“…where v n,F is the normal velocity of the fluid particle on the boundary; v n,s is the normal velocity of the structure surface; Y is the boundary admittance; and Z is the boundary impedance and Z = 1/Y. Substituting Equations ( 1)- (10) into Equations ( 1)-( 7), the following can be obtained:…”
Section: Set Boundary Conditions and Build Modelsmentioning
confidence: 99%
“…Processes 2022, 10, 1532 2 of 23 A lot of research has been conducted on sonic logging worldwide. On the one hand, the propagation characteristics of acoustic waves in the structure are studied [7][8][9][10][11][12][13][14][15][16]. Modave et al [7], for example, and Miller et al [8] demonstrate efficient finite element solutions of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers, combining projection-based model order reduction with an efficient time domain-impedance boundary condition formulation.…”
Section: Introductionmentioning
confidence: 99%
“…The parametric performance of the finite element simulation was optimized by comparing the amplitude and spectral characteristics of the ultrasonic waves generated by the phasedarray laser source at different element spacings. Lin et al [10] explored the feasibility and reliability of combining back-propagation neural networks (BPNN) and laser-generated surface acoustic waves (SAW) to detect the depth and length of subsurface cracks. The characteristic parameters of the emitted and reflected surface waves in the time and frequency domains were extracted by the Fourier transform and wavelet transform methods.…”
Based on the acoustic wave finite element (AWFE) method, one can establish an AWFE method and study the influence of mechanical parameters on the shale reservoir acoustic wave propagation characteristics. The different crack characteristics and different crack multi-physical coupling phenomena are studied by using the AWFE method on shale gas reservoir cracks. To calculate the shape and position along the crack near a side borehole, the model parameters are compared with the simulation results. The reflection waveform characteristics of adjacent cracks are studied by using the AWFE method. By considering the borehole axis of symmetry, for an acoustic impedance discontinuous interface on one side of the two-dimensional axisymmetric AWFE, one can establish a borehole cross-crack and an arc cross-crack reflection interface model with the AWFE method. By processing the waveform data received by different receiving points under the same source distance, the parameters, such as the reflection wave time and the distribution laws of the crack in the shale reservoir, are obtained. To verify the validity of the research method, the propagation of a reflected acoustic wave from the reservoir fracture by the filling with different media was also studied. The results show that a reflection wave arrival time changing with the source ordinate and present law, by side borehole fracture morphology, showed a suitable consistency. The well cross-crack angle range is 10~20°, according to the wave arrival time calculated by the side borehole fracture dip. For the acoustic signal propagation in the shale formation anisotropy, they found that an acoustic signal is always in the direction of the elastic modulus, with a further larger spread, a location of maximum amplitude, and a 45-degree direction to the axis of symmetry. In the lateral and longitudinal distance from an acoustic source of the same two receiver signal waves, the receiver vibration amplitude is bigger, and there is less attenuation. With the increase in the anisotropic index, the inside ovality amplitude distribution of the signal amplitude in this model is higher. When a side borehole has an arc crack and a reflected wave to time to obtain the coordinates of a reflecting interface and to compare with the results of the calculation model, the crack in the center position, and the reflection point coordinates, the relative error is less than 5%. Finally, the AWFE method could provide a new idea for the identification of the crack properties and also could be an inverse calculation of the position and morphological characteristics of fractures near the side borehole.
“…where v n,F is the normal velocity of the fluid particle on the boundary; v n,s is the normal velocity of the structure surface; Y is the boundary admittance; and Z is the boundary impedance and Z = 1/Y. Substituting Equations ( 1)- (10) into Equations ( 1)-( 7), the following can be obtained:…”
Section: Set Boundary Conditions and Build Modelsmentioning
confidence: 99%
“…Processes 2022, 10, 1532 2 of 23 A lot of research has been conducted on sonic logging worldwide. On the one hand, the propagation characteristics of acoustic waves in the structure are studied [7][8][9][10][11][12][13][14][15][16]. Modave et al [7], for example, and Miller et al [8] demonstrate efficient finite element solutions of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers, combining projection-based model order reduction with an efficient time domain-impedance boundary condition formulation.…”
Section: Introductionmentioning
confidence: 99%
“…The parametric performance of the finite element simulation was optimized by comparing the amplitude and spectral characteristics of the ultrasonic waves generated by the phasedarray laser source at different element spacings. Lin et al [10] explored the feasibility and reliability of combining back-propagation neural networks (BPNN) and laser-generated surface acoustic waves (SAW) to detect the depth and length of subsurface cracks. The characteristic parameters of the emitted and reflected surface waves in the time and frequency domains were extracted by the Fourier transform and wavelet transform methods.…”
Based on the acoustic wave finite element (AWFE) method, one can establish an AWFE method and study the influence of mechanical parameters on the shale reservoir acoustic wave propagation characteristics. The different crack characteristics and different crack multi-physical coupling phenomena are studied by using the AWFE method on shale gas reservoir cracks. To calculate the shape and position along the crack near a side borehole, the model parameters are compared with the simulation results. The reflection waveform characteristics of adjacent cracks are studied by using the AWFE method. By considering the borehole axis of symmetry, for an acoustic impedance discontinuous interface on one side of the two-dimensional axisymmetric AWFE, one can establish a borehole cross-crack and an arc cross-crack reflection interface model with the AWFE method. By processing the waveform data received by different receiving points under the same source distance, the parameters, such as the reflection wave time and the distribution laws of the crack in the shale reservoir, are obtained. To verify the validity of the research method, the propagation of a reflected acoustic wave from the reservoir fracture by the filling with different media was also studied. The results show that a reflection wave arrival time changing with the source ordinate and present law, by side borehole fracture morphology, showed a suitable consistency. The well cross-crack angle range is 10~20°, according to the wave arrival time calculated by the side borehole fracture dip. For the acoustic signal propagation in the shale formation anisotropy, they found that an acoustic signal is always in the direction of the elastic modulus, with a further larger spread, a location of maximum amplitude, and a 45-degree direction to the axis of symmetry. In the lateral and longitudinal distance from an acoustic source of the same two receiver signal waves, the receiver vibration amplitude is bigger, and there is less attenuation. With the increase in the anisotropic index, the inside ovality amplitude distribution of the signal amplitude in this model is higher. When a side borehole has an arc crack and a reflected wave to time to obtain the coordinates of a reflecting interface and to compare with the results of the calculation model, the crack in the center position, and the reflection point coordinates, the relative error is less than 5%. Finally, the AWFE method could provide a new idea for the identification of the crack properties and also could be an inverse calculation of the position and morphological characteristics of fractures near the side borehole.
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