Transport in a fully coupled asymmetric stratified system: Comparison of scale dependent and independent dispersion schemes

Abstract

Reactive solute transport in a stratified multi-layer system (such as a fracture-matrix or an aquifer-aquitard system) is a classical problem and serves as a benchmark for testing new ideas and theories in subsurface hydrology. This system resembles a “sandwich” model that includes a much permeable layer (such as a fracture or an aquifer) bounded by two much less permeable layers (such as rock matrixes or aquitards). Transport in such a system usually involves fully coupled processes at the interfaces of different layers. The system becomes asymmetric when the less permeable layers have different transport properties. The scale dependency of dispersion in a fully coupled stratified system has never been examined before. This study constructs new transport models and associated solutions to describe reactive solute transport in such a stratified system considering scale-dependent as well as scale-independent dispersion schemes. We will analyze the spatiotemporal concentration distributions based on the newly developed solutions. Breakthrough curves (BTCs) obtained from the models are tested against the experimental data to evaluate the effect of scale dependency of dispersion, and the analysis shows that dispersivity appears to be scale-independent in the experiments of concern. Meanwhile, this study reveals the possible existence of a dynamic diffusion phenomenon in the less permeable layers as the diffusion coefficients in those layers appear to decline with the advective time in the permeable layer. This may be attributed to the increasingly tortuous pathways for the diffusion to take place in those layers when advective time increases. However, theoretical understanding of such a dynamic diffusion phenomenon is still not available and needs further investigation.