Study on the Model and Law for Radial Leakage of Drilling Fluid in Fractured Formations

[Image: see text] 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.