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Within the existing leakage model accounting for drilling mud loss in naturally-fractured formations, the leak-off velocity is assigned to a fixed value or described by the Cater model, which does not consider the influence of dual-system hydromechanical coupling effects between fracture-wall and fracture-inner systems. The dual-system between the formation and fracture is controlled by the flowing net pressure inside the fracture, which determines the dynamic width of the natural fracture and leak-off velocity. In this study, first, the leak-off velocity under the hydromechanical coupling of the fracture-wall system was obtained based on the coupled governing equations of the solid and liquid phases of the natural fracture-wall, as well as Darcy’s law. Second, the leakage-front invasion velocity, leakage rate, and leakage volume under the hydromechanical coupling of the fracture-inner system were clarified according to the geometric governing of the natural fracture morphology. Finally, the dual-system coupling leakage model was developed considering the continuous equation, while the numerical solution was obtained through a time-step deduction. Results show that at a given time, a greater formation permeability leads to a greater leakage rate and volume, with a smaller leakage front distance. The leakage rate increases with an increase in formation permeability, well bottom differential pressure, and initial width of the natural fracture, while it decreases with an increase in the fracture normal stiffness, yield stress, and plastic viscosity. The new leakage model and numerical method concerning time-step deduction are assessed by solving the issues of fully coupled fracture-wall and fracture-inner systems considering drilling fluid leak-off. The new model may be utilized to simulate various problems related to the invasion of drilling fluids into the fractures, including predicting the dynamic width of natural fracture and borehole ballooning/breathing phenomena.

New Leakage Model for Naturally Fractured Formations Considering the Effects of Dual-System Hydro-Mechanical Coupling