Unstructured Grid Optimization to Achieve Monotonic Pressure Solutions Using Multipoint Flux Approximations
Abstract/Contents
- Abstract
- Multipoint flux approximation (MPFA) techniques are generally required to discretize the reservoir flow equations when the grid is unstructured and permeability is anisotropic. However, at high levels of permeability anisotropy, the coefficient matrix generated by MFPA may not be an M-matrix. The resulting pressures, therefore, may display unphysical oscillations or they may exceed boundary values. Unstructured grid optimization can be applied to improve the monotonicity of the pressure solution at high levels of anisotropy. An existing grid optimization method developed for this problem has been shown to be effective for two-dimensional reservoir systems with permeability anisotropy ratios up to about 100. The objectives of this work are to enhance the existing two-dimensional grid optimization algorithms to work for higher levels of permeability anisotropy and to develop and test new three-dimensional gird optimization algorithms. For two-dimensional cases, a new point-addition algorithm is developed and applied for permeability anisotropy up to the order of 1000. For three dimensional cases, an initialization algorithm and an edge-face swapping algorithm are developed in this study. Numerical results for a variety of examples show improvement in the monotonicity behavior of pressure solutions for both two-dimensional and three dimensional problems. This verifies the effectiveness of the new grid optimization algorithms for strongly anisotropic permeability fields. The examples include homogeneous or nearly homogeneous permeability fields, systems with continuously varying permeability orientations, and highly random permeability fields. In some cases, however, although the pressure solution is improved relative to that using the original gird, the optimization procedures do not provide completely monotonic pressure solutions.
Description
| Type of resource | text |
|---|---|
| Date created | June 2008 |
Creators/Contributors
| Author | Jin, Yulin |
|---|---|
| Primary advisor | Durlofsky, Louis J. |
| Degree granting institution | Stanford University, Department of Energy Resources Engineering |
Subjects
| Subject | School of Earth Energy & Environmental Sciences |
|---|---|
| Genre | Thesis |
Bibliographic information
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Preferred citation
- Preferred Citation
- Jin, Yulin. (2008). Unstructured Grid Optimization to Achieve Monotonic Pressure Solutions Using Multipoint Flux Approximations. Stanford Digital Repository. Available at: https://purl.stanford.edu/nq576hd9573
Collection
Master's Theses, Doerr School of Sustainability
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