On the effect of probabilistic nucleation on the distribution of mineral precipitates in porous media

The process of mineral precipitation and crystal growth begins with nucleation, which is usually overlooked in reactive transport simulators. Nucleation controls the location and timing of solid mineral formation in porous media. For an accurate prediction of the hydrodynamics of the porous medium after mineral precipitation, it is crucial to know the spatial distribution of stable secondary nuclei. We developed a novel probabilistic nucleation approach wherein induction time is treated as a random variable in order to better understand the nucleation process. The probabilistic induction time statistically spreads around the measured or reported induction time, either obtained from experiments or approximated by the exponential nucleation rate equation suggested by the classical nucleation theory (CNT). In this study, we used the classical nucleation theory. The location and time of nucleation are both probabilistic in our model, affecting transport properties at different time and length scales.

We developed a pore-scale Lattice Boltzmann reactive transport model incorporated with the new probabilistic nucleation model to investigate the effect of nucleation rate and reaction rate on the extent, distribution, and precipitation pattern of the solid phases. The simulation domain is a 2D substrate with an infinite source of the supersaturated solution. We use Shannon entropy to measure the disorder of the spatial mineral distributions. The results of the simulations show that all the reactions follow similar random behavior with different Gauss-Laplace distributions. The simulation scenarios start from a fully ordered system with no solid precipitation on the substrate (entropy of 0). Entropy starts to increase as the secondary phase precipitates and grows on the surface until it reaches its maximum value (entropy of 1). Afterward, the overall disorder declines as more surface areas are being covered, and eventually, entropy approaches a constant value. The results indicate that the slower reactions have longer windows of the probabilistic regime before entering the deterministic regime. The outcomes provide the basis for implementing mineral nucleation and growth for reactive transport modeling across time-scales and length-scales.