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

0

2 000

4 000

6 000

8 000

10 000

12 000

14 000

16 000

18 000

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

0

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

0

10

20

30

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

0

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