A micro-continuum approach is proposed to simulate the dissolution of solid minerals at the pore scale in the presence of multiple fluid phases. The approach employs an extended Darcy-Brinkman-Stokes formulation that accounts for the interfacial tension between the two immiscible fluid phases and the moving contact line at the mineral surface. The simulation framework is validated using an experimental microfluidic device that provides time-lapse images of the dissolution dynamics. The set-up involves a single-calcite crystal and the subsequent generation of CO2 bubbles in the domain. The dissolution of the calcite crystal and the production of gas during the acidizing process are analysed. We then show that the production of CO2 bubbles during the injection of acid in a carbonate formation may limit the overall dissolution rate and prevent the emergence of wormholes.