In this paper, we consider a finite volume approach for modelling multiphase flow coupled to geochemistry in porous media. Reactive multiphase flows are modelled by a highly nonlinear system of degenerate partial differential equations coupled with algebraic and ordinary differential equations. We propose a fully implicit scheme using a direct substitution approach (DSA) implemented in the framework of the parallel open-source platform DuMu X. We focus on the particular case where porosity changes due to mineral dissolution/precipitation are taken into account. This alteration of the porosity can have significant effects on the permeability and the tortuosity. The accuracy and effectiveness of the implementation of permeability/porosity and tortuosity/porosity relationships related to mineral dissolution/precipitation for single-phase and two-phase flows are demonstrated through numerical simulations.