A New Friction Factor Correlation for Laminar and Single-Phase Fluid Flow through Fractured Rocks K....
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![Page 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.](https://reader035.fdocuments.in/reader035/viewer/2022062714/56649d3a5503460f94a146ee/html5/thumbnails/1.jpg)
A New Friction Factor Correlation A New Friction Factor Correlation for Laminar and Single-Phase Fluid for Laminar and Single-Phase Fluid
Flow through Fractured RocksFlow through Fractured Rocks
K. Nazridoust, G. Ahmadi, and D.H. SmithK. Nazridoust, G. Ahmadi, and D.H. Smith
Department of Mechanical and Aeronautical EngineeringDepartment of Mechanical and Aeronautical Engineering Clarkson University, Potsdam, NY 13699-5725 Clarkson University, Potsdam, NY 13699-5725
National Energy Technology LaboratoryNational Energy Technology LaboratoryU.S. Department of Energy, Morgantown, WV 26507-0U.S. Department of Energy, Morgantown, WV 26507-0
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CT Scanning Procedures of Fractured RocksCT Scanning Procedures of Fractured Rocks- Geometric Features of Fractures- Geometric Features of Fractures
Single Phase Flows through FracturesSingle Phase Flows through Fractures
- Velocity and pressure contours- Velocity and pressure contours
Gas-Liquid FlowsGas-Liquid Flows- Water Flooding in Oil Saturated Fractures- Water Flooding in Oil Saturated Fractures
Conclusions Conclusions
OutlineOutline
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C.T. Scanning of C.T. Scanning of Fractured RocksFractured Rocks
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0.5 mm
HD-250 Medical C.T. ScannerHD-250 Medical C.T. Scanner
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Pore Space RenderingPore Space Rendering
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OMNI-X High Resolution Industrial ScannerOMNI-X High Resolution Industrial Scanner
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Source Source
Detector Detector
Rock sample inRock sample inthe pressure the pressure
vessel vessel
OMNI-X Scanner - Penn StateOMNI-X Scanner - Penn State
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Healed Natural FractureHealed Natural Fracture
Open Artificial FractureOpen Artificial Fracture
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Induced FractureInduced Fracture
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Fractures TopologyFractures Topology
Sample diameter is 25 mm. Inset size is 5x5 mm.
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aper
ture
length
Extracting Digital FractureExtracting Digital Fracture
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Fracture/SectionsFracture/Sections
C.T. Scan Images240 Micron Resolution
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Fracture SectionsFracture Sections
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Fracture SectionsFracture Sections
No-slip Wall
Inlets
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ParallelParallel Plate Model, Laminar FlowPlate Model, Laminar Flow
ijj
2
ii
jji U
xxP
x
1U
xUU
t
0Ux j
j
3i
ii
H
QL12P
1LLe
iP1P
2
3
Q)1(L
HP2f
CHH .avg
TortuosityTortuosity
For ith passage :
Friction FactorFriction Factor
Average aperture height Average aperture height
Governing EquationsGoverning Equations
ContinuityContinuity
MomentumMomentum
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TortuosityTortuosity
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Fracture Section
Avg. Aperture Height, Havg. (m)
Std. Deviation (m)
Avg. – Std. Deviation (m)
Tortuosity
Section (a) 606 302 3040.1457
Section (b) 573 296 2770.1705
Section (c) 590 304 2820.1513
Section (d) 637 325 3120.1533
.avg1 HH
Frequency – Passage Height DistributionFrequency – Passage Height Distribution
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Pressure for different flow rates, Section (a) - AirPressure for different flow rates, Section (a) - Air
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Pressure for different flow rates, Section (a) - WaterPressure for different flow rates, Section (a) - Water
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Velocity Magnitude, Section (a) - AirVelocity Magnitude, Section (a) - Air
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Air Water
Pressure DropPressure Drop
adcb PPPP
bavgcavgaavgdavg HHHH
acdb
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HRe
96f
QRe
H
Friction Factor for Laminar Flow between Parallel Friction Factor for Laminar Flow between Parallel PlatesPlates
Friction Factor for Laminar Flow in FracturesFriction Factor for Laminar Flow in Fractures
100Re , Re25.01Re
144f HH
H
687.0
Friction FactorFriction Factor
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Friction FactorFriction Factor
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Pressure Drop Ratio - AirPressure Drop Ratio - Air
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Pressure Drop Ratio - WaterPressure Drop Ratio - Water
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Two-Phase FlowsTwo-Phase FlowsWater-OilWater-Oil
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WaterWater OilOil
Volume Fraction during Water FloodingVolume Fraction during Water Flooding
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Shaded region is the fracture Shaded region is the fracture opening which is made transparent opening which is made transparent so that the flow can be observed. so that the flow can be observed. White regions are rock. The White regions are rock. The contours are shown on a plane contours are shown on a plane through the fracture.through the fracture.
Velocity Magnitude Contours During Velocity Magnitude Contours During Water-Oil Flow on a Plane across FractureWater-Oil Flow on a Plane across Fracture
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Volume Fraction of Oil During Water-Oil Flow on a Volume Fraction of Oil During Water-Oil Flow on a Plane across FracturePlane across Fracture
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Computational Grid – 3D – 37mmComputational Grid – 3D – 37mm
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Volume Fraction of OilVolume Fraction of Oil
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Two-Phase Air-WaterTwo-Phase Air-Water Flows though a Flows though a
Multi-Branch Fracture Multi-Branch Fracture
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Natural Multi-Branch FracturesNatural Multi-Branch Fractures
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Velocity Magnitude Velocity Magnitude ContoursContours
Air Volume Air Volume Fraction ContoursFraction Contours
Air-Water Flow in a Multi-Branch FractureAir-Water Flow in a Multi-Branch Fracture
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Air Volume Air Volume Fraction ContoursFraction Contours
Air-Water Flow in a Multi-Branch FractureAir-Water Flow in a Multi-Branch Fracture
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Water Volume Fraction Water Volume Fraction Contours on a PlaneContours on a Plane
Air-Water Flow in a Multi-Branch FractureAir-Water Flow in a Multi-Branch Fracture
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Velocity Magnitude Velocity Magnitude Contours on a PlaneContours on a Plane
Air-Water Flow in a Multi-Branch FractureAir-Water Flow in a Multi-Branch Fracture
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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.
ConclusionsConclusions
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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.
ConclusionsConclusions