Visualization of mixing processes in a heterogeneous sand box aquifer

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.