Drill String - Stuck Drill String - System Dynamics of Surface Resonant Vibrators

System Dynamics of Surface Resonant Vibrators

Surface Resonant Vibrators rely on the principle of counter rotating eccentric weights to impart a sinusoidal harmonic motion from the surface into the work string at the surface. Reference Three (above) provides a full explanation of this technology. The frequency of rotation, and hence vibration of the pipe string, is tuned to the resonant frequency of the system. The system is defined as the surface resonant vibrator, pipe string, fish and retaining media. The resultant forces imparted to the fish is based on the following logic:

• The delivery forces from the surface are a result of the static overpull force from the rig, plus the dynamic force component of the rotating eccentric weights
• Depending on the static overpull force component, the resultant force at the fish can be either tension or compression due to the sinusoidal force wave component from the oscillator
• Initially during startup of a vibrator, some force is necessary to lift and lower the entire load mass of the system. When the vibrator tunes to the resonant frequency of the system, the reactive load impedance cancels out to zero by virtue of the inductance reactance (mass of the system) equalling the compliance or stiffness reactance (elasticity of the tubular). The remaining impedance of the system, known as the resistive load impedance, is what is retaining the stuck pipe.
• During resonant vibration, a longitudinal sine wave travels down the pipe to the fish with an attendant pipe mass that is equal to a quarter wavelength of the resonant vibrating frequency.
• A phenomenon known as fluidization of soil grains takes place during resonant vibration whereby the granular material constraining the stuck pipe is transformed into a fluidic state that offers little resistance to movement of bodies through the media. In effect, it takes on the characteristics and properties of a liquid.
• During pipe vibration, Dilation and Contraction of the pipe body, known as Poisson's ratio, takes place such that that when the stuck pipe is subjected to axial strain due to stretching, its diameter will contract. Similarly, when the length of pipe is compressed, its diameter will expand. Since a length of pipe undergoing vibration experiences alternate tensile and compressive forces as waves along its longitudinal axis (and therefore longitudinal strains), its diameter will expand and contract in unison with the applied tensile and compressive waves. This means that for alternate moments during a vibration cycle the pipe may actually be physically free of its bond.