1 Introduction Definitions and some challenges of reservoir geomechanics. Modeling of coupled phenomena. 2 Constitutive Laws: Behavior of Rocks Fundamentals of Pore-Mechanics. 3 Constitutive Laws: Behavior of Fractures Geomechanics of Fractured Media. 4 Reservoir Geomechanics Elements of a geomechanical model and applications. 5 Unconventional Reservoirs Naturally fractured reservoirs, hydraulic fracture, proppant and fracture closure model, validation (microseismicity). 6 Advanced Topics Injection of reactive fluids and rock integrity. Introduction to Reservoir Geomechanics
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1 IntroductionDefinitions and some challenges of reservoir geomechanics.Modeling of coupled phenomena.
2 Constitutive Laws: Behavior of RocksFundamentals of Pore-Mechanics.
3 Constitutive Laws: Behavior of FracturesGeomechanics of Fractured Media.
4 Reservoir GeomechanicsElements of a geomechanical model and applications.
• Equilibrium restrictions (vapour pressure, air dissolution)
• Chemical equilibrium and kinetics for chemical species interaction
Thermo-hydro-mechanical joint element
Sequential and parallel versions
Staggered fully-coupled scheme THM – C
Compaction andsubsidence
Fault reactivation
Hydraulicfracturing Reservoir Geomechanics
Wellbore/Reservoir geomechanics
Creep in salt rocks
Geochemical Integrity of reservoir and cap rocks
RESEARCH LINES – LABORATORY TESTS
before
after
Matrix: Fracture:
Integrity of Carbonate Rocks Subjected to Mechanical and Chemical Actions
RESEARCH LINES – LABORATORY TESTS
Matrix: Fracture:
Integrity of Carbonate Rocks Subjected to Mechanical and Chemical Actions
Porosity
Injection of an under-saturated water
Dissolution frontof mineral
Pressure at the top: P + P ; P =0.1MPa
Pressure at the bottom: P
Initially:- porosity and permeability: constants- mineral: randomically distributed
2D and 3D MODEL
Injection of an under-saturated water
Dissolution frontof mineral
Pressure at the top: P + P ; P =0.1MPa
Pressure at the bottom: P
Initially:- porosity and permeability: constants- mineral: randomically distributed
2D and 3D MODEL
75 b)(m 10 218
)( 0
IK
KK
0
0be Tendency to develop
preferencial paths (channels for fluid flow)
DtDv
DtD
DtD Ts
s
u)1()1(
Injection of an under-saturated water
2D MODEL
Concentração do mineral Porosidade
Permeabilidade Fluxo
2D and 3D MODEL
(Pereira & Fernandes, 2009)
Clique aqui!
Clique aqui!
Clique aqui!
Clique aqui!
HM-C Couplings
Chemo-mechanical constitutive model:
Linear-elastic law including chemical (volumetric) strains:
parameter : mineral of rock) of (mol/mion concentrat:
mineral of /mol)(m memolar volu:
volumemineral total
3
3
mc
mv
cvv
m
m
mmmT
DtDv
DtD T
chevolche
vol )1(1
)( chevole mD
Cristal Growth
Chemical compaction
Iberian Range
Pyrenees
Cata
lan
Cost
al Ra
nge
B arcelona
MediterraneanSea
0 100 km50 45º
3º
High-speed Railway Madrid –Barcelona
TunnelLength
(m)
Maximum Cover
(m)
Excavated Cross-Section
(m2)
Camp Magre 954 52 140
Lilla 2034 110 117
Puig Cabrer 607 191 137
Madrid
Zaragoza Barcelona
Tunnels inStretches
IVb & V
length: 629 km
Camp Magre
Lilla Puig Cabrer
Tunnels in Section Lleida-MartorellRailway Authority
Case history: tunnel in sulphate bearing rock
Excavated in 2001-2002 by drill and blast (head and bench) from the two portals
Lilla Tunnel
R = 6.4
6 m
Case history: tunnel in sulphate bearing rock
280
320
360
400
440m a.s.l.
411+100 412+000 413+000 413+300
North portal(Lleida)
South portal(Martorell)
Quaternary Middle Eocene Early Eocene
Colluvion Limestone Claystone & Siltstone
Marl Anhydritic-Gypsiferous Claystone
cross-shaped fibrous gypsum veins
slickensidethe excavated material
The Tertiary Anhydritic-Gypsiferous Claystone from the Lilla Tunnel
Geological Profile
Case history: tunnel in sulphate bearing rock
Case history: tunnel in sulphate bearing rock
Heave in the flat slab section
9/20
/02
12/1
9/02
3/20
/03
6/19
/03
9/15
/03
12/1
5/03
2/2/
04
0 100 200 300 400 500Time (days)
0
100
200
300
400
500
600
700
800
Verti
cal d
ispl
acem
ent (
mm
)
411+380
411+420
411+540
Slab axis reference at 9/20/02
411+880
411+900
411+920
411+940
412+240
412+545
1/17
/03
12/1
/02
Con
stru
ctio
n of
the
inve
rt
Heave in Stations with severe expansive behaviour. Flat slab section
Lilla tunnel: field observations
0 100 200 300 400 500 600 700Time (days)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Tota
l rad
ial p
ress
ure
(MPa
)
411+589 CPTR-3
411+609 CPTR-1
411+629 CPTR-1
411+669 CPTR-1
411+749 CPTR-3411+769 CPTR-1
411+829 CPTR-3
Dec
-02
Jan-
03
Feb-
03
Mar
-03
Apr
-03
May
-03
Jun-
03
Jul-0
3
Aug
-03
Sep-
03
Oct
-03
Nov
-03
Dec
-03
Jan-
04
Feb-
04
Mar
-04
Apr
-04
May
-04
Jun-
04
Jul-0
4
Con
cret
ing
the
inve
rts
Invert: 40 cm
Invert: 60 cm
Total Radial Pressures at the invert sections
R = 6.46
m
CPTR-1CPTR-3CPTR-2
Lilla tunnel: field observations
Anhydrite/gypsum system
Heave in sulphate bearing rock: analysis
Anhydrite: Ca2+ + SO42- Gypsum: Ca2+ + SO4
2- + 2H2O
The molar volume of gypsum is 62% larger than that of anhydrite
Direct transformation is apparently not possible
Conversion from anhydrite to gypsum is via dissolution - precipitation
Anhydrite
Gypsum
2 H2O CaSO4 2 H2OCaSO4
Water2 mols36 cm3
Anhydrite1 mol
45.94 cm3
Gypsum1 mol
74.69 cm3
+
V = 62%
Orthorhombic Monoclinic
Anhydrite: Gs = 2.96
Gypsum: Gs = 2.32
Sulphate-Bearing Clayey Rocks
TRANSFORMATION OF ANHYDRITE INTO GYPSUM IN AN OPEN SYSTEM
Expansive Behaviour
Heave in sulphate bearing rock: analysis
HM-C Couplings
grain mass loss due to mineral dissolution produces a pronounced horizontal stress drop under zero lateral strain conditions
rearrangement of the internalgranular structure (discrete element simulation results confirm that the internal friction is fully mobilized at kmin )
Sample dimensions: 10x10x10cm
Injection of an under-saturated water
Dissolution frontof mineral
Pressure at the top: P + P ; P =0.1MPa
Pressure at the bottom: P
Initially:- porosity and permeability: constants
3D PLUG MODEL
HM-C Couplings
0 time (s) 1.0e8
verticaldispl.(cm)
0
0.3
0 time (s) 1.0e8
lateralstress(MPa)
0.44
2.34
Constant initial mineral concentration distribution
HM-C Couplings
0 time (s) 1.0e8
verticaldispl.(cm)
0.3
0
0 time (s) 1.0e8
lateralstress(MPa)
0.44
2.34
Randomic initial mineral concentration distribution
Higher vertical stresses inremaining mineral zones
HM-C Couplings
0 time (s) 1.0e8
verticaldispl.(cm)
0.34
0
0 time (s) 1.0e8
lateralstress(MPa)
0.44
2.34
Assuming elastoplasticMohr-Coulomb law:
)( chevol
p mD
HM-C Couplings
0 time (s) 1.0e8
lateralstress(MPa)
0.44
2.342.34
τ
h
How to increasethe lateral stress??
Introducing material degradation(eg., decreasing of cohesion)
v
At well and reservoir scales...
Cement dissolution under load can cause:
Chemically Induced Reservoir Compaction
Material degradation (decreasing of shear strength):
- Wellbore stability- Faults…
CONCLUSIONS
► A numerical tool capable to evaluate the integrity of reservoir and cap rockshas been presented considering a number of HM and HMC phenomena.
► Consideration of chemical effects requires the incorporation of:▪ New (environmental) variable: concentration of chemical species▪ New balance equation: reactive transport equation▪ Chemical models accounting for kinetics and chemical
equilibrium are required
► Mineral concentration was adopted as a state variable of a simplifiedchemo-mechanical constitutive model that was able to reproduce qualitativelydeformations induced by cement dissolution.