In this work, we analyzed the isothermal single-phase two-component flow in gas reservoirs for carbon dioxide storage and enhanced gas recovery. We considered heterogeneous media with fracture networks and permeability dependent on pressure change. In addition, inertial effects are incorporated using Barree and Conway’s model. The injection of carbon dioxide into a methane reservoir was studied using the Peng-Robinson equation of state. The discretization of the non-linear partial differential equations used in the physical-mathematical model is carried out by applying the Finite Volume Method with implicit formulation. This process leads to a coupled non-linear algebraic system for the unknown gas phase pressure and carbon dioxide molar fraction. After linearization by Picard’s method, the Conjugate Gradient and Biconjugate Gradient Stabilized (BiCGSTAB) methods are applied to solve two algebraic subsystems, respectively, one for the pressure and another for the molar fraction. Thus, the numerical solution is obtained using an operator splitting technique.