Speaker
Description
We study the effect of connectivity of two-dimensional heterogeneous porous media on
flow and transport by looking at line stretching and dispersion. A fluid is stirred by the
porous medium structure that leads to spatial flow variability and the deformation of fluid
elements. These mechanisms have been thoroughly analyzed in previous articles [Comolli
et al. (2019), Dentz et al. (2016b) and Feroukas et al (submitted)] where a single upscaled theoretical framework is proposed. Dispersion measures the extension of a solute distribution and stretching quantifies the fluid deformation of the flow leading to solute mixing, chemical reactions and biological activity. Despite this, much less is known about how connectivity impacts both theses mechanisms. To close to this gap, we analyze the effect of connectivity on dispersion and stretching in two-dimensional connected hydraulic conductivty fields, which are generated using the method of Zinn & Harvey (2003). We perform detailed numerical simulations of Darcy flow, particle transport and stretching. The Lagrangian flow properties are analyzed in terms of the copulas of particle speeds and correlation functions. Dispersion is measured in terms of first-passage time distributions of fluid elements and the temporal evolution of their displacement mean and variance. Deformation is studied in terms of the probability density function and average of the elongation of fluid elements. The stochastic dynamics of dispersion and stretching are quantified using a continuous time random walk (CTRW) approach based on an analytical model for the speed copulas. As for the unconnected fields, we find that dispersion is non-Fickian in the sense that breakthrough curves have strong long time tails, which increase for increasing heterogeneity, and dispersion grows superlinearly with time. Also, the mean elongation of fluid element grows algebraically in time and its distribution is skewed towards large values. Differences between connected an unconnected fields manifest in the copula densities and correlation functions. Suprisingly, the correlation lengths are
shorter for the connected than the unconnected fields. The upscaled CTRW model, which is based on these metrics, manages to predict both dispersion and stretching in the connected fields. These findings shed some new light on the link between geological heterogeneity and dispersion and fluid stretching.
| Country | Spain |
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