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

In an earlier work, we presented an experimental study wherein reaction-transport processes were forged in a real rock medium. Zonation of CaSO_{4}-rich and CaSO_{4}-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 H_{2}SO_{4}-acidization front propagating radially from a central source into a CaCO_{3} rock bed causes dissolution of the calcite mineral and precipitation of CaSO_{4} as either gypsum (CaSO_{4}·2H_{2}O) or anhydrite (anhydrous CaSO_{4}). The deposition of CaSO_{4} 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^{+}, Ca^{2+}, and SO_{4}^{2-}), the CaCO_{3} dissolution, and the deposition of CaSO_{4}, 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.