Informational Analysis of Invasion Percolation Model of Hydraulic - - PowerPoint PPT Presentation

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Informational Analysis of Invasion Percolation Model of Hydraulic - - PowerPoint PPT Presentation

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Informational Analysis of Invasion Percolation Model of Hydraulic Fracturing J. Quinn Norris May 31, 2013 Hydraulic Fracturing Simple

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Informational Analysis of Invasion Percolation Model of Hydraulic Fracturing

  • J. Quinn Norris

May 31, 2013

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

1

Hydraulic Fracturing

2

Simple Model

3

Invasion Percolation

4

Bursts

5

Information Theory

6

Tokunaga Branching

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Step 1: Drill a well

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Step 2: Inject fluid to generate fractures

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Step 3: Sand “props” fractures open allowing gas/oil to flow out

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Halliburton in the late 1940’s

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

USGS Potential Gas Committee (2011)

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Horizontal Drilling “Slickwater”

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

“Super Fracking” Today

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Potential Gas Committee (2011)

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Chattanooga

Eagle Ford

Western Gulf TX-LA-MS Salt Basin Uinta Basin Devonian (Ohio)

Marcellus

Utica

Bakken***

Avalon- Bone Spring San Joaquin Basin Monterey Santa Maria, Ventura, Los Angeles Basins Monterey- Temblor Pearsall Tuscaloosa Big Horn Basin Denver Basin Powder River Basin Park Basin Niobrara* Mowry Niobrara* Heath** Manning Canyon Appalachian Basin Antrim

Barnett

Bend New Albany

Woodford

Barnett- Woodford Lewis Hilliard- Baxter- Mancos Excello- Mulky

Fayetteville

Floyd- Neal Gammon Cody

Haynesville- Bossier

Hermosa Mancos Pierre Conasauga Michigan Basin

  • Ft. Worth

Basin Palo Duro Basin Permian Basin Illinois Basin Anadarko Basin Greater Green River Basin Cherokee Platform San Juan Basin Williston Basin Black Warrior Basin Ardmore Basin Paradox Basin Raton Basin Montana Thrust Belt Marfa Basin Valley & Ridge Province Arkoma Basin Forest City Basin Piceance Basin

Lower 48 states shale plays

200 400 100 300 Miles

±

Source: Energy Information Administration based on data from various published studies. Updated: May 9, 2011 Basins Shale plays Stacked plays Basins Current plays Prospective plays * Mixed shale & chalk play ** Mixed shale & limestone play ***Mixed shale & tight dolostone- siltstone-sandstone Intermediate depth/ age Shallowest/ youngest Deepest/ oldest

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Problem: Earthquakes known since 1976

  • C. B. Raleigh et al. Science 191(4233), 66-75
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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Problem: Earthquakes

− 10 − 8 − 6 − 4 − 2

H

  • riz
  • nta

l dis ta nc e(km ) D e pth(km ) S N w e ll # 1 w e ll # 5 E nde rsFa ult

15 10 5 –5

M 4.0 M 4.7 M 3.9 M a gnitude4.1 O z a rkA quife r Pre c a m bria n

  • R. A. Kerr. Science 335(6075), 1436-1437
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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Problem: Earthquakes from fluid reinjection Art McGarr (USGS)

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Problem: Contaminated Drinking Water

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing

Problem: Contaminated Drinking Water Osborn et al. PNAS, 108(20), 8172-8176.

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Hydraulic Fracturing Summary Main source of natural gas for the next 40 years Causes earthquakes May contaminate drinking water

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Simple Model

elastic region re rc damage shell uid lled cavity

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Simple Model

P = 0

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Simple Model

P = Pd

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Simple Model

P = Pd

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Simple Model

P = Pd

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Modified Invasion Percolation

0,0 0,1

  • 1,0

1,0 0,-1

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Modified Invasion Percolation

0,0 0,1

  • 1,0

1,0 0,-1 1,1 2,0 1,-1

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Modified Invasion Percolation

0,0 0,1

  • 1,0

1,0 0,-1 1,1 2,0 1,-1 1,2 2,1

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Modified Invasion Percolation

0,0 0,1

  • 1,0

1,0 0,-1 1,1 2,0 1,-1 1,2 2,1 0,2

  • 1,1
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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Modified Invasion Percolation

Sites Bonds Cluster

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Modified Invasion Percolation

t = 1000 t = 2000 t = 3000

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Modified Invasion Percolation

0.0 0.2 0.4 0.6 0.8 1.0

p

10000 20000 30000 40000 50000 60000

N

Stacked Histogram of Probabilites "Trapped" Bonds Broken Bonds

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Modified Invasion Percolation

0.4980 0.4985 0.4990 0.4995 0.5000 0.5005 0.5010

p

100 101 102 103

N

Histogram of Failed Strengths around p=0.5

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Waterlevel Bursts

5 10 15 20 25 30

N

+1.791e4 10-3 10-2 10-1 100

pc−p

lb =4 lb =1 lb =13

pb

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Waterlevel Bursts

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Waterlevel Bursts

100 101 102 103 104 105 mc 10-4 10-3 10-2 10-1 100 101 102 103 104 105 N

Frequency-Magnitude of Bursts(cutoff=0.49) Raw Data Binned Data Fit

N = 49349 t^-1.536633

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Information Theory Measures Reduce dimensionality by looking time-series of strengths

· · · p−2, p−1, p0, p1, p2 · · ·

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Information Theory Measures

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Information Theory Measures

0.6 0.4 0.2 0.0 0.2 0.4 0.6

p(t +1) pt

2 4 6 8 10 12

Probability

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Information Theory Measures Encodings Strength encoding: Temporal encoding: pt < pt+1 → 1 st n.n. st+1 → 1 pt > pt+1 → 0 st n.n. st+1 → 0

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Information Theory Measures Bayesian Inference: Strength Encoding

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Information Theory Measures Bayseian Inference: Spatial Encoding

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Information Theory Measures Permutation Entropy

5 10 15 20 25 L 5 10 15 20 25 HL

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Tokunaga Branching

1:1 1:1 1:1 1:1 1:1 1:1 1:1 1:1 2:2 2:2 2:2 2:2 3:3 3:3 4:4

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Tokunaga Branching

1:1 1:1 1:1 1:1 1:1 1:1 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:3 1:3 1:3 1:3 2:2 2:2 3:3

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Tokunaga Branching

2 4 6 8 10 12

i

10-1 100 101 102 103 104 105 106 107

Ni Ni =3957607 × 4.6278−i

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Tokunaga Branching

2 4 6 8 10 12

i

100 101 102 103 104 105 106

ri ri =2.03 × 2.6793i

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Tokunaga Branching

100 101 102 103 104 105

r

10-1 100 101 102 103 104 105 106 107

N N =11412703r−1.547762

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Tokunaga Branching

1 2 3 4 5 6 7 8 9

k

100 101 102 103 104

Tk Tk =1.10 × 2.71k +1

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Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching

Acknowledgments

In collaboration with John B. Rundle, Donald L. Turcotte, Mark R. Yoder Funded by US Department of Energy to UC Davis, #DE-FG02-04ER15568