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Simplified Predictive Models for CO 2 Sequestration Performance Assessment DEFE0009051 Srikanta Mishra Battelle Memorial Institute U.S. Departmentof Energy NationalEnergyTechnologyLaboratory Carbon Storage R&D Project Review Meeting Transforming Technology through Integration and Collaboration August 1820,2015 Priya Ravi Ganesh, Jared Schuetter, Doug Mooney Battelle Memorial Institute Louis Durlofsky Jincong He, Larry Zhaoyang Jin Stanford University
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Page 1: Simplified)Predictive)Models for)CO Sequestration ... Library/Events/2015/carbon storage... · Simplified)Predictive)Models for)CO 2 Sequestration) Performance)Assessment DE

Simplified Predictive Models for CO2 Sequestration

Performance AssessmentDE-­FE-­0009051

Srikanta MishraBattelle Memorial Institute

U.S. Department of EnergyNational Energy Technology Laboratory

Carbon Storage R&D Project Review MeetingTransforming Technology through Integration and Collaboration

August 18-­20, 2015

Priya Ravi Ganesh, Jared Schuetter, Doug Mooney

Battelle Memorial Institute

Louis DurlofskyJincong He, Larry Zhaoyang Jin

Stanford University

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2

Presentation Outline

§ Benefit to the Program / Stakeholders§ Project Overview§ Technical Status– Reduced physics based modeling– Statistical learning based modeling– Reduced order method based modeling– Uncertainty and Sensitivity Analysis

§ Accomplishments to Date§ Summary

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3

Benefit to the Program

§ Research will develop and validate a portfolio of simplified modeling approaches to predict the extent of CO2 plume migration, pressure impact and brine movement for a semi-­confined system with vertical layering

§ These approaches will improve existing simplified models in their applicability, performance and cost

§ The technology developed in this project supports the following programmatic goals: (1) estimating CO2 storage capacity in geologic formations;; (2) demonstrating that 99 percent of injected CO2 remains in the injection zone(s);; and (3) improving efficiency of storage operations

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4

Benefit to Stakeholders

§ Provide project developers with simple tools to screen sites and estimate monitoring needs

§ Provide regulators with tools to assess geological storage projects quickly without running full-scale detailed numerical simulations

§ Enable risk assessors to utilize robust, yet simple to implement, reservoir performance models

§ Allow modelers to efficiently analyze various CO2injection plans for optimal well design/placement

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5

Project Overview Goals and Objectives

Objective ð Develop and validate a portfolio of simplified modeling approaches for CO2 sequestration in deep saline formations

o Reduced physics-based modeling - where only the most relevant processes are represented

o Statistical-learning based modeling - where the simulator is replaced with a “response surface”

o Reduced-order method based modeling - where mathematical approximations reduce computational burden

o Uncertainty and sensitivity analysis – to validate the simplified modeling approaches for probabilistic applications

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Reduced Physics Based Models Background

§ Useful alternative to simulators if “macro” behavior is of interest

§ Analytical models of radial injection of supercritical CO2 into confined aquifers– (a) Fractional flow model (Burton et al., 2008;; Oruganti & Mishra;; 2013)

– (b) Sharp interface model (Nordbotten & Celia, 2008)

§ Require extension for semi-­confined systems with vertical permeability layering (based on detailed simulations) 6

(a)

(b)

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Reduced Physics Based Models Approach (using CMG-­GEM)

7

Average Gas Saturation in Swept Volume

CO2-­ BrineBrine

Injector

Sg,av

RCO2

Swept Volume

Unswept VolumeReservoir

ΔPjump

Injector

-­10,000 0 10,000

-­10,000 0 10,000

1,0001,100

1,2001,300

900

1,000

1,100

1,200

1,300

0.00 1.00 2.00 miles

0.00 2.00 4.00 km

File: 2D_Ref_Site7_3b.datUser: RAVIGANESHPDate: 10/11/2013Scale: 1:123684Z/X: 33.00:1Axis Units: m

0.020.030.050.070.120.180.280.430.671.041.612.503.886.029.3314.4822.4634.8354.0383.81130.00

CO2 injection: 25MMT in 30yearsPermeability I (md) 1970-­01-­01 J layer: 1

CAP ROCK (CR)

RESERVOIR (R)

Permeability (mD) contour map

CAP ROCK (CR)KCR = 0.02 mD

RESERVOIR (R)

Reservoir Permeability, mD

CAP ROCK PROPERTIESϕ, h, K, Pc

RESERVOIR PROPERTIESϕ, h, Kavg, Kv/Kh, krel

CMG-­GEM®

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Reduced Physics Based Models Simulation Scenarios

8

Parameter Description Units Reference value (0) Low value (-­1) High value (+1) Comments

1 hR Thickness of reservoir m 150 50 2502 hCR Thickness of caprock m 150 100 200

3 kavg,R (kR) Average horizontal permeability of reservoir mD 46 12 220

VDP Dykstra-­Parson’s coefficient -­-­ 0.55 0.35 0.75 Correlated with kavg,R

4 kavg,CR (kCR)Average horizontal

permeability of caprock mD 0.02 0.002 0.2

5 kV/kH Anisotropy ratio -­-­ 0.1 0.01 1

6 q CO2 Injection rate MMT/yr 0.83 0.33 1.33

L Outer radius of reservoir km 10 5 7 Correlated with q

7 fR Porosity of reservoir -­-­ 0.12 0.08 0.188 fCR Porosity of caprock -­-­ 0.07 0.05 0.1

9 IvIndicator for permeability

layering -­-­ Random Increasing from top

Increasing from bottom

Deriving insights into performance metric behavior

Quantifying functional relationships between variables based on sensitivity analysis

Validating simplified model to check for robustness

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0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

P D_p

rediction

PD_simulation

PD: predicted versus simulated values

Reduced Physics Based Models Dimensionless Injectivity – Predictive Model

9

1

100

1 10 100

(q/ΔP)_p

rediction, bbl/day/psi

(q/ΔP)_simulation, bbl/day/psi

Predicted versus simulated injectivities

Dataset

Blind Validation

(q/Δp)pred

(q/Δp)sim

𝑷𝑫 = 𝟏𝟎. 𝟑 +𝟎. 𝟓𝟗𝒅𝒇𝒈𝒅𝑺𝒈

+𝟑. 𝟒𝟏𝑽𝑫𝑷 +𝟏. 𝟐𝟑𝒅𝒇𝒈𝒅𝑺𝒈

𝑽𝑫𝑷 −𝟎. 𝟑𝟒𝒅𝒇𝒈𝒅𝑺𝒈

𝟐

− 𝟖. 𝟖𝟗𝑽𝑫𝑷𝟐

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0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Ref Rel Perm

Series1

one-­‐one

Reduced Physics Based Models Average Reservoir Pressure – Predictive Model

10

DAD tfP π2=

For a closed/ no-­caprock system

f depends on relative permeability

R² = 0.9985

0.840.850.860.870.880.890.90.910.920.930.940.95

20 25 30 35 40 45 50 55

Series1

Linear (Series1)

f

(Rmax/RCO2)2

DAD tfCP π2=

C depends on ratio of reservoir storativity to total storativity

C

SR/(SR+SCR)

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0

5

10

15

20

25

30

0 5 10 15 20 25 30

E S_p

rediction, %

ES_simulation, %

Reduced Physics Based Models Storage Efficiency – Predictive Model

11

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000

RCO

2_pred

ictio

n, m

RCO2_simulation, m

DataBlind Validation

(RCO2)pred

(RCO2)sim

𝑬𝑺

= 𝟑𝟎. 𝟕 +𝟎. 𝟒𝟑𝟓𝒅𝒇𝒈𝒅𝑺𝒈

+𝟐𝟗.𝟐𝟒𝑳𝑪 −𝟐𝟐.𝟎𝟐𝑽𝑫𝑷 −𝟏𝟏.𝟐𝑵𝒈 + 𝟒. 𝟓𝟗𝒅𝒇𝒈𝒅𝑺𝒈

𝑽𝑫𝑷− 𝟐𝟓. 𝟐𝟏𝑳𝑪𝑽𝑫𝑷− 𝟎. 𝟔𝟗𝟐𝒅𝒇𝒈𝒅𝑺𝒈

𝟐

+ 𝟔.𝟏𝟏𝑵𝒈𝟐

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Reduced Physics Based Models Sharp Interface Model Evaluation

12

Model M3: sharp interface model modified with average gas saturation and Bingham-­Reid mixing law used for plume tip calculation

(A) Reference rel perm

(B) Linear rel perm

(C) High rel perm

sharp interface model average gas saturationBingham-­Reid mixing law

0

200

400

600

800

1000

1200

1400

1600

1800

M0 M1 M2 M3

RMSE

, m

Model Type

(A) Reference

(B) Linear

(C) High

Model M0: sharp interface model Model M1: sharp interface model + average gas saturation Model M2: sharp interface model + Bingham-­Reid mixing lawModel M3: sharp interface model + average gas saturation + Bingham-­Reid mixing law

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Statistical Learning Based Models Background

§ Goal ð replace physics-­based model with statistical equivalent

§ Experimental design ðselection of points in parameter space to run limited # of computer experiments

§ Response surface ðfunctional fit to input-­output data to produce “proxy” models for plume radius and reservoir pressure buildup

§ Two common options– Box-­Behnken (BB) design 3-­pt + quadratic response surface

– Latin Hypercube sampling (LHS) multi-­point + higher-­order model 13

-1-0.5

00.5

1

-1

-0.5

0

0.5

1-1

-0.5

0

0.5

1

BB

LHS

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§ Data from 2-­D GEM simulations of CO2 injection into closed volume

§ 97 run Box-­Behnken design with 9 factors

§ 4 different meta-­models– Quadratic– Kriging– MARS– Adaptive regression

§ Cross validation using 5 mutually exclusive subsets (78 training + 19 test data points) with 100 replicates

Statistical Learning Based Models Box Behnken Design – Metamodeling

14

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Statistical Learning Based Models Proxy Models – Plume Radius

15Box-­Behnken Design LHS Design

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Statistical Learning Based Models Proxy Model Evaluation

16

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Reduced Order Method Based Models Background (1)

§ Proper Orthogonal Decomposition (POD)q Represent high-­dimensional state vectors (e.g., pressure & saturation in every grid block) with small number of variables by feature extraction

§ Trajectory Piecewise Linearization (TPWL)q Predict results for new simulations by linearizing around previous (training) simulations

Controls

Simulator

POD-TPWL

Production/Injection Rate

17

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POD + TPWL = POD-TPWL

Order reduction

Nonlinearity treatment

Linear expressions w/ 100s of variables

Reduced Order Method Based Models Background (2)

§ Retain the physics of the original problem

§ Overhead is required to build the POD-­TPWL model

§ Evaluation of POD-­TPWL model takes only seconds

§ Applied previously to oil-­water problems for optimization and history matching (Cardoso and Durlofsky 2010, 2011;; He et al. 2011, 2013 )

18

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Reduced Order Method Based Models 4-­Horizontal Well Problem (CO2 Storage)

19

Idealized problem based on CO2Storage in Mt Simon sandstone

planned for the FutureGen 2.0 site

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Reduced Order Method Based Models POD-­TPWL Performance: BHP Control for Wells

20

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Reduced Order Method Based Models POD-­TPWL Performance: Rate Control for Wells

21Runtime speedup factor ~ 370 for 3D POD-­TPWL case (compared to full-­order AD-­GPRS simulation)

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Reduced Order Method Based Models POD-­TPWL Performance: Geological Perturbation

22

Results demonstrate that the approach is able to capture basic solution trends

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Uncertainty and Sensitivity Analysis Problem Definition

23

Inputs:• Slope of CO2 fractional

flow curve• Initial P, T• CO2 injection rate• Time of injection• Reservoir thickness• Average porosity• Radial extent of reservoir• Reservoir permeability

anisotropy ratio• Total compressibility• Caprock thickness• Caprock porosity• Layer permeability

arrangement indicator

Models: ‘A’ – Box-­Behnken fitted with quadratic polynomial model‘B’ – Maximin LHS fitted with kriging model‘C’ – simplified physics-­based models

Cumulative distribution functions (CDFs) evaluated for

performance metrics:

RCO2, ∆PRavg

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Uncertainty and Sensitivity Analysis Simplified Model Performance

24

Model ‘A’ Model ‘C’Model ‘B’

Plume Extent at End of Injection

Simplified models can capture full range of outcomes predicted by full-­physics model

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Accomplishments to Date§ Developed simplified predictive models for dimensionless injectivity, average reservoir pressure buildup and CO2 plume migration extent (storage efficiency)

§ Compared performance of different metamodeling approaches for building proxy models

§ Evaluated experimental design (Box-­Behnken) and sampling design (Latin Hypercube sampling) schemes

§ Demonstrated applicability of POD-­TPWL for CO2 injection into saline aquifers using a compositional simulator

§ Evaluated different well constraints and effects of geologic reservoir heterogeneity

25

RPBM

SLBM

ROMBM

RPBM and SLBM models validated using uncertainty and sensitivity analysis

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Synergy Opportunities– Complements discussions on model complexity by Princeton U. vis-­à-­vis the limits of applicability of simplified v/s full physics models

– Complements discussions on response surface uncertainty analysis by U. Wyoming vis-­à-­vis various statistical techniques for model building

– Provides inputs to LANL discussion regarding use of science-­based simplified (abstracted) models in performance and risk assessment

26

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Summary

27

• Successful development of simplified predictive models for layered reservoir-­caprock systems

o Reduced physics models for injectivity and plume radius

o Improved proxy modeling workflow using BB/LHS designs

o Application of POD-­TPWL scheme to CO2-­brine systems

• Benefits to stakeholderso Site developers, regulators ð simplicity, limited data

o Modelers, risk assessors ð computational efficiency

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AppendixThese slides will not be discussed during the presentation, but are mandatory

28

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Organization Chart

Project Management (Task1)Principal Investigator:

Srikanta Mishra (Battelle)

Task 2Simplified Physics based Modeling

Srikanta Mishra(Battelle)

Task 3Statistical Learning based Modeling

Doug Mooney(Battelle)

Task 4ROM-­based Modeling

Lou Durlofsky(Stanford)

Task 5Validation using Uncertainty/Sensitivity Analysis

Srikanta Mishra & Doug Mooney(Battelle)

Sponsors

DOE ODOD

TechnicalAdvisor

Neeraj Gupta (Battelle)

Project Team

Project Manager – William O’Dowd (DOE)

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Gantt Chart BP1 BP2 BP3

Task Name 10/2012-­09/2013 10/2013-­09/2014 10/2014-­09/2015 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

Task 1: Project Management 1.1 Project Management & Planning 1.2 Update Project Mgmt. Plan X 1.3 Progress Reporting X X X X X X X ¨ ¨ ¨ ¨ ¨ 1.4 Project Controls 1.5 Deliverables and Reporting Task 2: Simplified physics based modeling 2.1 Numerical experiments 2.2 Models for two-phase region behavior 2.3 Models for pressure buildup Task 3: Statistical learning based modeling 3.1 Design matrix generation 3.2 Computer simulations 3.3 Analysis of computer experiments Task 4: ROM-based modeling 4.1 Black-oil ROM procedures 4.2 Compositional ROM procedures Task 5: Validation using UA/SA 5.1 Problem definition 5.2 Probabilistic simulation 5.3 Analysis of results

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Bibliography (1) Journals, multiple authors• Swickrath, M.J., Mishra, S. and Ravi Ganesh, P., 2015, An evaluation of sharp

interface models for CO2-­brine displacement in aquifers, Groundwater (in press)

• Ravi Ganesh, P. and Mishra, S., 2015, Simplified physics model of CO2 plume extent in stratified aquifer-­caprock systems, Greenhouse Gases: Science and Technology (in press)

• Schuetter, J., S. Mishra, and D. Mooney, 2015, Metamodeling techniques for a CO2geo-­sequestration problem, Computational Geosciences (in preparation).

• Ravi Ganesh, P. and S. Mishra, 2015, An algorithm for reduced-­physics modeling of CO2 storage in layered formations: Computers and Geosciences (in preparation).

• Jin, L., J. He and L. Durlofsky, 2015, Reduced-­order models for CO2 geologic sequestration using Proper Orthogonal Decomposition and Trajectory Piecewise Linearization, Intl. J. Greenhouse Gas Control (in preparation).

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Bibliography (2) Conference, multiple authors• Mishra, S., Ravi Ganesh, P., Schuetter, J., He, J., Jin, Z., and Durlofsky, L.J., 2015, Developing and

validating simplified predictive models for CO2 geologic sequestration, SPE-­175097, ATCE, Sept. 28-­30.• Schuetter, J. and S. Mishra, 2015. Experimental design or Monte Carlo simulation? Strategies for building

robust surrogate models, SPE-­174905, ATCE, Sept 28-­30. • Ravi Ganesh, P., and S. Mishra, 2015, Simplified model of CO2 injection-­driven pressure buildup in semi-­

closed layered formations, Carbon Capture Utilization & Storage Conference, Pittsburgh, PA, April 19-­22.• Schuetter, J., Mishra, S., Ravi Ganesh, P. and Mooney, D., 2014, Building statistical proxy models for CO2

geologic sequestration, Energy Procedia, Vol. 63, pp. 3702-­3714.• Ravi Ganesh, P., and Mishra, S., 2014, Reduced physics modeling of CO2 injectivity, Energy Procedia,

Vol. 63, pp. 3116-­3125.• Schuetter, J., Mishra, S., and Mooney, D., 2014, Evaluation of metamodeling techniques on a CO2

injection simulation study, Proc., 7th International Congress on Environmental Modelling and Software, San Diego, California, USA, D.P. Ames, N. Quinn (Eds.), June 16-­19.

• Mishra, S., P. Ravi Ganesh, J. Schuetter, D. Mooney, J. He, and L. Durlofsky, 2014, Simplified predictive models for CO2 sequestration performance assessment, 2014 European Geoscience Union General Assembly, Vienna, Austria, April 29 – May 2.

• Ravi Ganesh, P., and S. Mishra, 2014, Simplified predictive models of CO2 plume movement in 2-­D layered formations, Carbon Capture Utilization and Storage Conference, Pittsburgh, PA, April 28–May 1.

• Ravi Ganesh, P. and S. Mishra, 2013, Simplified predictive modeling of CO2 geologic sequestration in saline formations: Insights into key parameters governing buoyant plume migration and pressure propagation, Carbon Management Technology Conference, Arlington, VA, Oct 20-­22.

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