A Semi-analytical Solution of 1-D Diffusion–Convection Equation with Variable Convection Velocity
Bibliographic record
Abstract
Abstract Solvent-based EOR techniques, such as vapour extraction (VAPEX) and miscible/near-miscible flooding, have been studied and applied in petroleum industry. Diffusion–convection mass-transfer process is one of the most important EOR mechanisms in these techniques. This paper develops an accurate semi-analytical solution to a 1-D diffusion-convection mass-transfer model. The velocity term in the diffusion–convection equation has been assumed as a constant in previous works. This assumption is actually not valid in the solvent-based miscible flooding, since the velocity is a function of local viscosity and density, both of which depend on the local concentration. In this study, the spatially and temporally varying convection velocity is rigorously simulated through an accurate semi-analytical approach. First, we consider a sequence of time steps. In each time step, the convection velocity varies with space. Then the spatially varying velocity profile is divided into multiple sections. The velocity profile in each section is approximated with a linear function, so that the analytical solution for the diffusion-convection equation in each section can be obtained in Laplace domain. Then, the solutions in all sections are couped together and solved to obtain the mass-transfer rate through which the concentration distribution can be computed. Finally, a new convection velocity profile can be acquired by using Darcy's law for the next time step. The semianalytical solution is validated by an analytical solution for a special hyperbolic velocity case. In comparison with the numerical solution, the semi-analytical result is free from truncation error and numerical dispersion, thus it is more accurate and more reliable in computing the concentration distributions. The proposed method can be used in streamline simulation, or coupled with other functions to improve the simulation of solvent-based EOR techniques.
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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 | 0.000 | 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 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".