In this work, a novel globally implicit framework for reactive multiphase flow and transport has been implemented using the simulator DARTS and the geochemical package Reaktoro. This framework applies the Operator-Based Linearization (OBL) approach together with a Gibbs Energy Minimization (GEM) scheme to model complex nonlinear reactive transport and flow. Using component- to element-based transport allows for numerically stable equations. This formulation is used to model the dry-out effect and subsequent precipitation of minerals in the near-wellbore region of subsurface aquifers when injecting CO$_2$. A kinetic rate in combination with Reaktoro equilibrium calculations is implemented to achieve more accurate precipitation results. The kinetic products are not considered inside of Reaktoro and also not as an element. The consistency at the phase transition boundary has been corrected by using a projection of a plane within the hypercube of zero charge balance. Highly sensitive reactions such as pH, require a high resolution to produce physical results. The parameterization grid can be implemented such that some species have a high resolution within a small variation of concentration. Reaktoro is highly accurate for the complex multiphase thermodynamic and chemical equilibrium calculation, but at phase transition boundaries, the equilibration of the state can be nonphysical. The results have been benchmarked against the existing geochemical simulator from Shell, showing that more physics needs to be implemented, but gives an overall accurate result.