Two-Phase Formation Damage by Fines Migration
Several investigators including Muecke (1979), Sarkar (1988), and Sarkar and Sharma (1990) have determined that fine particles behave differently in a multi-phase fluid environment and formation damage follows a different course than the single-phase systems. However, the reported studies on the two-phase formation damage are very limited. Sutton and Roberts (1974) and Sarkar and Sharma (1990) have experimentally observed that formation damage in two-phase is less severe than in single-phase. Liu and Civan (1993, 1995, 1996) have shown that two-phase formation damage requires the consideration of other factors, such as the wettability affect and partitioning of particles between various phases.
Mutual interactions and affects between the two-phase flow systems, fine particles, and porous matrix are described mathematically to develop a predictive model for formation damage by fines migration in two-phase systems flowing through porous formations. The formulation is carried out by extending the Liu and Civan (1993, 1994, 1995, 1996) model for more realistic applications. The tests and case studies used by Liu and Civan (1995, 1996) are presented for demonstration and verification of the model. Although the model presented here involves some simplifications pertaining to the laboratory core damage experiments, it can be readily modified and generalized for the actual conditions encountered in petroleum reservoirs.
Formulation
The equations describing the various aspects for formation damage by fines migration during two-phase fluid flow through porous formations are formulated here. However, the formulation can be extended readily to multi-phase fluid systems. It is safe to assume that the gas phase does not carry any solid particles (i.e., it is nonwetting for all particles). For convenience in modeling, the bulk porous media is considered in four phases as schematically depicted in this article:
(1) the solid matrix,
(2) the wetting fluid,
(3) the nonwetting fluid, and
(4) the interface region.
These phases are indicated by S, W, N, and /, respectively. The porous matrix is assumed nondeformable. Therefore, it is stationary and its volumetric flux is zero. The wetting and nonwetting phases flow at the volumetric fluxes denoted, respectively, by uw and UN. The interface region is located between the wetting and nonwetting phases and is assumed to move at a flux equal to the absolute value of the difference between the fluxes of the wetting and nonwetting phases.
The various particles involving the formation damage are classified as
(1) the foreign particles introduced externally at the wellbore,
(2) the indigeneous particles existing in the porous formation, and
(3) the particles generated inside the pore space by various processes, such as the wettability alteration considered in this chapter.
Another classification of particles is made with reference to the wettability as
(1) the wetting particles,
(2) the nonwetting particles, and
(3) the intermediately wetting particles.
These particles are identified, respectively, by wp, np, and ip. The latter classification is more significant from the modeling point of view. Because, as explained by Muecke (1979), the wettability affects the behavior of these particles in a multi-phase fluid system. By means of experimental
investigations, Muecke (1979) has observed that particles tend to remain in the phases that can wet them. Ku and Henry, Jr. (1987) have shown that intermediately wet particles accumulate at the interface of the wetting and nonwetting phases, because they are most stable there. Therefore, in the following formulation, an interface region containing the intermediately wet particles is perceived to exist in between the wetting and nonwetting phases as schematically indicated in this article.
Further, it is reasonable to consider that the wettability of some particles may be altered by various processes, such as asphaltene, paraffin, and inorganic precipitation or by other mechanisms such as the turbulence created by rapid flow in the near-wellbore region. Consequently, these altered particles should tend to migrate into the phases that wet them as inferred by the experimental studies of Ku and Henry, Jr. (1979). In addition to the particles, the various phases may contain a number of dissolved species. The salt content of the aqueous phase is particularly important, because it can lead to conditions for colloidally induced release of clay particles when its salt concentration is below a critical salt concentration (Khilar and Fogler, 1983).
For convenience in formulation, the locations for particles retention can be classified in three categories:
(1) the wetting pore surface,
(2) the nonwetting pore surface, and
(3) the pore space behind the plugging pore throats.
The areal fractions of the wetting and nonwetting sites can vary as a result of the various rock, fluid, and particle interactions during formation damage, such as by asphaltene, paraffin, and inorganic deposition. Therefore, a parameter fks indicating the fraction of the pore surface, that is wetting for species k, is introduced in the formulation. Because the applications to describe and interpret the laboratory core damage data, conducted at mild temperature and pressure conditions are intended, the formulation is carried out for one-dimensional flow in homogeneous core plugs, isothermal conditions, and incompressible particles and fluids. This allows the use of a simplified formulation based on volumetric balances and a fractional flow concept. However, the derivation can be readily extended for compressible systems encountered at the prevailing elevated pressure conditions of the reservoir formations.
References
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.
