HR: 14:40h
AN: H13K-04    [Abstracts]
TI: Significance of Pre-Asymptotic Dispersion in Porous Media
AU: * Bijeljic, B
EM: b.bijeljic@imperial.ac.uk
AF: Imperial College, South Kensington Campus, London, SW7 2AZ, United Kingdom
AU: Blunt, M J
EM: m.blunt@imperial.ac.uk
AF: Imperial College, South Kensington Campus, London, SW7 2AZ, United Kingdom
AB: When chemically neutral tracer particles flow in a porous medium, the interplay of advection and diffusion (described by Peclet number, Pe) causes their spreading that is traditionally described by dispersion coefficients, D. Dispersion coefficients are defined by σ² = 2Dt, where σ² is the variance of the solute position and t is the time. In the asymptotic limit D is constant and can be used in an averaged advection- dispersion equation. However, it is highly important to recognize that, until the velocity field is fully sampled, the particle transport is non-Gaussian and D possesses temporal or spatial variation. We study spatial and temporal probability density functions of tracer particles by using a Lagrangian pore-scale network model that incorporates flow and diffusion in 2D and 3D network lattices representative of Berea sandstone. The pre-asymptotic and asymptotic dispersion are quantitatively described by the probability density functions and dispersion coefficients. The subtleties arising from comparison with the 2D lattice model that accurately predicts NMR, laser fluorescence and the classic breakthrough data for the experimental dependence of the longitudinal dispersion coefficient, D_L, on Pe are discussed. We show that, even in a statistically homogeneous medium where there is no spatial correlation of pore size, thousands of pores must be traveled before Gaussian behaviour is reached. This applies to the studies where there is a 100-fold range of velocities; in natural systems the heterogeneities at the larger scales will significantly increase this range thus significantly delaying the asymptotic approach to Gaussian behaviour. As a consequence, the asymptotic behaviour might not be reached at the reservoir scale. This opens up the question on how appropriate is the use of averaged advection-dispersion equation with constant dispersion coefficients in reservoir simulation.
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
SC: Hydrology [H]
MN: 2007 Fall Meeting