Methodologies and Robust Algorithms for Subsurface Simulators

Methodologies and Robust Algorithms
for Subsurface Simulators
April 27, 2016
Mary F. Wheeler
Acknowledge
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Andro Mikelic (U. of Lyon)
Thomas Wick (Ricam and Ecole Polytechnique)
Ben Ganis
Sanghyun Lee
Baehyun Min
Jing Ping
Gurpreet Singh
Ashwin Venkatraman
CSM Research Areas
§  CSM website: http://csm.ices.utexas.edu
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BIG DATA: Cross-cutting Initiative
Exascale Computing
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UT Strategic Partners
Center for Subsurface Modeling
Other Departments in UT
Director: Mary F. Wheeler
v  Faculty (6)
v  Graduate Students (11)
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Mary F. Wheeler
Todd Arbogast
Sanjay Srinivasan (Penn State U.)
Ivan Yotov (U. of Pittsburgh)
Andro Mikelic (U. of Lyon)
Thomas Wick (Ricam)
v  Research Associates (2)
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Ben Ganis
Gergina Pencheva
Tameem Almani
Yerlan Amanbek
Mohammed Reza Beygi
Saumik Dana
Recheng Dong
Mohammed Jammoul
Tea Mikelic
Morteza Naraghi
Azor Nwachukwu
Sogo Shiozawa
Deandra White
v  Postdoctoral Fellows (5)
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Sanghyun Lee
Baehyun Min
Jing Ping
Gurpreet Singh
Ashwin Venkatraman
v  Aerospace Engineering
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Laxminarayan Raja
Mark Mear
v  Bureau of Economic Geology
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Seyyed Hosseini
Susan Hovorka
Alexander Sun
v  Civil Engineering
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Chadi El Mohtar
v  Geosciences
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Mrinal Sen
v  Institute for Geophysics
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v  Staffs (2)
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Connie Baxter
Amy Manley
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Nick Hayman
v  Petroleum Engineering
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Matthew Balhoff
David DiCarlo
David Nicholas Espinoza
Collaborators
S. Barbeiro
H. Florez
M. Parashar
Z. Benjelloun-To
uimi, I. Faille
E. Gildin
J. Killough
T.F. Russell
T. Dewers
V. Girault
S. Sun
B. Dindoruk
R. Helmig
R. Tavakoli
H. van Duijn
K. Jordan
M. Vohralík
J. Eaton
K. Kumar
T. Wick
P. Eiseman
Y. Lee
G. Wittum
A.  Elsheikh
R. Liu
I. Yotov
A. Firoozabadi
A. Mikelić
D. Zhang
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Research Topics Covered
1. Engineering and Geophysical Applications
•  Accurate physics-based simulation for realistic porous media models
ü  CO2 storage and EOR
ü  Polymer and surfactant flooding and foam
ü  Geomechanics: domain decomposition (DD), elasticity, plasticity, and hydraulic fracturing
•  History matching and reservoir characterization
ü  Parameter estimation
ü  Verification & Validation
ü  Uncertainty quantification
2. Mathematical and Computational Modeling
•  Formulation & implementation of efficient & accurate parallel multiscale & multi-physics
algorithms based on
ü  Efficient solvers: multi-grid, multi-level multiscale preconditioners, non-linear acceleration
ü  Unstructured gridding and multipoint flux and mimetic methods
ü  Transport: DG, EG, CG post-processing
ü  Phase-field
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Research Initiative: Closed-loop Workflow
I. FLUID-DRIVEN
FRACTURE PROPAGATION
IV. UNCERTAINTY
QUANTIFICATION
II. PHASE & CHEMICAL
EQUILIBRIUM
III. SIMULATOR
DEVELOPMENT
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I. FLUID-DRIVEN FRACTURE PROPAGATION
Objectives
Develop a fracture propagation method (phase field)
driven by multiphysics, multiphase fluid flow
3-dimensional computations using mesh
adaptivity with coupling displacements,
phase field, and pressure system
In the phase field fracture propagation model,
primal-dual active set & fixed-stress
iteration is coupled to solve the whole system
Demonstrate the potential of the phase field
for treating practical engineering applications
by providing numerical examples
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Joining and branching of nonplanar hydraulic fractures
in
3D heterogeneous media.
Advantage of Phase Field Model
§  Classical theory of crack propagation [Griffith 1921]
§  Diffusive crack zones for free discontinuity problems
§  Γ-Convergent approximation [Ambrosio-Tortorelli 1992]
§  Variational methods based on energy minimization
-Marigo 1998], [Miehe et al. 2010]
Variation methods based energy minimization
[Real fractures]
[Interface approach]
[Diffusive approach using Phase field]
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[Francfort
Advantage of Phase Field Model
§  Fixed-topology approach avoiding re-meshing
§  Determine crack nucleation, propagation, and the path automatically
§  Simple to handle joining and branching of (multiple) cracks
§  Promising findings for future ideas as an indicator function
base
d on theory and numerical simulations
Before joining
After joining
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Branching
Governing System: Biot’s System
Biot’s system
Fracture with maximum pressure
•  Pressure Diffraction System
•  The pressure starts to decrease
when the fracture starts to propagate.
•  Mechanics and Phase Field
•  Linear Elasticity
•  Newton Iteration
(a) Phase Field
•  Primal-dual Active Set Method
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(b) Pressure
Numerical Examples of Phase Field
Multiple fractures propagating near the well bore
•  Fracture propagation
•  Pressure distribution
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Numerical Examples of Phase Field
3 parallel fractures in 3D domain
•  Not all fractures are growing because of the stress-shadowed effect.
Horizontal well
Fractures
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Numerical Examples of Phase Field
Multiple fractures propagating near the well bore
•  Dynamic mesh adaptivity: predictor-corrector method [Heister-Wheeler-Wick, 2014]
Heterogeneous Young’s Modulus
Fracture
Adaptive Mesh
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Numerical Examples of Phase Field
A fracture in layered media with different fracture toughness values
Fracture
= 1 Pa-m
Injection well
= 100 Pa-m
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II. GEOCHEMICAL REACTIONS
Objectives
Model geochemical reactions of injected CO2
in carbonate reservoirs during EOR or CO2 sequestration
In situ brines with reactive ionic species
Gas Phase
CO2, nC14,
& H 2O
Oleic Phase
CO2, nC14,
& H 2O
Study the effect of reactive species
on CO2 concentration
Aqueous Phase
Quantify the effect using changes in miscibilit
y conditions during CO2 EOR
CO2, CO32-, HCO3-, Ca2+, Cl-,
CaCO3, H+, OH-, & H2O
Solid Phase
CaCO3
[ Phase & Chemical Equilibrium of CO2 ]
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Coupling with a Compositional Simulator
Coupled phase and chemical equilibrium
•  Gibbs Free Energy Minimization
Gibbs free energy minimization
Phase behavior
Reactions
Stochiometric approach
•  Equation of State (EOS)
where rij : rate of change of component i in phase j due to chemical equilibrium
(rij = 0 if no reaction)
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Example: Effect of Reactions on CO2 Concentration
Concentration Profiles at Pavg = 2,200 psi after 0.12 hours of CO2 injection
•  Red curve
(
•  Black curve (
): concentration profiles with
equilibrium reactions
): concentration profiles without equilibrium reactions
•  Reactions in aqueous phase consume CO2 altering phase equilibrium and hence miscibil
ity conditions.
•  Higher in situ water saturation results in lower CO2 concentrations.
CO2 w/ reaction
CO2 w/o reaction
C14 w/ reaction
C14 w/o reaction
CO2 w/ reaction
CO2 w/o reaction
C14 w/ reaction
C14 w/o reaction
Sw = 0.3
Sw = 0.5
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III. SIMULATOR DEVELOPMENT
Objectives
Complete simulator development with numerical schemes f
or coupled processes
Develop computational methods for coupled p
rocesses based on multiscale discretization fo
r flow, geomechanics & geochemistry
Development of efficient
solvers & pre-conditioners
Model CO2 storage field sites
& perform compositional simulations
Cranfield site, Mississippi
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Framework of IPARS
§  IPARS (Integrated Parallel Accurate Reservoir Simulator)
Development of integrated
flow, geochemistry, and geomechanics framework
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Upscaling: Bridging Lab to Field
Upscale measured rock properties (fluid flow & geomechanics)
Objectives o scale relevant to field processes
t
Development of homogenization schemes c
ombining numerical and analytical approache
s, e.g. multiscale mortar method
Particular emphasis will be put on including n
atural fractures in effective properties and lo
calization effects
Obtain field scale constitutive parameters to p
erform coupled fluid flow and geomechanic
al numerical simulation
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⎧σ = C ε − αpc I
⎪
⎨
⎪⎩ϕ = pc / N + αε V
Model Field Sites
Objectives
Modeling, simulation & uncertainty analysis with application to CO2
storage sites (Cranfield, MS & Frio, TX)
Measure mechanical properties in laboratory
Site 1: Cranfield, MS
Collect other existing data
(seismic, well logs, etc.)
Measure impact of geochemical alteration on
mechanical properties
Study rock dissolution and its effect on weake
ning the rocks and creating leakage pathways
Enhanced simulation for studying and quantif
ying parameters, e.g. reservoir over pressure,
chemical and thermal loading
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Site 2: Frio, TX
Poro-plasticitiy
§  Geomechanical Effects of CO2 Injection with a Poro-plasticity Model
@(⇢(
Fluid Flow
1
0 + ↵"v + M (p
@t
Stress Equilibrium
@(⇢(
0
+ ↵"v + M1 (p
@t 00
Hooke’s Law
✓
p0)))
K
(rp ⇢grh)
q=0
µ
r · ( 00 + o ↵(p p0)I) + f = 0
+r· ⇢
◆
K
+ r · ⇢ (rp ⇢grh)
q=0
De : (" µ"p)
00
1 r · ( + o ↵(p p0)I) + f = 0
=
00
"˙ =
Plastic Strain Evolution
2
375581 [psi]
0.25
Druker-Prager Yield Surface
(ru + rT u)
= De : (" "p)
@F (" =00) 1 (ru + rT u)00
,2 at Y ( )
@ 00 00
@F ( )00
"˙p = "0,
˙p = at Y (00 , ) <
at Y0 (
Yield and Flow Functions
E
⌫
✓
p0)))
" =
Strain-Displacement Relation
p
◆
@
p
"˙ = 0, at Y (
00
)<0
Y = q + ✓ m ⌧0
Y = q+✓ m
0
F =F q=+q + m m ⌧00
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00
=0
)=0
Domain Decomposition for Geomechanics
Pay-zone / Nonpay-zone
Advantages of fixed stress splitting
Schematic of 3D domain
•  Mortar finite elements and interface iterati
ons are no longer required,
but still
possible to use.
Reservoir
•  We have a new parallel poro-plasticity
model that may be coupled with elastic a
nd poroelastic subdomains.
2D cross-section
!e,e
•  Savings with multi-rate methods have b
Ωe
s. We foresee it would be even greater in
np,e
!N
Ωp
poroelastic-elastic problems.
!D
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h
H
een demonstrated on poroelastic problem
!p,e
!p,p
nΩ
IV. UNCERTAINTY QUANTIFICATION
§  Calibration process of rock and fluid properties in subsurface models
A Priori Model
History Matching
(permeability, md)
(permeability, md)
Multi-modal
A Posteriori Model
Gaussian
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Multi-modal
Carbon Capture & Storage Projects Worldwide
Snohvit
Sleipner
K-12B
RECOPOL
CO2 SINK
Hokkaido
Nagaoka
Sibilla
In Salah
Qinshui Basin
Abu Dhabi 1st
CO2 EOR in Middle East
Teapot Dome
Rangely
Burlington
Zama
Penn West
Alberta ECBM
Weyburn
Mountaineer
West Pearl Queen
Cranfield
Frio
Gorgon
Otway Basin
Cerro Fortunoso
Coal Bed
Depleted Oil Field
ECBM Projects
EOR Projects
Gas Production Fields
Saline Aquifer
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Parameterization & Data Assimilation
§  History matching coupled w/ level-set parameterization, MFDFrac, and EnKF
1 Initialization
2 Level-Set Parameterization
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Generate initial fractured realizations
Experiments
Mesh generation
Realization
Convert non-Gaussian
to Gaussian parameters
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Φ: level set at the node
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r: fracture length
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θ: fracture orientation
3 Simulation using MFDFrac
4 Inverse Modeling using EnKF
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Mimetic Difference Approach
Internal Fracture
Boundaries
Intersecting
Fractures
Flow
EnKF for updating Gaussian parameters
Ensemble mean of
initial fracture realizations
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Ensemble mean of
final fracture realizations
Parameterization & Data Assimilation
Experimental setup
Numerical model
•  Collaboration w/ Dr. N. Espinoza
•  Injector: 5
•  Producers: 2, 3, 8, 9
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Parameterization & Data Assimilation
Numerical results
•  Blue straight lines indicate major fractures that mostly affect production rate.
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Parallel Multi-objective Optimization for CCS at Cranfield
Reservoir Characterization & Optimization
Simulator
IPARS
• Global-objective
evolution
ES
.exe
strategy
Stop
• Serial
• Multi-objective
algorithm
NSGA-II
.exe
Start
• Multi-objective
Builder
.exe
evolution
strategy
• PC
For i=1:N
Evaluate model
genetic
…
Evaluate model
algorithm
• Supercomputer
Start
Evaluate model
GA
.exe
Storage
• Parallel
• Global-objective
genetic
Run
Evaluate model
Algorithm
Evaluate model
OS
ε-MOES
.exe
Stop
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Simulation of Pulse Test for CO2 Leakage Detection
Permeability distribution in Cranfield, MS
•  661,760 = 20x188x176 grid cells
Permeability (md)
•  Grid size: 4 ft x 50 ft x 50 ft
DAS (drilled area of study)
80 ft
x
z
y
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Simulation of Pulse Test for CO2 Leakage Detection
Bottomhole pressure match at the monitoring well
Amplitude
•  Reproduction of both amplitude and wavelength of pulse patterns
Wavelength
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V. ONGOING WORKS
§  Modeling of proppant-filled fractures
Proppant-filled fractures in a poroelastic medium [L.-Mikelic-Wheeler-Wick 2016]
Fracture
Proppant
Proppant in a fracture
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Transport system is coupled
Enriched Galerkin (locally conservative)
Non-Newtonian flow (power-law)
Proppant
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V. ONGOING WORKS
§  Modeling of viscous fingering
Experimental results [S. Malhotra – E.R. Lehman – M.M. Sharma 2014]
Simulation results
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V. ONGOING WORKS
§  Stochastic fracture propagation
Coupling with probability map [L.-Wheeler-Wick-Srinivasan]
•  InSAR (surface deformation map)
•  Obtain probability map
•  Initialize hydraulic fractures
•  Interactions with natural fractures
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Concluding Remarks
Developing a coupled flow-geomechanics-geochemistry simulator
Capturing the coupled effect of non-ideal aqueous phase equilibrium
and reactions with traditional EOS calculations
Homogenization / Poro-plasticity / Fracture Propagation
/ Model calibration / Multi-rate coupling / Domain Decomposition
Synergy effects from combination of modules
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Acknowledgements
Thank you for your attention
Contact: mfw@ices.utexas.edu
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