Probabilistic nucleation governs time, amount, and location of mineral precipitation and geometry evolution in the porous medium

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.