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

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

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. Extracting Digital Fracture
aperture
length

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
Parallel Plate Model, Laminar Flow
For ith passage :
Tortuosity
Friction Factor
Average aperture height

16. Tortuosity

17. Frequency – Passage Height Distribution
Fracture Section
Avg. Aperture Height, Havg. (m)
Std. Deviation (m)
Avg. – Std. Deviation (m)
Tortuosity
Section (a)
606
302
304
0.1457
Section (b)
573
296
277
0.1705
Section (c)
590
282
0.1513
Section (d)
637
325
312
0.1533

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

33. Natural Multi-Branch Fractures

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

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

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

37. Velocity Magnitude Contours on a Plane
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.