During the chemical interactions between fluid and minerals in different geological processes, it is of high importance to predict where secondary precipitates form in the porous rocks as it helps correctly predict the hydrodynamic properties of the porous media. The reactive transport models developed for this purpose need to account for the nucleation process which is probabilistic by nature. To our knowledge, the probabilistic nature of nucleation based on the classical nucleation theory has not been accounted for previously in reactive transport models. In this study, we develop a new probabilistic nucleation model and incorporate it into a pore-scale reactive transport solver to simulate the mineral nucleation and growth in the porous media. Simulations are performed for different supersaturations, growth rates, and flow rates using a single-component mineral reaction. Simulations show that initial supersaturations strongly affect the pattern of secondary precipitate formation. Higher initial supersaturations lead to more uniformly dispersed nucleation on all the grains, while the lower initial supersaturations result in more isolated patterns. Decreasing the growth rate favors the formation of uniformly dispersed nuclei, whereas higher growth rates cause more isolated nucleation. Injection of fluid with a higher velocity gives rise to more precipitation. Moreover, comparison of probabilistic and deterministic nucleation showed that the isolated nucleation patterns cannot be modeled using the deterministic approach. The results showed that permeability for the porous media is influenced by the pattern of secondary precipitate growth and it is demonstrated that generally, the permeability has a direct relation with the initial supersaturation and an inverse relation with the growth rate and the flow rate. Finally, the model was applied for simulation of calcite nucleation and growth on quartz grains. The calcite nucleation and growth exhibit similar behavior to those observed for single-species simulations.

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One important unresolved question in reactive transport is how pore-scale processes can be upscaled and how predictions can be made on the mutual effect of chemical processes and fluid flow in the porous medium. It is paramount to predict the location of mineral precipitation besides their amount for understanding the fate of transport properties. However, current models and simulation approaches fail to predict precisely where crystals will nucleate and grow in the spatiotemporal domain. We present a new mathematical model for probabilistic mineral nucleation and precipitation. A Lattice Boltzmann implementation of the two-dimensional mineral surface was developed to evaluate geometry evolution when probabilistic nucleation criterion is incorporated. To provide high-resolution surface information on mineral precipitation, growth, and distribution, we conducted a total of 27 calcium carbonate synthesis experiments in the laboratory. The results indicate that nucleation events as precursors determine the location and timing of crystal precipitation. It is shown that reaction rate has primary control over covering the substrate with nuclei and, subsequently, solid-phase accumulation. The work provides insight into the spatiotemporal evolution of porous media by suggesting probabilistic and deterministic domains for studying reactive transport processes. We indicate in which length- and time-scales it is essential to incorporate probabilistic nucleation for valid predictions.

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