30 October 2013

Time and Apparent Time Effects on Compaction & Subsidence

Rune M Holt, NTNU & SINTEF

Leeuwarden, 29 October 2013

SC Meeting by Waddenacademie/KNAW & NAM

30 October 2013

Time Effects on Compaction & Subsidence • Creep • Consolidation

Apparent Time Effects:

• Stress Path / Arching-induced • Elasto-Plastic Transition

Both Reservoir and Surrounding Rocks are involved

30 October 2013

Creep • Creep is characterized by 3 phases: Transient, Steady-state, and Accelerating, where the rock may undergo failure • Creep mechanisms are not fully understood – a common assumption is stress-induced corrosion, which is strongly dependent on temperature & the distance in stress space to rock failure

Tran

sien

t

Stea

dy st

ate

Acc

eler

atin

g

time

strain

Rate dependent compaction model by de Waal & Smits, 1988

30 October 2013

Consolidation • Pore pressure equilibration in a depleting reservoir occurs at different rates, depending on permeability • The characteristic time for reaching equilibrium follows a classical diffusion law:

•100m sand with Darcy permeability ® seconds – minutes time-scale •10m shale layer with nanoDarcy permeability ® 10-100 years time-scale •100m shale with nanoDarcy permeability ® Myears time-scale • What if all permeabilities are present at all length scales (Mossop's hypothesis?)? • What about TenBoer?

2D

DD

ltC

»

1

2

( ) 1 4( )3

f fD

fr fr

K Kk CC MH K G

kh fh f

-é ùê ú

= - » +ê úê ú+ë û

10/30/2013

Stress Path

Reservoir stress path coefficients from Rudnicki (1999); reservoir is elastically matched to the surroundings (Poisson’s ratio = 0.20)

Notice: Stresses (and pore pressure) also change in the surrounding rocks

Dh

R e=Dh/2R

h

e=h/2R 0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,00 0,20 0,40 0,60 0,80 1,00

Aspect ratio

Stre

ss P

ath

Coe

ffici

ents

gv/a

gh/a

gv: "Arching" coefficient = Dsv/Dpf gh: Describes horizontal stress evolution = Dsh/Dpf (First defined by Schutjens, Hettema a.o.)

Reservoir

surface

compaction

S T R E S S A R C H

Stretching andreduction in v v

Increase in

Incresed shearstress

Casingsubject toshear

Reservoir Stress Path: Impact on Compaction

Compaction decreases with increasing reservoir aspect ratio, reflecting enhanced arching

If depleted area increases with depletion (aspect ratio decreases), compaction will accelerate with time

(1 ) 2 (1 )( )

v hfr

ffr

h ph E

g gna aa

- - --D= -D

An Apparent Time Effect

30 October 2013

Core vs. Virgin compaction: The "GRONstone" Experience

"Virgin" compaction, along a Reservoir Stress Path

"Coring" simulation, along 2 Coring Stress Paths + "Core" compaction, along a Reservoir Stress Path

Cementation: Sand & e.g. Sodium Silicate + CO2

Holt, Brignoli & Kenter; IJRM 2000

30 October 2013

Virgin vs. Simulated Core Compaction

ØPermanently reduced stiffness of well cemented cored material when reloaded above forming stress: Typical initial stiffness ratio ~ 2

Ø Apparently similar compaction after the virgin material has reached yield onset: For GRONstone typical 10 MPa (» UCS) above the forming ("in situ" stress)

Holt, Brignoli & Kenter; IJRM 2000

COMPETENT SYNTHETIC ROCK "GRONstone"

Uniaxial

30 October 2013

Virgin vs. Simulated Core Compaction STRONG SYNTHETIC ROCK "EPOXtone"

Ø As for GRONstone, but since EPOXtone is stronger (UCS ~ 15 MPa), yield onset occurs at higher stress

Ø Ratio between initial virgin : core stiffness ~ 3-4

Static vs Dynamic Moduli Ø Epoxy-cemented sandstone, formed at 30 MPa axial & 15 MPa

confining stress Ø Static = Dynamic Modulus directly after cementation; Undamaged

material Ø In simulated core, Dynamic > Static modulus, except during stress reversal

(unloading + reloading)

Uniaxial Strain (K0) Uniaxial Strain (K0)

Virgin Material Simulated Core

Holt et al., ARMA 2013

30 October 2013

NAM Core Compaction

• Field core from NAM tested in uniaxial strain conditions (no

pore fluid) • Note observed

nonlinearity (above 80 MPa axial stress) and

permanent strains

Why are Static ¹ Dynamic Moduli? Fluid contribution Static Dynamic

drained (normally) undrained (always)

( )

2

fr fr ff

s

K K K KK

a

f a f« +

+ -

Dispersion Ultrasonic: f ~ 1 MHz

Sonic: f ~ 10 kHz

Static: f ~ 1 Hz

+ Scale effects, Anisotropy, a.o.

Plasticity Static moduli are measured at finite strains and include elastic + plastic deformation; Dynamic moduli are measured at infinitesimal strain and are hence purely elastic.

Negligible for gas saturation

Static vs. Dynamic Moduli: Strain amplitude effects

Ø Experiments on dry sandstones show that:

Ø In hydrostatic loading (by grain contact plastification, crushing of asperities etc):

Ø In triaxial loading (by sliding cracks) :

0

1;1

dynstat

dyn

KK P

PK s s= µ

+ +

(1 )1

dynstat

z dyn

E FE

P E-

=+ z rF e eµ -

(e.g. ” Petroleum Related Rock Mechanics” by Fjær et al., 2008)

Creep can be modelled within the same framework by making the F-parameter time dependent – viscoplasticity relates to static moduli, viscoelasticity to dynamic

Reservoir Monitoring Aspects: Competent Synthetic Sandstone

ØPermanent drop of velocities after coring & reloading to forming stress

ØLow stress sensitivity during loading in the virgin material

ØLarger stress sensitivity during unloading

ØLarge stress dependence in the simulated core!

0.40

0.60

0.80

1.00

1.20

0 10 20 30 40 50 60 70

Effective vertical stress (MPa)

Verti

cal P

-wav

e ve

loci

ty (r

el.)

Simulated Core

Virgin Material

In situ stress

Discrete Particle Modelling: ”Best fit” between Laboratory and PFC3D simulations of GRONstone

30

35

40

45

50

55

60

0 1 2 3 4 5 6 7

Axial Strain [milliStrain]

Axi

al S

tres

s [M

Pa] Virgin GRONstone

Clump logick n /k s = 3.5 (uncemented) k n /k s = 1 (cemented)

5x2.5x2.5 mm sample

Epb=8 GPa; Shear = Tensile bond strength = 10 +- 10 MPa

Cored GRONstoneVirgin PFC

Cored PFC

Looked good.... Holt, Brandshaug & Cundall, NARMS 2000

6 Creep is implemented to mimick stress-induced corrosion by reducing the parallel bond extent depending on the stress level relative to bond strength at each contact

0 2 4 6 8 10 12

x 107

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time [s]

Cre

ep [m

illis

train

]

Creep (PFC2D - stress corrosion model)

75 % of peak

Steady state creep Accelerating creep

Transientcreep

Secondary creep

0 2 4 6 8 10 12

x 107

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time [s]

Cre

ep [m

illis

train

]

Creep (PFC2D - stress corrosion model)

75 % of peak

Steady state creep Accelerating creep

Transientcreep

Secondary creep

A similar approach has been presented by Potyondy (2005)

The model captures the three commonly observed

phases of transient, secondary and accelerating

(tertiary) creep

Time dependent deformation in Discrete Particle Modelling

Time dependent deformation in Discrete Particle Modelling

6 Long-term behaviour may be assessed from short-term simulations 6 Challenge: Appropriate calibration of microscopic creep parameters 6 Other physical mechanisms may play a vital role over long time scales

Darley Dale sst experiments (from Meredith, NYRocks 1997)

PFC3D

Application example: Creep under K0 conditions

0 50 100 150 200 250 3000

0.5

1

1.5

2

2.5

3

3.5

Time [years]

Axi

al c

reep

[mS

train

]

K0 creep

PFC simulationExperimental data

A tool for the

future...

0 50 100 150

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Time [days]

Axi

al c

reep

[mS

train

]

K0 creep

PFC simulationExperimental data

Concluding Remarks

Ø Time dependent compaction may be intrinsic (creep, consolidation; within reservoir & overburden) or apparent (stress arching induced, due to onset of plasticity)

Ø Rocks deform elasto-plastically – both in the Earth and in the Laboratory Ø Rock alteration due to stress relief during coring is well and

understood, and models for correction of core measured compaction exist

Ø Plastic strain evolves as failure is approached, and with it: Viscoplastic strain Ø Long term effects may be modelled, but require proper understanding

of mechanisms (hard to speed up…)