  Most of the lattice Boltzmann methods simulate an approximation of the sharp
interface problem of dissolution and precipitation. In such studies the
curvature-driven motion of interface is neglected in the Gibbs-Thomson
condition. In order to simulate those phenomena with or without
curvature-driven motion, we propose a phase-field model which is derived from a
thermodynamic functional of grand-potential. Compared to the free energy, the
main advantage of the grand-potential is to provide a theoretical framework
which is consistent with the equilibrium properties such as the equality of
chemical potentials. The model is composed of one equation for the phase-field
{\phi} coupled with one equation for the chemical potential {\mu}. In the
phase-field method, the curvature-driven motion is always contained in the
phase-field equation. For canceling it, a counter term must be added in the
{\phi}-equation. For reason of mass conservation, the {\mu}-equation is written
with a mixed formulation which involves the composition c and the chemical
potential. The closure relationship between c and {\mu} is derived by assuming
quadratic free energies of bulk phases. The anti-trapping current is also
considered in the composition equation for simulations with null solid
diffusion. The lattice Boltzmann schemes are implemented in LBM_saclay, a
numerical code running on various High Performance Computing architectures.
Validations are carried out with analytical solutions representative of
dissolution and precipitation. Simulations with or without counter term are
compared on the shape of porous medium characterized by microtomography. The
computations have run on a single GPU-V100.
