Drilling mud losses through fractures and excessive mud seepage into permeable zones can become the most impactful problem while drilling naturally fractured formations, increasing Non Productive Time. Currently, the modeling of this phenomenon is done assuming impermeable fracture walls, which are not connected to the rock matrix or modelling the mud seepage in permeable zones independently, without being coupled, which does not adequately represent what that is observed in the field. For this reason, in this research a new algorithm is developed, which represents the phenomenon of lost circulation through fractured formations coupled to permeable zones, allowing quantification of loss rates not only instantaneous but also, when maintaining a constant rate of loss over time, generated by the connection of fractures with permeable zones or another fracture network. For achieving greater accuracy, variables such as fracture deformation are analyzed, which can alter its width; mud rheology, a fundamental piece of information to derive the flow velocity within the fracture, petrophysical characteristics of the formation to determine the flow velocity in permeable zones and finally the coupling between the fractured zone and the permeable matrix is performed, showing that when the walls of the fracture plane are permeable, the rate of fluid loss is maintained over time. The proposed algorithm in this study allows estimating the fluid flow and fracture properties using finite differences, likewise, a linear relationship is assumed as a function of pressure to represent the fracture width, and the mud rheology by using power law. The implementation of this new model estimates the sludge loss phenomenon in a better way, allowing a improved understanding of the events reported in the field