An Improved Correlation to Estimate Productivity Index in Horizontal Wells
Bibliographic record
Abstract
Proposal Because their great efficiency in producing higher flow rates per unit pressure drawdown, horizontal wells have currently become a popular alternative for the development of hydrocarbon fields around the world. So far, most of the introduced correlations to estimate the productivity index for these wells have shown certain differences among their results. This does not allow us to properly establish which one of them provides the closest value to the actual one, since there is no evidence of a trustable enough reference point. Throughout the years, several investigations for the determination of horizontal-well productivity index have been carried out. These researches have been focused on the determination of steady-state solutions for the above-mentioned parameter, therefore, a diverse number of correlations have been introduced. These correlations have been presented by such very well-known researchers as Giger, Borisov3, Merkulov2, Renard & Dupuy2–5 and Joshi2–5. They are mainly based upon complex analytic solutions which may have some uncertainties when applying them. This paper proposes an improved steady-state correlation to calculate productivity index for horizontal wells and evaluates the most commonly used existing correlations to estimate this parameter by using numerical simulation. Besides that, a sensitivity analysis on the influence of the variation of each variable in the existing and proposed models was carried out. The analysis was conducted by generating a synthetic drawdown test by means of a commercial reservoir simulator. Using the pressure derivative curve, a time range where steady-state behavior takes place was defined. Then, a simulation was performed with the purpose of determining the pressure distribution in the reservoir within that range of time. This allows us to estimate the horizontal-well productivity index for any drainage radius. More than 500 simulation runs were performed to estimate the results obtained by the improved correlation introduced in this work and the existing ones. Several plots of productivity index versus each one of the model variables were constructed for comparison purposes. It was observed that Joshi's correlation matches well with the simulated results. However, the proposed correlation provides much better results than those provided by Joshi's within a very wide range of variation of the parameters involved in the different correlations.
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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".