Analysis of Experimental Data for Flow Thorough Fractures using Geostatistics

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Analysis of Experimental Data for Flow Thorough
Fractures using Geostatistics

• DICMAN ALFRED
• Dr. ERWIN PUTRA
• Dr. DAVID SCHECHTER

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Fracture model
Cubic law of fractures
From the experiments knowing pressure drop and
flow rate , the aperture b can be calculated.
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Actual core surface
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Actual fracture surface
Modified cubic law
Louis (1974) proposed that when e/D lt 0.033,
then f 1
e/D is defined relative roughness, where D is
the hydraulic diameter 22b
e/D gt0.033, then f (1 8.8(e/D)1.5)
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Previous Research
Tsang (1990) chose a statistical description of a
fracture with variable apertures by means of
three parameters , performed numerical flow and
transport experiments with them with particular
emphasis of correlate the fracture geometry
parameters. But concluded that the correspondence
between observations and the hydrological
properties is STILL AMBIGUOUS.
Detailed measurements of fracture apertures have
been obtained by joint surface profiling (Bandis
et al. 1981, Brown and Scholz 1985, Gentier
1986), low melting point metal injection
(Pyrak-Nole et al. 1987, Gale 1987), and resin
casting technique (Hakami 1988, Gentier et al.
1989). BUT THEY ARE EXPENSIVE AND THE DATA MAY
NOT BE A TRUE REPRESENTATIVE OF THE FRACTURE.
Work by researchers, such as Neuzil and Tracy
(1981), Brown (1987), Tsang and Tsang (1987),
Tsang et al. (1988) and Moreno et al. (1988),
have shown that the flow through a fracture
follows preferred paths or flow channels due to
the variation in fracture aperture.
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Our Approach
Experimental data-DP,K,Q,Kavg
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Probability Density Function for Log Normal
Distribution
To standardize this ,
Similar to the normal distribution
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Variogram and Kriging
Variogram summarises the relationship between
the variance of the difference between
measurements and the distance of the
corresponding points from each other. Kriging
uses the information from a variogram to find an
optimal set of weights that are used in
estimating a surface at unsampled locations.
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So lets get started !!!!
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Experimental Data
Pressure Drop
5 cc/min
10 cc/min
15 cc/min
500 1.2 2.7 4.15
1000 2.26 4.8 7.6
1500 4.6 9.3 15.1
Flow through fracture
500 3.75 6.75 10.24
1000 2.58 4.41 6.31
1500 0.64 0.82 0.69
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Core40 var 100
Core56 var 200
VARIOGRAM MODELING
Core20 var 30
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CORE 56.4 VAR 200
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CORE 40 VAR 100
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CORE 20 VAR 30
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PERMEABILITY DISTRIBUTION CORE 56.4 VAR 200
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PERMEABILITY DISTRIBUTION CORE 40 VAR 100
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PERMEABILITY DISTRIBUTION CORE 20 VAR 30
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The volume of the core is maintained constant
Grid definition 311515
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RESULTS

• Sensitivity studies
• Pressure Drop match
• Rate comparisons between theoretical and
• simulated flow
• Permeability comparison
• Variance vs Overburden pressure
• Comparison between cubic law and modified
  
• cubic law

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• Future Considerations
• Extending it to outcrop studies
• Modeling 2-phase flow.