The literature on studies of the mechanisms of wettability alteration and interface particle transfer is rather limited and insufficient to formulate these processes accurately and rigorously. Therefore, Liu and Civan (1996) have resorted to a simplified approach, which yielded reasonably good results. They have combined the rate processes of the wettability transformation and the phase to phase particle transfer into one step assuming that the particles would immediately migrate into the phases, which wet them once their wettabilities change from one type to another.

Based on the experimental observations and the studies of the mechanisms of interface particle transfer of Ku and Henry (1987), Liu and Civan (1996) assumed that the rate of the combined processes of wettability transformation and interface transfer of particles can be expressed as being proportional to the particle concentration according to:

Particle Retention in Porous Media

Although particle retentions may occur at various locations in porous media by various mechanisms, only the most likely mechanisms are considered here. The wetting and nonwetting particles preferentially deposit over the similar wettability type pore surfaces. They can also be captured at and detained behind the pore throats under favorable conditions. The intermediately wet particles most likely move directly towards the pore throats and are captured there under certain conditions, because they migrate along the interface.

Surface Deposition

The volumetric rate of deposition of the particle species j from phase J over a similar wetting pore surface can be expressed by (Civan, 1996):

Similar to Gruesbeck and Collins (1982), Liu and Civan (1996) assumed that the porosity variation by deposition of small amounts of particles is negligible (i.e., (|) is a constant). Liu and Civan (1996) considered a homogeneous wettability porous media, hence fjs = 1, and neglected the stationary deposition, therefore ocy =0.

Pore Throat Plugging

The volumetric rate of retention of particles in the pore space following the pore throat plugging can be expressed by (Gruesbeck and Collins, 1982, Civan, 1996):

Liu and Civan (1996) assumed the porosity change is negligible in Eq. 11-35 (i.e., (}) = constant). In Eq. 11-35, ktiJtS denotes the rate constant for deposition by pore throat plugging. Civan (1990, 1996) proposed a dimensionless correlation to determine the conditions favorable for pore throat plugging in single phase fluid media. This equation determines the critical ratio of the pore throat-to-particle diameters below which pore throat plugging by jamming of particles occurs. Thus,

where the pore throat-to-particle diameter ratio and the particle Reynolds numbers are given, respectively, by:

Liu and Civan (1993, 1995, 1996) have resorted to a simplified approach in an adhoc manner and demonstrated by comparison of the results with experimental data that it works. They assumed that the fraction of the plugged pore throats is proportional to the amount of particles detained behind the plugged pore throats. Therefore, their expression for the fraction of the nonplugged pore throats can be written as:

where ktjj are some empirical coefficients. They considered that there is a minimum characteristic value of (ƒt)min. for which the rpore throat blocking happens. Thus,


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

Civan, F., "A Multi-Phase Mud Filtrate Invasion and Well Bore 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., "A Multi-Purpose Formation Damage Model," SPE 31101 paper, Proceedings of the SPE Formation Damage Symposium, Lafayette, Louisiana, February 14-15, 1996, pp. 311-326.

Civan, F., "Convenient Formulations for Immiscible Displacement in Porous Media," SPE Paper 36701, Proceedings of the 71st SPE Annual Tech. Conf. and Exhibition, Denver, Colorado, October 6-9, 1996, pp. 223-236.

Collins, E. R., Flow of Fluids Through Porous Materials, Penn Well Publishing Co., Tulsa, Oklahoma, 1961, 270 p.

Craig, F. F., Jr., The Reservoir Engineering Aspects of Waterflooding, Third Printing, November 1980, Society of Petroleum Engineers of AIME, New York, 1971, 134 p.

Dake, L. P., Fundamentals of Reservoir Engineering, Elsevier Scientific Publ. Co., New York, 1978, 443 p.

Eleri, O. O., & Ursin, J-R., "Physical Aspects of Formation Damage in Linear Flooding Experiments," SPE 23784 paper, presented at the SPE Intl. Symposium on Formation Damage Control, Lafayette, Louisiana, February 26-27, 1992.

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

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

Jiao, D., & Sharma, M. M., "Formation Damage Due to Static and Dynamic Filtration of Water-Based Muds," SPE 23823 paper, presented at the SPE Intl. Symposium on Formation Damage Control, Lafayette, Louisiana, February 26-27, 1992.

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

Ku, C-A., & Henry, Jr., J. D., "Mechanisms of Particle Transfer from a Continuous Oil to a Dispersed Water Phase, J. Colloid and Interface ScL, 1987, Vol. 116, No. 2, pp. 414-422.

Liu, X., & Civan, F., "Characterization and Prediction of Formation Damage in Two-Phase Flow Systems, SPE 25429 paper, Proceedings of the SPE Production Operations Symposium, March 21-23, 1993, Oklahoma City, Oklahoma, March 21-23, 1993, pp. 231-248.

Liu, X., & Civan, F, "Formation Damage and Skin Factors Due to Filter Cake Formation and Fines Migration in the Near-Wellbore Region," SPE 27364 paper, Proceedings of the 1994 SPE Formation Damage Control Symposium, February 9-10, 1994, Lafayette, Louisiana, pp. 259-274.

Liu, X., & Civan, E, "Formation Damage by Fines Migration Including Effects of Filter Cake, Pore Compressibility and Non-Darcy Flow—A Modeling Approach to Scaling from Core to Field," SPE Paper #28980, SPE International Symposium on Oilfield Chemistry, February 14-17, 1995, San Antonio, TX.

Liu, X., & Civan, F., "Formation Damage and Filter Cake Buildup in Laboratory Core Tests: Modeling and Model-Assisted Analysis," SPE Formation Evaluation J., Vol. 11, No. 1, March 1996, pp. 26-30.

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.

Luan, Z., "Splitting Pseudospectral Algorithm for Parallel Simulation of Naturally Fractured Reservoirs," SPE Paper 30723, Proceedings of the Annual Tech. Conf. & Exhibition held in Dallas, TX, October 22-25.

Muecke, T. W., "Formation Fines and Factors Controlling their Movement in Porous Media," JPT, pp. 147-150, Feb. 1979.

Peng, S. J., & Peden, J. M., "Prediction of Filtration Under Dynamic Conditions," paper SPE 23824 presented at the SPE Intl. Symposium on Formation Damage Control held in Lafayette, LA, February 26-27, 1992, pp. 503-510.

Rahman, S. S., & Marx, C., "Laboratory Evaluation of Formation Damage Caused by Drilling Fluids and Cement Slurry," J. Can. Pet. Tech., November-December, 1991, pp. 40-46.

Richardson, J. G., "Flow Through Porous Media," In: V. L. Streeter (Editor), Handbook of Fluid Dynamics, Section 16, McGraw-Hill, New York, 1961, pp. 68-69.

Sarkar, A. K., "An Experimental Investigation of Fines Migration in Two-Phase Flow," MS Thesis, U. of Texas, Austin, 1988.

Sarkar, A. K., & Sharma, M. M., "Fines Migration in Two-Phase Flow," JPT, May 1990, pp. 646-652.

Sutton, G. D., & Roberts, L. D., "Paraffin Precipitation During Fracture Stimulation," JPT, September 1974, pp. 997-1004.

Ucan, S., & Civan, R, "Simultaneous Estimation of Relative Permeability and Capillary Pressure for Non-Darcy Flow-Steady-State," SPE Paper 35271, Proceedings of the 1996 SPE Mid-Continent Gas Symposium, Amarillo, TX, April 29-30, 1996, pp. 155-163.

Yokoyama, Y, & Lake, L. W., "The Effects of Capillary Pressure on Immiscible Displacements in Stratified Porous Media," SPE 10109 paper, presented at the 56th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME, San Antonio, TX, October 5-7, 1981.