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.

钻井时失水是一个具有挑战性的问题，可能会中断作业并污染地下地层。裂缝中流体流动的分析模型是一种工具，可以快速部署以评估钻探泥浆泄漏到裂缝中的情况。开发了一种新的半解析解决方案来模拟非牛顿钻井液在裂缝地层中的流动。该模型适用于表现出屈服-功率定律（Herschel-Bulkley）的各种流体类型。我们使用有限元模拟来验证我们的解决方案。我们还生成类型曲线，并将其与文献中的其他曲线进行比较。然后，我们证明了所提出的模型在两个遇到丢失环流的现场案例中的适用性。为了解决地下不确定性，我们将半解析解与蒙特卡洛相结合，并生成概率预测。