PRESSURE BEHAVIOR OF VERTICAL WELLS IN LOW-PERMEABILITY RESERVOIRS WITH THRESHOLD PRESSURE GRADIENT
Bibliographic record
Abstract
The threshold pressure gradient, which is associated with non-Darcy flow in low permeability reservoirs, is defined as the level of pressure gradient that must be attained to enable the fluid to overcome the viscous forces and start to flow. If the pressure gradient is small, then the flow velocity increases slowly and obeys a nonlinear relationship, but when the pressure gradient starts to exceed the threshold pressure gradient, it increases quickly and starts to obey the linear relationship. With low velocity and non-Darcy flow, the fluid flow boundary is controlled by the threshold pressure gradient and can extend outward continuously, while the fluid beyond this boundary cannot flow. This paper presents analytical solutions to the pressure transient equations of vertical wells in isotropic low-permeability reservoirs with threshold pressure gradient. These solutions are obtained by using Green's functions method with numerical approximations. A method to determine the location of the moving boundary front is also presented. It is concluded that, at any time, smaller threshold pressure gradient results in smaller resistance to flow; thus, a single-well control radius is larger and the moving boundary front is moving farther away from the wellbore. Furthermore, a greater threshold pressure gradient results in more resistance to flow, meaning a much stronger driving force is required to reach the same flow rate. Unlike the material balance equation, we conclude that both pressure transient radius and pressure drop at the wellbore are approximately linear functions of the cubic root of producing time and not the square root of producing time. Its proposed equations find that the moving boundary front is sensitive to the value of the threshold pressure gradients. Furthermore, at any given value of threshold pressure gradient, we calculate lower bottom-hole pressure than those calculated by the material balance equations. Finally, the solution procedure we propose is a fast tool to evaluate well performance in low permeability reservoirs.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 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 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".