Abstract
Hydrodynamic dispersion is a crucial mechanism for modelling contaminant transport in subsurface engineering and water resources management whose determination remains challenging. We use Digital Rock Physics (DRP) to evaluate the longitudinal dispersion of a sandpack. From a three-dimensional image of a porous sample obtained with X-ray microtomography, we use the method of volume averaging to assess the longitudinal dispersion. Our numerical implementation is open-source and relies on a modern scientific platform that allows for large computational domains and High-Performance Computing. We verify the robustness of our model using cases for which reference solutions exist and we show that the longitudinal dispersion of a sandpack scales as a power law of the Péclet number. The assessment methodology is generic and applies to any kind of rock samples.
Highlights
The accurate description of hydrodynamic dispersion according to the flow conditions is one of the long-standing challenges in hydrogeology and subsurface engineering [1, 2]
We verify that we recover Taylor–Aris law for the hydrodynamic dispersion within a single straight cylinder
We compute the dispersion tensor of a sandpack using 3D images obtained by microtomography
Summary
The accurate description of hydrodynamic dispersion according to the flow conditions is one of the long-standing challenges in hydrogeology and subsurface engineering [1, 2]. R:ð/DÃ rC AÞ; ð1Þ where / is the medium porosity (dimensionless), U is. Darcy’s velocity (in m/s) and D* is the so-called dispersion tensor (in m2/s). The spreading of a solute is not governed only by the molecular diffusion DA (in m2/s) and by the microstructure and the local velocity field. The tortuous feature of the porous structure characterizes by the medium tortuosity (dimensionless), s, tends to slow down the spreading. Hydrodynamic dispersion stretches a solute band in the flow direction during its transport
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