Abstract：The dynamic response of a drillstring that is limited in a wellbore is influenced by the bottom hole assembly (BHA), the drilling fluid inside and outside the drillstring, the drilling parameters, and so on. One of the major causes that lead to hole collapse and drilling tool damage is the severe drillstring vibrations in a state of dynamic instability. It is necessary to study the influences of various parameters, such as the structural parameters and drilling parameters, on the lateral vibrations of drillstring, and to take steps to improve its stability. In this paper, taking into account the big difference between drill pipe (DP) and drill collar (DC), the drillstring is modeled as a stepped pipe conveying drilling fluid that is pumped down to the bottom inside the drillstring and returns to the ground through the annulus. Meanwhile, the stabilizer is simplified as a linear spring. For the lateral vibrations of drillstring in a vertical well, an analytical model that considers the drillstring gravity, weight on bit (WOB) varying harmonically with time, arrangements of stabilizer, and hydrodynamic force and damping force of drilling fluid is established and discretized into the four order ordinary differential equations using the finite element method. The instable regions are determined by solving the critical frequency equation obtained using Bolotin’s method. The effects of WOB, length of drillstring, stabilizer location, and velocity and density of drilling fluid on the stability of drillstring system are studied. The results show that both the average value and the fluctuation amplitude of WOB can be the driving factors behind the system instability, and the stability of the system is not sensitive to the length of the drill pipe in tension. Furthermore, reducing the flow rate and density of drilling fluid, and shifting the stabilizer downward are all helpful in maintaining the stability of the system within the parameter ranges discussed in this paper.
2017, Vol. 38 
