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 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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".