Role of dead-end regions and transmitting pores in mixing and reactivity in unsaturated porous media

Abstract

Mixing-limited reactions in unsaturated porous media are controlled by complex pore-scale processes arising from air and water phases coexistence. Decreasing water saturation increases flow heterogeneity, creating preferential flow paths and dead-end regions (DER) that alter solute distribution and reaction efficiency. Transmitting pores (TP) enhance mixing via interface deformation driven by stretching and shrinking. Conversely, DER act as low-velocity traps, contributing to mixing through diffusion and delayed reactant release. A unified understanding of their distinct roles in mixing interface evolution and upscaled reaction rates remains limited. Using high-resolution multiphase flow simulations, we investigate how water saturation influences mixing interface evolution across Péclet numbers. We develop a two-compartment model that separately accounts for interface deformation in TP and solute trapping in dead-end regions. We show that, even under unsaturated conditions, the mixing interface deformation within TP eventually plateaus once a balance between stretching and diffusion is reached. In contrast, interface segments in DER are governed by the dynamic interplay between the generation of new trapped segments and the decay of existing ones. This controls the late-time behavior of interface length, which continues to grow until it reaches saturation. Our framework reproduces the observed mixing dynamics and provides a simple expression linking reaction rate to the total mixing interface length. The results demonstrate that under low saturation, the prolonged elongation of the interface substantially enhances reaction rates, highlighting the critical role of saturation-driven heterogeneity in reactive transport.

This research was funded by NSF Grant EAR2049688 and by the European Commission (MixUp, MSCA‐101068306). The authors gratefully acknowledge the Center for Research Computing (CRC) at the University of Notre Dame for providing the computational resources used to conduct the simulations in this work.

Peer Reviewed

Postprint (published version)