Impact of Physical Heterogeneity and Transport Conditions on Effective Reaction Rates in Dissolution

Abstract

A continuous-time random walk (CTRW) reactive transport model is used to study the impact of physical heterogeneity on the effective reaction rates in porous media in a sample of length 15 cm over timescales up to 10$$^8$$ 8 s (3 years). The model has previously been validated using nuclear magnetic resonance (NMR) measurements during dissolution of a limestone. The model assumes first-order reaction. We construct three domains with increasing physical heterogeneity and study dissolution at four Péclet numbers, Pe = 0.0542, 0.542, 5.42 and 54.2. We characterize signatures of physical heterogeneity in the three porous media using velocity distributions and show how these imprint on the signatures of particle displacement, namely particle propagator distributions. In addition, we demonstrate the ability of our CTRW model to capture the impact of physical heterogeneity on the longitudinal dispersion coefficient over several orders of magnitude in space and time. Reactive transport simulations show that the effective reaction rates depend on (i) initial physical heterogeneity and (ii) transport conditions. For all heterogeneities and Pe, the late-time reaction rate exhibits a time dependence $$t^{-a}$$ t - a with $$a \ne 0.5$$ a ≠ 0.5 that indicates the persistence of incomplete mixing. We show that the higher the initial heterogeneity, the lower the late-time reaction rate. A decrease in Pe promotes mixing by diffusion over advection, resulting in higher reaction rates. The post-dissolution propagators indicate an increase in the degree of non-Fickian transport. Overall, we establish a framework to demonstrate and quantify the impact of physical heterogeneity on transport and effective reaction rates in porous media.