ANALYTICAL STUDY ON A ONE-DIMENSIONAL MODEL COUPLING BOTH DARCY FLOW AND LOW-VELOCITY NON-DARCY FLOW WITH THRESHOLD PRESSURE GRADIENT IN HETEROGENEOUS COMPOSITE RESERVOIRS
Bibliographic record
Abstract
In the exploitation process of unconventional tight oil reservoirs in modern times, the involved heterogeneous composite reservoirs are common; in such reservoirs, different rock compartments indicate different permeability properties. In ultra-low-permeability compartments, non-Darcy flow with a threshold pressure gradient (TPG) happens, but in relatively high-permeability compartments, Darcy flow happens. The existence of TPG introduces a nonlinear motion boundary problem, which makes a composite reservoir model coupling both Darcy flow and non-Darcy flow much more challenging. Here, a new model of one-dimensional flow in a heterogeneous composite reservoir with TPG is presented in consideration of a boundary motion process. Relying on a previous exact analytic solution for such a motion boundary problem in a homogeneous reservoir, semi-analytic solutions for the heterogeneous composite reservoir model are obtained by adopting the Laplace transformation method and mathematical arguments. Significantly, applications of Duhamel's principle in compartments with Darcy flow serve as a key procedure to analytically solve the model. And their semi-analytic versions are also validated. Finally, by relying on these solutions, the necessity of incorporating the motion boundary process is demonstrated in the mathematical modeling, and the deviation degree of the transient pressure type curves is also analyzed when the boundary motion process is neglected.
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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 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".