Macroscopic Solute Dispersion at Multiple Length-scales: Impact of Spatial Heterogeneities

Transport properties in porous rocks are difficult to predict because they are geologically heterogeneous from the pore scale upwards. Solute transport in a porous medium is governed by the interplay of advection and diffusion (described by Peclet number, Pe) that cause dispersion of solute particles. 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 and spatial variation. Description of solute transport in geological porous media is inherently uncertain due to spatial distribution of the system properties. In order to study the impact of spatial heterogeneity on macroscopic solute dispersion we use pore-scale model with the geometry and topology based on the networks extracted from the micro CT images of sandstone core samples. We study temporal probability density functions of tracer particles by using a Lagrangian pore-scale network model that incorporates flow and diffusion in three-dimensional irregular network lattices. The impact of heterogeneity is presented in both pre-asymptotic and asymptotic dispersion regime by probability density functions and dispersion coefficients, for a range of Pe. We show that the length traveled by solute plumes before Gaussian behaviour is reached increases with an increase in heterogeneity and/or Pe. This opens up the question on the nature of dispersion in natural systems where the heterogeneities at the larger scales will significantly increase the range of velocities in the reservoir, thus significantly delaying the asymptotic approach to Gaussian behaviour. As a consequence, the asymptotic behaviour might not be reached at the field scale. This is illustrated by the multi-scale approach in which transport at core, gridblock and field scale is viewed as a series of particle transitions between discrete nodes governed by probability distributions. At each scale of interest a distribution that represents transport physics (and the heterogeneity) is used as an input to model a subsequent reservoir scale. The extensions to reactive transport are discussed.