Reactive transport modelling (RTM) is a powerful tool for understanding subsurface systems where fluid flow and chemical reactions occur simultaneously. RTM has been widely used to understand the formation of dolomite by replacement of calcite, which can be an important control on carbonate reservoir quality. Dolomitisation is a reactive transport process governed by slow dolomite precipitation and cannot be correctly simulated without a kinetic rate model. The new CSMP++ GEM coupled RTMcode uses the GEMS3K kernel for solving geochemical equilibria by the Gibbs energy minimisation method with the CSMP++ framework that implements a hybrid finite element-finite volume method to solve partial differential equations. The unique feature of the new coupling is the mineral reaction kinetics, implemented via additional metastability constraints. CSMP++ GEM is able to simulate single-phase flow and solute transport in porous media together with chemical reactions at different pressure, temperature, and water salinity conditions. This RTM assures mass conservation which is crucial when simulating transport of solutes with low concentrations over geological time. A full feedback of mineral dissolution/precipitation on the fluid flow is provided via corresponding porosity/permeability evolution and two source terms in the pressure equation. First, the mass source term accounts for the mass of solutes released during mineral dissolution or taken from the solution by mineral precipitation. The second source term attributes to the fact that the solution density is affected by mineral dissolution/precipitation, too. This effect is included through the equivalent water salinity, which is calculated from the total amount of dissolved solutes and is used to update the properties of saline water from the H2O-NaCl equation of state. This paper puts emphasis on the thorough mathematical derivation of the governing equations and a detailed description of the numerical solution procedure. Two sets of benchmarking results are presented. The first benchmark is a wellknown 1D model of dolomitisation by MgCl2 solution with thermodynamic reactions. In the second benchmark, CSMP++ GEM is compared with TOUGHREACT on a 1D model of dolomitisation by sea water taking into account mineral reaction kinetics. The results presented in this paper demonstrate the ability of the CSMP++ GEM code to correctly reproduce dolomitisation effects.