Natural fractures, carbonate reservoirs, fracture closure, topology, pseudo-coupling, numerical simulation, finite elements, double porosity/double permeability.

Naturally fractured reservoirs are present in the various lithostratigraphic units of shales, sandstones, carbonates, among others. Carbonate reservoirs stand out, representing a large part of the world's oil and gas reserves. In Brazil, the reservoirs of the Pre-Salt layer stand out for presenting challenging geological characteristics for Brazilian engineering. The Pre-Salt comprises an area of approximately 149 thousand square kilometers offshore, between the states of Santa Catarina and Espírito Santo, with a total depth of approximately 7 km (Petrobras, 2017). Usually the structure of these reservoirs is composed of two structures, the rock matrix and fractures, where fractures can function as channels or barriers to flow. When fractures develop high flow conductivity they cause premature water breakthrough in producing wells, compromising the efficiency of the reservoir matrix sweep (Bratton & Gillespie, 2006). The development of pre-salt carbonate reservoirs involves several problems such as: the coupling of mechanical deformation processes induced by fluid pressure on the matrix rock and fractures, the fluid flow inside the matrix and fractures, the interaction of fluid flows from the matrix and fractures, the deformations of the matrix rock and fractures, among others (Adachi et al., 2007; T. Chen et al., 2014). However, due to the large number of processes involved, the heterogeneity of the medium and the magnitude and direction of the in situ stresses make the modeling of the coupled hydromechanical problem very complex. The dual porosity approach is one of the computationally efficient and commonly used methods to model the flow in the fracture-matrix system. It was first introduced by (Barenblatt et al., 1960). In this model, the matrix and fracture are divided into two independent systems: the fractures are

conceptualized to serve as main global flow pathways (fractures have high permeability and low storage volume), while the continuous matrix, which acts as sinks or main sources of fluid storage (matrix blocks have high storage volume and low permeability), are locally connected to each other as well as interact directly or indirectly with the globally connecting fractures. Then, the dual porosity concept was extended and applied to the field of petroleum engineering by (Warren & Root, 1963) mainly for pressure test analysis. Within the dual porosity/permeability formulation is involved the fluid transfer term between the matrix and the fracture, related to the shape factor. As will be seen in the next chapters, this subject has been studied by several authors, who have developed constant values of the transfer term proper to the geometry of the model analyzed. However, these shape factor constants cannot fully explain the transient phenomenon of the system, because it is usually associated with the pseudo-stationary state, which would cause large calculation error at the initial stage of the flow. Therefore, the authors focused on the description of the transient pressure by solving the pressure diffusion equation inside the matrix block. In addition to the shape factor there are properties such as topology, equivalent permeability, which allows characterizing the natural fracture system, allowing to know the connectivity of this network and its importance in the flow of fluids. (Sævik & Nixon, 2017; Sanderson & Nixon, 2015a).In this work, a comparison between the DFN, Double porosity / double permeability and simple porosity

models is presented, with the aim of identifying, taking into account the considerations of each model, which one allows to have a real knowledge of the reservoir, for this purpose the concept of geomechanical pseudo-coupling tables is used where the volumetric deformation of the fracture system and matrix is considered.