Influence of diffusive porosity architecture on kinetically-controlled reactions in mobile-immobile models

Abstract:

Solute transport in porous media may be structured at various scales by geological features, from connectivity patterns of pores to fracture networks. This structure impacts solute repartition and consequently reactivity. Here we study numerically the influence of the organization of porous volumes within diffusive porosity zones on different reactions. We couple a mobile-immobile transport model where an advective zone exchanges with diffusive zones of variable structure to the geochemical modeling software PHREEQC. We focus on two kinetically-controlled reactions, a linear sorption and a nonlinear dissolution of a mineral. We show that in both cases the structure of the immobile zones has an important impact on the overall reaction rates. Through the Multi-Rate Mass Transfer (MRMT) framework, we show that this impact is very well captured by residence times-based models for the kinetic linear sorption, as it is mathematically equivalent to a modification of the initial diffusive structure; Consequently, the overall reaction rate could be easily extrapolated from a conservative tracer experiment. The MRMT models however struggle to reproduce the non-linearity and the threshold effects associated with the kinetic dissolution. A slower reaction, by allowing more time for diffusion to smooth out the concentration gradients, tends to increase their relevance.

Figure: Left: Representation of a mobile-immobile model with a complex immobile architecture. The mobile zone is indicated by an arrow. Right: Total remaining mass of mineral in mobile-immobile models and in their equivalent MRMT models during a flush by a highly under-saturated solution. The models only differ by the organization of their immobile porous volumes.