Relationship between numerical model grid spacing and accuracy of simulation results /
| Main Author: | |
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
[College Station, Tex.] :
Dokla,
1976.
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| Subjects: | |
| Online Access: | Link to ProQuest copy Link to OAKTrust copy |
| Abstract: | It is well known that use of very coarse grid patterns in numerical models can lead to large errors in simulated performance. There is very little quantitative information on the relationship between grid spacing and errors. This research is concerned with developing guidelines for optimizing the grid patterns and establishing some practical limits of the numerical errors. The study includes one dimensional, linear flow, radial flow, and two-dimensional flow in a well having a vertical infinite conductivity fracture. For the one dimensional system, uniform distance breakup was found better than non-uniform breakup. The use of the Crank-Nicolson scheme results in much smaller errors than with the fully implicit scheme. With 8 uniform cells, and using the Crank-Nicolson scheme, the error at the production end is within 0.2 percent as early as 0.05 dimensionless time (compared to 1.8 percent with the implicit scheme). It is not possible to get reasonable error values earlier than a dimensionless time of 0.05 with the 8 cell system, no matter how small the time steps are. A finer space breakup is necessary, and with 20 uniform cells the error was within 0.05 percent as early as 0.0001 dimensionless time. With the radial system, it was found that a distance breakup according to the relation [equation in PDF] where c is a constant, resulted in smaller errors than for any other breakup tested. A 10 cell system with breakup according to the above relation will yield results in the well within 5 percent of the analytical values or better starting at 0.0001 dimensionless time. During semi-steady state, the results are within 0.5 percent of the analytical. With a 20 cell system, the early time results are within 1.5 percent of the analytical values. The size c f the maximum cell should be less than 25 to 30 percent of the total volume of the system. It was possible to obtain small errors near the outer boundary (<0.01 psi) by refining the grid close to that boundary.. |
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| Item Description: | "Major subject: Petroleum Engineering." Vita. |
| Physical Description: | xii, 85 leaves : graphs ; 28 cm |
| Bibliography: | Includes bibliographical references (leaves 77-78). |