Pore-Scale Modeling of the Dissolution of Fractures

A pore-scale numerical model has been developed to study dissolution in rough fractures. The velocity field in the pore space is calculated by an implicit lattice-Boltzmann technique [1]. The transport of dissolved species is modeled by a random walk algorithm that efficiently incorporates the chemical kinetics at the solid surfaces [2]. The simulation has been validated by comparison with experimental data on an identical initial topography [3]. In this presentation we report studies of the evolution of porosity in numerically generated fracture geometries over a wide range of Peclet ( Pe) and Damkohler ( Da) numbers; these characterize the fluid flow and dissolution rate in the fracture. The geometrical characteristics of the pore space, the flow field and the increase in fracture permeability are followed over the course of the dissolution process. The dissolution patterns and flow characteristics are found to depend strongly on Pe and Da. Special attention is paid to the region of moderate Pe and Da where the nonlinear feedback mechanism leads to the formation of the pronounced dissolution channels. Here most of the flow is focused into a small number of channels while the rest of the pore space is eventually bypassed. [1] R. Verberg and A. J. C. Ladd, Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method. Phys. Rev. E, 60, 3366, 1999 [2] P. Szymczak and A. J. C. Ladd, Stochastic boundary conditions to the convection-diffusion equation including chemical reactions at solid surfaces, Phys. Rev. E., 69, 036704, 2004 [3] P. Szymczak, A. J. C. Ladd, Microscopic simulations of fracture dissolution, Geophys. Res. Lett., 31, L23606, doi:10.1029/2004GL021297, 2004