This work presents a very practical and simple technique to numerically simulate the multiphase flow in multiporosity naturally fractured petroleum reservoirs. A correct modeling of Naturally Fractured Reservoirs requires both good understanding of the physics of the flow through the formation and its correct implementation in a Numerical Reservoir Simulator. Some history matches in Naturally Fractured Reservoirs have showed that the traditional double porosity formulation used since the end of the 60's sometimes does not show good results. Even though the modeling of naturally fractured reservoirs has been developed through more than five decades, there is still and will be a considerable research activity to obtain a practical and robust modeling for this type of reservoirs. The proposed method assumes a nested serial flow among the different porosity systems that have been identified. Only the most outer porous medium is considered as continuous and therefore, it carries the flow to the producing wells. The rest of the systems are considered discontinuous, interacting themselves only locally. After applying the Newton method to the discretized system of nonlinear equations, a tri-diagonal matrix block structure is obtained, which is reduced by applying cyclically the Schur complement. This algorithm can be implemented straightforward in a non-fractured multiphase reservoir simulator. It is shown that this approach can model any multiporosity naturally fractured reservoir as long as the fluid transfer functions between mediums could be represented by the quasi-steady-state flow assumption, which is the Warren and Root model. Results show that the behavior of multiporosity reservoir simulated as double porosity systems result in non-realistic reservoir performance and therefore wrong make-decisions. Introduction Naturally Fractured Reservoirs (NFR) are of great interest worldwide because they contain huge reserves of oil and because its modeling faces many challenges that so far are not well developed and understood. In dealing with NFR, most of reservoir engineers have performed simulation by using the well known double porosity model introduced for Warren and Root in the 60´s. Since then, important contributions have been made to understand and modeling of multiphase fluid flow processes in NFR 1,2,3,4,5,6 However, most of these works have concentrated basically on NFR composed of two mediums: rock matrix and fracture network 7. Performing simulation studies in some NFR in Mexico, engineers have had some problems in doing history matching by using the traditional double porosity model 8, 9. The main reason is that some of these NFR present several types of media including macro fractures, micro fractures, caverns (vugs), contrasting matrix etc. In order to obtain a successful history matching by using the double-porosity model and provide reasonable reservoir performance, engineers spend too much work and time characterizing the two required porosity media, putting them together and performing a history matching, obtaining not always good results.
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