Notes

Outline

Spatial organization of natural fractures: A geomechanics approach

Fracture Spacing - Description describe fracture spacing from outcrop average perpendicular spacing clustering & saturation

Fracture Clustering & Spacing

Saturated Strike Joints

Unsaturated Cross-Fold Fractures

Saturated Cross-Fold Fractures

Fracture Zones – Potential Conduits for Flow

Fracture Spacing - Modeling analogue models for spacing stochastic crack models geomechanical analysis

Analogue Experiments for Fracture Spacing* brittle elastic coating on plexiglas sheet apply extension through bending increasing strain increases fracture intensity fracture spacing distribution changes with increasing intensity

Spacing Distributions - Experiments shape of spacing distributions changes as fractures grow distrib. moves from negative exponential toward normal with increasing intensity median/mean ratio approaches 1 normal distribution termed “saturated”

Stochastic Model (Rives et al., 1992)

Spacing Data from Outcrop

Can we learn about fracture spacing from geomechanics?

Why not statistics alone? Less insight into physical processes Not boundary condition driven LESS predictive? - can’t predict change between domains Cannot differentiate between non-unique answers with statistics alone (mechanics can help choose physically reasonable solution)

Mechanical Model Basis Fundamental physics elasticity fracture mechanics Estimation of input parameters boundary conditions material properties initial flaws Calibration to real data (statistical analysis)

What mechanism might cause natural, opening mode fractures (joints and veins) to grow?

"Natural Hydraulic Fracturing" fracturing can occur due to: increase in pore pressure tectonic extension reducing minimum stress initial stress conditions for the following simulations were: Pp = shmin  svert > sHmax > shmin

Stress Shadow and Fracture Spacing stress relief from existing fractures removes energy available for other cracks to grow fracture spacing should be proportional to size of stress shadow

Fracture Stress Perturbation Calculation body loaded in uniaxial tension one opening mode crack perpendicular to tension result symmetrical about crack (only show half)

Example - 2d, Plane Strain Crack stress shadow grows in size with increasing crack length (from 1 m to 6 m) plots show normal stress perpendicular to crack

2d Stress Shadow – Length = 1

2d Stress Shadow – Length = 3

2d Stress Shadow – Length = 6

Example - Finite Height Crack 3d fracture geometry width of stress shadow scaled to fracture height, unaffected by increasing length suggests closer fracture spacing than plane strain model

3d Elasticity Approximation Displacement discontinuity solution form

3d Influence Factor

For Bedded Sedimentary Rocks fractures confined to mechanical layers field data shows spacing depends on bed thickness => 3d stress shadow more appropriate

3d Stress Shadow – L = 1

3d Stress Shadow – L = 3

3d Stress Shadow – L = 6

Effect of ~3d Elasticity on Opening

The previous results were static, isolated cracks.  Let's look at the development of networks . . .

For modeling, we need . . .

“Critical Law” Crack Propagation Stress concentration at crack tip KI = (P-smin) (p a)1/2 Propagation when KI exceeds toughness High propagation velocity Start/stop propagation?

Propagation criterion

Propagation Criterion =  Subcritical Crack Growth Appropriate for Geologic Conditions long term loading (106 years) chemically reactive pore fluids Little evidence in rocks for dynamic propagation

Subcritical Propagation Law Stress Intensity Criterion (pure mode I) KI* < KI < KIc Velocity Rule v a (KI / KIc)n v = propagation velocity n = subcritical index

Dynamics of Crack Growth

Crack Path Criterion Cracks propagate perpendicular to local shmin Curving crack path (mixed mode I-II) implies low differential stress in horizontal plane Straight cracks imply high stress differential

Numerical Method Base code => 2-d displacement discontinuity (with 3d extension) Propagation accomplished by adding elements at crack tip (according to propagation criterion)

Simulation Boundary Conditions Displacement control, uniaxial extension Lateral boundaries - zero normal disp, zero shear stress Randomly located starter cracks All fractures are vertical

Results showing fracture spacing as affected by the subcritical exponent, n

Low Subcritical Exponent, n=1 all cracks propagate at similar velocity at same time to similar final length

Higher Subcritical Exponent, n=10 Cracks have: strong velocity contrast one crack propagates at a time

More Complex Simulations All simulations use IDENTICAL uniaxial loading Variations in patterns due to bed thickness and subcritical exponent effects Mixed mode propagation modeled

Example 1 thick bed = large stress shadows high velocity exponent, n=40, few cracks propagate at same time (body size = 10m x 10m)

Example 2 reduce bed thickness from 5 to 2 meters results in closer fracture spacing n=40

Example 3 same thin bed lower velocity exponent, n=10, more cracks propagate simultaneously

Multiple Fracture Orientations approximate randomly oriented starter cracks with orthogonal starter cracks late stage propagation parallel to extension (Poisson effect)

Example 4 thin bed, t=2 low velocity exponent, n=5

Summary Fracture Patterns

Summary Size of stress shadow exerts basic control on spacing, but only accounts for static effects Need to account for relative velocity / timing of crack propagation Experimental and field data suggests fracture pattern growth is not random but interactive Subcritical growth index, n, controls clustering and modifies spacing from simple bed thickness proportionality

Summary (cont.) Low subcritical index low velocity contrast many cracks growing simultaneously higher intensity for same strain clustered strain High subcritical index high velocity contrast one crack grows at a time lower fracture intensity for same strain regular spacing