• • •
Slope = 0.5 at high p Slope = 0.26 at p=pc At intermediate p values, at some time or distance to the wetting front,
the slope transitions from 0.26 to 0.50
14
Pore Connectivity and Diffusion • Same mathematics for diffusion and imbibition:
∂c ∂ ∂c = Ds (θ ) ∂t ∂x ∂x
Pore connectivity: Time-dependence: Distance to front Diffusion coefficient Distance-dependence: Diffusion coefficient
Pore Structure and Hydrocarbon Recovery in Fractured Shales
(Max) Qinhong Hu 胡钦红 maxhu@ Department of Earth and Environmental Sciences University of Texas, Arlington
(Spontaneous) Imbibition Test
• Rock sample epoxycoated along length → 1D flow • Imbibition rate monitored continuously over time
Balance
• Sample size (cm range) and shape • Different initial water contents • Tracer solution
Fracture‒Matrix Interaction
Field observation (preferential flow in a fracture network) of dye distribution in unsaturated fractured tuff at Yucca Mt.
1
2006
2004
2000 2008
/pub/oil_gas/natural_gas/analysis_publications/maps/maps.htm
2
http://www /tod ayinenergy/ detail.cfm?i d=2170 Updated June 1, 2011
Pore structure
Barnett Shale (7,219 ft)
pathways
Porosity: 5.5% k: nanodarcys (10-21 m2) Median pore dia.: 5 nm
• Gas deliverability from nanopores to well bore 5
3
Low gas recovery factor 15-30% for Barnett Shale (King, 2012)
4
Pore Structure and Low Hydrocarbon Production
RPSEA project: “Integrated • Amount of gas experimental and in place modeling approaches • Free vs. to studying the adsorbed gas fracture-matrix interaction in gas • Tortuous recovery from Barnett transport shale”
elliptical to completely rounded
Where is the porosity?
angular
rectangular
8
CH4 size: 0.375 nm
9
/customerexpress/docs/presentations_general/2009_ North_American_Shale_Gas_Overview_NECA.pdf
“Ant in a labyrinth”
p = 0.66
Solute in a pore system
↔
16
Multiple Approaches to Studying Pore Structure
• • • • • • • • • • • • Imbibition with samples of different shapes Edge-accessible porosity Liquid and gas diffusion Mercury injection porosimetry N2 adsorption/desorption isotherms Vapor absorption Nuclear Magnetic Resonance Cryoporometry SEM imaging after Wood’s metal impregnation Microtomography (high-resolution, synchrotron) Focused Ion Beam/SEM imaging Small-Angle Neutron Scattering (SANS) Pore-scale network modeling 1in) in log scale
0.5
1.5
2.5
3.5
19
Imbibition Results for Barnett Shale Samples Depth 7,109 ft (2,167 m) 7,136 ft (2,175 m) 7,169 ft (2,185 m) 7,199 ft (2,194 m) 7,219 ft (2,200 m)
18
Low Pore-Connectivity of Shale Samples
30 sec 5 min 2 hr 20 hr
Cumulative imbibition (mm) in log scale
0.0
-1.0
-2.0
Barnett Shale 2,166.8 m (7,109 ft) Rectangular prism (1.33 cm long × 1.76 cm wide × 1.43 cm tall)
Height/width
Imbibition slope
0.93 0.76 1.12 0.70 1.16 0.87 1.12 0.67 1.25 0.80
0.214 ±0.059 (N=3) 0.291 ±0.027 (N=3) 0.269 ±0.0045 (N=3) 0.216 ±0.040 (N=3) 0.273 ±0.050 (N=3) 0.357 ±0.006 (N=3) 0.284 ±0.062 (N=3) 0.282 ±0.047 (N=3) 0.306 ±0.019 (N=3) 0.264 ±0.046 (N=3) 20
Pore-Scale Network: Simulation Results (Ewing of ISU)
• p is pore connectivity probability; pc ≈ 0.2488 is the percolation threshold for cubic lattice
nanopore
0.375 nm
10
11
Fluid Flow and Mass Transport in Stimulated Reservoir Volume
~3×106 m3 for one frac stage (Curtis et al., 2012) 12
/customerexpress/docs/presentations_general/ 2009_North_American_Shale_Gas_Overview_NECA.pdf
21
height
Log mass imbibed
h φa (h ) = φp χ
β ν
1 Slope = = 0.5 2
Percolation Theory
The mathematics of how macroscopic properties result from local (microscopic) connections
p is the local connection probability
percolation threshold 0.5 < pc < 0.66 (for 2D square lattice) p = 0.5
Rock milling in 1998
My work on fracture transport starts with this rock
7
Intraparticle organic nanopores
Ar-ionbeam milling and fieldemissiongun SEM: resolve pores as small as 5 nm Loucks et al. (2009)
Sample dimension
1.33 cm L×1.76 cm W ×1.43 cm H (Vertical) 1.76 cm L×1.72 cm W ×1.32 cm H (Horizontal) 1.38 cm L×1.71 cm W ×1.72 cm H (Vertical) 1.73 cm L×1.73 cm W ×1.21 cm H (Horizontal) 1.35 cm L×1.79 cm W ×1.81 cm H (Vertical) 1.24 cm L×1.78 cm W ×1.32 cm H (Horizontal) 1.24 cm L×1.74 cm W ×1.67 cm H (Vertical) 1.74 cm L×1.72 cm W × 1.26 cm H (Horizontal) 1.37 cm L×1.74 cm W × 1.95 cm H (Vertical) 1.69 cm L×1.71 cm W ×1.36 cm H (Horizontal)