The geomechanical model for mud density optimization is essential to guarantee drilling success. This will allow to avoid problems such as: wellbore collapse, influx, induced fractures, pipe sticks, among other aspects that contribute on cost increasing and NPT. Normally, conventional wellbore stability models do not include mud losses effects through fractured zones. This research proposes a new algorithm (or methodology) for modeling the mud losses phenomenon through fractured and permeable formations. This model includes fracture deformation, mud rheology, flow through fractures and a coupling between fractured zone and permeable zone, considering that fracture plane walls are permeable, generating losses rate maintained over time when corrective actions are not taken at field. This proposed algorithm solves mathematical models in both analytical and numerical methods, using finite differences, in order to analyze the circulation losses in a more robust way. Therefore, differential equations were used for fluid flow modeling, and analytical equations for formation properties, when these are not available. For fracture behavior, a linear relationship is assumed as a function of pressure, and mud rheology is represented by power law behavior.

The mentioned algorithm allows to determine fracture width in real time, by circulation losses information. Moreover, it allows to calculate the maximum mud weight. Concluding, the mathematical model can be used in two way, when the fracture walls are impermeable and the fracture length is finite, ballooning phenomenon is modeled. Instead, when the fracture walls are permeable, it represents circulation losses phenomenon.

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