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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 Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing 1 Simple Model 2 Invasion Percolation 3 Bursts 4 Information Theory 5 Tokunaga Branching 6

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Step 1: Drill a well

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Step 2: Inject fluid to generate fractures

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

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Halliburton in the late 1940’s

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing USGS Potential Gas Committee (2011)

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Horizontal Drilling “Slickwater”

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing “Super Fracking” Today

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Potential Gas Committee (2011)

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Lower 48 states shale plays Niobrara* Montana Thrust Bakken*** Belt Heath** Cody Williston Basin Big Horn Powder River Gammon Basin Hilliard- Basin Baxter- Mowry Appalachian Mancos Michigan Basin Greater Basin Antrim Green Niobrara* River Park Forest Basin Basin Devonian (Ohio) City Basin Marcellus Illinois Uinta Basin Manning Basin Utica Canyon Piceance San Joaquin Denver Basin Mancos Basin Basin Excello- New Mulky Hermosa Cherokee Platform Albany Monterey- Paradox Basin Pierre Temblor Woodford Lewis Raton Fayetteville San Juan Anadarko Basin Chattanooga Basin Basin Ardmore Basin Monterey Black Warrior Arkoma Basin Palo Duro Bend Conasauga Santa Maria, Basin Basin Ventura, Los Floyd- Valley & Ridge Avalon- Angeles Neal Province Barnett Basins Bone Spring Permian TX-LA-MS Miles Basin Ft. Worth Salt Basin Barnett- Basin Tuscaloosa 0 100 200 300 400 Marfa ± Woodford Basin Eagle Haynesville- Ford Bossier Pearsall Shale plays Basins Western Basins Gulf Current plays * Mixed shale & chalk play Prospective plays ** Mixed shale & Stacked plays limestone play Shallowest/ youngest ***Mixed shale & Intermediate depth/ age tight dolostone- Deepest/ oldest siltstone-sandstone Source: Energy Information Administration based on data from various published studies. Updated: May 9, 2011

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

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Problem: Earthquakes S w e ll # 5 w e ll # 1 N 0 E nde rsFa ult − 2 O z a rkA quife r ) pth(km − 4 Pre c a m bria n e − 6 D M 3.9 − 8 M a gnitude4.1 M 4.7 M 4.0 − 10 –5 15 10 5 0 H oriz onta l dis ta nc e(km ) R. A. Kerr. Science 335(6075), 1436-1437

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Problem: Earthquakes from fluid reinjection Art McGarr (USGS)

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Hydraulic Fracturing Problem: Contaminated Drinking Water

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.

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

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Simple Model elastic region uid lled cavity r c r e damage shell

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Simple Model P = 0

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Simple Model P = P d

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Simple Model P = P d

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Simple Model P = P d

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Modified Invasion Percolation 0,1 -1,0 0,0 1,0 0,-1

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Modified Invasion Percolation 0,1 1,1 -1,0 0,0 1,0 2,0 0,-1 1,-1

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Modified Invasion Percolation 1,2 0,1 1,1 2,1 -1,0 0,0 1,0 2,0 0,-1 1,-1

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Modified Invasion Percolation 0,2 1,2 -1,1 0,1 1,1 2,1 -1,0 0,0 1,0 2,0 0,-1 1,-1

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Modified Invasion Percolation Sites Bonds Cluster

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Modified Invasion Percolation t = 1000 t = 2000 t = 3000

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Modified Invasion Percolation Stacked Histogram of Probabilites "Trapped" Bonds Broken Bonds 60000 50000 40000 N 30000 20000 10000 0 0.0 0.2 0.4 0.6 0.8 1.0 p

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Modified Invasion Percolation Histogram of Failed Strengths around p=0.5 10 3 10 2 N 10 1 10 0 0.4980 0.4985 0.4990 0.4995 0.5000 0.5005 0.5010 p

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Waterlevel Bursts 10 0 10 -1 p c − p p b 10 -2 l b =4 l b =1 l b =13 10 -3 5 10 15 20 25 30 +1.791e4 N

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Waterlevel Bursts

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Waterlevel Bursts Frequency-Magnitude of Bursts(cutoff=0.49) 10 5 10 4 N = 49349 t^-1.536633 10 3 10 2 10 1 N 10 0 10 -1 10 -2 Raw Data 10 -3 Binned Data Fit 10 -4 10 0 10 1 10 2 10 3 10 4 10 5 m c

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 , p 0 , p 1 , p 2 · · ·

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Information Theory Measures

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Information Theory Measures 12 10 8 Probability 6 4 2 0 0.6 0.4 0.2 0.0 0.2 0.4 0.6 p ( t +1 ) p t

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Information Theory Measures Encodings Strength encoding: Temporal encoding: p t < p t +1 → 1 s t n.n. s t +1 → 1 p t > p t +1 → 0 s t n.n. s t +1 → 0

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Information Theory Measures Bayesian Inference: Strength Encoding

Hydraulic Fracturing Simple Model Invasion Percolation Bursts Information Theory Tokunaga Branching Information Theory Measures Bayseian Inference: Spatial Encoding