Quantification of longitudinal dispersion by upscaling Brownian motion of tracer displacement in a 3D pore-scale network model

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 Peℓ 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 Peℓ, provided that for large Peℓ 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 Peℓ, including increased DL for increased porous medium heterogeneity.