ON MATHEMATICAL MODELLING OF THE 2-D FILTRATION PROBLEM IN POROUS AXIAL SYMMETRICAL CYLINDER
DOI:
https://doi.org/10.17770/etr2017vol3.2566Keywords:
absorption, analytical and numerical solution, diffusion problem, filtration, sorbents, special splinesAbstract
In this paper we study diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can derive the system of two partial differential equations (PDEs). One equation is expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetically equation for absorption. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM). This procedure allows reducing the 2-D axis-symmetrical mass transfer problem described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.Downloads
References
Aivars Āboltiņš, Harijs Kalis and Ilmārs Kangro, On Mathematical Modelling of Heat and MoistureDistribution in the Porous Multilayer Media: 15-th International Scientific Conference”ENGINEERING FOR RURAL DEVELOPMENT”, Jelgava, May 25-27, 2016.
A. Aboltins, Theoretical study of thin layer material, concentration depending drying coefficient: 13 Int. conf. ”Engineering for rural developmen”, Jelgava May 29-30,2013, Jelgava. Latvia University of Agriculture: Proc. of 13 Int. Conf., pp.1-7., 2013.
A.R. Appadu, Comparative Study of Three Numerical Schemes for Contaminant Transport with Kinetic Langmuir Sorption. International Conference of Numerical Analysis and Applied Mathematics 2015 (ICNAAM 2015), AIP Conf. Proc., doi: 10.1063/1.4951777, AIP Publishing.
M. Buike and A. Buikis. "Modelling 3-D transport processes in anisotropic layered stratum by conservative averaging method, " WSEAS Transactions on Heat and Mass Transfer, vol.1, No. 4,pp. 430-437, 2006.
A. Buikis, E.J. Titushkina. "Applied Makkormak`s method for calculation the filtration of liquid solutions in soil," Mathematical Modelling, applieds problems in mathematicai physics, No.2, Riga, University of Latvia, pp.71-80, 1991.
A. Buikis, H. Kalis and I. Kangro, Special Hyperbolic type spline for mass transfer problems in multi-layer 3-D domains: 3-rd Int. Conf. on Applied,Numerical and Cmputational Mathematics (ICANCM'15), Sliema, Malta, August 17-19, 2015, Sliema, Proc. of 3-rd Int. Conf., pp. 25-34., 2015.
A. Buikis, H. Kalis and I. Kangro. "Special splines of exponential type for the solutions of mass transfer problems jn multilayer domains," Mathematical Modelling and Analysis, vol. 21, No. 4, pp. 450-465, 2016.
J. Crank. The mathematics of diffusion. Oxford: Clarendon Press, 1956.
William Henry. "Experiments on the quantity of gases absorbed by water," Philosophical Trans. of the Royal Soc., 93, pp. 29-274, 1803.
Harijs Kalis, Andris Buiķis, Ilmārs Kangro and Aivars Aboltins. ”Special splines of hyperbolic type for the solutions of heat and mass transfer 3-D problems in porous multi-layered axial symmetry domain", journal: Mathematical Modelling and Analysis, Taylor & Francis, “submitted for publication” (manuscript ID: TMMA-2016_0394.R2, manuscript type: review).
H. Kalis, I. Kangro. "Calculation of heat and moisture sistribution in the porous media layer," Mathematical Modelling and Analysis, vol. 12, No. 1, pp. 91-100, 2007.
M. Kellow. Energy and Environment, Experiment instructions, CE 583, Adsorption, 2011.
Irvin Langmuir. "The adsorption of gases on plane surfaces of glass, mica and platinum," J. Am. Chem. Soc, 40, pp.1361-1403, 1918.
G. Limousin, J.P. Gaudet, L. Charlet, S. Szenknect, V. Barthes, M. Krinissa. "Sorptions isotherms: a review on physical bases, modeling and measurement," Aplied Geochemistry, 22, pp. 249-275, 2007.
S. Ripperger, W. Gosele, C. Alt. Ullman's Encyclopedia of industrial chemistry, Filtration, 1. Fundaments, vol.14. Germany, 2012.
Teirumnieka, Ē., Kangro, I., Teirumnieks, E. and Kalis, H., The analytical solution of the 3D model with Robin's boundary conditions for 2 peat layers: 10-th Int. Scientific and Practical Conference "Environment. Technology. Resources", Rezekne June 18-20, 2015, Rezekne. Rezekne Higher Education institution: Proc. of 10-th Int. Conf., Volume III, pp.186-192, 2015.
A.N. Tihonov, A.A. Samarsky, Equations of Mathematical Physics. Moskow, Press: Nauka, 1966, pp.163-173 (in Russian).
