Abstract
Anomalous transport in porous media is commonly believed to be induced by the highly complex pore space geometry. However, this phenomenon is also observed in porous media with rather simple pore structure. In order to answer how ubiquitous can anomalous transport be in porous media, we in this work systematically investigate the solute transport process in a simple porous medium model with minimal structural randomness. The porosities we consider range widely from 0.30 up to 0.85, and we find by lattice Boltzmann simulations that the solute transport process can be anomalous in all cases at high Péclet numbers. We use the continuous time random walk theory to quantitatively explain the observed scaling relations of the process. A plausible hydrodynamic origin of anomalous transport in simple porous media is proposed as a complement to its widely accepted geometric origin in complex porous media. Our results, together with previous findings, provide evidence that anomalous transport is indeed ubiquitous in porous media. Consequently, attentions should be paid when modelling solute transport by the classical advection-diffusion equation, which could lead to systematic error.
Highlights
Anomalous transport has been recognized as a common phenomenon in porous media whose complex pore space geometry strongly influences the flow and transport processes therein[1,2]
We find that anomalous transport is astonishingly prevalent in our simple porous medium model when advection plays a dominant role
By showing an extreme case of anomalous transport in two dimensional Poiseuille flow, we further argue that the emergence of anomalous transport is a result of the joint action of hydrodynamics and pore space geometry
Summary
Anomalous (or non-Fickian) transport has been recognized as a common phenomenon in porous media whose complex pore space geometry strongly influences the flow and transport processes therein[1,2]. On the other hand, we notice there has been experimental and numerical evidence that even for some structurally “simple” porous media, the solute transport process can be anomalous at high Péclet numbers[4,14,38,39] In such cases, the porous media are regular or very weakly complex in void space geometry; there can hardly be any non-trivial spatial structure that is complex enough to induce a highly heterogeneous velocity field. For structurally simple porous media, hydrodynamics plays a crucial role in inducing non-uniform velocity profiles, while the influence of geometry manifests itself by enhancing the heterogeneity of the flow field as structural complexity grows. If we consider porosity as some “mean-field” measure of the pore space complexity, we will see as the porosity φ is decreased, the exponent α follows, leading to a more heterogeneous flow field
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