The study of instable miscible displacement of chemical species is an important process for many environmental and reservoir engineering applications. A new coupled saturated porous media flow and reactive transport numerical model: RTAFF, has been developed for the assessment and analysis of complex feedback loops between physical transport, geochemistry, and fluid flows in such environments. The model accounts for changes of flowing phase mobility upon viscosity of individual species in the aqueous solution, and field permeability attributed mainly to mineral precipitation-dissolution reactions. An operator splitting framework sequentially couples a mixed-hybrid finite element flow model on quadrilateral/hexahedral grids, with a mass conservative advective-dispersive-reactive (ADR) model able to handle a full range of homogeneous and heterogeneous reactions, using a mixed kinetic equilibrium approach. The multi-component species ADR simulator workflow involves a time-split procedure adapted for each single process solver, thus advection and dispersion operators are also solved independently using other specialized computer models. Example applications are presented in one, and two space dimensions, showing the effectiveness of the numerical model for practical environmental applications. First results demonstrate the accuracy, efficiency and robustness of our approach. Therefore, the model may prove useful for many practical applications.