Estimating Effective Stress Parameter and Fracture Parameters in Shale-Gas Fractured Reservoirs Using Azimuthal Fourier Coefficients

Economic gas production from unconventional shale-gas reservoirs requires hydraulic fracturing to reconnect and open existing fractures which are lower than the actual fracture gradient. Estimating sensitive parameters of fractured sweet spots such as effective stress parameter and fracture properties from azimuthal seismic amplitude data can be useful to optimize the development of shale-gas fractured reservoirs. Based on the anisotropic Gassmann’s equation and the relationship between porosity and effective stress, we propose a simplified expression of the saturated stiffness tensor for a horizontal transverse isotropic (HTI) model formed by a single rotationally symmetric set of vertical fractures. Using the perturbation in the stiffness matrix, we derive a linearized reflection coefficient as a function of effective stress parameter and fracture parameters and corresponding Fourier series expression. The sensitivity analysis of Fourier coefficients (FCs) shows that the zeroth FC is sensitive to effective stress parameter, and the second FC is sensitive to fracture parameters. Thus, we propose to estimate the effective stress parameter and fracture weaknesses using a three-step azimuthal FCs inversion involving 1) estimating the FCs using azimuthal seismic data, 2) estimating the effective stress parameter using the zeroth FC, and 3) estimating the normal and tangential fracture weaknesses using the second FC. A synthetic seismic data example reveals that the effective stress parameter and fracture parameters can be reliably estimated even with moderate noise. Test on a real data set implies that the proposed inversion method can generate meaningful results that are useful for identifying abnormal pressure and fractures in reservoirs.