A comparative study of non-Darcy flows in naturally fractured gas reservoirs

Numerical reservoir simulation is applied to obtain forecasts for flow in hydrocarbon reservoirs under different production strategies. Considering heterogeneities, which may occur in different length scales, there is significant interest in fractures. In naturally fractured reservoirs (NFRs), for example, differences in permeability and porosity values are due to geological factors. In this work, a numerical reservoir simulator was built for the purpose of studying gas flow in NFRs. The physical–mathematical modeling considers single-phase and isothermal three-dimensional flow. Non-Darcy effects are incorporated using Forchheimer’s equation and the Barree and Conway’s model for considering the inertial effects. The nonlinear partial differential equations are discretized by means of the finite-difference method along with a time-implicit approach. The numerical code also allows grid refinement to represent fractures and providing a better capture of physical phenomena close to fractures and wellbores. A preconditioned approximate factorization technique was chosen for the numerical solution due its ability to solve matrix equations for problems where heterogeneity is an important feature. Different production scenarios were studied for hydrocarbons recovery. It was possible to conclude that spatial distribution and wide variation of heterogeneity values have direct influence in the pressure and velocity fields in porous media, and also impact on the wellbore pressure profile. When non-Darcy flow occurs in naturally fractured reservoirs there is a counterbalance between fracture effects, which reduce wellbore pressure drop, and the inertial effects, that increase wellbore pressure drop. Therefore, an accurate modeling of these interactions is fundamental to forecast reservoir performance.