Material Challenges in High Temperature Processes Material Challenges in High Temperature Processes for Hydrogen Productionfor Hydrogen Production

Bilge YildizBilge YildizDepartment of Nuclear Science and Engineering, MITDepartment of Nuclear Science and Engineering, MIT

GCEPGCEP--MIT Fission Energy WorkshopMIT Fission Energy WorkshopNovember 29, 2007November 29, 2007

Why nuclear hydrogen?Why nuclear hydrogen?

Hydrogen production using nuclear energy is a clean and Hydrogen production using nuclear energy is a clean and promising technology to decrease COpromising technology to decrease CO22--emissions. Potential emissions. Potential advantages compared to water electrolysis are:advantages compared to water electrolysis are:–– high efficiency and reduced electricity requirement,high efficiency and reduced electricity requirement,–– inexpensive materials.inexpensive materials.

Near-term markets

Fertilizers Oil Refining

Mid-term markets

Coal Liquefaction

Tar Sands

Long-term markets

Remote Power Transportation

Nuclear Energy

•CO2-free•Efficient and cost-

competitive•Size/location to address

the industry needs

Heat and electricity

Electrolysis and thermo-chemical processes:

H2O(g) ½ O2(g) + H2(g)

Co-electrolysis:

H2O(g) + CO2(g) O2(g) +

H2(g) + CO(g)

GoalGoal–– Enable durable, efficient, costEnable durable, efficient, cost--competitive, clean competitive, clean

hydrogen production technologies. hydrogen production technologies. OutlineOutline

–– Nuclear hydrogen production technologiesNuclear hydrogen production technologies–– High temperature steam electrolysis (HTSE)High temperature steam electrolysis (HTSE)–– Challenges, and fundamental research in:Challenges, and fundamental research in:

degradation mechanisms of the present devicesdegradation mechanisms of the present devicesinterfaces for higherinterfaces for higher--efficiency in the materialsefficiency in the materials

–– Concluding remarksConcluding remarks

Nuclear hydrogen production processesNuclear hydrogen production processes

HybridHybrid--SulfurSulfurCalciumCalcium--BromineBromineHybridHybrid

((ThemoThemo--electroelectro--chemical)chemical)

Steam electrolysisSteam electrolysisSteam electrolysisSteam electrolysisWater Water electrolysiselectrolysis

ElectroElectro--chemicalchemical

SulfurSulfur--IodineIodineCupperCupper--ChlorineChlorineThemoThemo--chemicalchemical

HighHigh(>800(>800ooC)C)

IntermediateIntermediate(500(500--700700ooC)C)

LowLow(RT)(RT)

Temperature Temperature rangerange

Research and development in the Nuclear Hydrogen Initiative Research and development in the Nuclear Hydrogen Initiative (NHI) of DOE(NHI) of DOE--NE on a range of hydrogen production NE on a range of hydrogen production technologies that can be supported by nuclear energy.technologies that can be supported by nuclear energy.

SulfurSulfur--Iodine (SI) ProcessIodine (SI) Process

Purpose: Splitting the HPurpose: Splitting the H22O into HO into H22 and Oand O22 using catalysis at using catalysis at lower temperatures than lower temperatures than pyrolysispyrolysis..SI cycle, with maximum temperature above 850SI cycle, with maximum temperature above 850ooC, using the C, using the thermal energy from the nuclear reactor thermal energy from the nuclear reactor

Heat

Sulfur-Iodine ThermochemicalWater-Splitting CycleHigh-temperature

nuclear reactor2H2O + I2 + SO2 2HI + H2SO4

H2SO4 H2O + SO2 + ½ O2

2HI I2 + H2

HybridHybrid--Sulfur (Sulfur (HyHy--S) CycleS) Cycle

Purpose: eliminating some of the corrosive chemical steps Purpose: eliminating some of the corrosive chemical steps from the thermochemical SI cyclefrom the thermochemical SI cycleHyHy--S, with maximum temperature above 850S, with maximum temperature above 850ooC, using the C, using the thermal and the electrical energy from the nuclear plant.thermal and the electrical energy from the nuclear plant.

HeatElectricity

High-temperature nuclear reactor

Hybrid-SulfurWater-Splitting Cycle

2H2O + SO2 H2SO4 + H2 (El.)

H2SO4 H2O + SO2 + ½ O2

High Temperature Steam Electrolysis (HTSE)High Temperature Steam Electrolysis (HTSE)Purpose: To split steam, HPurpose: To split steam, H22OO(g)(g), electrochemically while , electrochemically while spending >30% less electrical energy than water electrolysisspending >30% less electrical energy than water electrolysisHTSE, with maximum temperature at 830HTSE, with maximum temperature at 830ooC, using the thermal C, using the thermal and the electrical energy from the nuclear plant.and the electrical energy from the nuclear plant.

High Temperature Steam Electrolysis

HeatElectricity

High-temperature nuclear reactor

––Largest amount of hydrogen production rate, and the longest Largest amount of hydrogen production rate, and the longest duration of operation demonstrated within the NHI programduration of operation demonstrated within the NHI program..

H2O(g) H2(g) + ½ O2(g)

High temperature steam electrolysis (HTSE)High temperature steam electrolysis (HTSE)HTSE uses a solid oxide electrolysis cell (SOEC).HTSE uses a solid oxide electrolysis cell (SOEC).–– Materials are conducting ceramic oxides.Materials are conducting ceramic oxides.

–– Device is based on the solid oxide fuel cells (SOFC).Device is based on the solid oxide fuel cells (SOFC).

Cells are Cells are ““stackedstacked”” together in series for power management.together in series for power management.

Dense Electrolyte(Y2O3-ZrO2, YSZ)

Porous Anode (La0.8Sr0.2MnO3 composite)

Porous Cathode (Ni-YSZ)

H2O (+ H2) H2 (+ H2O)

O2

2O=

4e-

Solid oxide electrolysis cell, SOEC

AirAir

H2O(g)

O2(g)

O=

H2(g)

Cathode

Electrolyte

Anode

Interconnect

LongLong--term performance of present HTSEterm performance of present HTSE>1200 NL/hr of H>1200 NL/hr of H22 production was demonstrated by production was demonstrated by CeramatecCeramatec & & INL with a dual stack module for 2000 hrs.INL with a dual stack module for 2000 hrs.

Courtesy of Ceramatec, Inc.

Dual-stack SOEC module

O’Brien et al, Nuclear Technology, 2006

0 200 400 600 800 1000

Time (hours)

10

15

20

Cur

rent

(A) 800oC 830oC

0 200 400 600 800 1000

Time (hours)

10

15

20

Cur

rent

(A)

0 200 400 600 800 1000

Time (hours)

10

15

20

Cur

rent

(A)

0 200 400 600 800 1000

Time (hours)

10

15

20

Cur

rent

(A) 800oC 830oC

Degradation of the present SOEC stack performance is the Degradation of the present SOEC stack performance is the outstanding problem.outstanding problem.

Degradation mechanisms in SOECsDegradation mechanisms in SOECs

•Distribution and reaction species with Si•Specific position - on Ni or on Ni-zirconia interfaces.•Electrochemical nature where Si gets deposited.

Si-poisoning on the hydrogen/steam electrode(Si is coming from the cell seals)

•Between cobaltite-manganite layers•At manganite-zirconia particles•Decreasing electrical conductance of cobaltite due to decomposition

Decomposition / interdiffusionof cations at the interfaces, of the oxygen electrode

•Interface mechanical/adhesion stability against high flux of oxygen evolution•Interface chemical stability (interdiffusion)•Secondary blocking phase (zirconate) formation

Electrode – electrolyte interface delamination, in the oxygen electrode

•Distribution and reaction species with Cr•Getter agents for Cr to avoid its entry to the electrode.

Cr-poisoning, in the oxygen electrode(Cr is coming from the interconnect)

Specific Questions on:High-level Problem

CrCr--contamination in oxygen electrodecontamination in oxygen electrodeCr fluorescence spectra on the oxygen electrode showed presence Cr fluorescence spectra on the oxygen electrode showed presence of Cr in the bondof Cr in the bond--layer at ~10v%.layer at ~10v%.–– A large loss of active surface areaA large loss of active surface area

The preThe pre--edge peak shows evidence of Credge peak shows evidence of Cr6+6+ near the center of the near the center of the electrode electrode Multiple CrMultiple Cr--reaction speciesreaction species–– Cr transport mechanismCr transport mechanism –– solid state diffusion? Volatilization?solid state diffusion? Volatilization?

DelaminationDelamination between electrode and electrolytebetween electrode and electrolyte

Reasons for deformation at the electrode/electrolyte interfaceReasons for deformation at the electrode/electrolyte interface–– Secondary phase formation with high latticeSecondary phase formation with high lattice-- and thermaland thermal--mismatchmismatch–– SteamSteam--leak leading to reduction and decomposition of the manganiteleak leading to reduction and decomposition of the manganite

Tools to probe the reasons of deformationTools to probe the reasons of deformation–– HighHigh--resolution electron microscopy; in diffraction and spectroscopyresolution electron microscopy; in diffraction and spectroscopy–– HighHigh--resolution Auger electron spectroscopyresolution Auger electron spectroscopy

Electrolyte

Bond layer/Oxygen electrode

Steam electrode

SOEC oxygen-electrode side SOEC cross-section

900 µm

Avoiding degradation in SOECsAvoiding degradation in SOECsGoal: ensure the chemical stability Goal: ensure the chemical stability –– At the electrode/interconnect interfaceAt the electrode/interconnect interface

Protective coating on the interconnect to decrease Cr loss.Protective coating on the interconnect to decrease Cr loss.

Fundamental understanding of the degradation mechanisms in Fundamental understanding of the degradation mechanisms in SOECs are leading to SOECs are leading to evolutionary improvementsevolutionary improvements in the HTSE in the HTSE performance performance within the existing framework of materials, device within the existing framework of materials, device design, and operating temperature (>800design, and operating temperature (>800ooC).C).

–– At the electrode/electrolyte interfaceAt the electrode/electrolyte interfaceComposition gradient, with AComposition gradient, with A--site site deficiency, to avoid deficiency, to avoid zirconatezirconate formationformationThinThin--film protective interlayer, ceria, to film protective interlayer, ceria, to avoid interaction of the electrode avoid interaction of the electrode material with the zirconia electrolyte.material with the zirconia electrolyte.

AMnO3

Ceria-interlayerZirconia electrolyte

A0.98MnO3

Lower operating temperature for SOEC?Lower operating temperature for SOEC?There is the need to There is the need to reduce the operating temperature for reduce the operating temperature for prolonged lifeprolonged life--time, and thus reduced costtime, and thus reduced cost..Reduced temperature can allow the use of a wider range of Reduced temperature can allow the use of a wider range of nuclear reactors for supporting the SOECs.nuclear reactors for supporting the SOECs.

At lower temperatures, major source of energy loss is poor performance of the O2-electrode.

Goal:Revolutionary advances in

electrode materials (structures and compositions) for higher efficiency in H2 production at intermediate temperatures (500-700oC).

Singhal et al. HT-SOFCs, p281

AnodeElectrolyte

Cathode

800°C

650°C0

0.2

0.4

0.6

0.8

1

O2 electrodeH2 electrode

Res

ista

nce

Limiting reactions and pathways in oxygen electrodeLimiting reactions and pathways in oxygen electrodeOverall oxygen reactionOverall oxygen reaction(OR): (OR): OOOO ↔↔ ½½OO22 + 2e+ 2e-- + Vo+ Vo==

O=2e-

Os

O2(g)

O= O=

Electrode Bulk

Electrolyte

Elec

trode

Su

rface

O=

e-

e-

O-s

O=2e-

Os

O2(g)

O= O=

Electrode Bulk

Electrolyte

Elec

trode

Su

rface

O=

e-

e-

O-s

L -1.39

L -1.56

L -1.74

L -1.87

L -1.94

L -1.97

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

10 100 1000LSM Size, L (micro-m)

Res

ista

nce

(ohm

)

550600650700750800

T, oC

+ Exp.

At high temperature: limited by surface charge transfer – external interface

At low temperatures: limited by bulk transport –internal interfaces

1.4

1.9

2.4

2.9

0 100 200LSM Size, L (micro-m)

Effe

ctiv

e A

ctiv

atio

n En

ergy

(eV)

550-650 650-750700-800 750-850800-900 900-1000

T, oC

TPBBulk

SurfaceLSM

YSZ

For LaFor La0.80.8SrSr0.20.2MnOMnO3 3 at a microat a micro--scalescale

T

Opportunity for intermediate temperature SOECsOpportunity for intermediate temperature SOECs

Bulk

Electrolyte

Surface surface surface grain boundaries grain boundaries buried interfaceburied interface

Opportunity for improving the transport properties Opportunity for improving the transport properties through the understanding and tailoring of the interfaces:through the understanding and tailoring of the interfaces:

structural and structural and chemical naturechemical nature

AirAir

H2O(g)

O2(g)

O=

H2(g)

CathodeElectrolyteAnode

Interconnect

Anode

InterlayerElectrolyte

LSM

YSZ 100nm

Anode

InterlayerElectrolyte

Anode

InterlayerElectrolyte

Importance of interface structureImportance of interface structureDense thinDense thin--film electrodesfilm electrodes–– Fabricated by pulsed laser Fabricated by pulsed laser

deposition.deposition.–– Electrolyte substrate: (100) Electrolyte substrate: (100)

singlesingle--crystal YSZ.crystal YSZ.100nm

RMS R: 0.5-1nm

Represent particles as thin-films

Comparison of epitaxial and non-epitaxial LSM

Bulk

Electrolyte

Surface

LSM: Epitaxial (110)

100nm

Electrolyte

Surface

Bulk

LSM: No epitaxy,textured

100nm

Structure of the Structure of the surfacesurface and the and the grain boundaries grain boundaries is important.is important.

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

550 650 750 850 950Temperature (C)

ASR

(ohm

.cm

2)

No Epitaxy

Epitaxial (110)

Res

ista

nce

(ohm

) R

esis

tanc

e (n

orm

aliz

ed)

101

100

10-1

10-2

10-3

Ea(110)=2.04eV

Eano-ep = 1.24eV

X10 reduction in resistance

B. Yildiz, and K.C. Chang et al., Proc. 31st Int. Conf. Advanced Ceramics and Composites, January 2007

In situ x-ray characterization of the oxygen electrode materialsX-ray absorption spectroscopy: oxidation state, atomic environment

Grazing incidence-angle scattering geometry for surface sensitivity

Characterization of the electrode surfaceCharacterization of the electrode surface

Set-up, a first, shown here at the Advanced Photon Source.

TThe change in the he change in the chemical state of the Achemical state of the A--site site cationscations is occurring is occurring at the surface, associated with the at the surface, associated with the improvement of the electrode.improvement of the electrode.

0.00

0.01

0.02

0.03

5450 5500 5550Energy (eV)

Inte

nsity

(a.u

.)

After EP t4End of EP t3During EP t2During EP t1Before EP t0

to<t1<t2<<t3<t4t

tNormalized

La LIII edge XANES for La0.8Sr0.2MnO3

anodic polarization at 700oC.

B. Yildiz et al., Adv. Cer. and Comp., January 2007

Not Normalized

Interfaces in oxygen electrocatalysisInterfaces in oxygen electrocatalysis

Ionic conduction in CaF2/BaF2 nanoscale heterostructures, Sata et. al, Nature, 408, 2000

Conductivity Enhancement

Rela

tive

conc

entra

tion

1

1

1

δo

δo

δo

Normalized space coordinate0 2 4

L << λ

L ≤ λ

L > λ

λ: Debye lengthL: Film thickness

Electrolyte

Y2O3 – ZrO2

Electrode

(La0.8Sr0.2MnO3) O2-

σnanoσmicro >>

?

Nanoscale hetero-structures

Reactivity transport

Obtain fundamental level knowledge Obtain fundamental level knowledge about the about the layer/grain sizelayer/grain size--effecteffect::

Chemical, physical, and structural properties of theelectrode interfaces•Defect chemistry•Strain state

Charge transportCatalytic activity

Characterization of interface transport propertiesCharacterization of interface transport properties

SiteSite--specific highspecific high--resolution resolution microscopy and microscopy and spectroscopy is needed to characterizespectroscopy is needed to characterize::–– Important relationship between the Important relationship between the defect chemistry and strain defect chemistry and strain and the and the

conductivity and catalytic activity at the interfaceconductivity and catalytic activity at the interface and nearand near--interface regions interface regions (while under polarization):(while under polarization):

5 nm

90° [010] tilt GB

Structure and defect chemistry

Synthesis and nano-fabrication

Transport and electronic structure

in situNano-laminate

heterolayers

Electrode

Trench

Wire

Becker et al., PRL, 89, 2002

Modeling and simulations of transport propertiesModeling and simulations of transport properties

Predictive modeling capabilityPredictive modeling capability is needed for identifying the is needed for identifying the promising interface structures in a more efficient way.promising interface structures in a more efficient way.

Close coupling with the experiments using model material systemsClose coupling with the experiments using model material systems..

Goal: Elucidating and predicting the transport propertiesGoal: Elucidating and predicting the transport properties–– First principles calculations: First principles calculations:

formation energies for charged defects in a given interface confformation energies for charged defects in a given interface configurationigurationStrain state of the interfaceStrain state of the interface

–– Atomistic simulationsAtomistic simulationsCharge transfer and transport properties at the interfaceCharge transfer and transport properties at the interface

Model representation of the YSZ-CeO2 near-interface region. Sayle et al., J. Matls. Chem., 16 (11) 2006.

YSZ

CeO2

Multidisciplinary approach for studying Multidisciplinary approach for studying the conducting interfacesthe conducting interfaces

Reaction pathways, diffusivities; on model,

simple, clean microstructures.

Site-specificity, crystallography,microchemistry.

Atomistic:Reaction pathway &

mechanism, diffusivity Mesoscale, continuum:

Electrochemical response

Electronic Structure:Inter-atomic potentials

Atomistic:Dynamic & static re-

configuration.

Electronic Structure:Inter-atomic potentials,

full electronic structures, formation energies.

Reaction energetics, chemical bonding, electronic structure; at surfaces and interfaces.

Experiments Modeling / Simulations

Thermodynamic equilibrium re-

constructions near the interfaces

Structure of the transition states

Transport of oxygen, cations, and vacancies

Phenomena

With capabilities that we have and are developing at MIT, With capabilities that we have and are developing at MIT, and with external collaborations:and with external collaborations:

Concluding remarksConcluding remarksNuclear energy can provide clean nonNuclear energy can provide clean non--electric energy carriers.electric energy carriers.Hydrogen production processes at high temperature and corrosiveHydrogen production processes at high temperature and corrosiveenvironment have severe materials constraints.environment have severe materials constraints.Degradation of materials for steam electrolysis must be mitigateDegradation of materials for steam electrolysis must be mitigated.d.““ActivityActivity”” and and ““degradationdegradation”” are competing phenomena in are competing phenomena in determining the operating temperature of the SOECs.determining the operating temperature of the SOECs.A fundamental understanding is needed for the important role of A fundamental understanding is needed for the important role of interfaces on the activity of the conducting materials for steaminterfaces on the activity of the conducting materials for steamelectrolysis electrodes, using advanced scientific characterizatelectrolysis electrodes, using advanced scientific characterization ion tools.tools.A predictive capability is needed using advanced multiscale A predictive capability is needed using advanced multiscale modeling and simulations.modeling and simulations.

AcknowledgementsAcknowledgementsDrs. David Carter, Deborah Myers and Jennifer Mawdsley, ANL, Drs. David Carter, Deborah Myers and Jennifer Mawdsley, ANL, for SOEC materials and degradation.for SOEC materials and degradation.Drs. KeeDrs. Kee--Chul Chang and Hoydoo You, ANL, for Chul Chang and Hoydoo You, ANL, for in situin situ xx--ray ray characterization of surfaces.characterization of surfaces.Dr. Burc Misirlioglu, MIT, for transport at interfaces.Dr. Burc Misirlioglu, MIT, for transport at interfaces.

Backup slidesBackup slides

Internal / buried interface transport propertiesInternal / buried interface transport propertiesImportant relationship between: the Important relationship between: the phases and defect chemistry phases and defect chemistry and the and the conductivity and catalytic activity at the interfaceconductivity and catalytic activity at the interface and and nearnear--interface regions (while under polarization):interface regions (while under polarization):–– SiteSite--specific highspecific high--resolution microscopy and spectroscopy is needed.resolution microscopy and spectroscopy is needed.

(La0.85Sr0.15)2CoO4La0.6Sr0.4CoO3

Oxygen exchange profile using SIMSSase et al. Proc. 7th Eur. SOFC Forum, 2006

Oxygen Incorporation Enhancement

5 nm

90° [010] tilt GB

VT - STS / STM

Structure and defect chemistry

Synthesis and nano-fabrication

Transport and electronic structure

Nano-laminate heterolayers

Electrode

Trench

Wire

CrCr--CoCo--O particles found on the surface of the O particles found on the surface of the oxygen electrode bond coat oxygen electrode bond coat

Plan view of bond coat of Plan view of bond coat of a cell from the 2000 h a cell from the 2000 h stackstackXX--ray diffraction revealed ray diffraction revealed a spinel phase (ABa spinel phase (AB22OO44))

–– Cr:CoCr:Co ~ 9:7 by EDS~ 9:7 by EDS

CrCr--containing containing spinelspinel also also found using SEM and found using SEM and Raman spectroscopy in the Raman spectroscopy in the 1000 h stack1000 h stack

–– Particles ~ 1 Particles ~ 1 μμmm–– Cr:CoCr:Co ~ 2:3~ 2:3

Comparison of Four Nuclear Hydrogen TechnologiesComparison of Four Nuclear Hydrogen Technologies

Fixed hydrogen andFixed hydrogen andelectricity productionelectricity production

HighHigh--Temperature GasTemperature Gas--Cooled Cooled Reactor(HTGRReactor(HTGR))

Hybrid sulfur thermoHybrid sulfur thermo--electro electro chemical (chemical (HySHyS))

Pure hydrogenPure hydrogenHighHigh--Temperature GasTemperature Gas--Cooled Cooled Reactor (HTGR)Reactor (HTGR)

HighHigh--temperature sulfurtemperature sulfur--iodine iodine cycle with extractive HI (SI)cycle with extractive HI (SI)

YesYesHighHigh--Temperature GasTemperature Gas--Cooled Cooled Reactor (HTGR)Reactor (HTGR)

HighHigh--temperature steam temperature steam electrolysis (HTE)electrolysis (HTE)

YesYesAdvanced Light Water ReactorAdvanced Light Water Reactor(ALWR) (ALWR)

HighHigh--pressure, lowpressure, low--temperature temperature water electrolysis (HPE)water electrolysis (HPE)

Product FlexibilityProduct FlexibilityHydrogen/Electricity?Hydrogen/Electricity?Nuclear Reactor TypeNuclear Reactor TypeHydrogen Production ProcessHydrogen Production Process

2.972.97HySHyS--HTGRHTGR

3.263.26SISI--HTGRHTGR

2.932.93HTEHTE--HTGRHTGR

2.982.98HPEHPE--ALWRALWR

LevelizedLevelized CostCost[$/kg][$/kg]

PlantPlantCost and performance assumptions based on information from Technology Insights (06, 07).

Plant Evaluations: Summary of ResultsPlant Evaluations: Summary of Results

With current cost and performance estimates, the flexible electrWith current cost and performance estimates, the flexible electrochemical technologies (HPEochemical technologies (HPE--HTGR and HTGR and HPEHPE--ALWR) are the most profitableALWR) are the most profitable

–– Hydrogen remains the main product for these plants, but they swiHydrogen remains the main product for these plants, but they switch to electricity production a tch to electricity production a substantial amount of timesubstantial amount of time

100.0100.0100.0100.09.729.728418411919NoNoHySHyS--HTGRHTGR

100.0100.0100.0100.08.898.8912491249--348348NoNoSISI--HTGRHTGR

80.580.582.482.410.5210.5211701170295295YesYes

100.0100.0100.0100.09.809.80118311838383NoNoHTEHTE--HTGRHTGR

65.765.769.269.210.8510.8510781078283283YesYes

100.0100.0100.0100.09.999.99108410841717NoNoHPEHPE--ALWRALWR

Time Time [%][%]

Prod. Prod. [%][%]

Expected HExpected H22productionproduction

Expected IRRExpected IRR[%][%]

Std.DevStd.Dev. . ProfitProfit

[M $][M $]

Expected Expected ProfitProfit

[M $][M $]

Product Product FlexibilityFlexibility

TechnologyTechnology

Price assumptionsPrice assumptions–– Average prices: Electricity 50 $/Average prices: Electricity 50 $/MWhMWh, Hydrogen 3 $/kg, Hydrogen 3 $/kg–– Price volatility: 0.12 (per year), GBM processPrice volatility: 0.12 (per year), GBM process–– Hydrogen/electricity correlation: 0.5Hydrogen/electricity correlation: 0.5