Well-Test Analysis of Hydraulic Fractured Wells in Fracture-Vug Low-Permeability Carbonate Reservoirs

The naturally vuggy and fractured carbonate rock plays an important role in China's oil and gas resources. Therefore, it is of great significance to study the characteristics of well bottom pressure in fracture-vug carbonate rock for hydraulic fractured wells. According to the basic principle of seepage mechanics, the well test model for carbonate reservoirs in view of the stress sensitivity and the threshold pressure gradient was established. The point source function method, the Laplace integral transform and the Fourier cosine integral transform were used to obtain the point source solution with impermeable top and bottom and lateral infinite boundary in the Laplace space. The surface source solution was obtained with the integral of the point source solution; the real-space well bottom pressure solution was obtained through the Stehfest numerical inversion and the well test curves were drawn. The simplified model solution matches with the related literature calculation results as to the threshold pressure gradient. The larger the stress sensitivity coefficient is, the more obviously the pressure and the pressure derivative curve will go up; the larger the threshold pressure gradient is, the earlier the pressure derivative curve will rise up; the smaller the open degree is, the more obvious the spherical flow characteristics will be; the larger the interporosity flow coefficient is, the earlier the 'concavity' will appear; the larger the elastic storage ratio is, the wider and deeper the 'concavity' will be. The proposed model can be effectively applied to analyze the well test curves of hydraulic fractured wells in naturally vuggy and fractured carbonate reservoirs of low permeability.