introduction to reservoir geomechanics
TRANSCRIPT
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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.
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
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Earth Sciences and Engineering:
Problems Scales
micro lab
wellbore reservoir
basin
Earth
Reservoir Geomechnics
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micro lab
wellbore reservoir
basin
Earth
Reservoir Geomechnics
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micro lab
wellbore reservoir
basin
Earth
Reservoir Geomechnics
GeophysicsStructural GeologyReservoir Engineering
Geomechanics(mechanics of deformable porous media): integrating data from different scales…
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Underground stresses
Normally, an underground formation has to carry the weight of the overlying formations.
The vertical stress at the bottom of a homogeneous column of height z is:
σv = ρgz
where ρ is the density of the material and g is the acceleration of gravity.
If the density varies with depth, the vertical stress at depth D becomes:
The average density of sediments in the overburden is between 1.8 and 2.2 g/cm3, so as a rough number, the vertical stress increases downwards with about 20 MPa/km (typically 1 psi/ft).
Note: )()1( oowws SS
Off-shore
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The sedimentary rocks encountered during oil well drilling and production are porous and hence contain fluids. One refers to the pore pressure at depth D as normal if it is given by the weight of a fluid column above, the normal pore pressure pfn is
The pore fluid density in case of brine with sea water salinity is in the range 1.03–1.07 g/cm3, so the pore pressure increase with depth is roughly 10 MPa/km (0.45 psi/ft).
The effective vertical stress, σ’v, is then also increasing with approximately 10 MPa/km.In many important cases, however, the pore pressure deviates from the normal value pfn(abnormal pore pressures).
Effective stress tensor:
Fluid Pressure
σ’ =
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Underground stresses
L. Cabral (MSc, 2007)
Vertical stress - Integration of density values (obtained from the density profiles); r(z) -Specific weight along the depth.Pore Pressure - Direct measurement ; Bottom well pressure transducers
Density Profile Sonic Profile
DensityPressure
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Fluid Pressure
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Fluid Pressure
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Fluid Pressure
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Fluid Pressure
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Underground stresses
Horizontal Stress:
K’ (lateral earth stress coefficient) may vary significantly.
At shallow depths (0–150 m) it may vary from 1 to 10 or even higher.
At larger depths it may vary from 0.2 to 1.5.
Chemical compaction increases in importance at depths below 2–3 km (Bjørlykke and Høeg, 1997). It will contribute to horizontal stresses by altering the trend seen from pure mechanical compaction above this level.
It has been suggested that, with time, K’ → 1 , so that the stress state becomes hydro-static (Heim’s rule) due to creep (very slow process).
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Underground stresses
Models for estimating the in situ stress states:
Formation laterally constrained ( )rock behaves according to the theory of linear elasticity:
There are many reasons to apply the relationship above with great care...
(lateral stress coefficient at rest, K’=K0)
In a fluid, where νfr = 1/2, K0 = 1. For a rock with νfr = 1/3, K0 = 1/2
Stress history analysis must be performed (Warpinski, 1989), incorporating variations in mechanical properties over time:
Consolidation, diagenesis, changes in pore pressure due to gas generation, temperature gradients, and various tectonic and thermal episodes.
Viscoelasticity appeared to be more relevant for stresses in shale than in sandstone (Warpinski, 1989).
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Underground stresses
Models for estimating the in situ stress states:
Rock at failure: reasonable assumption in areas of active tectonics.
Mohr-Coulomb:
Assuming coesion=0:
If the friction angle is 30°, then K’ = 1/3. A lower friction angle will result in a higher value for K’.
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Relevant information from the faults: relative magnitude of principal stresses.
Faults and the stress state: Brittle behaviour leading to fault formation is characteristic of rocks subjected to low confining pressure, i.e. in some respect close to the surface of the Earth.
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Relevant information from the faults: relative magnitude of principal stresses.
Anderson, E. M. (1951):Fracturing will take place in one or both pairs of conjugate planes which are parallel to the direction of the intermediate principal stress, and are both at equal angles (ψ ) of less than 45° to the direction of the maximum principal stress.
Mohr-Coulumb Criteria (shear failure):
Faults and the stress state: Brittle behaviour leading to fault formation is characteristic of rocks subjected to low confining pressure, i.e. in some respect close to the surface of the Earth.
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Stress PolygonMohr-Coulomb Failure Surface
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Underground stresses
CONCLUSION: These are very simple examples of models for horizontal stress estimation. In reality, horizontal stresses are difficult to assess from mathematical models.The most direct method of obtaining horizontal stress is to measure it, for instance by a fracturing test of the formation.
Example: Gulf Coast Curve
Vertical stresswith density 2.1 g/cm3
Horizontalstress
pore pressurewith fluid density 1.05 g/cm3
“Gulf Coast Curve”
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Underground stresses
It is very common (and convenient) in the oil industry.
Assumptions:
- Three mutually orthogonal principal stresses, plus the pore pressure
- Vertical stress is a principal stress, governed by gravity, pointing towards the centre of the Earth.
Reasonable at large depth within a homogeneous Earth, in areas that have NOT been exposed to tectonic activity or are relaxed in the sense that there are no remnant stresses from previous tectonic activity.
Simple Stress Fields Complex Stress Fields
Be aware that there will be cases when this is not fulfilled, such as:
- Near the surface: Because the surface is stress free, the principal stress directions at and near it will be governed by the surface topography. In the case of a strongly sloping surface, evenat depth, the principal stress directions may be far from the vertical-horizontal directions.
- Near heterogeneities such as inclusions or faults, near underground openings such asboreholes, or near depleting reservoirs, principal stress directions will differ from the vertical–horizontal orientation.
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Leak-off test: obtainig the minimum principal stress (Smin)
LOP (leak-off point)
FBP (fracture breakdown pressure)
FPP (fracture propagation pressure)
ISIP (instantaneous shut-in pressure)
FCP (fracture closure pressure)
“the only practical and reliable”
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(Source: The Old Speak Journal, 2011)
Contamination of an aquifer caused by hydraulic fracturing
Enviromental Geomechanics:Geomechnics is often dealing with enviromental problems
Shale gas
Overpressure in
the reservoir due to fluid
injection (water, CO2,...)
Faults
Discontinuities in Reservoir Geomechanics
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• Hydraulic Fracturing: a subject of great interest of the oil industry• The Interaction between rock’s
mechanical properties, in-situstresses, and heterogeneitiessuch as natural fracturesinfluence the induced fracture.
Discontinuities in Reservoir Geomechanics
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Finite Element with Embedded Discontinuity
Mechanical Problem Hydraulic Problem
Strong Discontinuity Approach
t
S
n
u
t
e
The discontinuity path is placed insidethe elements irrespective of the sizeand specific orientation.
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Finite element with high aspect ratio
Weak/strong discontinuity kinematics
Same kinematics !!!
MANZOLI et al, 2012
Strong Discontinuity Approach
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Initial Finite Element mesh
Interface Elements
Interface finite elements are inserted throughout the mesh or in the mostrequested area of the mesh. Depending on the boundary conditions of theproblem and stress states resulting, the elements will be opening by apreferential path, forming a fracture and relaxing the stress in other candidateelements at the same time.
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Initial Finite Element mesh Interface Finite Elements
Interface finite elements are inserted throughout the mesh or in the mostrequested area of the mesh. Depending on the boundary conditions of theproblem and stress states resulting, the elements will be opening by apreferential path, forming a fracture and relaxing the stress in other candidateelements at the same time.
Interface Elements
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Interface Finite Elements
Fractures formation
Interface Elements
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Tensile damage model (mode I)
CONSTITUTIVE MODEL
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Constitutive relation
Damage criterion
Evolution law for the strain-type variable
Damage evolution
Softening lawFracture Energy
TENSILE DAMAGE MODEL
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NUMERICAL SIMULATION OF THE LEAK-OFF TEST
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tHhb fp ''3
EXAMPLE 1
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MPaH 5'
MPah 3'
skgQ /105 6
MPaft 1
EXAMPLE 1
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tHhb fp ''3
EXAMPLE 1
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Damage
EXAMPLE 1
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Fractureaperture
EXAMPLE 1
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64
QNode 34
σy = 1MPA
σx
Q=6x10-5kg/sσv=1MPaσx=2MPa
tensile strength of fracture material : (σy )=5 MPa
σy
► Hydro Mechanical application – Leakoff test
EXAMPLE 2
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EXAMPLE 2
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Strong Discontinuity Approach Interface Finite Element
Nodes 1595 10256Elements 2993 20162CPU time (s) 1210.51 6289.43
EXAMPLE 2
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NATURAL FRACTURES
Geomechanics of Fracturated Reservoirs
Much morecomplex behavior
of fractures...
?
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Improvement of constitutive of interface elements
Up to now: isotropic tensile damage model (mode I)
Improvements: shear modes (II and III) and inelastic effects due to dilatancy and compression
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• Coupled hydro-mechanical analysis of hydraulic fracturing consideringinfluence of rock and natural fracture properties, in-situ stresses andoperational conditions on the induced fracture trajectory.
interaction between natural and induced fractures
NATURAL FRACTURES
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1MPa
1MPa
Injection point
1.5MPa
1MPa
Injection point
NATURAL FRACTURES
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BREAKOUTS
A breakout is the evidence of wall yield (the formation strength at the borehole wall is exceeded). A breakout is not considered to be a borehole failure since the borehole remains useful. Borehole breakout can be measuredusing four- or six-arm caliper tools. The preferred tool, however, is the ultrasonic imaging tool, which makes up to 200-caliper measurements at every depth level.
L. C. Pereira (MSc, 2007)
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Geomechanics problem: elasto-plasticity Mohr-Coulomb
Drucker-Prager
F( ) ( ) 0tan
cJ p g
σ,κF( ) ( ) 0tan
cJ p g
σ,κsen( ) sen( )sencos( )
3
g
sen( ) sen( )sencos( )3
g
F( , ) 0tan JP
cJ p M
σ kF( , ) 0tan JP
cJ p M
σ k 30 2 3sen3 senJPM
30 2 3sen3 senJPM
BREAKOUTS
R. Sousa (MSc, 2004)
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Hardening/Softening Law
Linear Hardening
Perfect Plasticity
Linear Softening
Coesão Ângulo de Atrito
BREAKOUTS
Brittle rock
R. Sousa (MSc, 2004)
cohesion friction angle
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SIMULATION
Engineering Problem Horizontal well perforation Anisotropic and
bidimensional boundary conditions Adopted a finite element
excavation method (Brown e Booker, 1985) on 2D analysis
wpg
v
BREAKOUTS
K<1:
Vertical stress > Horizontal stress
R. Sousa (MSc, 2004)
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Shear Plastic Strains
BREAKOUTS
R. Sousa (MSc, 2004)
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Breakout
Imagem ultrasônica de perfil de poço apresentando breakout na
direção da tensão principal menor no plano normal ao poço
(Soliman e Boonen, 2000)
BREAKOUTS
R. Sousa (MSc, 2004)
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Results for Mohr-Coulomb Model with softening
BREAKOUTS
R. Sousa (MSc, 2004)
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Total Vertical Stress Redistribution
BREAKOUTS
R. Sousa (MSc, 2004)
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Impact on permeability and pressure distributions
BREAKOUTS
R. Sousa (MSc, 2004)
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INPUTS OF A GEOMECHANICAL MODEL (SUMMARY)
In situ stress field:
Vertical stress
Pore pressure
Minimum horizontal stress:-magnitude-direction
Maximum horizontal stress:-magnitude-direction
L. C. Pereira (MSc, 2007)
Density profile
Direct measurement (RTF, TRF)
Water hydrostatics
Hydraulic fracturing (LOT, XLOT)
Image profile
Retro-analysis
Image profile
ߪ = න ݖ ݖ.
ఙᇱ =0ܭఙᇲ௩
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INPUTS OF A GEOMECHANICAL MODEL (SUMMARY)
Rock parameters:
L. Cabral (MSc, 2007)
Deformability and strength parameters:
Elastic Modulus (E) and Poisson's ratio (n):
Sonic profile + Elasticity theory
Cohesion (c):
Samples or sonic profile + UCS correlation = f(tc)
Friction angle (f):
Literature
Equation:E and n = f(Vp and Vs)
= 30° (sandstone)= 20° (shale)
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RESERVOIR COMPACTION
(subsidence)
(compaction)
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RESERVOIR COMPACTION
Valhall Field - North Sea(SPE 83957, 2003)
L. C. Pereira (MSc, 2007)
carbonate reservoir with high porosity (between 42 and 50%)
1982 - beginning of production
1985 - first signs of subsidence
2003 - start of injection
2003 - accumulated subsidence of 4.9m at a rate of 25cm / year
compaction account for 50% of total recovery
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RESERVOIR COMPACTION
Ekofisk Field - North Sea(SPE 56426, 1999)
1971 - beginning of production
1984- first signs of subsidence
1987 - start of injection
Compaction causes:- Reservoir depletion- Waterweakening: incompatibility between carbonate rock and injected water
L. C. Pereira (MSc, 2007)
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Water induced reservoir compaction
1973
1984
Ekofisk oilfield
Start water flood
Subsidence
Reservoir pressure
Ekofisk 2/4 tank(from Hermansen et al., 2000)
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1973
1984
Start water flood
Ekofisk 2/4 tank(from Hermansen et al., 2000)
Secondary recovery:based on the effective stresses
concept, the resorvoir should expandwith injection!!
Primary recovery:compaction
explainedby the
effective stress principle
OK! ?Possible explanation:
water weakeningmechanism
(compactionunder injection)
Water induced reservoir compaction
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Capillary pressure as a new state variable for the rock stress-strain behavior
Water weakening
Water induced reservoir compaction
Destruction ofIntergranular links
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Chemo-mechanical Mechanism (ex: mineral dissolution)
Water weakening
Water induced reservoir compaction
Destruction ofIntergranular links
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Capillary pressure as a new state variable for the rock stress-strain behavior
Mineral dissolution and precipitation as chemo-mechanical
mechanism
Water weakening
Water induced reservoir compaction
Destruction ofIntergranular links
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Water induced reservoir compaction
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Chemical Mechanism
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RESERVOIR COMPACTION
Environmental damages in regional scale:
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RESERVOIR COMPACTION
Environmental damages in regional scale:
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RESERVOIR COMPACTION
Cap rock integrity during depletion:
Fault regimes induced by reservoir compaction:NF – Normal faultsRF – Reverse faultsThe upper part of the reservoir tends to move downwards while the lower part moves upwards
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RESERVOIR COMPACTION
and other consequences…
a good one!
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RESERVOIR COMPACTION
Hydraulic problem: two phase flow equations for deformable porous media
where:
owsqt
s, 0
)(
u
gpkkq r ~
s
u
q
g~
rkk
p
1 osws woc ppp
rk
cp
porosityfluid saturationfluid densityDarcy flowphase viscositySolid velocity
permeability tensorfluid relative permeabilityfluid mobilityFluid pressurecapillary pressuregravity
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RESERVOIR COMPACTION
Specific for each geomaterial
Mechanical problem for geomaterials:
Equilibrium Equation:
Principle of Effective Stresses:
Stress-strain relationship:
0bσ
Iσσ fp'
dσ' D dε
![Page 70: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/70.jpg)
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 FORMULATION
Other: Kozeny-Carman
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RESERVOIR COMPACTION
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02
vw
w
ww
w
wwDt
D εgKK
(Eq.7) Mass balance Final Equation
Volumetric strain in mass balance equations:
Compaction-driven mechanism
vss Dt
DDtD ε)1()1(
Pressure maintenance
Porositydecrease
qv
Increase of fluidflow apparent velocity
RESERVOIR COMPACTION
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SECONDARY OIL RECOVERY: WATER INJECTION
Sensitivity analysis of reservoir compaction parameters:
Elastic and Elasto-plastic (with CAP) reservoir
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Sensitivity analysis on cummulative oil production:
Fixed
Variable
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Sensitivity analysis of reservoir compaction parameters:
Injection
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Sensitivity analysis of reservoir compaction parameters:
Injection
Irreversible compaction
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Sensitivity analysis of reservoir compaction parameters:
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Sensitivity analysis of reservoir compaction parameters:Compaction-driven mechanism
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Sensitivity analysis of reservoir compaction parameters:
Elastic:
E
Poisson
Biot
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Sensitivity analysis of reservoir compaction parameters:
Elasto-plastic:
Coesion
Poisson
Biot
E
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Real case:
HT/HP reservoir
(Pereira, 2007)
L. C. Pereira (MSc, 2007)
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RESERVOIR COMPACTION
Real case:
L. C. Pereira (MSc, 2007)
DisplacementPlastic strains
![Page 83: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/83.jpg)
Is it correct to use in conventional reservoirsimulation Permeability as a function of Pressure?? K(P)?
It depends!! More critical close to wellbores.
Points at elastic regions
Points at elasto-plastic (compaction and dilation) regions
Permeability and pressure correlation in a coupled geomechanicalsimulation
Permeability and pressure correlation
RESERVOIR COMPACTION
L. C. Pereira (MSc, 2007)
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FAULT REACTIVATION
Why it is important to study fault reactivation?
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FAULT REACTIVATION
Why it is important to study fault reactivation?
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FAULT REACTIVATION
Why it is important to study fault reactivation?
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FAULT REACTIVATION
Why it is important to study fault reactivation?
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FAULT REACTIVATION
How to represent them properly?
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FAULT REACTIVATION
Criteria to define the maximum injection pressure:
Mohr-Coulomb
c
φ
' ' . tan 'n nc
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FAULT REACTIVATION
Mohr-Coulomb Total plastic work
c
φ
' ' . tan 'n nc
0
Pf
c Y pW d
cW
p
Criteria to define the maximum injection pressure:
Analytical analysis or FEM analysis only FEM analysis
![Page 91: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/91.jpg)
Oil Reservoir crossed by a fault
Example: Fault Reactivation Problem
![Page 92: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/92.jpg)
MPav 200
)( vh f
In situ stresses (estimated)Oil Reservoir crossed by a fault
MPaPf 100
Example: Fault Reactivation Problem
![Page 93: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/93.jpg)
MPav 200
)( vh f
In situ stresses (estimated)Oil Reservoir crossed by a fault
MPaPf 100
Mpac 818
Fault Properties:
Friction angle
Cohesion
Example: Fault Reactivation Problem
![Page 94: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/94.jpg)
MPav 200
)( vh f
In situ stresses (estimated)Oil Reservoir crossed by a fault
MPaPf 100
Mpac 818
Fault Properties:
Friction angle
Cohesion
Horizontal stress ratio4.00 k
Biot’s coefficient9.0Biot
Example: Fault Reactivation Problem
![Page 95: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/95.jpg)
MPav 200
)( vh f
In situ stresses (estimated)Oil Reservoir crossed by a fault
MPaPf 100
v 1
fBiot P 1'1
MPa110'1
'10
'3 k
MPa44'3
Mpac 818
Fault Properties:
Friction angle
Cohesion
Principal effective stresses
Horizontal stress ratio4.00 k
Biot’s coefficient9.0Biot
Example: Fault Reactivation Problem
![Page 96: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/96.jpg)
c
''3 '
1
sencF )(cos2 '3
'1
'3
'1
Mohr–Coulomb failure criteria(Potts e Zdravkovic, 1999
How much can the fluid pressure be increased??
Example: Fault Reactivation Problem
![Page 97: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/97.jpg)
'1 fail
Example: Fault Reactivation Problem
c
'P'1
sencF )(cos2 '3
'1
'3
'1
Mohr–Coulomb failure criteria(Potts e Zdravkovic, 1999)
How much can the fluid pressure be increased??
![Page 98: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/98.jpg)
'10
'3 k
'1 fail
Example: Fault Reactivation Problem
c
'P'1
Supposing:
sencF )(cos2 '3
'1
'3
'1
Mohr–Coulomb failure criteria(Potts e Zdravkovic, 1999)
How much can the fluid pressure be increased??
![Page 99: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/99.jpg)
'10
'3 k
'1 fail
0)(cos2 '10
'1
'10
'1 senkck
Example: Fault Reactivation Problem
c
'P'1
Supposing:
From failure criteria:
sencF )(cos2 '3
'1
'3
'1
Mohr–Coulomb failure criteria(Potts e Zdravkovic, 1999)
How much can the fluid pressure be increased??
![Page 100: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/100.jpg)
'10
'3 k
MPaMpac fail
9,90818 '
1
'1 fail
0)(cos2 '10
'1
'10
'1 senkck
Example: Fault Reactivation Problem
c
'P'1
Supposing:
From failure criteria:
sencF )(cos2 '3
'1
'3
'1
Mohr–Coulomb failure criteria(Potts e Zdravkovic, 1999)
How much can the fluid pressure be increased??
From the fault propeties:
![Page 101: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/101.jpg)
'10
'3 k
MPaMpac fail
9,90818 '
1
'1 fail
0)(cos2 '10
'1
'10
'1 senkck
Example: Fault Reactivation Problem
c
'P'1
)(1'1 PPfBiotfail
Supposing:
From failure criteria:
sencF )(cos2 '3
'1
'3
'1
Mohr–Coulomb failure criteria(Potts e Zdravkovic, 1999)
How much can the fluid pressure be increased??
From the fault propeties:
![Page 102: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/102.jpg)
'10
'3 k
MPaMpac fail
9,90818 '
1
'1 fail
0)(cos2 '10
'1
'10
'1 senkck
Example: Fault Reactivation Problem
c
'P'1
)(1'1 PPfBiotfail
Supposing:
From failure criteria:
sencF )(cos2 '3
'1
'3
'1
Mohr–Coulomb failure criteria(Potts e Zdravkovic, 1999)
How much can the fluid pressure be increased??
From the fault propeties:
remains constant
![Page 103: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/103.jpg)
'10
'3 k
MPaMpac fail
9,90818 '
1
'1 fail
MPaP 2,21
0)(cos2 '10
'1
'10
'1 senkck
Example: Fault Reactivation Problem
c
'P'1
)(1'1 PPfBiotfail
Supposing:
From failure criteria:
sencF )(cos2 '3
'1
'3
'1
Mohr–Coulomb failure criteria(Potts e Zdravkovic, 1999)
How much can the fluid pressure be increased??
From the fault propeties:
remains constant
![Page 104: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/104.jpg)
FAULT REACTIVATION MECHANISM
Producer (BHP=5MPa) Injector (BHP=35MPa)
Distribution of fluid pressure before fault reactivation
Well starting:
new pf distribution
new effective stress state:
Iσσ fp'
![Page 105: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/105.jpg)
FAULT REACTIVATION MECHANISM
Injector (BHP=5MPa) Producer (BHP=35MPa)
0bσ
Iσσ fp'
dσ' D dε
![Page 106: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/106.jpg)
FAULT REACTIVATION MECHANISM
Injector (BHP=5MPa) Producer (BHP=35MPa)
deformable porousrock compressibility media (geomechanics)
11s v
s
d dddt dt dt
ib expikk
Shear stresses
Dilatancy:
(more permeable medium)
![Page 107: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/107.jpg)
FAULT REACTIVATION MECHANISM
Injector (BHP=5MPa) Producer (BHP=35MPa)
gk
pkq r
dilatancy:
exp ib ik k
Fault reactivation:becomes permeable
![Page 108: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/108.jpg)
FAULT REACTIVATION MECHANISM
Injector (BHP=5MPa) Producer (BHP=35MPa)
gk
pkq r
Evolution of fluid pressure:
dilatancy:
exp ib ik k
Evolution of shear plastic strain in the fault:
![Page 109: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/109.jpg)
FAULT REACTIVATION MECHANISM
gk
pkq r
dilatancy:
exp ib ik k RESERVOIRCOMPACTION
LINKED PHENOMENA!
![Page 110: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/110.jpg)
Influence of a number of factors:
► Base 2D Case and sensitivity analysis.Influence of constitutive laws: evolution of permeability;
fluid compressibility.
► Influence of geometry: 3D modeling ;faults and wells interactions.
► Caprock integrity: hydraulic fracturing.
FAULT REACTIVATION
![Page 111: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/111.jpg)
Seismic image
FAULT REACTIVATIONPetroleum Engineering
In oil reservoirs with fault reactivationpossibility, definition of maximum bottomhole pressure of the injectors duringwaterflooding can only be safely conductedbased on a coupled hydro-geomechanicalanalysis tool with realist modeling of theconstitutive behavior of the materials.
MAXIMUM BHP?
G.S.C. (Geological Survey of Canada) (2009) Lithoprobe Seismic and Magnetotelluric Data Archive Geoscience Data Repository. (htpp://gsc.nrcan.gc.ca).
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FAULT REACTIVATIONPetroleum Engineering
In oil reservoirs with fault reactivationpossibility, definition of maximum bottomhole pressure of the injectors duringwaterflooding can only be safely conductedbased on a coupled hydro-geomechanicalanalysis tool with realist modeling of theconstitutive behavior of the materials.
MAXIMUM BHP?
![Page 113: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/113.jpg)
Finite Element Analysis of Fault Reactivation:
![Page 114: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/114.jpg)
MOHR COULOMB
![Page 115: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/115.jpg)
MOHR COULOMB
![Page 116: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/116.jpg)
PETROBRAS-UFPE Project:‘Coupled Hydro-geomechanics simulation of fault reactivation’
Researchers:UFPE: Leonardo Guimarães, Igor Gomes, Nayra Vicente, Renato de AlmeidaPETROBRAS: Leonardo Cabral
Other aspects studied:
► Influence of initial stressstate (stress anisotropy).
► Uncertainty analysisof fault parameters.
► Fault with differentlayers of materials.
Zona de dano 1
Zona de dano 2
Núcleo
Zona de dano 2
Zona de dano 1
FAULT REACTIVATION
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PETROBRAS-UFPE Project:‘Coupled Hydro-geomechanics simulation of fault reactivation’
FAULT REACTIVATION
Nuestro Colciencias
![Page 118: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/118.jpg)
(Mitchell and Faulkner, 2009)
(no subdivided) (subdivided)
Numerical Hydro-Mechanical Modelling of Fault Reactivation Composed byDifferent Zones – Fault Core and Damage Zones.
Geological fault reactivation
considering damage zones
![Page 119: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/119.jpg)
Numerical Study of the Influence of Filling Material Stiffness on the FaultReactivation Mechanism.
(Constantin et al, 2004)
Geological fault reactivation
considering damage zones
![Page 120: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/120.jpg)
Coupled Hydro-mechanical Modelling of the Permeability Change of SealingFaults in Oilfield Exploitation.
-HM modeling;-HMC modeling: filling material dissolution.
(Mitchell and Faulkner, 2009)
Geological fault reactivation
considering damage zones
![Page 121: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/121.jpg)
(no subdivided)
RESULTS
Injector well Producer wellReservoir
Reservoir Reservoir
Salt-2250 m
-306 m
-1439 m
Seabed level
33044 nodes65877 elements
CoreInternal damage zone
External damage zone
![Page 122: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/122.jpg)
(no subdivided)
RESULTS
33044 nodes65877 elements
CoreInternal damage zone
External damage zone
Material PropertiesFault elements Young Modulus
(MPa)Coesion (MPa) Friction Angle
(°)Permeability (m²)
External damage zone
7000 3.25 23 5x10-21 m²
Internal damage zone 6000 2.5 23 5x10-20 m²
Core 8000 4.0 23 5x10-22 m²
![Page 123: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/123.jpg)
Parameters of Sensitivity :
-Coesion and friction angle;-Stifness;
-K0, Poison Ratio;-Shear plastic strain limit;
-Fluid compressibility;-Permeability;
-Anisotropy;-Mechanical constitutive model;
-Wellbore position;...
(no subdivided)
RESULTS
![Page 124: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/124.jpg)
RESULTS
(≈ 6 years)
(≈ 8 years)
(≈ 4 years)
(≈ 2 years)
Time (seconds)
Shear Plastic Strain
![Page 125: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/125.jpg)
(Mitchell and Faulkner, 2009)
(no subdivided) (subdivided)
RESULTS
![Page 126: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/126.jpg)
(Mitchell and Faulkner, 2009)
(no subdivided) (subdivided)
RESULTS
Time (seconds)
Pressure (Mpa)
![Page 127: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/127.jpg)
(Mitchell and Faulkner, 2009)
(no subdivided)
RESULTS
![Page 128: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/128.jpg)
(Mitchell and Faulkner, 2009)
RESULTS
Cap-rock integrity
![Page 129: Introduction to Reservoir Geomechanics](https://reader035.vdocuments.us/reader035/viewer/2022062523/613cb717a3339922f86ee5c1/html5/thumbnails/129.jpg)
Material PropertiesFault elements Young Modulus
(MPa)Coesion (MPa) Friction Angle
(°)Permeability (m²)
External damage zone
7000 2.7 23 5x10-21 m²
Internal damage zone 6000 2.5 23 5x10-20 m²
Core 8000 4.0 23 5x10-22 m²
RESULTS
3.25
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Material PropertiesFault elements Young Modulus
(MPa)Coesion (MPa) Friction Angle
(°)Permeability (m²)
External damage zone
7000 2.7 23 5x10-21 m²
Internal damage zone 6000 2.5 23 5x10-20 m²
Core 8000 4.0 23 5x10-22 m²
RESULTS
3.25
Maximum injection pressure ???