Pore-scale simulation of dispersion

Tracer dispersion has been simulated in three-dimensional models of regular and random sphere packings for a range of Peclet numbers. A random-walk particle-tracking (PT) method was used to simulate tracer movement within pore-scale flow fields computed with the lattice-Boltzmann (LB) method. The simulation results illustrate the time evolution of dispersion, and they corroborate a number of theoretical and empirical results for the scaling of asymptotic longitudinal and transverse dispersion with Peclet number. Comparisons with nuclear magnetic resonance (NMR) spectroscopy experiments show agreement on transient, as well as asymptotic, dispersion rates. These results support both NMR findings that longitudinal dispersion rates are significantly lower than reported in earlier experimental literature, as well as the fact that asymptotic rates are observed in relatively short times by techniques that employ a uniform initial distribution of tracers, like NMR.

[1]  H. Brenner,et al.  Spatially periodic suspensions of convex particles in linear shear flows. II. Rheology , 1985 .

[2]  John F. Brady,et al.  Nonlocal dispersion in porous media: Nonmechanical effects , 1987 .

[3]  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.

[4]  Pierre M. Adler,et al.  GEOMETRICAL AND TRANSPORT PROPERTIES OF RANDOM PACKINGS OF SPHERES AND ASPHERICAL PARTICLES , 1997 .

[5]  Schwartz,et al.  Self-diffusion in a periodic porous medium: A comparison of different approaches. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Harihar Rajaram,et al.  Accuracy and Computational Efficiency in 3D Dispersion via Lattice-Boltzmann: Models for Dispersion in Rough Fractures and Double-Diffusive Fingering , 1998 .

[7]  Shiyi Chen,et al.  Stability Analysis of Lattice Boltzmann Methods , 1993, comp-gas/9306001.

[8]  Zanetti,et al.  Use of the Boltzmann equation to simulate lattice gas automata. , 1988, Physical review letters.

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

[10]  Joseph Klafter,et al.  Molecular dynamics in restricted geometries , 1989 .

[11]  R. E. Larson,et al.  A periodic grain consolidation model of porous media , 1989 .

[12]  George M. Homsy,et al.  Stokes flow through periodic arrays of spheres , 1982, Journal of Fluid Mechanics.

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

[14]  Reghan J. Hill,et al.  Brinkman screening and the covariance of the fluid velocity in fixed beds , 1998 .

[15]  Ruben G. Carbonell,et al.  Longitudinal and lateral dispersion in packed beds: Effect of column length and particle size distribution , 1985 .

[16]  J. Higdon,et al.  Oscillatory Stokes flow in periodic porous media , 1992 .

[17]  Robert S. Bernard,et al.  Simulation of flow through bead packs using the lattice Boltzmann method , 1998 .

[18]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[19]  Shiyi Chen,et al.  Lattice Boltzmann computations for reaction‐diffusion equations , 1993 .

[20]  Paul T. Callaghan,et al.  Generalized approach to NMR analysis of flow and dispersion in porous media , 1997 .

[21]  John F. Brady,et al.  Dispersion in fixed beds , 1985, Journal of Fluid Mechanics.

[22]  Robert S. Bernard,et al.  Accuracy of the Lattice-Boltzmann Method , 1997 .

[23]  Kroll,et al.  Simulation of Flow in Bidisperse Sphere Packings. , 1999, Journal of colloid and interface science.

[24]  J. Leblond,et al.  Experimental measurement of dispersion processes at short times using a pulsed field gradient NMR technique , 1997 .

[25]  Terukatsu Miyauchi,et al.  Axial dispersion in packed beds , 1975 .

[26]  Ernst,et al.  Simulation of diffusion in a two-dimensional lattice-gas cellular automaton: A test of mode-coupling theory. , 1989, Physical review letters.

[27]  R. Maier,et al.  Pore-Scale Flow and Dispersion , 1998 .

[28]  James D. Sterling,et al.  Accuracy of Discrete-Velocity BGK Models for the Simulation of the Incompressible Navier-Stokes Equations , 1993, comp-gas/9307003.

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

[30]  Claes Johnson Numerical solution of partial differential equations by the finite element method , 1988 .

[31]  D. Thomson,et al.  Reflection boundary conditions for random walk models of dispersion in non-gaussian turbulence , 1994 .

[32]  Using the FHP-BGK-Model to Get Effective Dispersion Constants for Spatially Periodic Model Geometries , 1997 .

[33]  Robert S. Bernard,et al.  Boundary conditions for the lattice Boltzmann method , 1996 .

[34]  A.F.B. Tompson,et al.  Numerical simulation of solute transport in randomly heterogeneous porous media: Motivation, model development, and application , 1987 .

[35]  Sankar Bhattacharja,et al.  Magnetic Resonance Relaxation Analysis of Porous Media , 1989 .

[36]  P. Sen Diffusion in a periodic porous medium with surface relaxation , 1994 .

[37]  Lowe,et al.  Do Hydrodynamic Dispersion Coefficients Exist? , 1996, Physical review letters.

[38]  Flekkoy Lattice Bhatnagar-Gross-Krook models for miscible fluids. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  John F. Brady,et al.  The effect of order on dispersion in porous media , 1989, Journal of Fluid Mechanics.

[40]  Pierre M. Adler,et al.  Spatial correlations and dispersion for fluid transport through packed glass beads studied by pulsed field-gradient NMR , 1998 .

[41]  K. J. Packer,et al.  NMR measurements and numerical simulation of fluid transport in porous solids , 1997 .

[42]  Sen,et al.  Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments: Simple pore geometries. , 1992, Physical review. B, Condensed matter.