Modeling the evolution of spectral induced polarization during calcite precipitation on glass beads

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1 Modeling the evolution of spectral induced polarization during calcite precipitation on glass eads Philippe Leroy Shuai Li Damien Jougnot André Revil Yuxin Wu

Complex conductivity in frequency or spectral induced polarization (SIP) > Sinusoidal electrical current injected. Electrical potential difference measured. Thesis A.

2 Complex conductivity in frequency or spectral induced polarization (SIP) > Sinusoidal electrical current injected. Electrical potential difference measured. Thesis A. Ghorani (2007) Pierre and Marie Curie University > Phase shift etween imposed current and measured voltage. > Method sensitive to conduction and polarization currents at the solid/water interface and inside conductive metals. jeudi 16 juin 2016 > 2

Complex conductivity (CC) > Method developed initially for the mining exploration ecause of its sensitivity to conduction and polarization currents in

Application of the CC method in hydrogeophysics to estimate for instance the transport properties of porous media for environmental and hydrogeological

3 Complex conductivity (CC) > Method developed initially for the mining exploration ecause of its sensitivity to conduction and polarization currents in conductive metals. > High increase of the accuracy of CC measurements, inversion and interpretation during the last decades. Application of the CC method in hydrogeophysics to estimate for instance the transport properties of porous media for environmental and hydrogeological investigations. > Example: monitoring remediation of groundwaters contaminated y organic pollutants using zero valent iron microparticles. Orozco et al. (2015) EST jeudi 16 juin 2016 > 3

4 Grain polarization model > However, frequency ehavior of SIP spectra still not exactly known.? > Necessity to develop mechanistic SIP models descriing key transport phenomena at the pore scale responsile for the measured SIP response. > Grain polarization model applied to calcite precipitation in porous media. jeudi 16 juin 2016 > 4

5 > Surface charge compensated y: - adsored counter-ions at the Stern, - adsored counter-ions and co-ions in

5 Electrical doule layer around calcite > Surface charge of the calcite particle in water due to the: - calcium surface sites >Ca-OH caronate surface sites >CO > Surface charge compensated y: - adsored counter-ions at the Stern, - adsored counter-ions and co-ions in the diffuse layer. > Assumed shear plane at the eginning of the diffuse layer. No water flow High viscosity Water flow Low viscosity jeudi 16 juin 2016 > 5

6 Triple layer model (TLM) of calcite (1) > Stoichiometric matrix of aqueous and surface reactions Li, Leroy et al. (2016), Influence of surface conductivity on the apparent zeta potential of calcite, Journal of Colloid and Interface Science jeudi 16 juin 2016 > 6

7 Triple layer model of calcite (2) > Parameters - total surface site density, - equilirium constants of adsorption, - capacitance C 1. > Measured data - surface charge densities Q 0, - sorption isotherms, - electrophoresis, streaming potential. Assumption: φ d ζ > Output data - electrical potentials, zeta potential, - surface site densities of adsored ions, - surface charge densities of the Stern and diffuse layer. Computed excess of charge controlling the SIP response. jeudi 16 juin 2016 > 7

8 Grain polarization model of Leroy et al. (2008) > Assumptions - continuous diffuse layer and discontinuous Stern layer. > Application of a sinusoidal electrical field - electromigration in the diffuse layer DC surface conductivity of the diffuse layer. Leroy et al. (2008), Complex conductivity of watersaturated packs of glass eads, Journal of Colloid and Interface Science - electromigration and diffusion in the Stern layer polarization, AC surface conductivity of the Stern layer. jeudi 16 juin 2016 > 8

9 Improvement of the grain polarization model of Leroy et al. (2008) > Multivalent and monovalent ions adsored at the Stern layer > Effects of the diffuse layer on Stern layer polarization Weak diffuse layer Strong diffuse layer decrease of the relaxation time of the polarization of the Stern layer increase of the associated characteristic frequency f τ 2 a / 2 D M f 1 /τ S D S : diffusion coefficient of the counter-ions in the Stern layer M: effects of the diffuse layer on Stern layer polarization (M 1) : angular frequency ω 2 πf jeudi 16 juin 2016 > 9

10 Grain polarization model theory (1) 1. TLM electrical potential at the onset of the diffuse layer surface charge density of the Stern layer Q ions surface site densities in the diffuse layer d Γ i φ d 2. Specific surface conductivities of the Stern and diffuse layer Σ s β Q d s 3. Complex surface conductivity of the particle N i 1 ez i B d i Γ d i β : ions surface moility in the Stern layer d B : ions effective moility in the diffuse layer i (electromigration+electroosmosis) σ s * (d, ω) σ s (d, ω) i ωε s ε s : dielectric permittivity of the particle (constant) 3 σ s * (d, ω) 4 d s 1 i ωτ i ωτ (d) (d) d s i ωαρ s ε 0 τ f 1 2 a D 2 M 8 d D 2 M 8 k d B 2 q T β M 1 2 jeudi 16 juin 2016 > 10

Grain polarization model theory (2) 4. Superposition principle: complex conductivity of particles of different sizes Q σ * f(d ) σ * (d, ω) s i s i i 1 f(d i ): particle size distriution 5.

11 Grain polarization model theory (2) 4. Superposition principle: complex conductivity of particles of different sizes Q σ * f(d ) σ * (d, ω) s i s i i 1 f(d i ): particle size distriution 5. Differential effective medium theory: porous medium complex conductivity m σ : water conductivity * /σ * w s w ε w : water dielectric permittivity * / σ* s F: formation factor σ * 1 - σ w σ * F 1 - σ σ * σ iω ε w F -m w w : porosity m: cementation exponent Self-similar model of rock (from Sen et al. (1981), A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass eads, Geophysics) jeudi 16 juin 2016 > 11

Grain polarization model - comparison with experimental data (1) > Spectral induced polarization (SIP) experiment of calcite precipitation Wu et

12 Grain polarization model - comparison with experimental data (1) > Spectral induced polarization (SIP) experiment of calcite precipitation Wu et al. (2010), On the complex conductivity signatures of calcite precipitation, Journal of Geophysical Research: Biogeosciences. jeudi 16 juin 2016 > 12

13 Grain polarization model - comparison with experimental data (2) > Measured sample complex conductivities s * () I()/(V()k) s * () s is se i s (s ² +s ²) 0.5 tan -1 (s /s ) s /s I(): injected sinusoidal current V(): measured electrical potential difference k: geometric factor : phase shift etween measured electric potential difference and imposed current s sensitive to conduction currents s sensitive to polarization currents > Imaginary conductivity response of calcite precipitation s f s f jeudi 16 juin 2016 > 13

14 Grain polarization model - comparison with experimental data (3) > Inverted particle size distriution jeudi 16 juin 2016 > 14

15 Grain polarization model - comparison with experimental data (4) > Adjusted cementation exponent 0.3 F -m (s ~ 0.06 S m -1 (day 2 - day 12)) jeudi 16 juin 2016 > 15

16 Grain polarization model - comparison with experimental data (5) > Modeled electrochemical properties of the calcite/water interface > Complex conductivity model parameters jeudi 16 juin 2016 > 16

17 Conclusions and perspectives > Complex conductivity model of the electrochemical polarization of the Stern layer surrounding calcite particles > Monovalent and multivalent counter-ions in the Stern layer > Effects of the diffuse layer on Stern layer polarization > Grain conductivity model comined with a triple layer model of the electrochemical properties of the calcite/water interface > Measured complex conductivity spectra of calcite precipitation on glass eads successfuly reproduced y our surface complexation and conductivity models > Particle size distriution and particle shape deduced from our models > Application of our models to estimate transport properties of sandstones containing saline solutions favoring calcite precipitation according to SIP measurements jeudi 16 juin 2016 > 17

18 Thank you for your attention!

Modeling the electrochemical properties and the complex conductivity of calcite

Modeling the electrochemical properties and the complex conductivity of calcite Shuai Li Philippe Leroy Damien Jougnot André Revil Nicolas Devau Frank Heberling Mohamed Azaroual Complex conductivity in