Multi-Well Analytical Solution for Coning Under Simultaneous Steady-State Flow of Three Phases
Bibliographic record
Abstract
Abstract Unwanted water or gas production from upward or downward coning can significantly erode profits in oil recovery processes. Simulation estimates of the magnitude and timing of coning can be erroneous owing to unknown reservoir heterogeneity, large grid blocks near the wells, and inaccuracies in simulation well models, such as that from Peaceman. This paper presents a multi-well steady-state analytical solution for coning of three phases (water, oil, and gas) flowing simultaneously. The solution for multiple wells is developed using superposition with a coning potential function that includes capillary pressure and relative permeability. The assumption of vertical equilibrium (VE) is made, which gives maximum crossflow vertically and therefore the largest possible coning. Any model for relative permeability and capillary pressure can be used, although we used Stone 2 for relative permeability and Brooks-Corey for capillary pressure. We give dimensionless inflow performance windows (IPW) to show the allowable physical window of three-phase rates and the maximum oil rate as a function of the water and the total well flow rate. The new potential functions are also used to demonstrate superposition for several well patterns with no-flow boundaries. Besides estimating critical oil rates, the solution could be important to benchmark numerical solutions and improve the accuracy of Peaceman's well model.
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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) | 0.001 | 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".