Bibliographic record
Abstract
Abstract Wormholes are believed to be generated during the initial phase of cold production and are responsible for enhanced production rates when sand cuts are reduced to their minimum. In this work, we present a theoretical model describing sand and fluids flow within a wormhole uniformly filled with sand. This model is based on the Darcy-Brinkman equations for fluids in mobile sand, a rheological equation for sand motion, and conservation laws. Velocity profiles of sand and fluid are calculated and used to establish the relation between the pressure drop and the flow rates. An estimation of wormhole size is also provided. This model provides understanding of the basic flow behavior in a wormhole during the massive sand production stage of cold production. It also provides some key parameters for field scale numerical simulations of cold production. Viscous Drag and Critical Radii The detailed mechanism of sand erosion is a complicated subject. It involves the geomechanical properties of the sand, the rheological properties of fluids, and the nature of sand-fluid and fluid-fluid interactions. However complicated, the key to flux erosion is that it happens when the drag force overcomes the resistance of the sand matrix. The drag force should be mainly the viscous body force due to flow of fluids through the sand matrix (Darcy flow). The resistance of the sand matrix is mostly a surface force. It is due to cohesion, adhesion and contact forces. It holds a chunk in place against the body force. The thickness of this chunk, ?, can be as small as the averaged grain size or orders of magnitude larger, depending on the sand properties and the viscous body force. In the former limiting case, "raining" of sand grains into a cavity occurs. In the latter limiting case, microcracks in the sand matrix may be observed just before the erosion. Assuming fluid flow into a cavity of radius R, the above-stated criterion can be expressed as: Equation (1) (Available In Full Paper) where σ is the surface strength of the sand, and P the fluid pressure. The geometry of the wormhole is assumed to be comprised of a straight cylindrical tube, with a hemispherical cap at the end, as illustrated in Figure 1. Computed tomography images(1) of the wormhole tip show that it is more pointed in reality, as shown by the dashed line in Figure 1. The assumption of hemispherical flow at the tip, however, seems reasonable. For a spherical geometry, FIGURE 1: Influx of fluid into a wormhole. The dashed line represents the actual shape of a wormhole tip (Available In Full Paper) the pressure gradient is inversely proportional to the square of the radius if the fluid is incompressible. Therefore, we can integrate the right-hand side of the inequality (1). Denoting the reservoir pressure as Pre, the pressure at the wall of the cavity as P, and the radius of the drainage zone beyond which the reservoir retains its original reservoir pressure as Rs, we find: Equation (2) (Available In Full Paper)
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How this classification was reachedexpand
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 | 0.003 | 0.001 |
| 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)
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 teacher head, 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".