Failure volume under particle water-jet impact in deep well drilling engineering: Mathematical modeling and verification analysis

•The rock failure volume model under particle jet impact is put forward and established.•Damage evolution and failure volume under particle jet impact are dynamically simulated and analyzed.•The correctness and applicability of mathematical model were verified by comparative analysis with experiment and simulation. There are some difficult problems in deep and ultra-deep oil and natural gas drilling process due to the complex stress environment and hard formation, such as slow drilling speed, well deviation and high cost. As one of the important parameters to measure rock-breaking efficiency, mathematical model of failure volume is proposed in this paper, which is suitable for deep-well rock-breaking technology. First, the particle jet impact rock-breaking laboratory experiment was conducted based on the self-developed experimental platform, and the strength of rock specimen was tested. Then, the failure volume model of particle jet impact rock-breaking which varied with particle size, and water-jet velocity was established based on contact mechanics. Meanwhile, the simulation model and method of particle jet impact rock was carried out and introduced, and damage evolution was dynamical simulated. Comparative analysis of experiment results, model calculation and dynamic simulation was used to analyze the failure volume, and it showed, failure volume would increase linearly with increase of water-jet velocity, while particle size has little effect on failure volume under the condition of constant nozzle diameter. The comparison results of theoretical modeling and rock-breaking experiment are basically consistent, which proves the correctness and applicability of failure volume model.