A framework for numerical modelling of miscible contaminant transport contained homogeneous /heterogeneous chemical reactions in porous media is presented. The mathematical model of the chemical-reacting processes integrates the homogeneous fast/slow and heteroneneous fast/slow governing phenomena. The transport behaviors of governing processes mainly include: convection

diffusion and degradation

adsorption etc. A finite element method based on the implicit characteristic Galerkin discretization is used to numerically solve the initial and boundary value problem for the model governing equations. The solving process separates the reactants and products in the homogeneous chemical reactions and the material in liquid and solid phases in heterogeneous reactions. The reactants in homogeneous reactions and chemical cations in liquid phase of heterogeneous reactions are simulated as the basic unknowns. The products in homogeneous reactions and the chemical cations in solid phase of heterogeneous reactions are solved individually. The different governing equations

then

can be classified as its intrinsic nature. The unknowns are also decreased by such treatments. The iterative operation is performed for the reason of the nonlinear right side contained the internal state variables. The numerical results and the stability analysis of the algorithm validate good performance of the present model and efficiency

accuracy and stability of the present numerical method.