Introduction to Reservoir Geomechanics - lmcg.ufpe.br Advanced Topics.pdf · 1 Introduction...
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Transcript of Introduction to Reservoir Geomechanics - lmcg.ufpe.br Advanced Topics.pdf · 1 Introduction...
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.
5 Unconventional ReservoirsNaturally fractured reservoirs, hydraulic fracture, proppant and fracture closure model, validation (microseismicity).
6 Advanced TopicsInjection of reactive fluids and rock integrity.
Introduction to Reservoir Geomechanics
Geochemical Coupling
Civil Engineering
Heave in a tunnel excavated in sulphate bearing rock (Belchen tunnel)
Mining Engineering
Effects of weathering of pillars in abandoned iron mines (Northern France)
Castellanza et al. (2005)
Chemical mechanism: new material characterization
Long term stability of mineworkins and quarries (De Genaro, 2006):
(and solid phase)
New Motivation:
Carbonatic Oil Reservoirs
Brazilian Pre-Salt Reservoirs(ultra-deep waters reservoir):
● Reservoir and cap rocks integrity(geomechanical and chemical)
● Reservoir properties(coupled HMC phenomena)
● CO2 injection(multiphase multispecies modeling)
Tupi Reservoir
CO2 underground geological storage:
Carbonate reservoirs: new deformational mechanisms can take place in the medium
Rock-fluidchemical
interactions
WaterweakeningChemo-mechanical
mechanism
CO2 underground geological storage:
Carbonate reservoirs: new deformational mechanisms can take place in the medium
WaterweakeningChemo-mechanical
mechanism
CO2 + H2O = HCO3- + H+
(water acidification)
CaCO3(s) + H+ = Ca2+ + HCO3-
(calcite dissolution)
How can the geological CO2 storage be done?
CO2 Storage in Geological Formations
Oil fields1- Depleted reservoirs (gas/oil)2- Enhanced oil recovery
Saline Aquifers;3- Deep unused saline water-saturated reservoir rocks.
Coal layers.4- Deep Unmineable coal5- ECBM Recovery
IPCC (2005)
How does CO2 behave when injected into geological formations?
Supercritical CO2(gas as a liquid density)
More reactive: Exhibit thepropensity to dissolve materials
CO2 Storage in Geological Formations
What can happen in porous media following CO2 injection?
CO2(g)
? ?
Fluid flow due to natural hydraulicgradientes andinjectionprocess;
Buoyancy causedby the densitydifferencesbetween CO2 and theformation fluid;
Diffusion, dispersion andfingering causedby constrastbetween CO2 injected andformation fluids;
Dissolution intothe formationfluid and porousmedia
Precipitation/ mineralizationinto the porousmedia
Pore spacetrapping
Adsorption ofCO2 onto organicmaterial
Others
Main mechanisms to storage CO2 into geological formations PhysicalChemical
CO2 Storage in Geological Formations
What can happen in porous media following CO2 injection?
234
1. CO2(g)
2. CO2(aq)
3. CO2(aq) + H2O(l)↔ H2CO3(aq)
4. H2CO3(aq) ↔ HCO3−
(aq) + H+(aq)
1
Dissolution of porous mediaabsorbedreactionized
CO2 Storage in Geological Formations
234 1
Dissolution of porous media
1. CO2(g)
2. CO2(aq)
3. CO2(aq) + H2O(l) ↔ H2CO3(aq)
4. H2CO3(aq) ↔ HCO3−
(aq) + H+(aq)
What can happen in porous media following CO2 injection?
5
absorbedreactionizedSolid phaseliquid phase
CO2 Storage in Geological Formations
5. CaCO3 (s)+ H+(aq) ↔ HCO3
−(aq)+ Ca2+
(aq)
What can happen in porous media following CO2 injection?
234
1. CO2(g)
2. CO2(aq)
3. CO2(aq) + H2O(l) ↔ H2CO3(aq)
4. H2CO3(aq) ↔ HCO3−
(aq) + H+(aq)
5. HCO3−
(aq)+ Ca2+(aq)↔ CaCO3 (s)+ H+
(aq)
5 1
Precipitation and mineralization into theporous media
absorbedreactionizedSolid phaseLiquid phase
CO2 Storage in Geological Formations
Efectiveness geological storage depends on a combination ofPhysical (hydrodinamic, structural and stratigrafic) and Geochemical processes
What can happen in porous media following CO2 injection?
Structural & stratigraphic trapping
Residual CO2 trapping
Solubility trapping
Mineral trapping
Capillarity
Under a layer withlow permeability
CO2 Storage in Geological Formations
Randhol & Larsen, 2010(SINTEF Petroleum Research)
III International Seminar on Oilfield Water Management
Challenges: quantify changes of porosity and permeability due to precipitation.
Distributed precipitation
Changes in Porosity andPermeability
The permeability is greatlyaffected, not porosity.
The only way to solve this problem is by perfomingexperiments
Precipitation locatedFormation of disconnected porous
CO2 Storage in Geological Formations
Coupled THM and Reactive Transport Problem
The species are:
• mineral (-) : main mineral
• water (w) : as liquid or evaporated in the gas phase
• air (a) : dry air, as gas or dissolved in theliquid phase
• chemical species : interacting (reactive) species
The three phases are:
• gas (g) : mixture of dry air and water vapour
• liquid (l) : water + air dissolved + dissolved chemical species
• solid (s) : main mineral + absorbed cations + precipitated mineralsSOLID
GAS LIQUID
Multiphase multispecies approach
Reactive transport equations
),...,1()( NiRcSt iiiww j
Chemical reactionsTotal Flow:
uDqj iwwiwwiwi cScc
Advective Non-advective(dispersion and diffusion)
Solid velocity
),...,1()( NiRcSt iiiww j
CHEMICAL INTERACTION OF N INTERACTING SPECIES
● Slow reactions: kinetics controlled
● Fast reactions: equilibrium controlled
PHENOMENA CONSIDERED● Homogeneous reactions
• Aqueous complex formation• Acid/base reactions• Oxidation/reduction reactions
● Heterogeneous reactions• Cation exchange • Dissolution/precipitation of minerals (equilibrium and kinetics)
● Other reactions• Radioactive decay• Linear sorption
Reactive transport equations
),...,1()( NiRcSt iiill j
CHEMICAL INTERACTION OF N INTERACTING SPECIES
Fast reactions: equilibrium controlled● A chemical equilibrium model is uses
based on the minimization of Gibbs free energy
xc
xi
cj
N
i
xi
xi
N
j
cj
cj
nnnnGminimize
11,
Slow reactions: kinetics controlled● Rate of species production in kinetics-
controlled reactions
Newton-Raphson algorithm Lagrange multipliers to incorporate the
restrictions of the system
),...,1(1
c
N
i
xiij
cj
Uj Njnnn
x
),...,1(0 ccj Njn
),...,1(0 xxi Nin
nrpmmllm kASr 1
c
mj
N
j
vjm
m
mp aQ
KQ
1
;
15.29811exp25 TR
Ekk am
Reactive transport equations
=
… …Mechanical problem:
Reactive transport problem:
local global
j
ii U
cEquation
Transportc
… …
0b
NUMERICAL IMPLEMENTATION
( ) 0 ( 1,..., )irrevl l j l j l l j l l j j cS U Ua Ua S U R j N
t
q D u
NEWTON-RAPHSON● Reactive Transport Equations
● Analogy with the mechanical problem
● Tangent matrix
,j
k k
Ua XU U
0bσ
Iσσ fp'
Specific for each geomaterial
dσ' D dε
Mechanical problem for geomaterials:
Equilibrium Equation:
Principle of Effective Stresses:
Stress-strain relationship:
+ L·dPc + H·dXd
New mechanisms!!!
HM-C Couplings
HYDRO-MECHANICAL COUPLINGS:
Rock porosity:
Rock permeability:
0.11 usst
u
tdtd
dt
ddt
ddtd vs
s
11
(mass conservation of solids)
(material derivative )
(changes of porosity as
a function of volumetric strains)
ib expikk
HM-C Couplings
HYDRO-MECHANICAL COUPLINGS:
Rock porosity:
Rock permeability:
0.11 usst
u
tdtd
dt
ddt
ddtd vs
s
11
(mass conservation of solids)
(material derivative )
ib expikk
HM-C Couplings
Chemical coupling:Porosity will change also due to mineral dissolution/precipitation!!!!! (new term in mass conservation equation)
f
+ dissolution/precipitation term
HM-C Couplings
Changes of porosity due to mineral dissolution/precipitation:
DtDv
DtD
DtD Ts
s
u)1()1(
chemical changes of porosity
mc
mv
cvv
m
m
mmmT
mineral of rock) of (mol/mion concentrat:
mineral of /mol)(m memolar volu:
volumemineral total
3
3
)problems chemical and thermical,mechanical()( kk
Intrinsic permeability changes:
Numerical implementation (Compiler: Intel Fortran; IDE: CodeBlocks; OS: Linux)
Numerical approach Finite elements in space
Finite differences in time
Implicit time integration
Simultaneous solution of the mechanical, hydraulic, thermal and reactive transport equations
Full Newton-Raphson for iterative procedure to solve the set of nonlinear equations
Solver (non-symmetric matrix)• LU decomposition and backsubstitution
• Conjugate Gradient Squared Method with block diagonal preconditioning
• PARDISO (MKL)
Convergence tolerances in terms of variable corrections and residuals
Coupled to a reactive transport module
Main features Coupled thermo-hydro-mechanical-
chemical (THMC) analyses in 1, 2 and 3 dimensions
Partial analyses are possible
General treatment of transport processes
Specific consideration of unsaturated porous media under non-isothermal conditions:
• Constitutive laws (thermal, hydraulic, mechanical)
• 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
Numerical implementation (Compiler: Intel Fortran; IDE: CodeBlocks; OS: Linux)
Numerical approach Finite elements in space
Finite differences in time
Implicit time integration
Simultaneous solution of the mechanical, hydraulic, thermal and reactive transport equations
Full Newton-Raphson for iterative procedure to solve the set of nonlinear equations
Solver (non-symmetric matrix)• LU decomposition and backsubstitution
• Conjugate Gradient Squared Method with block diagonal preconditioning
• PARDISO (MKL)
Convergence tolerances in terms of variable corrections and residuals
Coupled to a reactive transport module
Main features Coupled thermo-hydro-mechanical-
chemical (THMC) analyses in 1, 2 and 3 dimensions
Partial analyses are possible
General treatment of transport processes
Specific consideration of unsaturated porous media under non-isothermal conditions:
• Constitutive laws (thermal, hydraulic, mechanical)
• 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.