The Mathematical Model for Particle Suspension Flow through Porous Medium

Hooman Fallah, Hosein Barzegar Fathi, Hamed Mohammadi

Islamic Azad University, Firoozabad Branch, Iran.

DOI: 10.4236/gm.2012.23009                

Abstract

Transport of suspensions and emulsions in porous media occurs in numerous processes of environmental, chemical, petroleum and civil engineering. In this work, a mass balance particle transport equation which includes filtration has been developed. The steady-state transport equation is presented and the solution to the complete advective-dispersion equation for particulate suspension flow has been derived for the case of a constant filter coefficient. This model in-cludes transport parameters which are particle advective velocity, particle longitudinal dispersion coefficient and filter coefficient. This work recommends to be investigated by particle longitudinal dispersion calculation from experimental data, directly. Besides, the numerical model needs to be developed for general case of a transition filter coefficient.

Keywords

Particulate Suspension Flow; Filtration Theory; Filtration Coefficient; Transport; Porous Medium; Mathematical Model

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Pang and M. M. Sharma, “A Model for Predicting Injectivity Decline in Water-Injection Wells,” SPE Paper 28489, Vol. 12, No. 3, 1997, pp. 194-201.
[2]	T. Iwasaki, “Some Notes on Sand Filtration,” Water Works Association, 1937, pp. 1591-1602,
[3]	J. W. A. Foppen and J. F. Schijven, “Evaluation of Data from the Literature on the Transport and Survival of Escherichia coil in Aquifers under Saturated Conditions,” Journal of Water Research, Vol. 40, No. 3, 2006, pp. 401-426. doi:10.1016/j.watres.2005.11.018
[4]	J. F. Schijven and S. M. Hassanizadeh, “Removal of Viruses by Soil Passage: Overview of Modeling Processes, and Parameters,” Critical Reviews in Environmental Science and Technology, Vol. 30, No. 1, 2000, pp. 49-127
[5]	R. Farajzadeh, “An Experimental Investigation into Internal Filtration and External Cake Build Up,” MSc. Thesis, Delft University of Technology, 2004.
[6]	J. P. Herzig, D. M. Leclerc and P. Le Goff, “Flow of suspension through porous media-application to deep filtration,” Journal of Industrial and Engineering Chemistry, Vol. 65, No. 5, 1970, pp. 8-35
[7]	M. Elimelech and O’Melia, “Effect of Particle Size on Collosion Efficiency in the Deposition of Brownian Particles with Electrostatic Barriers,” 1990, pp. 1153-1163
[8]	J. E. Houseworth, “Longitudinal Dispersion in Nonuniform, Isotropic Porous Media,” Ph.D. Thesis, W.M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Report No. KH-R-45, 1984.
[9]	A.C. Paytakes and C. Tien, “Particle Deposition in Fibrous Media with Dendritic Pattern: Apreliminary model,” Journal of Aerosol Science, Vol. 7, No. 2, 1976, pp. 85-94. doi:10.1016/0021-8502(76)90067-7