Numerical methods are used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. In particular, the temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAC and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed. The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, it is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper. The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.