Analysis of three-dimensional nonlinear fluid-solid coupling vibration characteristics of coalbed methane abandoned well plugging string

Objective The plugging quality of cement plug in abandoned coalbed methane wells is critical to preventing pollutant leakage. Current standards for handling these wells involve simple mud pump injection, which often results in cement plugs with issues like particle agglomeration, bubbles, and micropores. These defects reduce the strength of the cement plug and compromise its sealing performance. Methods To address this, vibration technology is applied to the plugging operation, using a specialized tool to induce vibrations in the pipe string. This process enhances the fluidity of the cement slurry via the transmission of vibration energy, thereby improving the plugging quality of the cement plug. A three-dimensional nonlinear coupling vibration control model of the pipe string-cement slurry system during plugging operations was established based on Euler-Bernoulli beam theory and the Hamilton variational principle, taking into account nonlinear factors. The Lagrange function and cubic Hermite interpolation function were used to discretize the pipe string system. The Newmark-β method was employed to calculate and analyze the vibration characteristics of the pipe string under cement slurry conditions. An experimental test platform was constructed, and orthogonal tests were conducted to study the effects of vibration frequency, vibration time, and vibration amplitude on the mechanical properties of the cement stone under various parameter combinations. Optimal vibration parameters were identified, and the influence of individual factors on the mechanical properties of the cement stone was further examined. Results and Conclusions The results indicate that: (1) Considering the vertical and horizontal coupling effect transforms the string from a linear to a nonlinear structure. The applied load significantly increases the natural frequency of vibration, which changes in real-time along with the vibration mode, exhibiting periodic changes over time. (2) The length of the string is inversely proportional to the natural frequency of the vibration; longer strings show smaller variations in natural frequency. (3) The coupling effect between the pipe string and the cement slurry significantly impacts the natural frequency of vibration. In the presence of cement slurry, the natural frequency of the pipe string system decreases, with higher slurry density further reducing the natural frequency. (4) Mechanical vibration enhances the uniformity and density of the cement slurry system, substantially increasing the strength of the cement stone. When the vibration frequency is 15 Hz, vibration time is 5 minutes, and vibration amplitude is 3 mm, the compressive strength of the cement increases by 38.45%, tensile strength by 24.14%, and bonding strength by 52.9% compared to non-vibration conditions. The research findings provide guidance for designing vibration parameters for plugging tools and determining field construction parameters, improving cement slurry performance to enhance plugging quality, and offering significant engineering insights.