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Mass transfer, mixing, and therefore reaction rates during transport of solutes in porous media strongly depend on dispersion and diffusion. In particular, transverse mixing is a significant mechanism controlling natural attenuation of contaminant plumes in groundwater. The aim of the present study is to gain a deeper understanding of vertical transverse dispersive mixing of reaction partners in saturated porous media. Multitracer laboratory experiments in a quasi two-dimensional tank filled with glass beads were conducted and transverse dispersion coefficients were determined from high-resolution vertical concentration profiles. We investigated the behavior of conservative tracers (i.e., fluorescein, dissolved oxygen, and bromide), with different aqueous diffusion coefficients, in a range of grain-related Peclet numbers between 1 and 562. The experimental results do not agree with the classical linear parametric model of hydrodynamic dispersion, in which the transverse component is approximated as the sum of pore diffusion and a compound-independent mechanical dispersion term. The outcome of the multitracer experiments clearly indicates a nonlinear relation between the dispersion coefficient and the average linear velocity. More importantly, we show that transverse mechanical dispersion depends on the diffusion coefficient of the compound, at least at the experimental bench-scale. This result has to be considered in reactive-transport models, because the typical assumption that two reactants with different aqueous diffusive properties are characterized by the same dispersive behavior does not hold anymore.

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[1] Transverse mixing of solutes in steady state transport is of utmost importance for assessing mixing-controlled reactions of compounds that are continuously introduced into the subsurface. Classical spatial moments analysis fails to describe mixing because the tortuous streamlines in heterogeneous formations cause plume meandering, squeezing, and stretching, which affect transverse spatial moments even if there is no mass transfer perpendicular to the direction of flow. For transverse solute mixing, however, the decisive process is the exchange of solute mass between adjacent stream tubes. We therefore reformulate the advection-dispersion equation in streamline coordinates (i.e., in terms of the potential and the stream function values) and analyze how flux-related second central moments of plumes increase with dropping hydraulic potential. We compare the ensemble behavior of these second central moments in random two-dimensional heterogeneous flow fields with the moments in an equivalent homogeneous system, thus defining an equivalent effective transverse dispersion coefficient. Unlike transverse macrodispersion coefficients derived by traditional moment analysis, our mixing-relevant, flux-related coefficient does not increase with travel distance. We present closed-form solutions for the mean enhancement of transverse mixing by heterogeneity in two-dimensional isotropic media for linear laws of local-scale transverse dispersion. The mixing enhancement factor increases with the log conductivity variance but remains fairly low. We also evaluate the variance of our cumulative measure of transverse mixing, showing that heterogeneity causes substantial uncertainty of mixing. The analytical expressions are compared to numerical Monte Carlo simulations for various values of log conductivity variance, indicating good agreement with the analytical results at low variability. In the numerical simulations, we also consider nonlinear models of local-scale transverse dispersion.

Groundwater plumes originating from continuously emitting sources are typically controlled by transverse mixing between the plume and reactants in the ambient solution. In two-dimensional domains, heterogeneity causes only weak enhancement of transverse mixing in steady-state flows. In threedimensional domains, more complex flow patterns are possible because streamlines can twist. In particular, spatially varying orientation of anisotropy can cause steady-state groundwater whirls. We analyze steadystate solute transport in three-dimensional locally isotropic heterogeneous porous media with blockwise anisotropic correlation structure, in which the principal directions of anisotropy differ from block to block. For this purpose, we propose a transport scheme that relies on advective transport along streamlines and transverse-dispersive mass exchange between them based on Voronoi tessellation. We compare flow and transport results obtained for a nonstationary anisotropic log-hydraulic conductivity field to an equivalent stationary field with identical mean, variance, and two-point correlation function disregarding the nonstationarity. The nonstationary anisotropic field is affected by mean secondary motion and causes neighboring streamlines to strongly diverge, which can be quantified by the two-particle semivariogram of lateral advective displacements. An equivalent kinematic descriptor of the flow field is the advective folding of plumes, which is more relevant as precursor of mixing than stretching. The separation of neighboring streamlines enhances transverse mixing when considering local dispersion. We quantify mixing by the flux-related dilution index, which is substantially larger for the nonstationary anisotropic conductivity field than for the stationary one. We conclude that nonstationary anisotropy in the correlation structure has a significant impact on transverse plume deformation and mixing. In natural sediments, contaminant plumes most likely mix more effectively in the transverse directions than predicted by models that neglect the nonstationarity of anisotropy.