The economic loss caused by fracture leakage accounts for 90% of all leakage costs; thus, it is necessary to find the factors that affect the leakage and to study the leakage laws of fractured strata. The advantage of this article is that we introduced fracture index deformation and fracture tortuosity parameters to characterize fracture roughness and fracture characteristic parameters using the logging data analysis method. To explore the mechanism of leakage in essence, this paper, based on fluid mechanics, improves the radial leakage model by adopting the Herschel–Bulkey (H–B) flow type drilling fluid with high calculation accuracy and comprehensively considering the factors such as drilling fluid performance parameters, fracture roughness characteristic parameters, pressure difference between the wellbore and formation, and radial extension length of the drilling fluid. The advantage of the model is that it is solved in an absolutely stable backward Euler difference format. The numerical simulation is carried out by MATLAB. The simulation results revealed that the leakage rate increased as the fracture index deformation coefficient and the fracture opening increased. The leakage rate also increased as the fracture tortuosity parameters decreased and as the fracture smoothened. However, the leakage rate decreased as the drilling fluid consistency coefficient increased. Drilling fluid dynamic shear force had a minor effect on the leakage rate. The higher the pressure difference between the wellbore and the formation, the higher the leakage rate. As the drilling fluid intrusion depth increased, the leakage rate decreased until it reached 0. Two parameters were mainly controlled in order to control the degree of leakage: differential pressure and fracture static width, which has important guiding for adjusting the drilling fluid density and predicting leaks in the field. The solution method of the model in this paper has a certain reference value for the solution of other models in the future. The conclusion can provide reference for numerical simulation, laboratory test, and field application in the future.

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Wellbore leakage mostly occurs in structurally developed fractured formations. Analyzing the real-time leakage rate during the drilling process plays an important role in identifying the leakage mechanism and its rules on-site. Based on the principles of fluid mechanics and using Herschel-Bulkley (H-B) drilling fluid, by reasonably simplifying the drilling fluid performance parameters, fracture roughness characteristic parameters, pressure difference between the wellbore and formation, and the radial extension length of drilling fluid, the radial leakage model is improved to improve the calculation accuracy. Using the Euler format in numerical analysis to solve the model and with the help of numerical analysis software, the radial leakage law of this flow pattern in the fractures is obtained. The results show that the deformation coefficient of the fracture index, fracture aperture, pressure difference, leakage rate, and cumulative leakage rate are positively correlated. The larger the curvature of the fracture, the rougher the fracture, and the smaller the leakage rate and cumulative leakage rate. The larger the consistency coefficient of the drilling fluid, the greater the additional resistance between the fractures, and the smaller the leakage rate and cumulative leakage rate. As the extending length of the fracture increases, the invasion of drilling fluid decreases, the leakage rate slows down, and eventually reaches zero, with the maximum cumulative leakage rate.