Simulation of three-dimensional chemical dissolution of limestone

The development of prediction techniques for the evolution of karstic caves is essential for geohazard prevention because limestone collapse commonly accompanies their complex dissolution process. Previous studies to understand the dissolution mechanisms focus on field-based and/or small-scale experimental approaches. Although several large-scale numerical simulations have been conducted due to improved computing capabilities, mathematical modelling and numerical simulation for the three-dimensional dissolution of limestone remains unavailable. In this study, we examine the three-dimensional dissolution phenomenon of calcium carbonate in limestone and propose mathematical and numerical models based on an advection, reaction, and diffusion system involving Darcy’s law. Additionally, we implement the models using a finite difference method involving the constrained interpolation profile with conservative semi-Lagrangian scheme, and dissolution patterns of the calcium carbonates obtained by the proposed model are presented. The simulation demonstrates that the dissolution of calcium carbonate is strongly related to the groundwater flow, with increasing pores and cavities toward the groundwater flow direction, and the dissolution rate depends on the contact area between the groundwater and limestone.