A New Friction Factor Correlation for Laminar and

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 13699 -5725 National Energy Technology Laboratory U. S. Department of Energy, Morgantown, WV 26507 -0

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

C. T. Scanning of Fractured Rocks

HD-250 Medical C. T. Scanner 0. 5 mm

Pore Space Rendering

OMNI-X High Resolution Industrial Scanner

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

Healed Natural Fracture Open Artificial Fracture

Induced Fracture

Fractures Topology Sample diameter is 25 mm. Inset size is 5 x 5 mm.

aperture Extracting Digital Fracture length

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

Fracture Sections

Fracture Sections No-slip Wall Inlets

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

Tortuosity

Frequency – Passage Height Distribution Fracture Section Avg. Aperture Height, Havg. ( m) Std. Deviation ( m) Avg. – Std. Deviation ( m) Section (a) 606 302 304 Section (b) 573 296 277 Section (c) 590 304 282 Section (d) 637 325 312 Tortuosity 0. 1457 0. 1705 0. 1513 0. 1533

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

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

Velocity Magnitude, Section (a) - Air

Pressure Drop Air Water

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

Friction Factor

Pressure Drop Ratio - Air

Pressure Drop Ratio - Water

Two-Phase Flows Water-Oil

Volume Fraction during Water Flooding Water Oil

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.

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

Computational Grid – 3 D – 37 mm

Volume Fraction of Oil

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

Natural Multi-Branch Fractures

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

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

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

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

Conclusions Ø The computer simulation technique is capable of capturing the features of the flow through the fracture. Ø The simulation results are in qualitative agreement with the parallel plate model. Ø 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. Ø A significant portion of the fracture pressure drop occurs in the areas with smallest passage aperture.

Conclusions Ø 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. Ø The tortuosity of the fracture passage is an important factor and needs to be included in the parallel plate model.