Forces Acting Upon Particles
Ives (1985) classified the various forces acting on particles in a flowing suspension in three categories as
a forces related to the transport mechanisms,
b forces related to the attachment mechanisms, and
c forces related to the detachment mechanisms, and characterized them in terms of the relevant dimensionless groups.
- 1 Forces Related to the Transport Mechanisms
- 2 Forces Related to the Attachment Mechanisms
- 3 Forces Related to the Detachment Mechanisms
- 4 References
Forces Related to the Transport Mechanisms
The important relevant quantities governing the particle behavior in a suspension can be summarized as following: d and D are particle and porous media grain diameters, respectively; p5 is the density of particles; p and \JL are the density and viscosity of the carrier liquid, respectively; va is the convective velocity; g is the gravitational acceleration coefficient; and T is the absolute temperature.
The inertia of a particle forces it to maintain motion in a straight line. The inertia force can be expressed by the dimensionless group as (Ives, 1985):
As a result of the density difference between the particle and the carrier liquid, particles tend to move in the gravity direction according to Stokes' law. The velocity of a spherical particle undergoing a Stokes' motion is given by:
The gravity force acts upward when particles are lighter and, therefore, buoyant. The gravity force acts downward when particles are heavier and, therefore, tend to settle. The gravity force can be expressed by a dimensionless group, which relates the Stokes and convection velocities as (Ives, 1985):
The centrifugal forces are generated by external acceleration. The centrifugal force created with an angular velocity of w and a radius of R is expressed in dimensionless form by
Particles smaller than 1 mm diameter tend to move irregularly in a liquid media and disperse randomly. This phenomena is called the Brownian notion. The diffusivity of fine particles undergoing a Brownian notion is given by Einstein (McDowell-Boyer et al., 1986):
The diffusion force can be expressed by the Peclet number as the ratio of the convection velocity to the average Brownian velocity given by (Ives, 1985).
Hydrodynamic forces are the fluid shearing and pressure forces (Wojtanowicz et al., 1987, 1988). Ives (1985) explains that during fluid flow econdary circulation flows can be formed around the particles, which can generate out-of-balance hydrodynamic forces acting on the particles to move them across the flow field. Ives (1985) states that a proper dimensionless group rigorously expressing the hydrodynamic force is not available. Ives (1985) points out that the Reynolds number given by:
and its other forms such as those "relating to the shear gradient, the relative velocity between particle and liquid, the angular velocity of the rotating particle, and the frequency of pulsation liquid have been suggested." Khilar and Fogler (1987) expressed the hydrodynamic lift force pulling a spherical particle off the pore surface by the following equation given by Hallow (1973):
where us is the slip velocity, K is the linearized velocity gradient near the particle, and d is the diameter of the spherical particle.
Forces Related to the Attachment Mechanisms
These forces act on the particles when they are near the grain surface less than a 1 Jim distance (Ives, 1985). These forces and the characteristic dimensionless groups are described below.
London—van der Waals Force
This is the attractive force due to the electromagnetic waves generated by the electronic characteristics of atoms and molecules. The attraction force is expressed by (Ives, 1985):
in which X is a dimensionless wavelength of the dispersion force divided by nd product and Fn is a function assuming different forms for (s - 2)/X less and greater than unity.
Friction—Drag Force and Hydrodynamic Thinning
Particles approaching the grain surfaces experience a flow resistance because they must displace the liquid at the surface radially as they attach to the grain surface (Ives, 1985; Khilar and Fogler, 1987).
Forces Related to the Detachment Mechanisms
This is the friction or drag force. When the shear stress of the liquid flowing over the deposited particles creates a shearing force greater than those attaching the particles to the grain surface, then the particles can be detached and mobilized (Ives, 1985):
Electrostatic Double-Layer Force
These forces are created due to the ionic conditions measured by pH and ionic strength. When the particle and grain surfaces carry the electrostatic charges of the same sign, they repel each other. The repulsive force is expressed by (Ives, 1985):
where s is the dimensionless separation distance expressed as the ratio of the radial separation distance divided by the particle radius (d/2), k is the Debye reciprocal double-layer thickness, and d is the particle diameter. When the ionic strength is higher, then the double-layer thickness is smaller, and hence k is larger.
Born Repulsion Force
This force is generated as a result of the overlapping of the election clouds (Wojtanowicz et al., 1987, 1988).
Amaefule, J. O., Kersey, D. G., Norman, D. L., & Shannon, P. M., "Advances in Formation Damage Assessment and Control Strategies," CIM Paper No. 88-39-65, Proceedings of the 39th Annual Technical Meeting of Petroleum Society of CIM and Canadian Gas Processors Association, June 12-16, 1988, Calgary, Alberta, 16 p.
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.
Chang, F. F., & Civan, F., "Modeling of Formation Damage due to Physical and Chemical Interactions between Fluids and Reservoir Rocks," SPE 22856 paper, Proceedings of the 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, October 6-9, 1991, Dallas, Texas.
Chang, F. E, & Civan, E, "Predictability of Formation Damage by Modeling Chemical and Mechanical Processes," SPE 23793 paper, Proceedings of the SPE International Symposium on Formation Damage Control, February 26-27, 1992, Lafayette, Louisiana, pp. 293-312.
Chang, F. E, & Civan, E, "Practical Model for Chemically Induced Formation Damage," J. of Petroleum Science and Engineering, Vol. 17, No. 1/2, February 1997, pp. 123-137.
Civan, E, "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, E, "Evaluation and Comparison of the Formation Damage Models," SPE Paper 23787, Proceedings of the SPE International Symposium on Formation Damage Control, February 26-27, 1992, Lafayette, Louisiana, pp. 219-236.
Civan, E, "Predictability of Formation Damage: An Assessment Study and Generalized Models," Final Report, U.S. DOE Contract No. DE-AC22- 90BC14658, April 1994.
Civan, E, "A Multi-Phase Mud Filtrate Invasion and Well Bore Filter Cake Formation Model," SPE 28709 paper, Proceedings of the SPE International Petroleum Conference & Exhibition of Mexico, October 10-13, 1994, Veracruz, Mexico, pp. 399-412.
Civan, E, "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, E, "A Multi-Purpose Formation Damage Model," SPE 31101paper, Proceedings of the SPE Formation Damage Symposium, Lafayette, Louisiana, February 14-15, 1996, pp. 311-326.
Civan, E, 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.
Dullien, F. A. L., Porous Media Fluid Transport and Pore Structure, Academic Press, London (1979), 396 p.
Gruesbeck, C, & Collins, R. E., "Particle Transport Through Perforations," SPEJ, December 1982, pp. 857-865.
Gruesbeck, C., R. E. Collins, "Entrainment and Deposition of Fine Particles in Porous Media," SPEJ, December 1982, pp. 847-856.
Hallow, J. S., "Incipient Rolling, Sliding, and Suspension of Particles in Horizontal and Inclined Turbulent Flow," Chem. Eng. Sci., Vol. 28, 1973, pp. 1-12.
Himes, R. E., Vinson, E. E, & Simon, D. E., "Clay Stabilization in Low- Permeability Formations," SPE Production Engineering, August 1991, pp. 252-258.
Ikoku, C. U., & Ramey, Jr., H. J., "Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media," Supri-TR-9, Report No. E(04- 3)1265, U.S. Department of Energy (February 1979) 257.
Ivanov, I. B., Kralchevsky, P. A., & Nikolov, A. D., "Film and Line Tension Effects on the Attachment of Particles to an Interface," J. Colloid and Interface ScL, Vol. 112, No. 1, 1986, pp. 97-107.
Ives, K. J., "Deep Bed Filters," in Rushton, A. (Ed.) Mathematical Models and Design Methods in Solid-Liquid Separation, 1985 Martinus Nijhoff Publishers, pp. 90-332.
Khilar, K. C., & Fogler, H. S., "Colloidally Induced Fines Migration in Porous Media," in Amundson, N. R. and 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.
Kia, S. E, Fogler, H. S., & Reed, M. G., "Effect of Salt Composition on Clay Release in Berea Sandstones," SPE 16254, February 1987.
King, R. W., and Adegbesan, K. O., "Resolution of the Principal Formation Damage Mechanisms Causing Injectivity and Productivity Impairment in the Pembina Cardium Reservoir," SPE Paper 38870, Proceedings of the 1997 Annual Technical Conference and Exhibition held in San Antonio, Texas, October 5-8, 1997, pp. 277-288.
Lichtner, Water Resources Research, Vol. 28, No. 12, December 1992, pp. 3135-3155.
McDowell-Boyer, L. M., Hunt, J. R., & Sitar, N., "Particle Transport Through Porous Media," Water Resources Research, Vol. 22, No. 13, December 1986, pp. 1901-1921.
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.
Millan-Arcia, E., Civan, F. "Characterization of Formation Damage by Particulate Processes," J. Canadian Petroleum Technology, Vol. 31, No. 3, March 1992, pp. 27-33.
Muecke, T. W., "Formation Fines and Factors Controlling their Movement in Porous Media," JPT, April 1979.
Ochi, J., & Vernoux, J.-F., "Permeability Decrease in Sandstone Reservoirs by Fluid Injection-Hydrodynamic and Chemical Effects," /. of Hydrology, Vol. 208, 1998, pp. 237-248.
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 19420 paper, Proceedings of the 1990 SPE Symposium on Formation Damage Control, Lafayette, Louisiana, February 22-23, 1990, pp. 185-200.
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.
Pautz, J. F, Crocker, M. E., & Walton, C. G., "Relating Water Quality and Formation Permeability to Loss of Injectivity," SPE 18888 paper, Proceedings of the SPE Production Operations, Oklahoma City, Oklahoma, March 13-14, 1989, pp. 565-576.
Rushton, A., "Mathematical Models and Design Methods in Solid-Liquid Separation," NATO ASI, 1985, No. 88, Ed. A. Rushton, Martinus Nijhoff.
Wojtanowicz, A. K., Krilov, Z. and Langlinais, J. P., "Study on the Effect of Pore Blocking Mechanisms on Formation Damage," Paper SPE 16233, presented at Society of Petroleum Engineers Production Operations Symposium, Oklahoma City, Oklahoma, March 8-10, 1987, pp. 449-463.
Wojtanowicz, A. K., Krilov, Z. and 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.