Water Suspension Infiltration with Adsorption in Unsaturated-Saturated Porous Media
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Abstract
Transportation of contaminated water suspension (water and silt) in unsaturated-saturated porous media is considered. Moreover, the water in suspension is contaminated and this contaminant is adsorbed by the porous media matrix. The deposition of silt in the matrix is characterized by a filtration function, and the contaminant adsorption is modeled by a sorption isotherm. The mathematical model includes a coupled system for the water suspension infiltration, silt, and contaminant (uniformly mixed in the water) transport with dispersion and their deposition and adsorption in porous media. Filtration function expresses the rate of silt deposition depending on the amount of (immobile) deposited silt. Contaminant adsorption is modeled in terms of the contaminant concentration in suspension, the amount of adsorbed contaminant, and the rate of adsorption. The main goal is to develop a suitable numerical approximation that can be applied to the solution of direct and inverse problems. In the numerical experiments, we demonstrate the correctness and the effectiveness of the used method.
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How to Cite
Kačur, J., & Mihala, P.
(2020).
Water Suspension Infiltration with Adsorption in Unsaturated-Saturated Porous Media.
Proceedings Of The Conference Algoritmy, , 229 - 239.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1587/840
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References
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[4] M.T. Van Genuchten, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil science society of American Journal, vol 44, (1980), p. 892-898.
[5] J. Kačur, P. Mihala and M. Tóth, Determination of soil parameters in hydraulic flow model for porous media, International journal of mechanics, Vol. 11, (2017), p. 36–42.
[6] J. Kačur and J. Minár, A benchmark solution for infiltration and adsorption of polluted water into unsaturated-saturated porous media, Transport in porous media, vol. 97, (2013), p. 223–239.
[7] T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. Dewitt, Fundamentals of heat and mass transfer, John Wiley and Sons, 7th edition, (2011).
[8] M. Koniorczyk and D. Gawin, Heat and moisture transport in porous building materials containing salt, Journal of building physics, vol. 31, no. 4, (2008), p. 279-300.
[9] N.-Z. Sun, Inverse problems in Groundwater modelling., Kluwer, Academics. Dordrecht, (1994).
[10] N.-Z. Sun and A. Sun, Mathematical Modeling of Groundwater Pollution, Springer-Verlag, New York, (1996).
[11] A.C. Alvarez, G.Hime, J.D.Silva and D.Marchesin, Analytic regularization of an inverse filtration problem in porous media, Inverse Problems 29, (2013).
[12] Z.Mesticou, M.Kacem and PH.Dubujet, Flow of suspensions through porous media - application to deep filtration, Indust.Eng.Chem. 65, (1970), p. 8–35.
[13] J.P.Herzig, D.M.Leclerc and P.L.Golf, Krylov subspace methods for solving large unsymmetric linear systems, Math. Comp., 37 (1981), pp. 105–126.
[14] P. Bedrikovetsky et al., Particle detachment under velocity alternation during suspension transport in porous media, Transport in Porous Media volume 91, (2012), 173–197.
[15] J. Kačur, P. Mihala and M. Tóth, Numerical modeling of heat exchange and unsaturated- saturated flow in porous media, Computers and Mathematics with Applications, Vol. 77, No. 9 (2019), pp. 1668–1680.