Calculation and research of fundamental frequency of casing string in shale gas horizontal wells

In view of the fact that the fundamental frequency of the casing string in shale gas horizontal wells is difficult to be accurately obtained by numerical simulations and experimental methods, a research method is proposed based on the similarity model theory and the transfer matrix method. According to the similarity criterion from the similarity theory, a similarity model is established, and the similarity ratio of the natural frequency is obtained. Through the use of the transfer matrix method, the fundamental frequency of the experimental model of the casing string in horizontal wells with rigid support is analyzed, and its mathematical model is established. Through the calculation of the fundamental frequency of the experimental model and the result of the vibration experiment, the correctness of the model is verified. Besides, the fundamental frequency of a 2500 m long shale gas horizontal well casing string with 20 rigid centralizers is calculated. The calculation results show that the combination of the similarity theory and the transfer matrix method can realize the solution of the natural frequency of the casing string in large-scale horizontal wells, which is reliable, accurate and easy to be programmed.