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
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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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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 | 0.001 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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 it