An efficient boundary control for porous media equation: Motivated by water coning problem
Bibliographic record
Abstract
Abstract The porous media equation is a nonlinear partially differential equation (PDE) that is extensively applied in industries. One such case is regarding the water coning problem in oil reservoirs. This phenomenon may result in decreasing oil production rates and increasing water cut production as well as costs that may lead to the early closure of an oil well. Conventionally, well shutting‐in is the only treatment approach when a well faces this problem; however, this does not lead to full reservoir depletion. Recently, the boundary control approach has been proposed to solve the water coning problem. The most important and challenging question is the following: which controllers guarantee that this issue will be resolved? To deal with the water coning issue, first, several types of controllers were considered and applied on the nonlinear PDE. Next, to investigate the stability behaviour of each controller, the direct Lyapunov approach was employed. Finally, to support the results of the analytical part of this paper and to compare the performance of those controllers, numerical simulations were performed. The results show that only for those control laws that guarantee the asymptotic and exponential stability of the nonlinear PDE, the thickness of the oil column tends to zero as time tends to infinity for the whole spatial domain. In addition, a novel controller, which is introduced in the present study, fulfills the exponential stability and is more efficient than other presented controllers. Using the controller, the whole oil column is drained out about 16 % faster without water breakthrough.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".