Reactive fluid flow in porous media significantly impacts ore mineralisation, carbon dioxide sequestration, and contaminant spread in aquifers. These processes, driven by complex rock-fluid interactions, alter fluid and rock properties such as permeability and porosity. However, accurately modelling the transport of chemical species in this process is challenging due to the inherent heterogeneity of porous media and the nonlinearity of chemical reactions. Existing software tools for geochemical modelling and advective flow simulations often struggle with sharp reaction fronts when advection dominates or when high diffusivity contrasts occur. These limitations introduce highly oscillatory solutions when the meshes are not sufficiently fine, and thus, accuracy could be significantly affected over long periods or large spatial scales. We address these challenges by extending the stabilisation technique proposed in [1-2] to a reactive transport model. We use a Sequential Non-Iterative Approach (SNIA) to couple the diffusive-advective transport processes with chemical reactions. We minimise the transport residual onto a discontinuous Galerkin (dG) dual norm to obtain a stable approximation and an on-the-fly error estimator for each species. We weight each estimator by the reactivity of the species to produce a global indicator that guides mesh refinement to regions with significant chemical activity, such as reaction fronts. We use FEniCS to solve the resulting diffusion-advective transport equations and PHREEQC to model geochemical interactions. We validate our method using 1D and 2D simulations of advective-dominated calcite-dolomite precipitation under different conditions. Our framework improves the resolution of precipitation fronts, allowing us to precisely characterise their spatial evolution and impact on porosity and permeability.