Productivity Index for Arbitrary Well Trajectories in Laterally Isotropic, Spatially Anisotropic Porous Media
Why this work is in the frame
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Bibliographic record
Abstract
Summary For an anisotropic medium, the permeability is a second-order tensor. As such, permeability is an entity that is dependent upon the coordinate system used to describe the flow quantitatively, although the flow itself is independent of this system. In particular, this means that when a well is producing fluids from a porous medium, the coordinate system must be specified for descriptive purposes and, consequently, the permeability tensor relative to that coordinate system is determined. It is impossible to simultaneously align a 3D orthonormal coordinate system and a cylindrical well segment defined by a single axis except for special cases. Because the permeability tensor will introduce different formulations depending on the defined coordinate system, its complexity will vary accordingly. The objective of this paper is to define an optimal coordinate system with respect to the simplicity of the flow description into the well with an arbitrary trajectory for the special situation of a laterally isotropic, spatially anisotropic medium. The derivation for this optimization strategy is dependent on a sequence of flow-rate-preserving geometric transformations. The resulting virtual medium has isotropic attributes in the transformed 2D plane. Under this transform, known closed-form models are applicable by use of a single permeability value.
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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 | 0.000 | 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 it