Loss of circulation is a major problem that often causes interruption to drilling operations, and reduction in efficiency. This problem often occurs when the drilled wellbore encounters a high permeable formation such as faults or fractures, leading to total or partial leakage of the drilling fluids. In this work, we present a novel semi-analytical solution and type-curves that offer a quick and accurate diagnostic tool to assess the lost-circulation of Herschel-Bulkley fluids in fractured media. Based on the pressure and mud loss trends, the tool can estimate the effective fracture conductivity, the cumulative mud-loss volume, and the leakage period. The behavior of lost-circulation into fractured formation can be assessed using analytical methods that can be deployed to perform flow diagnostics, such as the rate of fluid leakage and the associated fracture hydraulic properties. In this study, we develop a new semi-analytical method to quantify the leakage of drilling fluid flow into fractures. The developed model is applicable for non-Newtonian fluids with exhibiting yield-power-law, including shear thickening and thinning, and Bingham plastic fluids. We propose new dimensionless groups and generate novel dual type-curves, which circumvent the non-uniqueness issues in trend matching of type-curves. We use numerical simulations based on finite-elements to verify the accuracy of the proposed solution, and compare it with existing analytical solutions from the literature. Based on the proposed semi-analytical solution, we propose new dimensionless groups and generate type-curves to describe the dimensionless mud-loss volume versus the dimensionless time. To address the non-uniqueness matching issue, we propose, for the first time, complimentary derivative-based type-curves. Both type-curve sets are used in a dual trend matching, which significantly reduced the non-uniqueness issue that is typically encountered in type-curves. We use data for lost circulation from a field case to show the applicability of the proposed method. We apply the semi-analytical solver, combined with Monte-Carlo simulations, to perform a sensitivity study to assess the uncertainty of various fluid and subsurface parameters, including the hydraulic property of the fracture and the probabilistic prediction of the rate of mud leakage into the formation. The proposed approach is based on a novel semi-analytical solution and type-curves to model the flow behavior of Herschel-Bulkley fluids into fractured reservoirs, which can be used as a quick diagnostic tool to evaluate lost-circulation in drilling operations.

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