Assessment of turbulence effects on effective solute diffusivity close to a sediment-free fluid interface

Abstract

Our work is focused on the analysis of solute mixing under the influence of turbulent flow propagating in a porous system across the interface with a free fluid. Such a scenario is representative of solute transport and chemical mixing in the hyporheic zone. The study is motivated by recent experimental results (Chandler et al. Water Res Res 52(5):3493–3509, 2016) which suggested that the effective diffusion parameter is characterized by an exponentially decreasing trend with depth below the sediment-water interface. This result has been recently employed to model numerically downstream solute transport and mixing in streams. Our study provides a quantification of the uncertainty associated with the interpretation of the available experimental data. Our probabilistic analysis relies on a Bayesian inverse modeling approach implemented through an acceptance/rejection algorithm. The stochastic inversion workflow yields depth-resolved posterior (i.e., conditional on solute breakthrough data) probability distributions of the effective diffusion coefficient and enables one to assess the impact on these of (a) the characteristic grain size of the solid matrix associated with the porous medium and (b) the turbulence level at the water-sediment interface. Our results provide quantitative estimates of the uncertainty associated with spatially variable diffusion coefficients. Finally, we discuss possible limitations about the generality of the conclusions one can draw from the considered dataset.

Modeling solute transport and mixing in heterogeneous porous media under turbulent flow conditions

“…• Case 2: a system mimicking an erosimeter, consisting by a porous medium underlying a water column 41,42 .…”

“…Our aim is to simulate vertical solute exchange taking place in the system as driven by diffusion and mixing. Experimental 10 and numerical 42 results document an exponential reduction of the diffusion coefficient with increasing depth below the sediment-water interface. For the purpose of our study, the porous domain is then segmented into 6 layers (see Figure 7).…”

“…These parameters are considered as independent and identically distributed random variables, each characterized by a uniform distribution within selected intervals, chosen considering a coefficient of variation of 0.2. The mean values of the parameters A and B are determined upon relying on the results of Baioni et al 42 , while average values of λ min and λ max are set on the basis of existing experimental data 10 . The mean value of Ct C ′ φ is set to the value employed in Meyer 29 .…”