During the drilling process, horizontal drill strings are often subject to stick-slip and back-pressure phenomena, which undermine drilling safety and affect drilling costs. However, most of the models proposed in the existing literature apply only to the analysis of the drill string motion state and are irrelevant to the rotary drilling process in coal mines. This paper presents a lumped-mass model of a drill string in a horizontal coal mine well. First, based on reasonable assumptions, the drill-string system was considered as four lumped-mass units. The lateral-torsional dynamics model was established based on the Lagrange dynamics theory. Further, combined with lateral movement, the intermittent contact between the drill string and borehole wall is described, and the friction torque due to this intermittent contact is calculated. Combined with the Karnopp bit-rock interaction, a drill-string dynamics model of horizontal wells that considers intermittent contact friction was developed. The proposed horizontal well drill-string model is more suitable for rotary drilling in a coal mine, and the nonlinear influencing factors are considered more comprehensive.

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