Two-dimension multi-phase fluid flow numerical simulations which include drilling fluid, injected gas, formation fluids and cuttings were carried out for different well geometry taking into account both inlets and outlets throughout boundary system. Simulations were made for fields whose formation and fracture pressure profiles are characteristic of the naturally fractured Mexican fields. During simulations different gas injection systems to get underbalanced conditions such as parasite tubing string, annular gas injection and drill-pipe gas injection were proved in order to establish their feasibility for application in the case of study. Pressure and velocity fields together with phase distribution along the well are analyzed in each case to determine their technical and operative applicability as well as to evaluate advantages or disadvantages of this technique respect to the present circumstances during drilling. From the results it is possible affirm that drill-pipe gas injection is the best option to get underbalanced conditions during drilling as is explain in the extent work. A comparative survey against other model results (R.R. Angel, Machado-Ikoku, Poettmann & Berman and Okpöribi) is realized in the final of this work from which it is possible to observe the improvements of this work in regarding those of obtained by mentioned models. According to observed results underbalanced drilling is a good-available solution to total lost circulation and formation damage problems faced presently during drilling-wells in the naturally fractured low-pressure Mexican fields. The main contributions of this work consist of its capability to design drilling performance and quantify lost circulation by means of numerical simulation of volume-average general mass and momentum conservation equations.

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