Dynamic stability of a stepped drillstring conveying drilling fluid

Taking into account differences between a drill pipe (DP) and a drill collar (DC), the drillstring in a vertical well is modeled as a stepped pipe conveying a drilling fluid downwards to the bottom inside the string and then upwards to the ground from the annulus. An analytical model that describes lateral vibration of the drillstring and involves the drillstring gravity, weight on bit (WOB), hydrodynamic force and damping force of the drilling fluid is established. By analysis of complex frequencies, the influences of WOB, borehole diameter, DP length, velocity and density of the drilling fluid on the stability of the system are discussed.