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Vivek Muralidharan

Simulation and imaging experiments of fluid flow through a fracture surface: a new perspective. Vivek Muralidharan. Fractured Reservoirs. Log Analysis. Fracture Characterization. Poor recovery. Simulation. Fracture Model. X-ray CT scanner. Laboratory Experiments. Aperture distribution.

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Vivek Muralidharan

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  1. Simulation and imaging experiments of fluid flow through a fracture surface: a new perspective Vivek Muralidharan

  2. Fractured Reservoirs Log Analysis Fracture Characterization Poor recovery Simulation Fracture Model X-ray CT scanner Laboratory Experiments Aperture distribution

  3. Presentation Outline • Historical Perspective • Objectives and Approach • Applications • Conclusions

  4. w Constant fracture aperture Historical perspective Fracture Model

  5. Cubic Law Aperture Size Historical perspective

  6. Single Fracture Aperture Parallel Plate Assumption w

  7. Realistic simulation model Fracture Aperture Fracture roughness Better History Match

  8. Fracture Aperture Distribution Fracture aperture distribution Tsang et al., 1987 Pyrak-Nolte et al., (1987) Keller, (1996) Gale, 1987 Lognormal distribution for natural fractures

  9. Log-Normal Mean Variable Log-Normal Deviation ( Aperture ) Lognormal Function Apertures distributed log-normally

  10. Generation of apertures

  11. Aperture Distribution Smooth fracture surface

  12. Aperture Distribution Slightly rough fracture surface

  13. Larger Aperture Size Aperture Distribution Highly rough surface fracture

  14. Problems • Aperture distribution is proved for fractures without experiencing any stress. • Aperture distribution has not yet been investigated under different stress condition. • Single fracture aperture does not represent the actual flow through fracture

  15. Presentation Outline • Historical Perspective • Objectives and Approach • Applications • Conclusions

  16. Stress Aperture distribution? Objectives Problem: Aperture distribution has not yet been investigated under different stress condition. X-ray CT scanner

  17. Gravity drainage experiment X-ray CT scanner Objectives Problem: Single fracture aperture does not represent the actual flow through fracture

  18. Aperture distribution under stress using X-ray CT scanner

  19. Approach Experiments in X-ray CT scanner Scan Aperture Distribution Scans at multiple locations Calibration

  20. X-ray CT Scanner Density of fluid in fracture Density of rock CT scanner analyzes density differences between objects Matrix and fracture identification

  21. X-ray CT Scans Matrix 1600 CT numbers are different from actual aperture size Calibration Technique to correlate CT to obtain fracture aperture size 1400 CT number Fracture 1200 No direct measurement of fracture aperture 1000 0 20 40 60 80 Pixel number

  22. Smooth surface Feeler gauge of known size Scanned the core between feeler gauges Calibration Procedure

  23. Calibration Procedure Matrix Fracture

  24. Calibration Procedure Min rock CT Integrated CT area

  25. Calibration Curve Feeler gauge size

  26. Fracture aperture Scans of fractured core of unknown apertures Integrated CT area Calibration curve

  27. Calibration Curve Determination of fracture aperture

  28. Aperture Distribution

  29. Scans taken along the length of the core

  30. Animation Apertures along the length of the core No stress 1500 psi 1000 psi 500 psi

  31. 70 locations 90 sections Four different stress conditions 24000 apertures Apertures Apertures are calculated from calibration curve Around 6000 sections

  32. Aperture Distribution without stress Lognormal distribution Mean = 370.527 σ = 211.772

  33. Aperture Distribution with stress Mean = 197.997, σ = 172.573 Mean = 370.527, σ = 211.772

  34. Aperture Distribution with stress Mean = 157.418, σ = 162.395 Mean = 197.997, σ = 172.573 Mean = 370.527, σ = 211.772

  35. Aperture Distribution with stress Mean = 138.656, σ = 150.33 Mean = 157.418, σ = 162.395 Mean = 197.997, σ = 172.573 Mean = 370.527, σ = 211.772

  36. Aperture Distribution with stress Aperture distribution follows Lognormal distribution at all conditions

  37. Larger Aperture Size Lognormal Distribution Highly rough surface fracture Fracture apertures have to be distributed

  38. Presentation Outline • Historical Perspective • Objectives and Approach • Applications • Conclusions

  39. Pressure Drop 500,1000,1500 p Injection rate 5 cc/min qinj Km qinj/ p Matrix Permeability Experimental Procedure Unfractured Core

  40. Average Pressure Drop pavg Injection rate qinj 5 cc/min Kavg qinj/ pavg Average Permeability Experimental Procedure Fractured Core fracture l matrix

  41. Analytical Equations

  42. Area of fracture Area of matrix Total area of core Fracture Permeability Matrix Permeability Average Permeability Analytical Equations

  43. Cubic Law Combining above equations to determine w Analytical Equations Fracture Permeability matrix fracture w d A

  44. Fracture Aperture

  45. Fracture Permeability

  46. Fracture Flowrate 500 Psi 1000 Psi 1500 Psi

  47. Flow through fracture and matrix Flow through fracture

  48. Flow through fracture and matrix Flow through matrix Flow through fracture

  49. Modeling Laboratory Experiment Simulation model using aperture distribution

  50. Simulation Model j i k Model Description • 10x10x15 grids • Fracture in 8th block in K dirn

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