An Investigation of the Explicit Correction Scheme for Local Grid Refinement
Abstract/Contents
- Abstract
- Classical cell centered discretization of the reservoir simulation pressure equation on a locally refined grid results in an O(1/h) leading truncation error at the local grid interface between local grids of different refinement level. This error can become significant in the case of large pressure gradient tangential to the local grid interface. Most commercial simulators use a three-point explicit correction scheme for eliminating this leading error. The leading error coefficient has been shown to be proportional to grid refinement ratio, grid aspect ratio and permeability anisotropy ratio. The primary purpose of this work is to understand the limitations of the conventional three-point explicit error correction and the effect of relevant parameters on the performance of the correction scheme.This work shows that large refinement ratios and grid aspect ratios can have adverse effects on results in the presence of large pressure gradient tangential to a local grid interface. For larger grid refinement and aspect ratios, the correction is less effective. A grid ratio of two is shown to have the least error (consistent with analysis of previous studies) and the explicit correction scheme is shown to be most effective in this case. Use of nested local grid refinement (LGR) is therefore recommended.In addition to local errors, the LGR error can cause numerical instability at the saturation front and lead to a numerical 'pseudo-fingering' effect. In the case of adverse mobility ratio problems pseudo-fingers elongate with time and have a width equal to that of the underlying coarse grid block. In the case of favorable mobility ratio the errors are more localized.A case study with dynamic LGR is also considered and it is shown that the results obtained are comparable with uniform fine grid results at a reduced cost. Static LGR is shown to resolve pressure fields while dynamic LGR is shown to resolve saturation fields.
Description
| Type of resource | text |
|---|---|
| Date created | June 2001 |
Creators/Contributors
| Author | Malik, Inam-Ur-Rehman |
|---|---|
| Primary advisor | Aziz, Khalid |
| Primary advisor | Edwards, Michael G. |
| Degree granting institution | Stanford University, Department of Petroleum Engineering |
Subjects
| Subject | School of Earth Energy & Environmental Sciences |
|---|---|
| Genre | Thesis |
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Preferred citation
- Preferred Citation
- Malik, Inam-Ur-Rehman. (2001). An Investigation of the Explicit Correction Scheme for Local Grid Refinement. Stanford Digital Repository. Available at: https://purl.stanford.edu/ys781vp9990
Collection
Master's Theses, Doerr School of Sustainability
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