Lattice-Boltzmann Simulations of Carbonate Systems

Carbonate bedrocks encompass a vast range of primary porosities and permeabilities, which are further modified by the addition of secondary porosities as a result of fissure, fracture, and conduit development. The wide variety of primary and initial secondary porosities found in carbonates further complicate the already difficult task of modeling speleogenic processes. Understanding carbonate dissolution requires consideration of the aqueous speciation of a host of chemical elements (e.g., H, O, C, Ca, Mg, and S). It also requires simultaneous solution for the complex, typically non-Darcian, flow field over a wide range of spatial and temporal scales as the flow field affects the degree of advection and diffusion of the chemical species to and from the host rock. Lattice-Boltzmann methods are particularly suited to modeling the complex fluid dynamics involved in carbonate dissolution. Lattice-Boltzmann simulations are adept at reproducing complex and changing boundary geometries, as well as turbulent and laminar flows, multiphase-multicomponent flow, and buoyancy-induced convection due to solute and thermal gradients. Here, we present some preliminary numerical models, using lattice-Boltzmann simulations, to reproduce permeability development over a range of length and time scales for two different karst systems: continental Paleozoic systems and modern carbonate platforms.