Implementation and Application of a Hybrid Multipoint Flux Approximation for Reservoir Simulation on Corner-Point Grids
Bibliographic record
Abstract
Abstract Accurate and robust discretization of the fluid flow equations is required to account for the extreme heterogeneity of oil and gas reservoirs, and the combined effect of anisotropy and grid distortion, necessary to adapt the grid to the geology. There is a growing need for handling distorted unstructured grids and full permeability tensors that appear after upscaling of the fine-scale permeability field. The classical cell-centered finite difference method results in a 7-point stencil and is insufficient to account for these effects. A number of closely related methods, coined as multipoint flux approximations (MPFA), have been proposed recently and are currently under active development. The basic principle of MPFA is that the flux across an interface between two gridblocks depends on the state variables (pressure and saturations) of more than two gridblocks. MPFA leads naturally to an enhanced finite volume method with a 27-point stencil. In this paper, we implement a variant of the MPFA method for corner-point geometry hexahedral grids. Motivated by the very high aspect ratio of gridblocks in typical reservoir models (ratios as high as 100:1 are not uncommon), we propose a hybrid method that employs a multipoint flux approximation in the areal direction and a two-point flux approximation in the vertical direction. This restricted MPFA method leads to an 11-point stencil, therefore reducing the computational effort significantly. We discuss the implementation of the method in detail. We evaluate its performance on a number of test cases and show that, for typical applications, this simplification does not greatly compromise the accuracy of the 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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".