Simulation of wave propagation in boreholes and radial profiling of formation elastic parameters

Chi, Shihong
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Modern acoustic logging tools measure in-situ elastic wave velocities of rock formations. These velocities provide ground truth for time-depth conversions in seismic exploration. They are also widely used to quantify the mechanical strength of formations for applications such as wellbore stability analysis and sand production prevention. Despite continued improvements in acoustic logging technology and interpretation methods that take advantage of full waveform data, acoustic logs processed with current industry standard methods often remain influenced by formation damage and mud-filtrate invasion. This dissertation develops an efficient and accurate algorithm for the numerical simulation of wave propagation in fluid-filled boreholes in the presence of complex, near-wellbore damaged zones. The algorithm is based on the generalized reflection and transmission matrices method. Assessment of mudfiltrate invasion effects on borehole acoustic measurements is performed through simulation of time-lapse logging in the presence of complex radial invasion zones. The validity of log corrections performed with the Biot-Gassmann fluid substitution model is assessed by comparing the velocities estimated from array waveform data simulated for homogeneous and radially heterogeneous formations that sustain mud-filtrate invasion. The proposed inversion algorithm uses array waveform data to estimate radial profiles of formation elastic parameters. These elastic parameters can be used to construct more realistic near-wellbore petrophysical models for applications in seismic exploration, geo-mechanics, and production. Frequencydomain, normalized amplitude and phase information contained in array waveform data are input to the nonlinear Gauss-Newton inversion algorithm. Validation of both numerical simulation and inversion is performed against previously published results based on the Thomson-Haskell method and travel time tomography, respectively. This exercise indicates that the numerical method is stable and efficient for the simulation of wave propagation in boreholes surrounded by complex invasion zones. Additional tests of the inversion algorithm are performed on array waveform data acquired in a low-porosity gas field. Mud-filtrate invasion effects are not measurable on the estimated P- and S- wave velocities for depths of invasion around 2-3 borehole diameters. Acoustic log corrections performed with the Biot-Gassmann fluid substitution model can only be used for the case of deep invasion. The inversion examples indicate that physically consistent radial profiles of formation density and P- and S-wave velocities can be reconstructed from array waveform data.