Multiphase Flow in Fractures: Co-Current and Counter-Current Flow in a Fracture
Bibliographic record
Abstract
Abstract Multiphase flow through fractures is important not only for naturally fractured petroleum reservoirs but also for underground disposal of radioactive waste and geothermal ydrotransport, cap rock integrity, as well as underground water and aquifer flow. For instance, naturally fractured reservoirs located in Northern Alberta contain large quantities of heavy oil and bitumen. It still remains unclear how multiple phases flow in fractures and how to determine the relative permeability of each phase that can be used in reservoir simulators. In typical practice, simulation of fractured reservoirs uses, in general, very crude and unproven hypotheses such as a linear relative permeability curves. However, by using inaccurate relative permeability curves, large errors of the predicted oil recovery can result. In this work, a relatively simple flow model is derived to determine analytic functions for the relative permeability curves versus phase saturation in a single fracture. The results show that relative permeability is not just a function of the fluid saturations but also the fluid properties and flow pattern within the fracture itself. The analysis reveals that at certain viscosity ratios and flow pattern conditions, the relative permeability of one phase can exceed unity due to lubrication effects. The available experimental data confirms the validity of the proposed model Introduction Fracture dominated flow is not only important for naturally fractured petroleum reservoirs but also for underground disposal of radioactive waste, geothermal hydrotransport, cap rock integrity, and underground water and aquifer flow. In naturally fractured reservoirs, fractures are highly conductive flow pathways that dominate fluid transport throughout the reservoir. To examine flow of multiphase flow in fractures, many different experimental1,2,9,20,27,33,43,44, theoretical3,4,24,41,42 and numerical studies13,25,26,28,32,35,46 have been done. However flow structure and momentum transfer between flowing phases in fractures are not yet well understood9,10,14. Transport parameters such as relative flow rates of phases and the relationship between fracture geometryand flow remain unclear. The relative permeability concept can be used to describe behaviour of multiple phases flowing together through porous media, interfering and aiding each other to move under the action of a pressure gradient. Despite the importance of relative permeability in fracture flows, still there is no unique and consistent theory which provides an easy, yet computationally inexpensive, method to calculate relative permeability curves in fractures. In this research, a new model is derived for multiple phase layer flow in a single fracture to demonstrate how relative permeability in fractures depends on flow structure as well as fluid properties. Background: Modelling of multiphase flow in fractures is usually based on three common methods: porous medium approach, pipe flow model and the equivalent homogeneous single-phasemodel8,9,14,18. For phase i, from Darcy's law, the velocity in the x direction is given by: Equation (1) (Available in full paper) where K is absolute permeability of the fracture, kri is relative permeabilityPi is pressure, and µi is viscosity of phase i, respectively. The origin of relative permeability arrives from the relative resistance to flow of each phase and interference between phases as they flow under their individual pressure gradients.
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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 | 0.001 | 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 | 0.001 |
| 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".