Zhang, Yanbin (2013-08). Dynamic Reservoir Characterization Using Complex Grids Based on Streamline and Fast Marching Methods. Doctoral Dissertation.
Thesis
Dynamic reservoir characterization of large three dimensional earth models has become an increasingly important topic in recent years. Conventional finite difference reservoir simulation may not always be the optimal choice in such applications. Alternative methods such as the streamline method and the Fast Marching Method (FMM) could be advantageous in many cases. A comprehensive study to extend these methods to more complex grids is both theoretically interesting and practically beneficial. The ability to use complex grids greatly increases the applicability of these methods, for example, to model complex geologic structures, horizontal and multilateral wellbores, and complex hydraulic/natural fractures.
We present a comprehensive study of various velocity interpolation methods in polygons. These methods extend the widely used velocity interpolation algorithms, such as the Pollock's algorithm, to more complex geometries such as perpendicular bisection (PEBI) grids, unstructured triangular grids and grids with local refinement. We analyze important issues such as local conservation, velocity continuity, and orders of interpolation. Based on our analysis, we recommend a lower order locally conservative method for the most robust and numerically efficient calculation of streamline trajectories on unstructured grids. The proposed method is then applied to generate streamline visualizations for various grids.
Previous studies have demonstrated the use of the FMM and the diffusive time of flight for drainage volume visualization and pressure depletion estimation for un- conventional reservoirs. In the current study, we first extend the FMM to corner point grids and anisotropic permeabilities. We then propose a new formulation of the diffusivity equation using the diffusive time of flight ? as a spatial coordinate. This new ? -coordinate formulation reduces the problem from 3D to 1D in space. The basic formulation is extended by incorporating additional physical processes which are potentially important in shale gas reservoirs. The new formulation is validated by comparing with both analytical solution and traditional finite difference simulation. Our expectation is that the new formulation will become an efficient and versatile tool for pressure depletion and associated reservoir characterization applications.
