In this paper, we formulate and test numerically a fully coupled fully implicit finite volume (FV) method for solving the nonlinear coupling between two-phase flows and geochemical reactions in porous media on a reservoir scale. The problem is modeled by a highly nonlinear system of degenerate partial differential equations (PDEs governing a compositional two-phase flow model) coupled to ordinary and/or algebraic differential equations (modeling kinetic and equilibrium chemical reactions respectively). The spatial discretization uses a cell-centered FV scheme. After discretizing in time with an implicit Euler scheme, the resulting systems of nonlinear algebraic equations are solved with Newton’s method and the systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. We discuss two strategies for selecting local time steps. We have developed and implemented this scheme in a new module in the context of the parallel open source platform DuMuX . Parallelization is carried out using the DUNE parallel library package. Two numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed solver for 3D problems modeling scenarios of CO2 geological storage into a deep saline aquifer. We also report the parallel scalability of the proposed algorithm on a supercomputer with up to 768 processor cores. The proposed method is accurate, numerically robust and exhibits the potential for tackling realistic problems. Lastly, a comparison with a sequential method consisting in decoupling the original problem into a two-phase flow and a reactive transport problem, is performed in term of accuracy.