Numerical simulation of single-phase two-component non-Darcy flow in naturally fractured reservoirs for enhanced gas recovery and carbon dioxide storage

In this work we analyze the isothermal single-phase two-component non-Darcy flow in naturally fractured reservoirs (NFRs) for enhanced gas recovery (EGR) and carbon dioxide storage. The Peng-Robinson equation of state is used to evaluate the thermodynamic properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Volume Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After linearization and use of an operator splitting, the Conjugate Gradient (CG) and the Biconjugate Gradient Stabilized (BCGS-Stab) methods are used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. Non-Darcy effects are included using the Barree and Conway's model for inertial effects. The numerical code also allows grid refinement to represent fractures and provides an improved capture of physical phenomena close to fractures. The effects of hydrodynamic dispersion in our simulations were also considered.