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TECHNICAL PAPERS

Flow in Porous Media of Variable Permeability and Novel Effects

[+] Author and Article Information
D. A. Siginer

College of Engineering, Wichita State University, 105 Wallace Hall, 1845 N. Fairmount, Wichita, KS 67260-0044e-mail: siginer@engr.twsu.edu

S. I. Bakhtiyarov

Mechanical Engineering Department, Auburn University, 202 Ross Hall, Auburn, AL 36849

J. Appl. Mech 68(2), 312-319 (Aug 15, 2000) (8 pages) doi:10.1115/1.1349120 History: Received May 23, 2000; Revised August 15, 2000
Copyright © 2001 by ASME
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References

Dauben, D. L., and Menzie, D. E., 1967, “Flow of Polymer Solutions Through Porous Media,” J. Pet. Technol., pp. 1065–1072.
Marshall,  R. G., and Metzner,  A. B., 1967, “Flow of Viscoelastic Fluids Through Porous Media,” Ind. Eng. Chem. Fundam., 6, No. 3, pp. 393–400.
James,  D. F., and McLaren,  D. R., 1975, “The Laminar Flow of Dilute Polymer Solutions Through Porous Media,” J. Fluid Mech., 70, pp. 733–752.
Mirzajanzade, A. Kh., 1959, Hydrodynamics of Viscoplastic and Viscous Fluids Used in Oil Production, Aznefteizdat, Baku (in Russian).
Christopher,  R. K., and Middleman,  S., 1965, “Power-Law Flow Through a Packed Tube,” Ind. Eng. Chem. Fundam., 4, pp. 422–426.
Kulicke,  W. M., and Haas,  R., 1984, “Flow Behavior of Dilute Polyacrylamide Solutions Through Porous Media. 1. Influence of Chain Length, Concentration and Thermodynamic Quality of the Solvent,” Ind. Eng. Chem. Fundam., 23, No. 3, pp. 308–315.
Dharmadhikari,  R. V., and Kale,  D. D., 1985, “Flow of Non-Newtonian Fluids Through Porous Media,” J. Chem. Eng. Sci., 40, No. 3, pp. 527–529.
Bakhtiyarov, S. I., and Suleymanzade, N. S., 1991, “Herschel-Bulkley Fluid Flow in Porous Medium,” J. Oil Gas, Baku, No. 7, pp. 50–53 (in Russian).
Farinato,  R. S., and Yen,  W. S., 1987, “Polymer Degradation in Porous Media Flow,” J. Appl. Polym. Sci., 33, pp. 2353–2368.
Rodriguez,  S., Romero,  C., Sargenti,  M. L., Müller,  A. J., Sáez,  A. E., and Odell,  J. A., 1993, “Flow of Polymer Solutions Through Porous Media,” J. Non-Newtonian Fluid Mech., 49, pp. 63–85.
Kutateladze,  S. S., Popov,  V. I., and Khabakhpasheva,  E. M., 1966, “The Hydrodynamics of Fluids of Variable Viscosity,” J. Appl. Mech. Tech. Phys., 1, pp. 45–49 (in Russian).
Bird, R. B., Armstrong, R. C., and Hassager, O., 1987, Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics, 2nd Ed. John Wiley and Sons, New York.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 1960, Transport Phenomena, John Wiley and Sons, New York.
Scheidegger, A. E., 1974, The Physics of Flow Through Porous Media, University of Toronto Press, New York.
Muskat, M., and Wyckoff, K. D., 1946, The Flow of Homogeneous Fluids Through Porous Media, Edwards, Ann Arbor, MI.
Tanner, R. I., 1985, Engineering Rheology, Clarendon Press, Oxford, U.K.
Williams,  M. C., and Bird,  R. B., 1962, “Steady Flow of an Oldroyd Viscoelastic Fluid in Tubes, Slits, and Narrow Annuli,” AIChE J., 8, pp. 378–382.
Fredrickson, A. G., 1964, Principles and Applications of Rheology, Prentice-Hall, Englewood Cliffs, N.J.
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Figures

Grahic Jump Location
Experimental set-up: (1) filling tank; (2) test tube; (3) valve, (4) measuring cylinder
Grahic Jump Location
Fluidity as a function of the shear stress for two aqueous solutions of polyacrylamide (▵–one percent, □–two percent) and for the spacer fluid (⋄)
Grahic Jump Location
Viscosity as a function of the shear rate for two aqueous solutions of polyacrylamide (▵–1 percent, □–2 percent) and for the spacer fluid (⋄)
Grahic Jump Location
Friction factor as a function of the Reynolds number. Tests I: (•)–distilled water, (◂)–glycerol/water, (▴)–one percent PAA, (▪)–two percent PAA, (♦)–spacer fluid; Tests II: (○)–distilled water, (◃)–glycerol-water, (▵)–one percent PAA, (□)–two percent PAA, (⋄)–spacer fluid. Solid curves correspond to theoretical predictions obtained using Eqs. (13) and (14) or Eqs. (7): (—) Oldroyd model, one percent PAA, η0=0.133 Ns/m2,n=0.286,σ1=3.10−5 s−2,C=1.3; (— - —) Oldroyd model, two percent PAA, η0=0.150 Ns/m2,n=0.250,σ1=3.10−5 s−2,C=3.0; ([[dashed_line]]) spacer fluid, θ/φ0=0.06 m2/N; ([[ellipsis]]) Newtonian fluids, distilled water, and glycerol/water solution.
Grahic Jump Location
Resistance coefficient as a function of the Reynolds number. Tests I: (•)–distilled water, (◂)–glycerol/water, (▴)–one percent PAA, (▪)–two percent PAA, (♦)–spacer fluid; Tests II: (○)–distilled water, (◃)–glycerol-water; (▵)–one percent PAA, (□)–two percent PAA, (⋄)–spacer fluid. Solid curves correspond to theoretical predictions obtained using Eqs. (13) and (14) or Eqs. (7): (—) Oldroyd model, one percent PAA, η0=0.133 Ns/m2,n=0.286,σ1=3.10−5 s−2,C=1.3; (— - —) Oldroyd model, two percent PAA, η0=0.150 Ns/m2,n=0.250,σ1=3.10−5 s−2,C=3.0; (-•-) KPK model, one percent, PAA; (–○–) KPK model, 2 percent PAA; ([[dashed_line]]) spacer fluid, θ/φ0=0.06 m2/N; ([[dotted_line]]) Newtonian fluids, distilled water, and glycerol/water solution.
Grahic Jump Location
The variation of the Deborah number (De) with the Reynolds number (Re): (—) spacer fluid; ([[dashed_line]]) one percent PAA; (— - —) two percent PAA

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