Quantitative understanding of microseismicity

for reservoir characterization

Serge Shapiro and the PHASE-Project Team.

We greatly acknowledge support of the PHASE project sponsors

A recent book:

Serge A. Shapiro, 2015,

Fluid-Induced Seismicity,

Cambridge Univ. Press, pp 289.

http://www.cambridge.org/9780521884570

Physical Concept

- In some locations the state of stress is nearly critical.

- Seismicity triggering process is a dynamic perturbation of

this stress state: Pressure diffusion & Hydraulic fracturing.

Exponential ACF

distribution of criticality events and their occurrence times

events and their occurrence times distribution of criticality

Gaussian ACF

distance vs. time

distance vs. time

model diffusivity

model diffusivity

Numerical modelling of seismicity: linear diffusion

Triggering Front and Back Front: linear diffusion

r=√4π Dt rbf=√6 Dt (1−t / t0 ) ln(1−t0 /t )

2

1

original coordinate system

Tensor of hydraulic diffusivity: linear diffusion

scaled coordinate system

x̄=x

√4πt

x̄1

2

D11

+x̄

22

D22

+x̄

32

D33

=1

Top South East

Fenton Hill Soultz-sous-Forêts

Event Density: linear diffusion

Perkins-Kern-Nordgren (PKN) Model of Hydraulic Fracture

Cotton Valley: data courtesy of J. Rutledge

Volume Balance Principle

Volume of injected fluid = fracture volume + lost fluid volume

QI t = 2 L G + 6 L hf CL t1/2

t injection time,

QI average injection rate,

CL fluid loss coefficient,

G = w*hf vertical cross section of the fracture.

Stage 2Microseismicity induced by hydraulic fracturing

The straight lines: fracture reopening

Triggering Front and Back Front

Basic Equations: non-linear diffusion

∂ ρϕ∂ t

=−∇Uρ≈ρS∂ p∂ t

Mass conservation (in terms of density, porosity, and filtration velocity):

Darcy law (in terms of pressure, permeability and viscosity):

Hydraulic diffusivity :

U=−kη

∇ p

D( p )=k ( p )

Sη

Non-Linear Diffusion

∂rd−1 p∂ t

= ∂∂ r

D( p )rd−1 ∂∂r

p

Diffusion equation:

Hydraulic diffusivity and injection rate:

D∝D0 pn Q∝QI ti

Triggering Front

r=√4π Dt

r∝(D0Q In tn( i+1 )+1 )1/ (dn+2)

r∝d√QI t

i+1

Linear diffusion, n=0

Strong non-linearity, n>>1 (volume balance)

Fisher et al, 2002

Fisher et al, 2004

Barnett Shale

r =At^1/2

r =At^1/3

Data courtesy of Shawn Maxwell, Pinnacle Technologies

Hydraulic Fracturing in Barnett Shale

Factorized anisotropy and non-linearity

∂ p∂ t

= ∂∂ x i

Dij( p ) ∂∂ x j

p

Dij( p )=[D011 0 0

0 D022 00 0 D033

] f ( p )

∂ p∂ t

=D011∂∂ x1

f ( p )∂∂ x1

p

+D022∂∂ x2

f ( p )∂∂ x2

p+D033∂∂ x3

f ( p )∂∂ x3

p

Rescaling of the cloud

Factorized non-linearity: Anisotropy vs time-dependence

Barnett Shale: modelling using engineering data

The back front of seismicity

N. Hummel, 2011,2012

N. Hummel, 2015

Conclusions

• Qantitative information on rock-physics: e.g., initial and stimulated

permeability.

• Non-linear diffusion helps to understand fracturing of shale.

• Back front of seismicity is indicative for a pressure-dependence of

the stimulated permeability.

• r-t plots can help to control the quality of microseismic dots.