Spatial heterogeneity in natural subsurface systems governs water fluxes and residence time in reactive zones and therefore determines effective rates of mineral dissolution. Extensive studies have documented mineral dissolution rates in natural systems, although a general rate law has remain elusive. Here we fill this gap by answering two questions: (1) how and to what extent does spatial heterogeneity affect water residence time and effectively-dissolving surface area? (2) what is the upscaled rate law that quantifies effective dissolution rates in natural, heterogeneous media? With data constraints from experimental work, 240 Monte-Carlo numerical experiments of magnesite dissolution within quartz matrix were run with spatial distributions characterized by a range of permeability variance σ2lnκ (0.5–6.0) and correlation length (2–50 cm). Although the total surface area and global residence time (τa) are the same in all experiments, the water fluxes through reactive magnesite zones varies between 0.7 and 72.8% of the total water fluxes. Highly heterogeneous media with large σ2lnκ and long λ divert water mostly into non-reactive preferential flow paths, therefore bypassing and minimizing flow in low permeability magnesite zones. As a result, the water residence time in magnesite zones (i.e., reactive residence time τar) is long and magnesite dissolution quickly reaches local equilibrium, which leads to small effective surface area and low dissolution rates. Magnesite dissolution rates in heterogeneous media vary from 2.7 to 100% of the rates in the equivalent homogeneous media, with effectively-dissolving surface area varying from 0.18 to 6.83 m2 (out of 51.71 m2 total magnesite surface area). Based on 240 numerical experiments and 45 column experiments, a general upscaled rate law in heterogeneous media, [Formula presented], was derived to quantify effective dissolution rates. The dissolution rates in heterogeneous media are a function of the rate constants k being those measured under well-mixed conditions, effective surface area in equivalent homogeneous media Aehm, and the heterogeneity factor [Formula presented]. The heterogeneity factor quantify heterogeneity effects and depends on the relative magnitude of global residence time (τa) and reactive residence time ([Formula presented] of the gamma distribution for reactive residence times. Exponential forms of rate laws have been used at the micro-scale describing direct interactions among water and mineral surface, and at the catchment scale describing weathering rates and concentration-discharge relationships. These observations highlight the key role of mineral-water contact time in determining dissolution rates at different scales. This work also emphasizes the importance of critical interfaces between reactive and non-reactive zones as determined by the details of spatial patterns and effective surface area as a scaling factor that quantifies dissolution rates in heterogeneous media across scales.
All Science Journal Classification (ASJC) codes
- Geochemistry and Petrology