Evaluating Long Term CO 2 Storage in Saline Aquifers
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Transcript of Evaluating Long Term CO 2 Storage in Saline Aquifers
Evaluating Long Term CO2 Storage in Saline Aquifers
Mary Fanett WheelerCenter for Subsurface ModelingThe University of Texas at Austin
Acknowledge
Collaborators:
Algorithms: UT-Austin ( B. Ganis, G. Pencheva, G.. Xue, H. Florez, B. Wang, R. Tavakoli) ; Pitt (I. Yotov); Paris VI (V. Girault, M. Vohralik); Lyon (A. Mikelic)
Parallel Computation: IBM (K. Jordan), Rutgers (M. Parashar)
Phase Behaviour and Compositional Modeling : UT-Austin ( M. Delshad, X. Kong); Chevron (S. Thomas)
Support of Projects: NSF, DOE (DE-FG02-04ER25617 and EFRC-DE-SC0001114), CSM Industrial Affiliates
Outline
Motivation Why Carbon Capture and Storage (CCS)? Mechanisms, Questions Needing Answers
Mathematical and Computational Models Benchmarks Investigate applicability of existing oil/water/gas models
to supercritical C02/water strategy Calibrate and history match demonstration sites
Mathematical and Computational Challenges Discretizations and Solvers Multiscale, Multiphysics, Multinumerics & Data
Assimilation Conclusions
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2 000
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1980 1990 2000 2010 2020 2030
Mto
e
Other renewables
Hydro
Nuclear
Biomass
Gas
Coal
Oil
World energy demand expands by 45% between now and 2030 – an average rate of increase of 1.6% per year – with coal accounting for more than a third of the overall rise
World Primary Energy Demand
From: Joan MacNaughton (Alstom Power Company)
Units:1 Gt = 10^12 kg
1Source: IEA/OECD (200)
Year
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10
20
30
1880 1900 1920 1940 1960 1980 2000 2020
Total: 26,6 Gt in 2005
Source: Alstom, adapted from CDIAC 2004
Coal generates 70% of the CO2 emissions from power generation
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41 %
22 %
22 %
Power
Industry
Transport
16 % Others
Wor
ld C
O2 f
ossi
l em
issi
ons
GtCO2 by sector
Gto
n of
CO
2
70 %
8 %3 %
Coal
GasOil
Power by fuel
From: Joan MacNaughton (Alstom Power Company)
CO2 from Fossil Fuel Combustion
Center for Frontiers of Subsurface Energy SecurityThe University of Texas
Summary statement: Our goal is scientific understanding of subsurface physical, chemical
and biological processes from the very small scale to the very large scale so that we can
predict the behavior of CO2 and other byproducts of energy production that may need
to be stored in the subsurface.
RESEARCH PLAN AND DIRECTIONS• Challenges and approaches: Integrate and expand our knowledge of
subsurface phenomena across scientific disciplines using both experimental and modeling approaches to better understand and quantify behavior far from
equilibrium. • Unique aspects: The uncertainty and complexity of fluids in geologic media
from the molecular scale to the basin scale. • Outcome: Predict long term behavior of subsurface storage.
Multi-Scale Investigation
Dissolved CO2
Aquifer Brine
SC-CO2
Geographical location of Denbury Resources,Incorporated’s Cranfield Unit east of Natchez, Mississippi
Gulf Coast Stacked Storage Project(SECARB)
Research Questions
?How can we represent the essential features of large-scale behavior that emerge from small-scale phenomena?
Can we engineer solutions to mitigate contaminant
leakage pathways?
What are the relevant physics, biology, and chemistry of CO2 transport in the subsurface?
How does supercritical CO2 behave in the subsurface?
Goal of CO2 Geological Sequestration
Permanently store CO2 in deep saline aquifers by different trapping mechanism:
ResidualDissolutionMineralStructural
Precipitated Carbonate Minerals
Confining Layer(s)
Injection Well
SupercriticalCO2
Dissolved CO2
Celia et al., 2002
Modeling CO2 Storage
Accurate prediction of the CO2 fate is a challenge CO2 injection in subsurface brings a weighty list of
variables, parameters, and potential outcomes CO2 properties of density, viscosity, solubility depend on
pressure, temperature, and water salinity Relative permeabilities are functions of rock properties
such as wettability and permeability Relative permeability and capillary pressure are
hysteretic Relative permeability and capillary pressure are
influenced by pressure, interfacial tension, and flow rate
Forces Controlling the Movement of CO2
Pressure Gradient (Driving Force)
Buoyancy Force (Driving or Trapping Force)
Capillary Pressure (Trapping Force)
Mobilization Condition of Trapped CO2 Globule
Lw gD Pc 2 cosnRn
cosR
Rb
Pr essureForce
Buoyancy
Force
Capillary
Force
Compositional Modeling
Compositional Flow andThermal Formulation
IPARS-COMP Flow Equations
Mass Balance Equation
Pressure Equation
Solution Method• Iteratively coupled until a volume balance convergence criterion is met
or a maximum number of iterations exceeded.
ii i i i
N. u S D q
t
Thermal & Chemistry Equations
Energy BalanceSolved using a time-split scheme
(operator splitting)Higher-order Godunov for advectionFully implicit/explicit in time and
Mixed FEM in space for thermal conduction
ChemistrySystem of (non-linear) ODEsSolved using a higher order
integration schemes such as Runge-Kutta methods
Tp H
T
T s vs v
M T. C u T T q
tInternal energy : MM 1 C C S
EOS Model
CO2 Properties
Fugacity (T, P)
Density (T, P)
Viscosity (T, P)
Aqueous Solution Properties
CO2 Solubility (T, P)
Aqueous Density (T, P)
Effect of salinity
a TRTPv b v v b b v b
Peng-Robinson EOS
Parallel
Subsurface Compositional Framework
Thermal2 or 4- P Flash
Geomechanics
Numerics
Visualization
EOS Comp. GeochemicalReaction
Gridding
Solvers
Physical Prop
EOS Compositional Flow Simulations
6 Component Compositional BenchmarkLarge Scale CO2 Simulation
Calibration: Resid. Sat & TrappingCore Studies and Scaling
Preliminary – Matching Cranfield Field Studies
M. Delshad, X. Kong, and W
EOS Compositional Simulations
Modified SPE5 WAG injection, 6 non-aqueous components-solved using EOS compositional model
SPE10 permeability distribution 50x480x480 cells (~11 million) Linear Solver: BiCGS or GMRES
+ MG preconditioner.
Water Saturation
Gas Saturation Propane Concentration
After Three Years
Permeability
Oil Pressure
HardwareLonestar: Linux cluster system
Blue GeneP: CNK system, Linux I/O
1,300 Nodes / 5,200 cores
262,144 Nodes / 1,048,576 cores
Processor Arch: 2.66GHz, Dual core, Intel Xeon 5100, Peak: 55
TFlops/s
Processor Arch: 850MHz,
IBM CU-08, Peak: ~1 PFlop/s
8 GB/node 2 GB/node
Network: InfiniBand, 1GB/s
Network: 10Gb Eth,1.7GB/s
SoftwareGMRES, BCGS, LSOR, Multigrid.
MPI: MVAPICH2 library for parallel communication
Texas Advanced Computing Center The University of Texas at Austin
Parallel Scalability
Large-Scale High Resolution Simulation --- 3.3 million cells
6581 ft
5304 ft
1080
ft
480 ft
320 ft
Aquifer, Sandstone
Cap rock, Shale
Aquifer, Sandstone
Cap rock, Shale
Aquifer, Sandstone
160 ft
6581 ft
5304 ft
1080
ft
480 ft
320 ft
Aquifer, Sandstone
Cap rock, Shale
Aquifer, Sandstone
Cap rock, Shale
Aquifer, Sandstone
160 ft
CO2 Injection wells Permeability, md
CO2 saturation after 2 years
Permeability and well locationsVertical cross section
Case 1: 3.34 million grids,3 leaky points
Aquifer size, L, W, H 5304 ft× 6581 ft × 1080 ft
Mesh 3,342,336 (128× 256×102), (40ft x25ft x15 ft)
Dip, Depth (top corner) 0 degree, 3000 ft
Residual gas and water in aquifer 0.103, 0.197
Initial pressure 1800 psi at injection layer
Aquifer temperature 43 C (110 F)
Well position four wells in the center of bottom aquifer
Vertical well perforated length 240 ft, bottom half depth of bottom aquifer
Injection rate 7000 mscfd each well
Aquifer permeability heterogeneous with average 96 md
Leaky points 2 ft x 2 ft
Shale permeability 0.0003 md
permeability at leaky paths 3000 md
injection time 2 years
Residual Saturation vs. Trapping Number
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0.05
0.1
0.15
0.2
0.25
0.3
1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06
Res
idua
l CO
2 sa
tura
tion
Trapping number
TG = 97x106
t = 1.05
Points: data from Bennion and BachuLine: Model
Generate heterogeneous permeability and porosity data with FFTSIM (geostatistics software)
Permeability and porosity are highly heterogeneous with a Dykstra-Parson coefficient of 0.6
Honor average permeability and porosity of experimental data (Ref. SPE 126340)
Isotropic permeability
IPARS Coreflood Simulation
Permeability along the core Permeability in a cross section
T (oC) 50 CO2 dissolution (mass fraction)
0.04873
Pressure (MPa) 12.41 CO2 density (kg/m^3) 608.38
Salinity (ppm) 6500 CO2 viscosity (cp) 0.06
Porosity 0.185 Brine Density (kg/m^3) 993.33
Permeability (md) 85 Interfacial tension (N/m) 0.0285
Core length (cm) 20 Injection rate (ml/min) 3
Core Diameter (cm) 4.064 Total pore volume injection 7
Residual saturationOf both water and CO2
0.2 Final average gas saturation 0.54
Simulation Data
• Set up simulation model with same parameters as the experiment (SPE 126340)
Relative permeability and capillary pressure used in simulation
Core is initially saturated with 100% water, residual of both CO2 and water is assumed to be 0.2
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Sw
Rela
tive
perm
eabi
lity
Krw
Krg
Relative Permeability andCapillary Pressure
0
1
2
3
0 0.2 0.4 0.6 0.8 1
Sw
Capi
llary
pre
ssur
e(ps
i)
Drainage relative permeability Drainage capillary pressure
Numerical Experiment
• Total injection: 7 pore volumes• Fine mesh cylindrical case, required very small time steps• Coarse grids used for testing purpose
Gas Saturation at 0.3 Pore Volume with Mesh (32x32x64)
Cube and Coarse GridComparison Cases
Permeability for coarse case Porosity for coarse case
• Cube and coarse grid was used to test sensitivity of simulation to model parameters.
• Grid : 8x8x32
CO2 narrowly distributed and uniform
Case 1… Without Pc Scaling
CO2 histogram shows log normal distribution
Case 2… With Pc Scaling UsingJ-Leverret
Summary
For case without J-Leverret capillary pressure, CO2 saturation is more uniform and continuously distributed than that of experiment‘
Locally non-uniform distribution of CO2 is shown in Case 2
Final gas saturation with Pc scaling is close to experimental results of 0.54 (ref. Paper 126340).
Results indicate that J-Leverret function based capillary pressure is important for core flood simulation.
MFMFE for General Hexahededraand Simplices
Formulation: W, Xue and Yotov
Solvers: Siefert, Tuminaro (Sandia), Pencheva (UT Austin - EFRC)
Frio BrinePilot Site
Injection interval: 24-m-thick, mineralogically complex fluvial sandstone, porosity 24%, Permeability 2.5 D
Unusually homogeneous Steeply dipping 16 degrees 7m perforated zone Seals numerous thick shales,
small fault block Depth 1,500 m Brine-rock, no hydrocarbons 150 bar, 53 C, supercritical CO2
Injection interval
Oil productionFrom Ian Duncan
Corner Point Grid for Frio Pilot Test
Permeability
Multipoint Flux Mixed Finite Element
ˆ V ( ˆ E ) 1 ˆ x 1 ˆ y 1 rˆ x 2 2sˆ x ̂ y
2 ˆ x 2 ˆ y 2 2rˆ x ̂ y sˆ y 2
(DFE )ij Fi
ˆ x j
JE det(DFE )
Vh (E) 1JE
DFEˆ V ( ˆ E )oFE
1
Wh (E) const
BDM1 Space on reference element:
Multipoint Flux Mixed Finite Element(MFMFE) on General Hexahedra
Convergence Test for MFMFE on General Hexahedra
Solver Performances for SPE 10Benchmark Problems
SPE 10 permeability on 220 x 65 x 50 highlyperturbed hexahedral mesh
• Model 1: Symmetric multipoint flux• Model 2: Non-symmetric multipoint flux
AMG solvers:HYPRE (developed by researchers at LLNL)SAMG (developed by the group of K. Stüben)FASP (developed by the group of J. Xu from Penn State)ML in Trilinos (developed by researchers at Sandia) (tested in a different code)
Stopping criteria: relative residual less than 10-9.
ML 21 - 28 ML 23 - 29
Parallel Non-Overlapping DD for MFMFE Using ML (Trilinos)
Smoothed Aggregation (SA) with standard SA dropping Symmetric Gauss-Seidel for pre- and post-smoother within the W cycle Drop tolerance discourages aggregates that traverse large material jumps
- give a sense for both total storage and total cost per iteration
Increasing the drop tolerance tends to reduce iterations but increases complexity
Parallel EnKF for Reservoir History Matching
G. Pencheva, R. Tavakoli, W, K. Jordan, M. Parashar
Continuous Measurement and Data Analysis for Reservoir Model Estimation
Source: E. Gildin, CSM, UT-Austin
Recent Award
1st Place, IEEE SCALE 2011 Challenge, “A Scalable Ensemble-based Oil-Reservoir Simulations using Blue Gene/P-as-a-Service”, with Rutgers and IBM.
Ensemble Kalman Filter (EnKF) Monte Carlo approach for recursively updating the model
parameters (as well as primary variables) based on an ensemble of prior realizations and observation data.
The EnKF consists of two steps:1) Forecast step: running a set of reservoir simulations (IPARS) to predict
data at the next update step
2) Update step: computing Kalman gain matrix and updating state vectorsm
timet0 t1 t2 t3
True Model
Pro
duct
ion
pred
ictio
n
Serial vs. Parallel EnKF
Sequentially run each of the realizations one after another for j=1, 2, …, Ne
Run Ne realizations simultaneously where each simulation run is
performed in parallel
Linear and Nonlinear Solvers
Reservoir simulation application uses models for multiphase flow in porous media: time-dependent, highly nonlinear, conserve mass.
We would like each realization to run efficiently (parallel scalable), so must utilize good solvers and preconditioners.
Moreover, need to synchronize multiple simulation runs during the EnKF process.
(The update step is a barrier).
Solver with Preconditioning
In IPARS, linear system is solved using preconditioned generalized minimum residual (GMRES).
Two-stage preconditioning: decoupling preconditioner stage: allows us to
precondition the diagonal pressure block of the Jacobian independently of the saturation blocks
At the second stage, the pressure block is preconditioned
GMRES preconditioner in IPARS
GMRES-PREC
DESCRIPTION
3 Block Gauss-Siedel (GS)4 LSOR with N_GS_STEP iterations5 Truncated NS + CG inner iterations6 Truncated NS + BCGstab inner
iterations7 Truncated NS + GMRES inner iterations8 Un-accelerated truncated NS11 Two-stage: SEP-PREC + LSOR
smoother13 Multilevel incomplete LU (MLILU)14 Two-stage: MLILU + LSOR smoother 15 Algebraic Multigrid (AMG)16 Two-stage: AMG+LSOR17 SPARSE FACTORIZATION
Dynamic Tolerance
In addition to proper choice of a preconditioner in solving a Jacobian equation (AX=B), the problem of an adequate tolerance in the linear solver appears.
The forcing term technique is used in IPARS to dynamically adjust the tolerance in the course of the Newton process (start with loose tolerance and tighten the condition as we proceed for further iterations)
The optimal choice of forcing factor has appeared to be 0.1 (FORCING=0.1)
Results: EnKF
Observation data: oil flow rate, water oil ratio (WOR), bottom hole pressure (BHP)
Assimilate time: 1550 days (with variable assimilation interval) followed with prediction phase till 2800 days
Uncertain Model parameters: Horizontal permeability and porosity.
Ensemble size: 100 realizations
Computational Results Example: water saturation distribution after 1550 days
3D reservoir, 80x60x5 gridblocks, two-phase (oil-water) 4 inverted five-spot patterns 9 production wells with liquid rate constraint of 4000 STB/day 4 injection wells with constant water injection rate of 8000 STB/day
Horizontal permeability and porosity are uncertain model parameters
3D View Layer # 4
Results: EnKF
True porosity
Final average porosity
Results: EnKF
True horizontal log-permeability
Final average horizontal log-permeability
Results: EnKF
Cumulative wall-clock computational time (sec) for EnKF run with 100 ensemble members on ICES-BVO2 cluster
Number of Simulation Run at a Time (NRun)
1 2 4 5 10 20
Number of Processors per Each
Simulation (NpSim)
1 63,381 32,102 16,433 13,281 7,069 3,899
2 47,298 23,998 12,406 10,020 5,397 3,056
3 35,772 18,223 9,469 7,673 4,181 2,461
4 32,425 16,535 8,646 7,019 3,882 2,272
Total Computational Time: Total Sim. Time (forecast step) + EnKF update steps Time
The total time of update steps is less than 4% of the total .
Results: EnKF
As we increase Nrun>10, the efficiency gets far from the ideal Two main reasons are; 1) additional waiting time due to the slowest
simulation run, 2) the update step is done in a serial mode
1 2 4 5 10 200
10
20
30
40
50
60
70
80
90
100NpSim=4
NpSim=3
NpSim=2
NpSim=1
NRun
Para
llel E
ffici
ency
, %
Summary
Calibration of the linear and nonlinear solvers help to reduce and synchronize the simulation times of each forward run.
We employ two levels of parallelism in EnKF:
Multiple processors per ensemble member Multiple concurrent ensemble members.
The EnKF algorithm helps to reduce uncertainty in reservoir simulation by assimilating production data.
The combination of parallelizing the EnKF algorithm with an efficient choice of solver gives over 40% parallel efficiency.
On Prediction of Realistic CO2 Tests
Fluid properties as a function of pressure, temperature, compositionViscosity, density, interfacial tension, phase behavior
Rock dependent relative permeability and capillary pressure as a function of Saturation, composition, saturation history (hysteresis), IFT
Rock reaction to pressure changes and subsequent impact on pore volumes and permeability (geomechanics)
Reactions of rock minerals and injected CO2 (geochemistry) Model estimators that include upscaling and downscaling for
property manipulations for coarse/fine grid Upscale strategy for CO2 storage (if needed) Increase grid resolution to improve the quality of model results
Increase CPU and memory requirementsFaster numerical methods – dynamic grid refinement based on a
posteriori error estimators that include upscaling and down scaling, efficient solvers
Efficient parallelization methodsOptimization and Uncertainty analysis
Summary
Renewables all have major problems – cost, energy efficiency, reliable, location, ….
CCS May Be Best Hope for Handling Greenhouse Gases Until Solar Becomes Economically Feasible-- Buys Time
Conclusions