A Method for Determining DepositionRates in an ElectrorefinerUsing Electrode Potentials

D. S. Rappleye, M. S. Yim, R. M. Cumberland

2012 International Pyroprocessing Research ConferenceAugust 26 – 29, 2012

Fontana, WI

Objective

• Determine species deposition rates at thecathode

– Product optimization

– Safeguards

• Selected measures:

– Electrode potentials

– Cell current

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Background

• “Normal” operating condition

– Only uranium

U U

U U

Zr Zr

U

U

U

U

U U

U

U

U

Pu

Pu

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Background

• Two “abnormal” scenarios

– Zirconium co-deposition

U

Zr Zr

U

U

U

U

U U

U

U

U

Pu

Pu

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Background

• Two “abnormal” scenarios

– Plutonium co-deposition

Pu Pu

U Pu

U U

U

U

Pu

U

U

U

U

Pu

Pu

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Theory

• Notation and Symbols

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electrode area electrode potential Faraday’s constant

current i current density c mass transfer coefficient

n electrons transferred universal gas constant reaction rate

temperature mole fraction

Symbols

α transfer coefficient activity coefficient η overpotential

Subscripts & Superscripts

concentration equilibrium j species

current step exchange/standard s surface

Theory

• Cell Current

– Species current density

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Theory

• Electrode Potential

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Theory

• Cell Current

– Additional relationship

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Assumptions

• At low current

– Bulk concentrations are constant• 3∙1F (289,455C) to reduce one mole of U and Pu

– 4/3 as much for Zirconium

– Bulk concentration is equivalent to surfaceconcentration

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Method

1. Set current to zero

2. Step current up incrementally

3. Measure potential at each current setting

• Two-species example:

Istep

Iop

EstepOCP

Eop

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Method

• General Approach

– Solve for bulk mole fractions at low current• = # of species, = # of low current steps

– Validate mole fractions at operating conditions

Mole Fractions are constantbetween current steps

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Method

DepositionRates

Assume“normal”operation

1. MeasureOCP

2. Solve forXU

3+ usingOCP

3. Determinecurrent at Eop

Match?

4. Step upcurrent

7. Solve forXS

3+ at Estep

8. Solve forXU

3+ at OCP

9. Solve IT atEstep

Match?

Yes

No

No

Yes

6. Differencedue to side

reaction

5. Determinecurrent at

Estep

10. Determineηc,U

3+ and ηc,Sn+

11. Solve IT

at Eop

Match?

12. Additionalor AlternativeSide Reaction

YesNo

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Validation

• No experimental data

• Tested versus an existing model– Enhanced REFIN with Anodic Dissolution (ERAD)

– Based on current and

potentials from ERAD,

mole fractions were

predicted

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0

50

100

4 5 6 7

Cu

rre

nt

(A)

Time (hr)

Results

• Unknown variables– Species mole fractions

• Deposition rates based on mole fractions

Species Predicted Mole Fraction ERAD Mole Fraction

U 0.0194 0.0113

U, Zr 0.0210, 4.99E-4 0.0175, 4.48E-4

U, Pu 1.91E-3, 3.00E-3 2.08E-3, 4.22E-4

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Limitations

• Number of species

• Low current steps

• High concentration of inactive species

• Solid cathode

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Limitations

• Number of species

• Low current steps– Finite number of “low” current steps

• High concentration of inactive species

• Solid cathode

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Limitations

• Number of species

• Low current steps

• High concentration of inactive species

• Solid cathode

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Limitations

• Number of species

• Low current steps

• High concentration of inactive species– Actinide build-up

• Solid cathode

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Limitations

• Number of species

• Low current steps

• High concentration of inactive species

• Solid cathode

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Limitations

• Number of species

• Low current steps

• High concentration of inactive species

• Solid cathode– Liquid cathode

• Additional concentration

• Additional current step

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Limitations

• Relax constant bulk mole fractionassumption

– Requires• Analysis of anode potentials

• Account of all species in molten salt

– Resolves the first three limitations

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Summary

• Molten salt compositions from

– Cell current

– Electrode potentials

• Initial modeling attempt

– Constant salt composition

• Results are comparable to ERAD

• Potential resolutions to model limitations

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Acknowledgements

• David McNelis

• Jun Li

• Michael Simpson

• Robert Hoover

• Supathorn Phongikaroon

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References

• Hoover, R. O. (2010). Development of a Computational Model for theMark-IV Electrorefiner. Idaho Falls, ID: University of Idaho.

• Park, B.-G. (1999). A time-dependent simulation of molten saltelectrolysis for nuclear wastes transmutation. Seoul, South Korea:Seoul National University.

• Prentice, G. (1991). Electrochemical Engineering Principles.Englewood Cliffs, NJ: Prentice Hall.

• Zanello, P., Fabrizi de Biani, F., & Nervi, C. (2012). InorganicElectrochemistry:Theory, Practice and Application, 2nd Edition.Cambridge: The Royal Society of Chemistry.

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