Impact of flow conditions on pore-scale solute mixing: experiments in heterogeneous 2D porous media

<p>Solute mixing mediated by flow in porous media plays a significant role in controlling reaction rates in subsurface environments. In many practical cases, incomplete mixing—inhomogeneous solute concentrations—occurs at the pore-scale, limiting local and thus upscaled reaction rates, and renders their prediction based on effective dispersion coefficients derived from dispersion models (or by assuming Taylor-Aris dispersion) inaccurate. We perform solute transport experiments in transparent, quasi-two-dimensional, soil analog models to investigate the relationships between pore-scale solute dispersion and mixing under different flow conditions. We use Fluorescein as a conservative tracer and record its fluorescence intensity in monochrome images at fixed time intervals. We convert the fluorescence intensity to solute concentration fields based on a calibration curve obtained with various homogeneous solute concentrations and subsequently compute concentration gradients. Our images provide evidence for incomplete mixing at the pore-scale and show strong gradients transverse to the overall flow direction. We fit the mean longitudinal concentration profile to an analytical solution of the advection-dispersion equation and compute the effective longitudinal dispersion coefficient. Based on the lamellar mixing theory, we also infer an effective diffusion coefficient relevant to the mean concentration gradient’s dynamics. By comparing these two diffusion/dispersion coefficients in saturated flow conditions, we show that while their values are similar at low Péclet, their scaling behaviors as a function of Péclet are different. Hence, as pointed out by several previous studies, modeling reactive transport processes requires accounting for a mixing behavior driven by a diffusive process that cannot entirely be described by the solute dispersion coefficient. We extend this work by varying the saturation degree in the experiments and our samples' structural heterogeneity to investigate how flow desaturation and porous medium structure impact solute mixing.</p>

Experimentally Determined Solute Mixing under Laminar and Transitional Flows at Junctions in Water Distribution Systems

The water quality model in water distribution systems adopted in EPANET and other commercial simulation programs assumed perfect mixing of solute at pipe junctions. However, imperfect solute mixing at pipe junctions at turbulent flow has been reported. Yet, the mixing under laminar and transitional flow is rarely reported and thus is the focus of experimental study reported here. The experimental results show that the average Reynolds number and the outflows Reynolds number ratio controls degrees of the mixing at the pipe junctions. For cross junctions, the mixing degree is a function of the average Reynolds number in three regions; each has different mixing mechanisms and mathematical relationship. For double-Tee junctions, the dimensionless connecting pipe length plays a more important role than the Reynolds number ratios of outflows and average Reynolds number on mixing because a longer connecting pipe length gives more mixing space and time for the water flow mixing.

Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model

In this work, we develop a novel Lagrangian model able to predict solute mixing in heterogeneous porous media. The Spatial Markov model has previously been used to predict effective mean conservative transport in flows through heterogeneous porous media. In predicting effective measures of mixing on larger scales, knowledge of only the mean transport is insufficient. Mixing is a small scale process driven by diffusion and the deformation of a plume by a non-uniform flow. In order to capture these small scale processes that are associated with mixing, the upscaled Spatial Markov model must be extended in such a way that it can adequately represent fluctuations in concentration. To address this problem, we develop downscaling procedures within the upscaled model to predict measures of mixing and dilution of a solute moving through an idealized heterogeneous porous medium. The upscaled model results are compared to measurements from a fully resolved simulation and found to be in good agreement.