The Nonlinear Dynamic Characteristics of Straddle Packer Fracturing Tool String Considering Collision Constraints

The straddle packer fracturing technique represents a core technology for reservoir stimulation in horizontal wells targeting deep shale gas formations. However, the fracturing string constrained by dual packers is highly susceptible to severe vibrations induced by high-pressure pulsating fluid flow, which subsequently leads to collisions between the string and the casing. These collisions may compromise the sealing integrity of the packers or cause fatigue damage to the string. The existing design of packer spacing primarily relies on static mechanical experience and lacks the support of nonlinear dynamics theory. As a result, it is difficult to maximize operational efficiency while ensuring safety. Therefore, this paper establishes a fluid–solid coupling fracturing string model that takes into account fluid pulsation, geometric nonlinearity and gap collision constraints. Using the Galerkin discretization and the fourth-order Runge–Kutta algorithm, the influence laws of packer spacing and flow rate on the system stability are systematically studied. Studies have shown that the spacing of packers non-monotonically controls the system stability. Both too short or too long packer spacings will induce chaotic instability. However, there exists a highly robust, stable contact window near the ratio. Within this interval, the fracturing string is locked onto a stable period-doubling orbit. Based on this proposed optimization criterion, compared with the traditional conservative design, the spacing of the packers can be extended by approximately 90%. This not only avoids the risk of chaos but also significantly improves the efficiency of the fracturing operation.