optimization of fluid injection and extraction for ... · max buildup along a fault . no co 2 flow...

EARTH AND ENVIRONMENTAL SCIENCES • LAWRENCE BERKELEY NATIONAL LABORATORY

September 27, 2016 ARB’s Carbon Capture and Sequestration (CCS) Program

CCS Technical Discussion Series: Health and Environmental Risks, and Environmental Justice

Abdullah Cihan and Jens Birkholzer

Energy Geosciences Division, Lawrence Berkeley National Laboratory

Optimization of Fluid Injection and Extraction for Reservoir Management and Risk Mitigation during CO2 Sequestration


Reduced Storage Capacity

Interference Between Storage Sites

Pressure Buildup and Brine Displacement

Caprock Damage

Permitting and AoR

Effect on Other Georesources

Reservoir Management Via Brine Extraction

Induced Seismicity

Reservoir Integrity Issues Related to Industrial-Scale CO2 Injection

Beneficial Use of Extracted Brine


• Objective − Manage reservoir pressure with optimum extraction volumes and infrastructure needs

• Approach − Define specific reservoir performance criteria (e.g., maximum pressure near fault

zone, maximum caprock pressure, minimum AoR size, maximum CO2 trapping) − Via smart optimization algorithms, automatically find most suitable CO2 injection and

brine extraction solutions that meet performance criteria and constraints − Optimization searches for optimum number of wells, well locations, and rates

• Optimization − Optimization is based on a suite of gradient-based and global algorithms. − Global algorithms are preferred for coupled optimal well placement and control

problems − Must be conducted both during the planning stage and during the operation stage for

‘real-time’ management

Optimized Reservoir Management

BIRKHOLZER, J.T., CIHAN, A., ZHOU, Q. (2012): Impact-Driven Pressure Management Via Targeted Brine Extraction – Conceptual Studies of CO2 Storage in Saline Formations, International Journal of Greenhouse Gas Control, 7, pp. 168-180

CIHAN, A., BIRKHOLZER, J.T., BIANCHI, M. (2015): Optimal well placement and brine extraction for pressure management during CO2 sequestration, International Journal of Greenhouse Gas Control, 42, pp. 175-187


Example Description of Constrained Global Optimization Problem

4

Minimize

Subject to

A general constrained optimization problem for pressure control using brine extraction can be formally expressed as

Extraction Ratio (if no brine extraction, f is chosen as 1/Vinj)

Pressure buildup constraints, e.g. max buildup along a fault

No CO2 flow into extraction wells (for brine extraction schemes)

Range of Cartesian coordinates for vertical wells (for partially penetrating and horizontal wells, additional parameters can be included)


Example Description of Constrained Global Optimization Problem

5

Minimize

Subject to

A general constrained optimization problem for pressure control using brine extraction can be formally expressed as

Extraction Ratio (if no brine extraction, f is chosen as 1/Vinj)

Pressure buildup constraints, e.g. max buildup along a fault

No CO2 flow into extraction wells (for brine extraction schemes)

Range of Cartesian coordinates for vertical wells (for partially penetrating and horizontal wells, additional parameters can be included)

Other or Additional Objective Functions: • Minimize well number • Minimize size of AoR • Maximize CO2 trapping • Maximize EOR efficiency

Other or Additional Constraints: • Bottom hole pressure • Leakage rate in abandoned well field • TDS of extracted brine


Design and Optimization of Injection, Extraction, and Monitoring Using a Suite of Forward Models

• Recently developed a constrained differential evolution (CDE) algorithm was coupled with a suite of forward models for solving global optimization problems involving well placement, injection and brine extraction.

• In addition, other local and global optimization algorithms built in Itough2 are available to use, depending on the nature of the optimization problems.

Forward Predictors

(1) Analytical Solutions

(2) Vertically Integrated Numerical Two-Phase Flow Models – Sharp-Interface Models – Vertically Integrated

Multi-Phase Models

(3) Multi-phase flow in full 3D systems


Application to Hypothetical CO2 Injection in the Vedder Formation (Southern San Joaquin Valley,

California)

Sier

ra N

evad

a

Southern San Joaquin Basin

g(

)

260 270 280 290 300 310 320 330 340

3890

3900

3910

3920

3930

3940

3950

3960

3970

3980

3990

4000

GreeleyPond

New

Hope

1 New

Hop

e2

Poso Creek

Kern Front

Kern Gorge

km

km

Top of Vedder Elevation

Major faults not to experience pressure buildup above 1 MPa

Injection Target: 5 Mt CO2 per Year Over 50 Years


Injection of 5 Mt CO2 per Year Over 50 Years Without Pressure Management

Pressure-buildup contour lines (black) in MPa and CO2 plume extent (red) CO2 Saturation

Results for Realization 1


Optimal Well Placement and Pressure-Buildup

Maximum pressure buildup w/ and w/o brine extraction Results for Realization 1


R

Optimal Injection Rates without Brine Extraction for ΔPmax=1MPa along

the Faults

Optimal Extraction Ratios for 5Mt/year injection and ΔPmax=1MPa along the

Faults 1 1.968 Mt/yr 0.672 2 2.739 Mt/yr 0.393 3 3.229 Mt/yr 0.380 4 2.061 Mt/yr 0.654 5 2.451 Mt/yr 0.538

Optimized Extraction Rates for all Realizations

Realization-1 Lower permeability zones between the faults result in stronger pressure buildups and thus higher volume of brine extraction

Realization-3 Higher permeability zones exist between the faults. One extraction well achieves the performance goal


Heterogeneity plays a significant role for optimal well placement and injection/extraction rate control, which points to:

• Importance of site characterization

• Use of adaptive management strategies combining monitoring+inversion+optimization in an integrated framework


Optimization Framework and Integrated Management

Objectives • Develop and apply an adaptive optimization framework for CO2 storage projects which utilizes

advanced automated optimization algorithms and suitable process models for coupled multi-phase behavior,

• Use this new framework to investigate process behavior and then develop optimal schemes for key technical challenges in CO2 sequestration


Aquifer 1

Aquitard

Q1(t)

Aquifer 2

Injection well

Obs. well

An Example Application of Adaptive Approach to Project Control and Optimization

Parameters assumed to be Unknown

Actual Values

K1 (m/d) 1.015E-01 S1 (Specific Storage Coef, 1/m) 1.693E-06

Horizontal Anisotropy Ratio 2.000E+00

K2 (m/d) 1.037E-01 S2 (1/m) 1.704E-06 K’ (aquitard) 1.028E-06 S’ (aquitard) 1.988E-06

Objective: • Critical pressure buildup is assumed

to be 0.2 MPa along the fault • Fluid injection rate is 1Mt/yr over 30

yrs • A adaptive optimization algorithm

involving optimization +monitoring + model update is applied to manage the system, minimizing extraction rates while attempting to reduce risk of fault slippage.

Extraction Well


1. Optimization With Existing Model(s)

2. Monitoring/Model

Testing

3. Model Calibration

Input (Planning

Stage)

High pressure in violation of constraint indicates: • Importance of site

characterization at the planning stage

• Monitoring and model update need to be done at a higher temporal frequency at earlier times to detect higher pressures and change extraction rates accordingly

For Observed vs. Predicted at Step 2


1. Optimization With Existing Model(s)

2. Monitoring/Model

Testing

3. Model Calibration

Input (Planning

Stage)

Constraint violation eliminated by higher-frequency monitoring and model update at earlier times


• Developed an optimization method that minimizes brine extraction volumes while meeting defined reservoir management targets

• Applied optimization method to realistic complex problems involving pressure control near faults and other management objectives

• Optimization allows for significant reduction in brine extraction volumes (extraction ratios < 1)

• Heterogeneity plays a significant role for optimal well placement and injection/extraction rate control for minimizing risks

Summary

• Investigation and development of adaptive management strategies for pressure control and mitigation

• Optimization and risk management under uncertainty conditions

Ongoing Work


BACKUP SLIDES

17


There is a need for robust and efficient optimization strategies for large-scale pressure

management problems

• Selections of well locations and injection/extraction rates are critical for maximizing storage and minimizing brine extraction.

• Objective functions can have multiple local optima in the solution space.

• Global optimization methods are needed.

Global minimum

f

xi


Brine extraction can be a significant factor in economic viability of a CCS project

Based on Harto et al., 10th Annual Conference on CCS, Pittsburgh, May 2011

• Construction of wells and treatment/disposal facilities • Operating cost (pumping, treatment, disposal, discharge) • Transportation • Permitting, monitoring, reporting

• Optimization can minimize extraction volumes and beneficial use can ease economic burden


Constrained Differential Evolution Algorithm

Implementation of Constraints in CDE Objective function evaluations in the original DE is reformulated in the CDE based on the following criteria:

1. Any feasible (satisfying constraints) solution is preferred to any infeasible solution 2. Among feasible solutions, the one having the better objective function value is preferred 3. Among the infeasible solutions, the one having smaller constraint violation is preferred

Main Stages of Differential Evolution Algorithm (Storn and Price, 1997)

Initialization Selection Mutation Crossover

• A constrained differential evolution (CDE) algorithm was developed for solving optimization problems involving well placement, injection, and brine extraction.

• The DE algorithm is a very powerful evolutionary algorithm with good convergence properties, ease of use and suitability for parallelization.

• The original DE method is in general applicable to unconstrained optimization problems.


Demonstration and Testing of Constrained Differential Evolution (CDE) Method

Impact Point (x=0, y=-20km) (Critical ΔP=0.2MPa)

Injection Well (x=0, y=0)

Extraction Well

Impact Point (x=20 km, y=0) (Critical ΔP=0.2MPa)

x

-y

Optimal Location

(10 km, -10 km)

A Simple Optimization Problem with Known Optimal Extraction Well Location

Norm

alized Extraction R

ate N

ormalized

Extraction Rate


Comparison with Results from Gradient-Based Method for Extraction Rates

SQP: Sequential Quadratic Programming

• CDE finds optimal well location • CDE and SQP optimum extraction rates agree well • CDE needs much larger number of forward runs, but easily parallelizable


Example application case - using different models for estimating optimal injection rates

Two-phase Flow in 3D Two-phase Vertical-Equilibrium (VE)

(Saturation distribution at the top layer, vertical

resolution~5m, average thickness~100m)

Model Type

Optimal Injection Rates without Brine Extraction for

ΔPmax=1MPa along the Faults

Two-phase 3D 0.051 Mt/yr Two-phase VE 0.048 Mt/yr


Effects of Critical Pressure and Fault Permeability on ‘Extraction Ratio’

Critical ∆P (bar)

Extr

actio

nR

atio

(m3 /m

3 )

2 4 6 8 100

0.2

0.4

0.6

0.8

1

kfault/kreserv=0kfault/kreserv=10-4

kfault/kreserv=10-2

Extraction Ratio: Total Volume of Extracted Brine Divided by Injected CO2


A Generic Optimization Problem for CO2 Injection and Brine Extraction

Model Easting (m)40000 60000 80000

Facies

4321

CO2 InjectionWellFault-1

Model Easting (m)

Mod

elN

orth

ing

(m)

40000 60000 80000

10000

20000

30000

40000

50000

54.543.532.521.510.5

CO2 InjectionWell

∆P (MPa)

• Injection target: 5 Mt CO2 per year over 30 years • Threshold pressure to prevent caprock fracturing: 8 MPa • Threshold pressure to prevent fault activation: 0.55 MPa • Optimization goal: Inject target amount of CO2 while honoring pressure constraints, with

minimum number of injection/extraction wells and minimum brine extraction volume

Pressure contours for single-well injection of 1.5 Mt CO2 at 30 years (both pressure constraints are violated)


5

5

55

5

5

5

10

10

10

10

10

20

20

2030

30

30

40

4050

70

Model Easting (m)

Mod

elNo

rthin

g(m

)

40000 60000 80000

10000

20000

30000

40000

500000.40.350.30.250.20.150.1

Ave SCO2

Injection Zone

Extraction Wells


Optimization Results Involving Four Injection Wells and Two Extraction Wells with Time-Dependent Extraction Rate



Time (yr)

Opt

imiz

edPu

mpi

ngR

ates

(m3 /s

)

0 10 20 30 400

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Injection

Extraction

Time (yr)

Max

imum

Pres

sure

Bui

ldup

(bar

)

0 10 20 300

20

40

60

80

100

Injection ZoneFault Zone

Threshold for Fracking

Threshold for Fault Activation

Extraction Ratio: 22%

optimization of fluid injection and extraction for ... · max buildup along a fault . no co 2 flow...

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