Adaptive control design for a nonlinear parabolic PDE: Application to water coning
Bibliographic record
Abstract
Abstract Water coning is usually responsible for the production of undesirable water from oil wells. This phenomenon may cause a decrease in oil production rate, increase in water cut production, and costs, which subsequently leads to early shutdown of the well. Although the boundary control of the production rate was suggested for managing the problem, due to the uncertainty associated with the physical nature of petroleum reservoirs, it failed to be implemented in practice. To overcome this issue, the paper employs the adaptive control approach for the distributed parameter system, which is modelled using a nonlinear partial differential equation (PDE). For this purpose, an adaptive control law and an update law for estimating the uncertain parameter are developed using the direct Lyapunov method. Next, the global stability of the closed‐loop system with the abovementioned laws is proven. Finally, the effectiveness and performance of the proposed idea is demonstrated by numerical simulations. The results show that the thickness of an oil column tends to zero as time tends to infinity for the whole spatial domain. In other words, as time elapses, the whole oil column will be depleted before the cone breakthrough. The numerical simulation demonstrates that though water cone breakthrough is inevitable in the conventional way of production, the adaptive control approach successfully controls the cone growth up, even with no knowledge of reservoir permeability. The results of this study can be applied to any type of reservoir subjected to water coning.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".