The evolution of the surface topography of a calcite crystal subject to dissolution is documented through in situ real-time imaging obtained via atomic force microscopy (AFM). The dissolution process takes place by exposing the crystal surface to deionized water. AFM data allow detection of nucleation and expansion of mono- and multilayer rhombic etch pits and are employed to estimate the spreading rate of these structures. Spatially heterogeneous distributions of local dissolution rate are evaluated from the difference between topographic measurements taken at prescribed time intervals. We rest on a stochastic framework of analysis viewing the dissolution rate as a generalized sub-Gaussian (GSG) spatially correlated random process. Our analysis yields: (i) a quantitative assessment of the temporal evolution of the statistics of the dissolution rates as well as their spatial increments; (ii) a characterization of the degree of spatial correlation of dissolution rates and of the way this is linked to the various mechanisms involved in the dissolution process and highlighted through the experimental evidences. Our results indicate that the parameters driving the statistics of the GSG distribution and the spreading rate of the multilayer pits display a similar trend in time, thus suggesting that the evolution of these structures imprints the statistical features of local dissolution rates. Article Highlights We investigate dynamics of dissolution patterns on a calcite crystal in contact with deionized water via AFM imaging Temporal behavior of parameters of our statistical model is consistent with surface pattern evolution A nested model for the spatial correlation of rates embeds multiple mechanisms driving dissolution rate.

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<p>Carbonate dissolution processes are key in many environmental areas as well as in the industrial sector. In subsurface environments, a detailed knowledge of mineral dissolution/precipitation kinetic rate laws is a critical component in the context of, e.g., aquifer contamination assessment, geologic carbon sequestration, toxic waste disposal, or hydraulic fracturing of hydrocarbon reservoirs. The recent employment of advanced measurement instruments such as Atomic Force Microscopy (AFM) and Vertical Scanning Interferometry (VSI) enables direct observations of the mechanisms occurring on the mineral surface during the reaction, providing evidence that the dissolution process is strongly affected by several sources of variability at the local (i.e., micro-scale) mineral-fluid interface. In this context result, marked spatial heterogeneities in the dissolution rate are documented. Therefore, a change of perspective towards a quantification based on a stochastic approach is of primary importance. We propose to employ geostatistical tools to characterize the spatial heterogeneity of dissolution rate maps obtained from in-situ and real-time AFM imaging. We collect datasets of the surface topography of a millimeter-scale calcite sample subject to dissolution, from which we evaluate reaction rate maps. Our work is aimed at (1) characterizing the statistical behavior of topography and dissolution rate data and their spatial increments; (2) identifying an appropriate interpretive model for such statistics; and (3) evaluating quantitatively, through observed trends of model parameters, the temporal evolution of the spatial heterogeneity of reaction kinetics.</p>

<p>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.</p>