1. MMC
  2. All Volumes and Issues
  3. Volume 5, Number 2, 2018
  4. Spatial modeling of multicomponent pollution removal for liquid treatment under identification of mass transfer coefficient

Spatial modeling of multicomponent pollution removal for liquid treatment under identification of mass transfer coefficient

MMC.
2018;
Volume 5, Number 2
: 108-118
https://doi.org/10.23939/mmc2018.02.108
Received: October 02, 2018

Math. Model. Comput. Vol. 5, No. 2, pp. 108-118 (2018)

Authors:
  1. A. Bomba
  2. A. Safonyk
  3. V. Voloshchuk
1
Rivne State Humanitarian University
2
Department of Automation, Electrical and Computer-Integrated Technologies, National University of Water and Environmental Engineering
3
National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"

A generalized spatial mathematical model of the multicomponent pollutant removal for a liquid treatment is proposed. Under the assumption of domination of convective processes over diffusive ones, the model considers an inverse influence of the determining factor (pollution concentration in water and sludge) on the media characteristics (porosity, diffusion) and takes into account the specified additional condition (overridden condition) for estimation of the unknown mass transfer coefficient of a small value.

The algorithm for solving the corresponding nonlinear singularly perturbed inverse problem of the type "convection--diffusion--mass transfer" is developed. A computer experiment has been carried out based on this methodology.

multicomponent pollutant
inverse problem
overdeterminatiom condition
asymptotic solution
identification
spatial modeling
  1. Berg C. Permeability description by characteristic length, tortuosity, constriction and porosity. Transport in Porous Media. 103 (3), 381–409 (2014).
  2. Calo V., Iliev O., Lakdawala Z., Leonard K., Printsypar G. Pore-scale modeling and simulation of flow, transport, and adsorptive or osmotic effects in membranes: The influence of membrane microstructure. International journal of advances in engineering sciences and applied mathematics. 7 (1), 2–13 (2015).
  3. Chetti A., Benamar A., Abdelkrim H. Modeling of Particle Migration in Porous Media: Application to Soil Suffusion. Transport in Porous Media. 113 (3), 591–606 (2016).
  4. Civa F. Modified formulations of particle deposition and removal kinetics in saturated porous media. Transport in Porous Media. 111 (2), 381–410 (2016).
  5. Gravelle A., Peysson Y., Tabary R., Egermann P. Experimental investigation and modelling of colloidal release in porous media. Transport in Porous Media. 88 (3), 441–459 (2011).
  6. Husseinab M., Lesnica D., Ivanchov M., Snitkod H. Multiple time-dependent coefficient identification thermal problems with a free boundary. Appl. Num. Math. 99, 24–50 (2016).
  7. Mittal R., Jain R. Numerical solutions of nonlinear Fisher’s reaction-diffusion equation with modified cubic B-spline collocation method. Math. Sci. 7 (1), 12 (2013).
  8. Peng Ch., XuG., WuW., YuH., Wangc Ch. Multiphase SPH modeling of free surface flow in porous media with variable porosity. Computers and Geotechnics. 81, 239–248 (2017).
  9. Shi M., Printsypar G., Iliev O., Calo V., Amy G., Nunes S. Water flow prediction based on 3D membrane morphology simulation. J. Membr. Sci. 487, 19–31 (2015).
  10. Orlov V., Martynov S., Kunitskiy S. Energy saving in water treatment technologies with polystyrene foam filters. Journal of Water and Land Development. 31 (X-XII), 119–122 (2016).
  11. Orlov V., Martynov S., Kunitskiy S. Water defferrization in polystyrene foam filters with sediment layer. LAP LAMBERT Academic Publishing, Saarbrucken. 94 p. (2016).
  12. Bomba A., Safonyk A., Fursachik E. Identification of mass transfer distribution factor and its account for magnetic filtration process modeling. Journal of Automation and Information Sciences. 45 (4), 16–22
    (2013)    .
  13. Orlov V., Safonyk A., Martynov S. Simulation the process of iron removal the underground water by polystyrene foam filters. International Journal of Pure and Applied Mathematics. 109 (4), 881–888
    (2016)    .
  14. Safonyk A. Modelling the filtration processes of liquids from multicomponent contamination in the conditions of authentication of mass transfer coefficient. Int. J. Math. Models and Methods in Appl. Sciences. 9, 189–192 (2015).
  15. Safonyk A. Modelling of biological purification process taking into account the temperature mode. Int. J. Math. Models and Methods in Appl. Sciences. 12, 68 (2018).
  16. Bomba A., Klymiuk Yu., Prysiazhniuk I., Prysiazhniuk O., Safonyk A. Mathematical modeling of wastewater treatment from multicomponent pollution by using microporous particles. AIP Conference Proceedings. 1773 (1), 040003 (2016).
  17. Bomba A., Safonik A. Mathematical simulation of the process of aerobic treatment of wastewater under conditions of diffusion and mass transfer perturbations. Journal of Engineering Physics and Thermophysics. 91 (2), 318–323 (2018).
  18. Safonyk A., Martynov S., Kunytsky S., Pinchuk O. Mathematical modelling of regeneration the filtering media bed of granular filters. Advances in Modelling and Analysis C. 73 (2). 72–78 (2018).