Bibliographic record
Abstract
ABSTRACT: Hydraulic fracture and fracture flow simulations are almost exclusively based on Poiseuille flow (the cubic law). A key assumption embedded in our models is that flow is steady, inertial effects are negligible, the fracture surfaces are parallel and the rate of change of the fracture aperture does not impact flow. However, in many practical applications most and sometimes all of these assumptions are violated. In this paper, we will discuss various phenomena that may be observed in experiments and the newly derived Reduced Dimension Fracture Flow (RDFF) model which are not captured by simulations based on the cubic law. These include (1): fracture fluid flow induced by seismic waves, (2) phase shifts between pressure, aperture, and flux fields, (3) non-Darcian flow in the direction of positive pressure gradients, (4) negative near well bore fluid pressures induced by high velocity radial flow. 1 INTRODUCTION Modern large-scale simulations of fracture flow and hydraulic fracture operations are based almost exclusively on the cubic law (also known as Poiseuille flow). The cubic law is popular because it provides a constitutive relationship between the fluid flux and the fluid pressure, but this model is accompanied by a number of limiting physical assumptions. The cubic law is the analytical solution to flow through rigid parallel plates and makes the assumptions: a) that flow is steady, b) inertial effects are negligible, c) fracture surfaces may be locally approximated using parallel plates, d) that flow is laminar, and e) that the rock mass is impermeable. In many applications of the cubic law, most and sometimes all of these assumptions are violated. The recently derived Reduced Dimension Fracture Flow (RDFF) model (Gee and Gracie, 2022b) provides an alternative to the cubic law. The RDFF model is derived from the Navier-Stokes equations by integrating over the fracture aperture and making simplifying assumptions about the flow behaviour to generate a model that, at the cost of increased model complexity, is not subject to the same physical limitations as the cubic law. The RDFF model is capable of capturing inertial and transient flow behaviours, and has been shown to conserve energy in fractures of varying aperture where the cubic law does not.
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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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".