Stochastic modeling of the multimodal behavior of spatially heterogeneous calcite dissolution rate at the nanoscale

Mineral dissolution/precipitation reactions are critical in several contexts (e.g., geologic sequestration of CO2 or reservoir hydraulic fracturing). High-resolution imaging techniques such as Atomic Force Microscopy (AFM) allow direct observation of the (nanometer-scale) evolution of the crystal topography during the reaction, thus enhancing our knowledge on the various dissolution mechanisms occurring at the liquid-solid interface. These mechanisms are imprinted onto the highly heterogeneous patterns observed and are originated from the presence of inhomogeneities and defects in the mineral lattice, resulting in a broad range of local reaction rate values. We rely on a multimodal Gaussian model to capture the spatial heterogeneity of dissolution rates from AFM (in-situ and in real time) topography measurements collected on calcite samples subject to dissolution at far from equilibrium conditions. We resort to an imaging segmentation technique to cluster reaction rate data into regions associated with diverse dissolution mechanisms and relate each region to a component of the Gaussian mixture. We analyze the temporal trend of model parameters to provide quantitative insights on the dynamic evolution of the spatial heterogeneity of dissolution rate.