Doctor of Philosophy (PhD)


Petroleum Engineering

Document Type



Dimensionless space provides a tool for analyzing the behavior of complex systems described by mathematical relationships. The limited application of dimensionless variables in numerical reservoir simulation and experimental design motivated the development of a complete set of dimensionless scaling groups. Inspectional analysis yielded 8 dimensionless groups completely describing the flow system. Further analysis of fluid interaction reduced the number of dimensionless groups to 7. The newly developed dimensionless equations and groups were used for analytical and numerical reservoir characterization, quantifying the behavior of differential and difference equations employed in fluid flow in three-dimensional porous media. The behavior of the dimensionless scaling is demonstrated for breakthrough time in an immiscible displacement in three dimensions. Numerical simulations were designed in dimensionless space and converted to dimensional space using several approaches. The resulting estimates of stability limits, numerical dispersion, and regime boundaries were in excellent agreement. The application of the dimensionless groups to upscaling was investigated using designed reservoir simulations to estimate dimensionless regions corresponding to different flow regimes. Analytical development, simulation runs and literature data were in good agreement. This application demonstrates the potential benefits of the proposed dimensionless groups for upscaling, sensitivity analysis, stability analysis, and reservoir characterization.



Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Christopher D. White