Visualization of Mixing Processes in a Heterogeneous Sand Box Aquifer

Abstract

Mixing is increasingly recognized as a critical process for understanding and modeling reactive transport. Yet, mixing is hard to characterize because it depends nonlinearly on concentrations. Visualization of optical tracers in the laboratory at high spatial and temporal resolution can help advance the study of mixing processes. The solute distribution is obtained by analyzing the relationship between pixel intensity and tracer concentration. The problem with such techniques is that grain borders, light fluctuations, and nonuniform brightness contribute to produce noisy images of concentrations that cannot be directly used to estimate mixing at the local scale. We present a nonparametric regression methodology to visualize local values of mixing from noisy images of optical tracers that minimizes smoothing in the direction of concentration gradients. This is achieved by weighting pixel data along concentration isolines. The methodology is used to provide a full visualization of mixing dynamics in a tracer experiment performed in a reconstructed aquifer consisting of two materials with contrasting hydraulic properties. The experiment reveals that mixing is largest at the contact area of regions with different permeability. Also, the temporal evolutions of mixing and dilution rates are significantly different. The mixing rate is more persistent than the dilution rate during tracer invasion, and the opposite is true during flushing, which helps in understanding the complementary nature of these two measures.

Enhancement of plume dilution in two‐dimensional and three‐dimensional porous media by flow focusing in high‐permeability inclusions

“…Due to the small spatial scale at which mixing occurs, resolving steep concentration gradients at the field scale remains challenging despite the rapid development of improved monitoring techniques [e.g., Annable et al ., ; Anneser et al ., ; Devlin et al ., ]. Therefore, laboratory experiments [e.g., Castro‐Alcala et al ., ; de Anna et al ., ; Haberer et al ., ; Rolle et al ., ] and numerical simulations at multiple scales [e.g., de Dreuzy et al ., ; Herrera and Valocchi , ; Hochstetler et al ., ; Porta et al ., ; Rolle et al ., ; Tartakovsky et al ., ] are fundamental for the understanding of dilution in porous media. Most of these studies, however, focused on (quasi) two‐dimensional systems, while detailed experimental and modeling investigations in three‐dimensional domains are less common [e.g., Herrera et al ., ; Rashidi et al ., ; Silliman , ; Yoon and McKenna , ; Cirpka et al ., ].…”

Measurements and models of reactive transport in geological media

“…Even without strongly defined preferential pathways, heterogeneity affects tracer transport, dispersion, and dilution. Castro‐Alcalá et al [] report visualization experiments of a (conservative) tracer migrating in a 2‐D flow cell containing a rectangular sand lens of fine sand (with relatively low K ) embedded in a coarse sand (higher K ) matrix. Careful image analysis demonstrated that the largest degree of mixing occurs along contacts between regions with different permeability and that rates of mixing and dilution evolve differently over time.…”

Scalar dissipation rates in non-conservative transport systems

“…This often requires complete knowledge of the concentration over time and is impossible to monitor a field scale plume with sufficient resolution to fully resolve the detailed concentration field. The SDR can be applied to numerical and laboratory scale studies that quantify the spatio-temporal concentration field such as Gramling et al, [2002], Zinn et al, [2004], Acharya et al, [2007], Tartavkosky et al, [2008], and Castro-Alcala et al, [2012], but upscaling methods to connect the scales are needed. One simple method of doing so is outlined in section 4.4, but prior to considering that case we develop analytical tools for determining the effects that different limits on the problem domain will have on the dissipation rates.…”