Dispersion in spatially periodic porous media

Abstract. The method of volume averaging is applied to ordered and disordered spatially periodic porous media in two dimensions in order to compute the components of the dispersion tensor for low Peclet numbers ranging from 0.1 to 100. The effect of different parameters on the dispersion tensor is studied. The longitudinal dispersion coefficient decreases with an increase in disorder while the transverse dispersion coefficient increases. The location of discs in the unit cell influences the longitudinal dispersion coefficient significantly, compared to the transverse dispersion coefficient. Under a laminar flow regime, the dispersion coefficient is independent of Rep. The predicted functional dependency of dispersion on the Peclet number agrees with experimental data. The predicted longitudinal dispersion coefficient in disordered porous media is smaller than that of the experimental data. However, the predicted transverse dispersion coefficient agrees with the experimental data.

[1]  Stephen Whitaker,et al.  Dispersion in pulsed systems—II: Theoretical developments for passive dispersion in porous media , 1983 .

[2]  F. Dullien Porous Media: Fluid Transport and Pore Structure , 1979 .

[3]  William G. Gray,et al.  General conservation equations for multi-phase systems: 1. Averaging procedure , 1979 .

[4]  Pierre M. Adler,et al.  Porous media : geometry and transports , 1992 .

[5]  S. Whitaker Diffusion and dispersion in porous media , 1967 .

[6]  S. Whitaker The method of volume averaging , 1998 .

[7]  Stephen Whitaker,et al.  Dispersion in pulsed systems—I: Heterogenous reaction and reversible adsorption in capillary tubes , 1983 .

[8]  Pierre M. Adler,et al.  Taylor dispersion in porous media. Determination of the dispersion tensor , 1993 .

[9]  William G. Gray,et al.  General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow. , 1980 .

[10]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[11]  Stephen Whitaker,et al.  Dispersion in pulsed systems—III: Comparison between theory and experiments for packed beds , 1983 .

[12]  R. Wooding Instability of a viscous liquid of variable density in a vertical Hele-Shaw cell , 1960, Journal of Fluid Mechanics.

[13]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[14]  G. Taylor Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[15]  H. Brenner,et al.  Dispersion resulting from flow through spatially periodic porous media , 1980, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[16]  A. E. Sáez,et al.  Prediction of effective diffusivities in porous media using spatially periodic models , 1991 .

[17]  Helio Pedro Amaral Souto,et al.  Dispersion in two-dimensional periodic porous media. Part II. Dispersion tensor , 1997 .

[18]  D. A. Edwards,et al.  Dispersion of inert solutes in spatially periodic, two-dimensional model porous media , 1991 .

[19]  A. Chorin A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[20]  J. J. Fried,et al.  Dispersion in Porous Media , 1971 .

[21]  William G. Gray,et al.  General conservation equations for multi-phase systems: 2. Mass, momenta, energy, and entropy equations , 1979 .

[22]  Helio Pedro Amaral Souto,et al.  Dispersion in periodic porous media. Experience versus theory for two-dimensional systems , 1997 .

[23]  J. Bear Dynamics of Fluids in Porous Media , 1975 .