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

Abstract

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.

Probabilistic Nucleation and Crystal Growth in Porous Medium: New Insights from Calcium Carbonate Precipitation on Primary and Secondary Substrates

“…Relatively uniform surface coverage exhibits similar physiochemical conditions in the portrayed substrate region that supported stochastic but compact nucleation sites. The enlarged regions provide evidence for the probabilistic spatial distribution of nuclei and crystals, as addressed in our newly developed probabilistic nucleation model . The top-row subfigures suggest that 3 h elapsed time from the onset of the experiment was not long enough to transform a nucleus to the primitive form and subsequently to the geometrical crystalline form (Figure c).…”

“…The entropy ( E ) then increases until it reaches a maximum value, approaching one for an entirely random system. We expect the measure of randomness to decline afterward when crystals start covering more and more surface area, and the entropy eventually reaches a constant minimum value if the substrate is fully covered . The higher number of crystals and larger surface coverage are translated into greater Shannon entropy values.…”

“…It indicates that large solid accumulations can attract and consume more supersaturated fluid in their peripheral region. According to the probabilistic nucleation model, there is a similar probability for nucleation at various sites on the substrate, under similar conditions ( T and Ω). However, the nuclei may not find the opportunity for growth and realization as stable isolated crystals when there is insufficient solute available to support continued growth.…”

“…During solute transport and flow of a reactive fluid within a porous medium, crystal nucleation and growth may change the pore geometry and thus transport properties of the porous medium. − Solid precipitation and accumulation also change the available surface area for nucleation and growth, which leads to alterations in the reactivity of the system, reaction rates, and therefore, overall progress. − Predicting potential events and the evolution of transport properties of a porous medium is paramount in many natural and engineered systems dealing with reactive transport processes coupled with thermo–hydro–mechanical effects. Fluid flow, solute transport, chemical reactions, and fluid–solid interactions may vary markedly over different time- and length-scales in such systems and processes. ,− Prediction of such complex natural or engineered perturbations is far from trivial in geo-environments.…”

“…Mineral nucleation is a probabilistic process, where crystals can nucleate anywhere under similar conditions such as surface properties, supersaturation, and temperature. Therefore, it is imperative to use a probabilistic approach or an upscaled physically sound representation to understand the effect of mineral nucleation on the dynamics of fluid flow and solute transport in porous media …”