With the increasing complexity of shale gas extraction conditions, a large number of high-strength collapse-resistant casing is applied to the extraction of unconventional oil and gas resources. There are errors in the traditional API collapse strength formula. A high-precision and low-computational-cost model is needed for predicting the strength of high-collapsible casing. The key influencing factors of casing anti-collapse strength were determined as outer diameter, wall thickness, yield strength, ovality, wall thickness unevenness, and residual stress by analyzing the casing collapse mechanism. In response to the key factors mentioned above, a dataset was formed by measuring the geometric parameters of the full-size casing and collecting data on the results of the anti-collapse strength experiment, which was divided into a training set (70%) and a testing set (30%). Three machine-learning algorithms, a neural network, random forest, and support vector machine, were trained to predict the anti-extrusion strength. The correlation coefficient R², root mean square error RMSE, and average relative MRE were used to evaluate the indexes for model preference evaluation. The results show that machine-learning algorithms have unique advantages in casing anti-collapsing strength prediction. Within which, the neural network prediction model has the best prediction effect, and its characteristics of high precision, low cost and high efficiency are more suitable for the prediction of casing extrusion strength. Its testing set R² is 0.9733, RMSE is 0.0267 and MRE is 0.0782, and the prediction accuracy can reach 92.2% which is much higher than the API calculation result (63.3%). The network prediction model is suitable for casing anti-collapsing strength prediction and meets the actual prediction requirements.

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.