Mineral Deposition on the Rough Walls of a Fracture

Modeling carbonate growth in fractures and pores is important for understanding carbon sequestration in the environment or when supersaturated solutions are injected into rocks. Here we study the simple but nontrivial problem of calcite growth on fractures with rough walls of the same mineral using kinetic Monte Carlo simulations of attachment and detachment of molecules and scaling approaches. First we consider wedge-shaped fracture walls whose upper terraces are in the same low energy planes and show that the valleys are slowly filled by propagation of parallel monolayer steps in the wedge sides. The growth ceases when the walls reach these low energy configurations, so that a gap between the walls may not be filled. Secondly we consider fracture walls with equally separated monolayer steps (vicinal surfaces with roughness below $1$~nm) and show that growth by step propagation will eventually clog the fracture gap. In both cases, scaling approaches predict the times to attain the final configurations as a function of the initial geometry and of the step propagation velocity in the chosen supersaturation. The same reasoning applied to a random wall geometry shows that step propagation leads to lateral filling of surface valleys until the wall reaches the low-energy crystalline plane that has the smallest initial density of molecules. Thus, the final configurations of the fracture walls are much more sensitive to the crystallography than to the roughness or to the local curvature. The framework developed here may be used to determine those configurations, the times to reach them, and the mass of deposited mineral.