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A New Friction Factor Correlation for Laminar and Single-Phase Fluid Flow through Fractured Rocks

Explore a groundbreaking research on fluid flow in fractured rocks, using CT scanning and computer simulations to analyze single-phase and two-phase flows in fractures. The study introduces a novel empirical equation for fracture friction factor and provides detailed insights on pressure drops and velocity profiles through fractures.

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A New Friction Factor Correlation for Laminar and Single-Phase Fluid Flow through Fractured Rocks

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  1. A New Friction Factor Correlation for Laminar and Single-Phase Fluid Flow through Fractured Rocks K. Nazridoust, G. Ahmadi, and D.H. SmithDepartment of Mechanical and Aeronautical Engineering Clarkson University, Potsdam, NY 13699-5725National Energy Technology LaboratoryU.S. Department of Energy, Morgantown, WV 26507-0

  2. Outline • CT Scanning Procedures of Fractured Rocks - Geometric Features of Fractures • Single Phase Flows through Fractures - Velocity and pressure contours • Gas-Liquid Flows - Water Flooding in Oil Saturated Fractures • Conclusions

  3. C.T. Scanning of Fractured Rocks

  4. 0.5 mm HD-250 Medical C.T. Scanner

  5. Pore Space Rendering

  6. OMNI-X High Resolution Industrial Scanner

  7. OMNI-X Scanner - Penn State Source Detector Rock sample in the pressure vessel

  8. Healed Natural Fracture Open Artificial Fracture

  9. Induced Fracture

  10. Fractures Topology Sample diameter is 25 mm. Inset size is 5x5 mm.

  11. aperture length Extracting Digital Fracture

  12. Fracture/Sections C.T. Scan Images 240 Micron Resolution

  13. Fracture Sections

  14. Fracture Sections No-slip Wall Inlets

  15. Governing Equations Continuity Momentum ParallelPlate Model, Laminar Flow For ith passage : Tortuosity Friction Factor Average aperture height

  16. Tortuosity

  17. Frequency – Passage Height Distribution

  18. Pressure for different flow rates, Section (a) - Air

  19. Pressure for different flow rates, Section (a) - Water

  20. Velocity Magnitude, Section (a) - Air

  21. Pressure Drop Air Water

  22. Friction Factor Friction Factor for Laminar Flow between Parallel Plates Friction Factor for Laminar Flow in Fractures

  23. Friction Factor

  24. Pressure Drop Ratio - Air

  25. Pressure Drop Ratio - Water

  26. Two-Phase Flows Water-Oil

  27. Volume Fraction during Water Flooding Water Oil

  28. Velocity Magnitude Contours During Water-Oil Flow on a Plane across Fracture Shaded region is the fracture opening which is made transparent so that the flow can be observed. White regions are rock. The contours are shown on a plane through the fracture.

  29. Volume Fraction of Oil During Water-Oil Flow on a Plane across Fracture

  30. Computational Grid – 3D – 37mm

  31. Volume Fraction of Oil

  32. Two-Phase Air-Water Flows though a Multi-Branch Fracture

  33. Natural Multi-Branch Fractures

  34. Air-Water Flow in a Multi-Branch Fracture Velocity Magnitude Contours Air Volume Fraction Contours

  35. Air-Water Flow in a Multi-Branch Fracture Air Volume Fraction Contours

  36. Air-Water Flow in a Multi-Branch Fracture Water Volume Fraction Contours on a Plane

  37. Air-Water Flow in a Multi-Branch Fracture Velocity Magnitude Contours on a Plane

  38. Conclusions • The computer simulation technique is capable of capturing the features of the flow through the fracture. • The simulation results are in qualitative agreement with the parallel plate model. • The newly proposed empirical equation for fracture friction factor provides reasonably accurate estimates for the pressure drops in fractures for range of Reynolds numbers less than 100. • A significant portion of the fracture pressure drop occurs in the areas with smallest passage aperture.

  39. Conclusions • The order of the magnitude of the pressure in various sections of the fracture is consistent with the number of passages with smallest aperture that are present in those sections. • The tortuosity of the fracture passage is an important factor and needs to be included in the parallel plate model.

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