Transverse mixing in three-dimensional nonstationary anisotropic heterogeneous porous media

Abstract

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.

Observations of 3-D transverse dispersion and dilution in natural consolidated rock by X-ray tomography

“…Several notable studies, however, have shown that transverse dispersion can not be neglected as it plays a key role in the dilution and mixing of solutes and mixing-limited reactive transport [14,13,31,15,7,8,16,20]. The main goal of our study is to devise an experimental technique capable of quantifying three-dimensional 10 transverse dispersion and dilution in natural porous media by providing several quantities such as the transverse dispersion coefficient [41], the dilution index, and the reactor ratio [29].…”

Subsurface flow mixing in coarse, braided river deposits

“…Kitanidis, 1994;Mattle et al, 2001;Mays and Neupauer, 2012;Cirpka et al, 2015). Subsurface flow mixing is generally decomposed into an advective transport process combined with diffusion/dispersion (e.g.…”

“…Janković et al (2009) coined the phrase advective mixing to describe these phenomena. Cirpka et al (2015) identified three advective mixing phenomena that enhance solute mixing: (i) streamline focusing/defocusing, (ii) depth-dependent streamline meandering (i.e. streamline deviation), and (iii) secondary motion consisting in persistent twisting, folding, and intertwining of streamlines.…”

“…Chiogna et al (2015) demonstrated the occurrence of macroscopic helical flow in subsurface flow simulations where the hydraulic conductivity field was heterogeneous and locally isotropic. Despite the importance of advective mixing in solute mixing processes that enhance diffusion/dispersion (Hemker et al, 2004;Janković et al, 2009;Cirpka et al, 2015;Ye et al, 2015), volumetric concentration measurements on the field cannot distinguish between advective mixing and dispersion/diffusion (Janković et al, 2009).…”

Impact of the spatial structure of the hydraulic conductivity field on vorticity in three-dimensional flows

“…Sposito [26], and more recently Chiogna et al [27], studied vorticity in both locally isotropic and anisotropic conductivity fields. Several studies [28,29] showed how non-uniformity in the statistical properties of the hydraulic conductivity field can lead to spiralling flows, which affect solute mixing rates. Similar kinematics analysis was conducted by Raats [30].…”