The objectives of the experimental studies were threefold:

1. Determine an empirical relationship between permeability and porosity in the form of Eq. 10-92.

2. Determine the values of the deposition and entrainment rate constants, kp and k'e.

3. Study the effects of the length of porous media and the rate and concentration of the particle suspension injected into the porous media.

The pressure difference across the porous media and the particle concentration of the effluent were measured as functions of time during the injection of a suspension of finely ground limestone particles at a given concentration and rate. The porous material was prepared by using nonwoven felt of filaments of polypropylene. The porous material samples of 4 cm diameter and 0.5,1.0, 1.5, and 2.0 cm lengths were used. The particle suspension was prepared using finely ground limestone of 2,825 kg/m3 density in water. The porosity was determined by the weighting method. The discrete times at which measurements are taken are denoted by the subscript i = 2,3,...,N and the initial time is denoted by / = 1. The permeability was determined by Darcy's equation by neglecting the effect of gravity for short samples:

The volume of particles deposited per unit volume of porous media was calculated, by integrating Eq. 10-84 and applying the mean value theorem:

where £0 =0 for an initially particle-free porous material. Eq. 10-172 is evaluated numerically by applying the trapezoidal rule of integration as, for a constant injection suspension particle concentration:

Eqs. 10-170 and 173 were applied at different times and the data were plotted in Figure 10-16. As shown in Figure 10-16, virtually the same results were obtained for different injection velocities of u = 0.5 and 1.0 cm/s. The E and G parameter values were determined as a function of the length of porous media by nonlinear regression of Eq. 10-92 to the data given in Figure 10-16. Plot of E and G vs. the length are given in this article exponential regressions of these data indicate that E = 0.14 and G = 5.3 as the length approaches zero, although the data are of low

quality, as indicated by the coefficients of regressions R2 = 0.78 and R2 = 0.18, respectively. The mean diameter of particles is 20.2jam and the estimated dimension of pores 50jom. The porosity is (j>0=0.31. The concentration of the injected suspension is cin =0.lkg/m3 or <5in = 0.1&g/ra3)/(2,825£g/m3) = 3.54xlO-5m3/m To determine the deposition and entrainment rate constants, in Eq. 10-91 i'cr - 0 was substituted and the derivative with respect to time was evaluated numerically using the central and backward finite difference approximations given below, respectively, for the interior and the final points:

The average concentration was estimated as the logarithmic mean value of the injection and the effluent suspension concentrations according to:

The rate parameters, kp and k'e, in Eq. 10-91 were determined for different injection velocities using the method of least squares with the values calculated by Eqs. 10-170 and 174-176. The results presented in this article indicate that the retention rate coefficient, kp, decreases and the entrainment rate coefficient, ke, increases with the injection velocity. These calculations were repeated for different length porous media and the results are summarized. These values can be extrapolated to zero core length, however, again the quality of data is not good.

The effect of the suspension particle concentration and particle size on the pressure drop. For a given injection suspension particle concentration and rate, at equilibrium,


Cernansky, A., & Siroky, R. "Deep-bed Filtration on Filament Layers on Particle Polydispersed in Liquids," Int. Chem. Eng., Vol. 25, No. 2, 1985, pp. 364-375.

Cernansky, A., & Siroky, R., "Hlbkova Filtracia Polydisperznych Castic z Kvapalin na Vrstvach z Vlakien," Chemicky Prumysl, Vol. 32 (57), No. 8, 1982, pp. 397-405.

Civan, F. "A Generalized Model for Formation Damage by Rock-Fluid Interactions and Particulate Processes," SPE Paper 21183, Proceedings of the SPE 1990 Latin American Petroleum Engineering Conference, October 14-19, 1990, Rio de Janeiro, Brazil, 11 p.

Civan, F. "Evaluation and Comparison of the Formation Damage Models," SPE 23787 paper, Proceedings of the SPE International Symposium on Formation Damage Control, February 26-27, 1992, Lafayette, Louisiana, pp. 219-236.

Civan, F., & Knapp, R. M. "Effect of Clay Swelling and Fines Migration on Formation Permeability," SPE Paper No. 16235, Proceedings of the SPE Production Operations Symposium, Oklahoma City, Oklahoma, 1987, pp. 475-483.

Civan, F. "A Multi-Phase Mud Filtrate Invasion and WellBore Filter Cake Formation Model," SPE Paper No. 28709, Proceedings of the SPE International Petroleum Conference & Exhibition of Mexico, October 10-13, 1994, Veracruz, Mexico, pp. 399-412.

Civan, F., Knapp, R. M., & Ohen, H. A. "Alteration of Permeability by Fine Particle Processes," J. Petroleum Science and Engineering, Vol. 3, Nos. 1/2, October 1989, pp. 65-79.

Civan, F., Predictability of Formation Damage: An Assessment Study and Generalized Models, Final Report, U.S. DOE Contract No. DE-AC22- 90BC14658, April 1994.

Civan, F. "Modeling and Simulation of Formation Damage by Organic Deposition," Proceedings of the First International Symposium on Colloid Chemistry in Oil Production: Asphaltenes and Wax Deposition, ISCOP'95, Rio de Janeiro, Brazil, November 26-29, 1995, pp. 102-107.

Civan, F. "A Multi-Purpose Formation Damage Model," SPE 31101, Proceedings of the SPE Formation Damage Symposium, Lafayette, Louisiana, February 14-15, 1996, pp. 311-326.

Civan, F. "Interactions of the Horizontal Wellbore Hydraulics and Formation Damage," SPE 35213, Proceedings of the SPE Permian Basin Oil & Gas Recovery Conf., Midland, Texas, March 27-29, 1996, pp. 561-569.

Gruesbeck, C, & Collins, R. E. "Particle Transport Through Perforations," SPEJ, December 1982b, pp. 857-865.

Gruesbeck, C., & Collins, R. E. "Entrainment and Deposition of Fine Particles in Porous Media," SPEJ, December 1982a, pp. 847-856.

Khilar, K. C., & Fogler, H. S. "Colloidally Induced Fines Migration in Porous Media," in Amundson, N. R. & Luss, D. (Eds.), Reviews in Chemical Engineering, Freund Publishing House LTD., London, England, January-June 1987, Vol. 4, Nos. 1 and 2, pp. 41-108.

Khilar, K. C., & Fogler, H. S. "Water Sensitivity of Sandstones," SPEJ, February 1983, pp. 55-64.

Liu, X., Civan, F, & Evans, R. D. "Correlation of the Non-Darcy Flow Coefficient, J. of Canadian Petroleum Technology, Vol. 34, No. 10, 1995, pp. 50-54.

Metzner, A. B., & Reed, J. C. "Flow of Non-Newtonian Fluids—Correlation of the Laminar, Transition, and Turbulent Flow Regions," AIChE J., Vol. 1, No. 4, 1955, pp. 434-440.

Nayak, N. V, & Christensen, R. W. "Swelling Characteristics of Compacted Expansive Soils," Clay and Clay Mineral, Vol. 19, No. 4, December 1970, pp. 251-261.

Ohen, H. A., & Civan, F. "Predicting Fines Generation, Migration and Deposition Near Injection and Production Wells," Proceedings of the First Regional Meeting, American Filtration Society, Houston, Texas, October 30-November 1, 1989, pp. 161-164.

Ohen, H. A., & Civan, F. "Simulation of Formation Damage in Petroleum Reservoirs," SPE Advanced Technology Series, Vol. 1, No. 1, April 1993, pp. 27-35.

Ohen, H. A., & Civan, F. "Simulation of Formation Damage in Petroleum Reservoirs," SPE 19420 paper, Proceedings of the 1990 SPE Symposium on Formation Damage Control, Lafayette, Louisiana, February 22-23, 1990, pp. 185-200.

Schechter, R. S., Oil Well Stimulation, Prentice Hall, Englewood Cliffs, New Jersey, 1992, 602 p.

Seed, H. B., Woodward, Jr., R. J., & Lundgren, R. "Prediction of Swelling Potential for Compacted Clays," /. Soil Mech. Found. Div., Proc. Am. Soc. Civ. Eng., 88(SM3), June 1962, pp. 53-87.

Wojtanowicz, A. K., Krilov, Z., & Langlinais, J. P. "Study on the Effect of Pore Blocking Mechanisms on Formation Damage," SPE 16233 paper, presented at Society of Petroleum Engineers Production Operations Symposium, Oklahoma City, Oklahoma, March 8-10, 1987, pp. 449-463.

Wojtanowicz, A. K., Krilov, Z., & Langlinais, J. P. "Experimental Determination of Formation Damage Pore Blocking Mechanisms," Trans, of the ASME, Journal of Energy Resources Technology, Vol. 110, 1988, pp. 34-42.