Physical models for seismicity triggered during hydrofracture Physical models for seismicity triggered during hydrofracture experimentsexperiments

Asaf InbalAsaf Inbal Spatiotemporal distribution of induced seismicity in hydrofracture experiments will

be explored via 2 models:Model #1 : Pore-pressure diffusion controls seismicity distributionModel #2 : Seismicity is triggered by stresses due to an opening fracture

Shapiro et al. (1999)Fischer et al. (2008)

100 hr 200 hr 300 hr 400 hr

Shapiro et al. (1999)

Model #1 : Seismicity controlled by pore-pressure diffusionModel #1 : Seismicity controlled by pore-pressure diffusion

∂ p∂ t

=D∇ 2 p

The pore-pressure perturbation is relaxed due to diffusion (Shapiro et al., 1999):

where D is hydraulic diffusivity.

For a step-function-like pore-pressure

perturbation at the injection source, the

triggering front is given by (Shapiro et al.,

1997):

r=4 Dt

Model #1 : Seismicity controlled by pore-pressure diffusionModel #1 : Seismicity controlled by pore-pressure diffusion

Can pore-pressure diffusion explain the seismicity back-front?

Parotidis et al. (2005)

Combining poroelastic effects and fluid leakage from the fracture may explain the temporal evolution of seismicity. The fracture half-length as a function of time is:

Lt =Q I t

4h f C L2t2h f w

Model #1 : Seismicity controlled by pore-pressure diffusionModel #1 : Seismicity controlled by pore-pressure diffusion

Shapiro et al. (2005)

Lt ∝t If fluid loss is significant (e.g. during long-term injections): Lt ∝t Otherwise, during the initial injection phase:

Q I : ave. injection rateh f : ave. fracture heightw : ave. fracture widthC L : fluid-loss coefficient

Brief introduction to Linear Elastic Fracture MechanicsBrief introduction to Linear Elastic Fracture Mechanics

U =−W U e U s

dUda

=0

Energy balance for a static crack in an elastic medium:

Griffith criteria for crack propagation:

stable :

unstable propagation:

healing:

dUda

0

dUda

0

2a δa

σ

Brief introduction to Linear Elastic Fracture MechanicsBrief introduction to Linear Elastic Fracture Mechanics

U =−W U e U s

dUda

=0

Energy balance for a static crack in an elastic medium:

Griffith criteria for crack propagation:

stable :

unstable propagation:

healing:

dUda

0

dUda

0

2a δa

σ

x

σ

=K 1

2 r

Brief introduction to Linear Elastic Fracture MechanicsBrief introduction to Linear Elastic Fracture Mechanics

U =−W U e U s

dUda

=0

Energy balance for a static crack in an elastic medium:

Griffith criteria for crack propagation:

stable :

unstable propagation:

healing:

dUda

0

dUda

0

2a δa

σ

x

σ

=K 1

2 r

G=−d −WU e

daGc∝K c

2

We relate the fracture criteria to Griffith energy balance by introducing the energy release rate:

Model #2 : Fluid filled crack in an elastic mediumModel #2 : Fluid filled crack in an elastic medium

Dahm et al. (2010)

Dahm et al. (2010)

Phase 1 : Bidirectional growth under driving stress gradients (during injection)Phase 1 : Bidirectional growth under driving stress gradients (during injection)

a∝ t3 / 4

Crack tip velocity and crack length during phase 1:

Dahm et al. (2010)

Phase 2 : Bidirectional growth due to decompression (post-injection)Phase 2 : Bidirectional growth due to decompression (post-injection)

K=K c

Crack growth is maintained by remaining driving pressures

The post-injection length scales with the overpressure, and thus can be used to estimate

Kc of the formation.

g v=−g , g eff =0

Dahm et al. (2010)

Phase 3 : Unidirectional growth (post-injection) Phase 3 : Unidirectional growth (post-injection)

Dahm et al. (2010)

Coulomb stress changesCoulomb stress changes

Phase 2 (post-injection, g=0)

Phase 3 (post-injection, g>0)

Phase 1 (during injection, g=0)

Application to hydrofracturing dataApplication to hydrofracturing data

Dahm et al. (2010)

Application to hydrofracturing dataApplication to hydrofracturing data

Dahm et al. (2010)

Calo et al. (2011)

Is seismicity triggered by aseismic slip during the 2000 Soultz experiment?Is seismicity triggered by aseismic slip during the 2000 Soultz experiment?

Points for discussionPoints for discussion

How do we identify which physical model explains the majority of the observations?

Application to natural earthquakes

What happens if the stress drop is not instantaneous as assumed

in the fluid filled crack model?

List of references used:

Calo M., Dorbath C., Cornet F. H., and Cuenot, N. (2011). Large-scale aseismic motion identified through 4-D P-wave tomography, GJI, 186 (3), 1295-1314. doi: 10.1111/j.1365-246X.2011.05108.x

Dahm T., Hainzl S. and Fischer T. (2010). Bidirectional and unidirectional fracture growth during hydrofracturing: Role of driving stress gradients, JGR, 115, doi:10.1029/2009JB006817

Fischer T., Hainzl S., Eisner L., Shapiro S. A. and Le Calvez J. (2008). Microseismic signatures of hydraulic fracture growth in sedimentformations: Observations and modeling. JGR, 113(B2), doi:10.1029/2007JB005070

Parotidis M., Shapiro S.A. and Rothert E. (2005). Evidence for triggering of the Vogtland swarms 2000 by pore pressure diffusion. JGR, 110(B5), doi: 10.1029/2004JB003267

Shapiro S. A., Dinske C. and Rothert, E. (2006). Hydraulic-fracturing controlled dynamics of microseismic clouds. GRL, 33(114), doi: 10.1029/2006GL026365

Shapiro S.A., Huenges E. and Borm G (1997). Estimating the crust permeability from fluid-injection-induced seismic emission at the KTB site. GJI, 131(2).

Shapiro S.A., Audigane P. and Royer J.J. (1999). Large-scale in situ permeability tensor of rocks from induced microseismicity. GJI, 137(1), 207-213, doi: 10.1046/j.1365-246x.1999.00781.x