TY - JOUR
T1 - Quantfication of longitudinal dispersion by upscaling Brownian motion of tracer displacement in a 3D pore-scale network model
AU - Acharya, R.C.
AU - van Dijke, M.I.J.
AU - Sorbie, K.S.
AU - van der Zee, S.E.A.T.M.
AU - Leijnse, A.
PY - 2007
Y1 - 2007
N2 - We present a 3D network model with particle tracking to upscale 3D Brownian motion of non-reactive tracer particles subjected to a velocity field in the network bonds, representing both local diffusion and convection. At the intersections of the bonds (nodes) various jump conditions are implemented. Within the bonds, two different velocity profiles are used. At the network scale the longitudinal dispersion of the particles is quantified through the coefficient DL, for which we evaluate a number of methods already known in the literature. Additionally, we introduce a new method for derivation of DL based on the first-arrival times distribution (FTD). To validate our particle tracking method, we simulate Taylor¿s classical experiments in a single tube. Subsequently, we carry out network simulations for a wide range of the characteristic Péclet number Pe¿ to assess the various methods for obtaining DL. Using the new method, additional simulations have been carried out to evaluate the choice of nodal jump conditions and velocity profile, in combination with varying network heterogeneity. In general, we conclude that the presented network model with particle tracking is a robust tool to obtain the macroscopic longitudinal dispersion coefficient. The new method to determine DL from the FTD statistics works for the full range of Pe¿, provided that for large Pe¿ a sufficiently large number of particles is used. Nodal jump conditions should include molecular diffusion and allow jumps in the upstream direction, and a parabolic velocity profile in the tubes must be implemented. Then, good agreement with experimental evidence is found for the full range of Pe¿, including increased DL for increased porous medium heterogeneity
AB - We present a 3D network model with particle tracking to upscale 3D Brownian motion of non-reactive tracer particles subjected to a velocity field in the network bonds, representing both local diffusion and convection. At the intersections of the bonds (nodes) various jump conditions are implemented. Within the bonds, two different velocity profiles are used. At the network scale the longitudinal dispersion of the particles is quantified through the coefficient DL, for which we evaluate a number of methods already known in the literature. Additionally, we introduce a new method for derivation of DL based on the first-arrival times distribution (FTD). To validate our particle tracking method, we simulate Taylor¿s classical experiments in a single tube. Subsequently, we carry out network simulations for a wide range of the characteristic Péclet number Pe¿ to assess the various methods for obtaining DL. Using the new method, additional simulations have been carried out to evaluate the choice of nodal jump conditions and velocity profile, in combination with varying network heterogeneity. In general, we conclude that the presented network model with particle tracking is a robust tool to obtain the macroscopic longitudinal dispersion coefficient. The new method to determine DL from the FTD statistics works for the full range of Pe¿, provided that for large Pe¿ a sufficiently large number of particles is used. Nodal jump conditions should include molecular diffusion and allow jumps in the upstream direction, and a parabolic velocity profile in the tubes must be implemented. Then, good agreement with experimental evidence is found for the full range of Pe¿, including increased DL for increased porous medium heterogeneity
KW - porous-media
KW - hydrodynamic dispersion
KW - molecular-diffusion
KW - solute transport
KW - flow
KW - transition
KW - advection
KW - aquifers
KW - length
KW - beds
U2 - 10.1016/j.advwatres.2005.04.017
DO - 10.1016/j.advwatres.2005.04.017
M3 - Article
SN - 0309-1708
VL - 30
SP - 199
EP - 213
JO - Advances in Water Resources
JF - Advances in Water Resources
IS - 2
ER -