Phase Transition in a Self--Gravitating Planar Gas

We consider a gas of Newtonian self-gravitating particles in two-dimensional space, finding a phase transition, with a high temperature homogeneous phase and a low temperature clumped one. We argue that the system is described in terms of a gas with fractal behaviour.Comment: corrections made and discussions enlarged; to appear P.L.

Analysis and mitigation of wellbore breakout and fracturing

Mechanical wellbore integrity problems while drilling are mainly due to wellbore shear failure or tensile failure. To ensure wellbore integrity, breakout and fracture geomechanical analysis is conducted to estimate minimum and maximum drilling fluid densities. Currently, there is no agreement as to which rock failure criterion to use for estimating breakout or fracture criteria to use for analyzing drilling induced fractures. However, when wellbore integrity issues arise while drilling, mitigation strategies can be applied to rectify these problems. This dissertation analyzes criteria for wellbore breakout and fracturing. Also, mitigation strategies for breakout and fracturing while drilling were experimentally investigated. Thirteen rock failure criteria were compared based on estimating borehole breakout for field reported wellbore failure cases. Five fracture width models were investigated, compared, and experimentally evaluated. Hydraulic fracturing experiments were carried out to evaluate the impact of LCM addition on enhancing both; breakdown and re-opening pressure. Coal Combustion Residuals particles evaluated as shale inhibitor additive in water-based drilling fluid system using pressure transient test. The results showed the estimated borehole breakout by Mogi-Coulomb, Modified Lade, and Modified Wiebols Cook criteria is close to field reported shear failure. Carbonell and Detournay\u27s fracture width model estimated close to the measured fracture width of core samples. The addition of different LCM blends enhanced the breakdown pressure up and the re-opening pressure. Using fine grained Coal Combustion Residuals in water-based drilling fluid reduced the pressure transient rate in Catoosa shale samples --Abstract, page iv