ABSTRACT Deep bed filtration of carrier water with particles occurs in numerous processes of environmental, chemical, petroleum and civil engineering. For example in the petroleum industry, deep bed filtration of drilling fluid happens during well drilling; it also takes place near to injection wells during seawater injection or produced water re-injection causing in- jectivity reduction. In this work, the filtration theory and its mathematical model are given and the filtration coefficient will be discussed. Then the transition time, the time at which the initial layer of external filter cake is completely formed has been derived mathematically. The transition time can be obtained by calculating the trapping efficiency as a function of the number of previously deposited particles where very few particles can invade the rock and the external filtration begins to build. The prediction of particle capturing and particle retention by mathematical model is an essen- tial stage during planning and design of above-mentioned industrial processes.
Cite this paper
H. Fallah, A. Ahmadi, M. Karaee and H. Rabbani, "External Cake Build Up at Surface of Porous Medim," Open Journal of Fluid Dynamics, Vol. 2 No. 4, 2012, pp. 145-148. doi: 10.4236/ojfd.2012.24015.
 R. Farajzadeh, (PWRI), “An Experimental Investigation into Internal Filtration and External Cake Build Up,” MSc. Thesis, Delft University of Technology, Delft, 2004.
 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.
 T. Iwasaki, “Some Notes on Sand Filtration.” Journal of the American Water Works Association, Vol. 29, 1937, pp. 1591-1602.
 P. Bedrikovetsky and F. D. Siqeira, “Modified Particle Detachment Model for Colloidal Transport in Porous Media,” Transport in Porous Media, Vol. 86, No. 2, 2011, pp.383-413.
 Z. I. Khatib, “Prediction of Formation Damage Due to Suspended Solids: Modeling Approach of Filter Cake Build up in Injectors,” Paper SPE 28488, 1994.
 S. Pang and M. M. Sharma, “Supplement to SPE 28489, A Model for Predicting Injectivity Decline in Water Injection Wells,” SPE Formation Evaluation, Vol. 12, No. 3, 1997, pp. 194-201.
 J. H. Barkman and D. H. Davidson, “Measuring Water Quality and Prediction Well Impairment,” Journal of Petroleum Technology, 1972, pp. 865-868.
 F. Al-Abduwani, W. M. G. van den Broek and P. K. Currie, “Laboratory and Mathematical Study of Produced Water Re-Injection in Oil Reservoirs,” European Water Management Symposium, Aberdeen, 21-22 May 2004.