Semianalytical Model for Reservoirs With Forchheimer's Non-Darcy Flow
Bibliographic record
Abstract
Abstract This paper presents a semi-analytical model to investigate the effect of Forchheimer's non-Darcy flow on the transient pressure behavior of vertical well in an infinite homogeneous reservoir. This model uses the Forchheimer number, defined as the product of the reservoir non-Darcy flow coefficient and a reference rate, to quantify the non-Darcy flow in reservoirs accurately. The traditional non-Darcy skin factor, generally applied to model the non-Darcy flow in reservoirs, is employed to describe the non-Darcy flow across completions only. This study shows that the non-Darcy flow effect may influence the local flow rate profile over a reservoir region of several hundred times the wellbore radius. Therefore, it is not satisfactory to merely use the traditional non-Darcy skin factor to model non-Darcy flow in reservoirs. Type curves are documented for both drawdown and buildup tests for the first time using the semi-analytical model proposed. It is observed that, when non-Darcy flow in reservoirs and/or across completions are considered, the dimensionless pressure derivative curves of drawdown tests have a wider-transition region with gentler slopes, while those of buildup tests exhibit a shorter transition region with steeper slopes. In the radial flow period, compared to the cases with only non-Darcy flow across completions, the cases with non-Darcy flow in reservoirs for drawdown and buildup tests possess dimensionless pressure derivatives that are moving downwards to approach 0.5 at decreasing rates more gradually and smoothly. In general, the pressure derivatives of drawdown tests are larger than those of buildup tests before they converge to 0.5. With this model, the skin factor for non-Darcy flow across completions and the dimensionless Forchheimer number for non-Darcy flow in reservoirs can be estimated from a common drawdown or buildup test. Guidelines for interpreting field test data are presented. Several typical cases from the literature are analyzed, and better type curve matches and more reliable results are obtained.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".