Hybrid Simulation of the Eulerian Method and the Streamline Method: Investigating the Role of Cross-Product in Cross-Over Time Between the Two Methods
Abstract/Contents
- Abstract
- The streamline method is ideally suited for simulating large 3D heterogeneous multi-well systems when fluid transport is dominated by convection. For such systems the Eulerian method becomes too expensive because of strong non-linearity. Decoupling of the 3D problem into a set of 1D problems reduces the computational time in the streamline method. However, the streamline method cannot address the cross-flow effect effectively when it is strong. In field scaled problems, the cross-flow effect is not always strong and one can still benefit from using the streamline method. Motivated by this, the possibility of a hybrid approach was investigated. The hybrid approach consisted of using the Eulerian method when the cross flow was strong and shifting to the streamline method when the cross flow was negligible. The present research dealt with the finding of a robust measure for the cross-over time in the hybrid approach. The cross-product of phase fluxes was found to be a reasonable measure to determine the cross-over time in the hybrid simulation. It was observed that the cross-product decreased at a faster rate initially and it stabilized at later times. The time when the cross-product stabilized was considered the optimal cross-over time. However, the optimal cross-over times were found to be very large due to very low relative error tolerance. The rate of decrease in relative error was not linear with the increase in cross-over time. The relative error decreased at a faster rate initially. Therefore, to benefit from the computational efficiency of the streamline method and also to have an acceptable relative error tolerance, a cross-over time less than the optimal cross-over time was considered. The maximum reducible cross-product is the difference of the maximum cross-product and the stabilized cross-product. A criterion for selecting the cross-over time was found to be the time when the maximum reducible cross-product reduces by 90%. This criterion resulted in 70% and 98% reduction in the relative error for gas injection and water injection cases, respectively. The average run time using the Eulerian method in the hybrid simulation was around 30% and 10% of the total simulation time for gas injection and water injection cases, respectively.
Description
| Type of resource | text |
|---|---|
| Date created | June 2010 |
Creators/Contributors
| Author | Kumar, Archana |
|---|---|
| Primary advisor | Gerritsen, Margot |
| Degree granting institution | Stanford University, Department of Energy Resources Engineering |
Subjects
| Subject | School of Earth Energy & Environmental Sciences |
|---|---|
| Genre | Thesis |
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Preferred citation
- Preferred Citation
- Kumar, Archana. (2010). Hybrid Simulation of the Eulerian Method and the Streamline Method: Investigating the Role of Cross-Product in Cross-Over Time Between the Two Methods. Stanford Digital Repository. Available at: https://purl.stanford.edu/qj348bf3395
Collection
Master's Theses, Doerr School of Sustainability
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