Simulation of geochemical banding: Theoretical modeling and fractal structure in acidization-diffusion-precipitation dynamics

Abstract

In an earlier work, we presented an experimental study wherein reaction-transport processes were forged in a real rock medium. Zonation of CaSO4-rich and CaSO4-depleted domains were obtained and characterized. In the present study, we present a theoretical model to simulate the reaction-diffusion processes underlying the dynamics of the system. An H2SO4-acidization front propagating radially from a central source into a CaCO3 rock bed causes dissolution of the calcite mineral and precipitation of CaSO4 as either gypsum (CaSO4·2H2O) or anhydrite (anhydrous CaSO4). The deposition of CaSO4 is shown to exhibit a banded texture (irregular concentric rings in two dimensions). The model involves reaction-diffusion evolution equations for three aqueous species (H+, Ca2+, and SO42-), the CaCO3 dissolution, and the deposition of CaSO4, which is taken to obey a scaled Cahn-Hilliard equation. The output captures the zonation observed experimentally. Fractal analysis of the experimental contour shapes of the deposits reveals an oscillation in the fractal dimension over successive band numbers. Such oscillation is interpreted in terms of the precipitation-depletion tug scenario, not observable in regular two-dimensional Liesegang systems with high circular symmetry. ©2019 American Physical Society.