Mass transfer between recirculation zone and main flow domain in fractures: Is the first order rate law valid?

Abstract

• Recirculation zones (RZs) are present and grow with Reynolds number ( Re ) in fractures when inertial forces are significant. • Mass transfer between RZ and main flow channel results in a late time tailing in residence time distributions. • The first order rate law is robust for describing mass transfer between RZs and main flow channel. A better understanding of solute transport in fractures with immobile zones is critical for many geophysical processes and engineering applications. Although the roles of immobile zones in capturing and releasing solutes leading to non-Fickian transport are well-acknowledged, the mass transfer between immobile and mobile domains using the first order rate law has never been explicitly validated. To this end, we solved fluid flow and solute transport through direct numerical simulations with Reynolds number ( Re ) ranging from 10 to 40, where one kind of immobile zone, i.e., recirculation zones (RZs), are noticeably present and grow with Re . By fitting the analytical solution using the first order rate law to the numerically-derived concentration in RZs, we find that the first order rate law is applicable whenever RZs are noticeably present. Moreover, the mass transfer coefficient increases with Re , and decreases from upstream to downstream in the direction of fluid flow. Hence, the mass transfer coefficient should be precisely determined to accurately capture non-Fickian transport via the first order rate law.