Four-component Gas/Oil Displacement with Constant Pressure Boundaries
Bibliographic record
Abstract
Summary This paper presents the analytical solution of four-component gas/oil displacements under constant pressure boundary conditions. All the previous studies in gas/oil displacement problems have been accomplished under the assumption of constant flux boundaries. In practice however, gas flooding projects are often conducted with constant injection pressure and constant producing well pressure. In this work, a novel generation of Buckley-Leverett’s classic fractional flow theory is applied to solve the problem of four-component gas/oil displacements under constant pressure boundaries. Conservation of mass in a one-dimensional, dispersion-free medium, for a four-component gas/oil displacement system leads to a set of partial differential equations. The solution of the corresponding initial value problem under constant flux boundary conditions consists of rarefaction waves, shock waves and constant states connecting the injection state to the production state. In incompressible systems with constant pressure boundaries, the total volumetric flux is a function of time and hence, the classical Buckley-Leverett theory is not valid. However, the saturation wave structure obtained from the constant flux boundary condition problem can be used in the solution of the associated problem with constant pressure boundaries by determining the flux analytically as a function of time. The solution for a four-component gas/oil displacement case study is presented. The determination of time dependent volumetric flux from the solution of the constant flux problem is demonstrated. Results are also obtained using a numerical approach and are compared to the analytical results. This indicates that the analytical solution is indistinguishable from the numerical solution as the number of grid blocks in the numerical method approaches infinity. However, a very fine grid is needed for an acceptable solution.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".