Search

The infinitesimal algebra of Lie symmetries of the Eikonal equation is shown to be isomorphic to o ( n + 1 , 2 ) when there are n independent variables. An explicit basis is found that is aligned with the standard basis coming from the standard matrix representation of o ( n + 1 , 2 ) thereby making it possible to read off inequivalent one-dimensional symmetry vector fields. The symmetries are used to construct various solutions of the Eikonal equation. [ABSTRACT FROM AUTHOR]

Simulation of fluid flow in porous media is an indispensable part of oil and gas reservoir management. Accurate prediction of reservoir performance and profitability of investment rely on our ability to model the flow behavior of reservoir fluids. Over the years, numerical reservoir simulation models have been based mainly on solutions to the normal diffusion of fluids in the porous reservoir. Recently, however, it has been documented that fluid flow in porous media does not always follow strictly the normal diffusion process. Small deviations from normal diffusion, called anomalous diffusion, have been reported in some experimental studies. Such deviations can be caused by different factors such as the viscous state of the fluid, the fractal nature of the porous media and the pressure pulse in the system. In this work, we present explicit and implicit numerical solutions to the anomalous diffusion of single-phase fluids in heterogeneous reservoirs. An analytical solution is used to validate the numerical solution to the simple homogeneous case. The conventional wellbore flow model is modified to account for anomalous behavior. Example applications are used to show the behavior of wellbore and wellblock pressures during the single-phase anomalous flow of fluids in the reservoirs considered. [ABSTRACT FROM AUTHOR]