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Loss of circulation while drilling is a challenging problem that may interrupt operations and contaminate the subsurface formation. Analytical modeling of fluid flow in fractures is a tool that can be quickly deployed to assess drilling mud leakage into fractures. A new semi-analytical solution is developed to model the flow of non-Newtonian drilling fluid in fractured formation. The model is applicable for various fluid types exhibiting yield-power law (Herschel-Bulkley). We use finite-element simulations to verify our solutions. We also generate type curves and compare them to others in the literature. We then demonstrate the applicability of the proposed model for two field cases encountering lost circulations. To address the subsurface uncertainty, we combine the semi-analytical solutions with Monte Carlo and generate probabilistic predictions. The solution method can estimate the range of fracture conductivity, parametrized by the fracture hydraulic aperture, and time-dependent fluid loss rate that can predict the cumulative volume of lost fluid.

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