To ensure a successful drilling is essential to design a geomechanical model in order to determine a mud weight which avoids problems such as well collapse, flux of cavings and among other aspects that contribute to increase costs and non-productive times (NPT). Considering that conventional wellbore stability models don't include the effect of circulation losses through fractured zones, this research aims to design a new algorithm that models the phenomenon of circulation and filtered loss through fractured formations. Additionally, an integrated model which includes aspects like: fracture deformation, mud rheology, and flow through fractures is implemented. This new algorithm takes into account the most important considerations in this area published in the literature The algorithm proposed in this research enables to solve mathematical models analytically and numerically in order to analyze all the possible solutions integrated in the model which includes differential equations for the fluid flow and analytical equations for the formation properties, fracture behavior and mud rheology. This new algorithm allows to determine fracture widths in real time, using information of the circulation loss or the required mud weight, if the known fracture width to maintain losses at its minimum permitted movement. These results are important to select the lost circulation material (LCM), reservoir engineering, secondary permeability log and the operation simulation can be optimized. This paper extents the knowledge of naturally fractured reservoirs especially during drilling, and modeling the phenomenon of circulation lost using a new algorithm that solves an integrated model is easy to implement.


Based on Ali Ghalambor et al (2014), the circulation loss could be the major problem during drilling increasing the non-productive time (NPT). According to Murchison, (2006), Ivan et al., (2003), this NPT cost to the petroleum industry US$ 800 million per year approximately.

Ghalambor et al (2014), also established that this circulation loss occur through the rock matrix, natural and induced fractures, and vugs. With the implementation of mathematical models to represent this phenomenon, the flux is classified into filtered through the rock generating a mud cake along the wellbore wall and flux through the fractured zones regarding the mud rheology.

Parn-Anurak and Engler (2005), studied the filtered loss through the rock matrix considering the filtered influence radio and cake thickness. This model analyze the erosion and formation rate of the cake constituted by mud filtered.

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