Presented in this dissertation are novel models and techniques to analyze the whirling vibration of drillstrings during oil and gas (O&G) operations. Mathematical models are developed to solve for the dynamic whirl response. For this purpose, the drillstring is modeled by a system of nonlinear ordinary differential equations (ODEs), which are derived using established mechanics theory. The ODEs form a lumped parameter representation accounting for the physical system. Improvements are made to these equations, such as asymmetry, Hertzian friction contact, non-Hertzian contact, geometrical misalignment, and coupling of patterns of vibration. The equations are solved using numerical integration, but analytics technique are also applied when possible.

Further, stochastic techniques are introduced to solve for drillstring whirl with random process excitation. In this regard, Auto-Regressive-Moving-Average (ARMA) digital filters enable the synthesis of artificial time-histories that are compatible with a target excitation power spectrum. The target spectrum is obtained from downhole torque-on-bit (TOB) measurements, which are common excitation sources during drilling. Through Monte-Carlo simulation, the response of the dynamical system to artificial TOB time-histories is determined in a statistical sense.

Furthermore, the drillstring whirl behavior is elucidated through finite element analysis (FEA) and experimental measurements. A transient FEA model is developed using a commercial software package to represent a three-dimensional (3D) whirling system. An experimental testing system is presented for the purpose of acquiring dynamic data during controlled drillstring whirl events. The FEA model and experimental data are compared against the mathematical whirl models. The efficacy of the models to characterize drillstring whirl is determined from this comparison.

From a holistic perspective, the endeavor of this work is to enrich the field of drillstring dynamics by introducing novel models and techniques to better understand drillstring whirl in deterministic and stochastic systems. With the inclusion of modeling and experimental measurement the thesis seeks to strengthen the correlation between theory and reality.