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K. Nazridoust, G. Ahmadi, and D. H

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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. 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.


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