Comput. math. appl., 7, 43-58, (1981) · Zbl 0456.65036
[4] Blodau, C., A review of acidity generation and consumption in acidic coal mine lakes and their watersheds, Sci. total environ., 369, 307-332, (2006)
[5] Brézis, H., Analyse fonctionnelle. théorie et applications, (1983), Masson · Zbl 0511.46001
[6] Castendyk, D.N.; Webster-Brown, J.G., Sensitivity analyses in pit lake prediction, martha mine, New Zealand 2: geochemistry, water-rock reactions, and surface adsorption, Chem. geol., 244, 56-73, (2007)
[7] Crouzeix, M.; Mignot, A., Analyse numérique des équations différentielles, (1989), Masson · Zbl 0709.65054
[8] Delgado, J.; Juncosa, R.; Padilla, F.; Rodríguez-Vellando, P.; Delgado, J., Predictive modeling of the water quality of the future meirama open pit lake (cerceda, a coruña), Macla, 10, 122-125, (2008)
[9] Eary, L.E., Geochemical and equilibrium trends in mine pit lakes, Appl. geochem., 14, 963-987, (1999)
[10] Evangelou, V.P.; Zhang, Y.L., A review: pyrite oxidation mechanisms and acid mine drainage prevention, Crit. rev. env. sci. tec., 25, 141-199, (1995)
[11] L. García-García, Numerical resolution of water quality models: application to the closure of open pit mines, Ph.D. thesis, University of Santiago de Compostela, 2010.
[12] R. Herbert, Sulfide oxidation in mine waste deposits - A review with emphasis on dysoxic weathering, Technical Report, MIMI, 1999.
[13] Morel, F.; Hering, J., Principles and applications of aquatic chemistry, (1993), John Wiley and Sons
[14] Nordstrom, D.; Alpers, C., (), 133-157
[15] Nordstrom, D.; Southam, G., (), 361-382
[16] Pares, C.; Castro, M.; Macias, J., On the convergence of the bermudez-moreno algorithm with constant parameters, Numer. math., 92, 113-128, (2002) · Zbl 1003.65069
[17] D. Parkhurst, C. Appelo, Userʼs Guide to pHreeqC (Version 2) - A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport and Inverse Geochemical Calculations, USGS, 1995.
[18] Smith, W.; Missen, R.W., Análisis del equilibrio en reacciones químicas. teoría y algoritmos, (1987), Limusa
[19] Tikhonov, V.A.; Sveshnikov, A.N.A., Differential equations, (1985), Springer-Verlag
[20] Waage, P.; Guldberg, C., Forhandl. videnskabs-selskabet christiana, 35-45, (1865)
[21] Werner, E.K.G.B.; Mueller, F.M., Pit lake baerwalde revisited: comparing predictions to reality, ()
[22] Werner, M.M.; Graupner, F.B., Predicted and observed water quality data from the coal mine pit lake Bärwalde, laustz, Germany, (), 2333-2343
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.