Scale dependence of surface complexation capacity and rates in heterogeneous media

Reactive solutes flow, transport, and transform in natural subsurface that is ubiquitously heterogeneous. How much are the heterogeneity effects on solute reactive transport? At what spatial scale heterogeneity effects diminish? Answers to these questions are important to understand controls of and to predict solute reactive transport in natural environments. Although these questions have been explored for non-reactive tracers and solutes that go through relatively simple single-component sorption, heterogeneity effects remain poorly understood for solutes that go through surface complexation. These reactions typically include multi-component and are subject to influences of local geochemical conditions. This work aims to address these questions and to understand how and how much effective capacity (C_sc,m), early (k_c1) and late (k_c2) rates of Cr(VI) surface complexation are influenced by heterogeneity characteristics and length scales. A two-dimensional model with Cr(VI) surface complexation were calibrated using column data. Numerical experiments were carried out in heterogeneous media characterized by different permeability variance σ²_lnκ (0.2, 4.5), correlation length λ_L (0-6.0 cm), and domain length (0.1-1.0 m). Results show that long λ_L and high σ²_lnκ facilitate the formation of preferential flow and elongate the diffusion length, leading to high connectivity that minimizes C_sc,m and k_c1. In highly connected media (>2.0), C_sc,m and k_c1 can be >2 orders of magnitude lower than those in corresponding homogeneous media. Connectivity however is not a good indicator for k_c2 that is predominantly controlled by diffusion. The heterogeneity effects are scale dependent. As the domain length increases, C_sc,m and k_c1 values approach those of homogeneous media due to longer mixing lengths and continued pH increase during Cr(VI) surface complexion. The "critical length" at which heterogeneity effects disappear occurs at about 20λ_L and differs only slightly at different σ²_lnκ values. The heterogeneity effects however linger at much longer lengths for k_c2, the values of which are >2 orders of magnitude lower in heterogeneous media even at 20λ because of the longer characteristic times of diffusive transport. These results underscore the strong regulation of solute reactive transport by mineral spatial patterns, suggesting the importance of subsurface characteristics and spatial scales at which they are important in estimating natural attenuation, residence times, and natural system capacity to sorb chemicals.