Sharif Digital Repository

Vertical drilling methods have been often used for oil and gas extraction so far. In some places, for further extraction and access to the locations that cannot be obtained by the vertical drilling (due to its restrictions); horizontal drilling has become more popular. In horizontal drilling, a variety of longitudinal, torsional and lateral vibrations occur. These vibrations, if left uncontrolled, can damage the drilling rig and equipment, as well as reduce the efficiency of the drilling process and increase the processing time. The purpose of this research is to obtain the coupled axial and torsional vibration equations by analysing the vibrational modes in the horizontal section of the... 

We derive a new non-linear two dimensional model for melt flows and interface instability in aluminum reduction cells. This model is based on non-linear de St. Venant shallow water equations and contains the main features of an aluminum reduction cell. In this model we consider linear friction terms but in a new way that has not been considered in previous works. Our results are in good agreement with the results of simulation of viscous flow. This model is applicable both in determination of melt flows in molten aluminum and cryolite layers and also in finding the extreme limit for stability of interfacial waves in an aluminum reduction cell