Paul Glover & Emilie Walker Universit Laval, Qubec, Canada , Q - - PowerPoint PPT Presentation

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Paul Glover & Emilie Walker Universit Laval, Qubec, Canada , Q - - PowerPoint PPT Presentation

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Paul Glover & Emilie Walker Universit Laval, Qubec, Canada , Q , Matthew Jackson Imperial College, London, UK The classical Helmholtz Smoluchowski equation relates the streaming potential coupling coefficient (SPCC) to li ffi

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SLIDE 1

Paul Glover & Emilie Walker

Université Laval, Québec, Canada , Q ,

Matthew Jackson

Imperial College, London, UK

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SLIDE 2

The classical Helmholtz‐Smoluchowski equation relates the streaming potential li ffi i t (SPCC) t coupling coefficient (SPCC) to

  • zeta potential
  • Pore fluid dielectric permittivity

( )

2

f s f f s

C ε ζ η σ = + Σ Λ

Pore fluid dielectric permittivity

  • Pore fluid conductivity
  • Pore fluid viscosity

( )

Developped for capillary tubes Commonly applied to rocks H b lid t d f k ( f t t ti l) However, never been validated for rocks (no measure of zeta potential) Never even been a theoretical model applied to real rocks DESPITE most of the theoretical tools being available since 1998

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 4. Plenary
  • 5. Individual
  • 6. Conclusions

2/18

g

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SLIDE 3

In this presentation: D l t f th i d Development of the required theoretical tools Compilation of a SPCC dataset for p rocks Compilation of a zeta potential dataset f k for rocks Modelling SPCC of rocks as a function

  • f salinity
  • f salinity

Modelling ζ of rocks as a function of salinity

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

3/18

  • 4. Plenary
  • 5. Individual
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SLIDE 4

SPCC vs. Pore fluid salinity Silica, glass, Silica, glass, sand and sandstone 11 sources

Acknowledgments to Jaafar (2009)

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

4/18

  • 4. Plenary
  • 5. Individual
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SLIDE 5

Zeta potential

  • vs. Pore fluid

salinity salinity Silica, glass, sand and sandstone 7 so rces 7 sources

Acknowledgments to Jaafar (2009)

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

5/18

  • 4. Plenary
  • 5. Individual
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SLIDE 6

The method is as follows: 1. Calculate the pore fluid conductivity (salinity and temperature)

Sen and Goode (1992)

( ) (

)

3 2 2 4 5 1 2 3 6

, 1

f f f f f

d d T T C d d T d T C C d C σ ⎛ ⎞ + = + + − ⎜ ⎟ ⎜ ⎟ + ⎝ ⎠

Sen and Goode (1992)

2. Calculate the pore fluid relative permittivity (salinity and temperature)

( )

( )

2 3 2 3

T C a a T a T a T c C c C c C ε ε + + + + + +

Olhoeft (1980)

3 Calculate the pore fluid viscosity (salinity and temperature)

( )

( )

1 2 3 1 2 3

,

f f

  • f

f f

T C a a T a T a T c C c C c C ε ε = + + + + + +

3. Calculate the pore fluid viscosity (salinity and temperature)

( )

( )

( ) ( )

1 2 1 3 2 4 3 4

, exp exp exp

m m f f f f

T C e e T e C e T C η α α α α = + + + +

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

6/18

Phillips et al. (1978)

  • 4. Plenary
  • 5. Individual
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SLIDE 7

4. Define the physical chemistry of the double layer

( )

  • SiOH

SiO + H

K − +

> ⇔ >

5 Calculate or set the pore fluid pH (SiO ‐H O‐CO )

  • SiOH + Me

SiOMe + H

M e

K + +

> ⇔ >

5. Calculate or set the pore fluid pH (SiO2‐H2O‐CO2)

( ) ( )

3 2 1 1 2

2

a b w H H H

C C C C K K C K K

+ + +

− − − + − =

Lide (2009); Revil et al. (1999)

6 Calculate the Debye screening length and shear plane distance

16 16 17 2 19 3

6.9978 10 5.0178 10 2.4434 10 7.1948 10

w

K T T T

− − − −

= × + × − × + × 6. Calculate the Debye screening length and shear plane distance

χζ = 2.4×10-10 m

2

and 2000

  • r b

d f

k T e I ε ε χ = Ν

2

1 2

n f f i i

I Z C = ∑

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

7/18

ζ

  • 4. Plenary
  • 5. Individual

2000

f

e I Ν 2 i

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SLIDE 8

7. Calculate the Stern plane potential

( )

3

8 10 10 pH

H

k C ⎛ ⎞ ⎡ ⎤

( )

3

8 10 10 10 2 ln 3 2

pH pH r o b Me f a b f b d

  • f

s

k T K C C C C k T e I e K ε ε ϕ

− − −

⎛ ⎞ ⎡ ⎤ × Ν + + + + ⎜ ⎟ ⎢ ⎥ = ⎜ ⎟ Γ ⎢ ⎥ ⎜ ⎟ ⎣ ⎦ ⎝ ⎠

Revil and Glover (1997; 1998)

8. Calculate the zeta potential

( )

exp

d d ζ

ζ ϕ χ χ = −

Revil and Glover (1997; 1998)

( )

exp

d d ζ

ζ ϕ χ χ

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

8/18

  • 4. Plenary
  • 5. Individual
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SLIDE 9

9. Calculate the surface conductance

EDL Prot Stern s s s s

Σ = Σ + Σ + Σ

  • s

s Me f Stern

e K C β Γ Σ

( )

2 3 3

8 10 10 10 10 2

s pH pH r o b Me f a b f pH Me f

  • f

s

k T K C C C C K K C I e K ε ε

− − − − − −

Σ = ⎛ ⎞ ⎛ ⎞ ⎡ ⎤ × Ν + ⎜ ⎟ + + + ⎜ ⎟ ⎢ ⎥ + + ⎜ ⎟ ⎜ ⎟ Γ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎣ ⎦ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

( )

1 3

10 10 1 2

pH f Me EDL pH s f Na H

  • s

C K R B C B S e K

+ +

− − − −

⎛⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ + ⎜⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Σ = + − + ⎜⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Γ ⎜ ⎟ ⎜ ⎝ ⎠ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎝

( )

1 3

10 10 1 2

f

s pH pH pK f Me f Cl OH

  • C K

B C B S e K

− −

+ − −

⎜ ⎟ ⎜ ⎝ ⎠ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎝ ⎞ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ + ⎟ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ + − ⎟ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Γ ⎜ ⎟ ⎟ ⎝ ⎠ ⎢ ⎥ ⎝ ⎠

( )

2

s

e K− ⎜ ⎟ ⎜ ⎟ Γ ⎜ ⎟ ⎟ ⎝ ⎠ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦⎠

3

2 10 10

r o b pH f

k T R C ε ε

− −

× Ν = +

( )

3

8 10 10 10

w

pH pK pH r o b f

S k T C ε ε

− − −

= × Ν + +

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

9/18

Revil and Glover (1997; 1998)

  • 4. Plenary
  • 5. Individual

10

f

C +

( )

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SLIDE 10
  • 10. Calculate the SPCC

( )

F m d d P V C

s f f f s

Σ + = Δ Δ = 4 σ η ζ ε

Glover and Déry (in press)

Fundamental constants (kb and NA etc.).

f f

Environmental conditions (T etc.). Fluid parameters (salinity, pH, pKw, pK1 and pK2 etc.). Rock microstructure parameters (F, m, φ, d etc.). Rock-fluid interface parameters, i.e., the electro-chemical parameters

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

10/18

associated with surface adsorption reactions (pKme, pK– etc.).

  • 4. Plenary
  • 5. Individual
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SLIDE 11

Parameter Symbol Value or range Units Reference Model variables Temperature T 25

  • C

Experimental condition Pore fluid salinity Cf 10‐5 – 3.98 mol/L Varied between limits Pore fluid pH pH 6 ‐ 8 (‐) Varied between limits F d t l t t Fundamental constants Dielectric permittivity in vacuo εo 8.854×10‐12 F/m Lide (2009) Boltzmann’s constant kb 1.381×10‐23 J/K Lide (2009) Charge on an electron e 1 602×10‐19 C Lide (2009) Charge on an electron e 1.602×10 19 C Lide (2009) Avagadro’s number N 6.02×10+23 /mol Lide (2009) Fluid parameters Added acid concentration Ca variable mol/L Calculated from pH Added acid concentration Ca variable mol/L Calculated from pH Added base concentration Cb variable mol/L Calculated from pH Surface mobility βs 5×10‐9 m2/s/V Revil and Glover (1997) Reaction constant carbonisation pK1 7.53 (‐) Wu et al. (1991)

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

11/18

  • 4. Plenary
  • 5. Individual

1

Reaction constant dehydrogenisation pK2 10.3 (‐) Wu et al. (1991)

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SLIDE 12

Parameter Symbol Value or range Units Reference Rock parameters Grain size (diameter) d 2×10‐4 m St Bee's SST (Jaafar et al., 2009) Cementation exponent m 1.86 (‐) Calculated Formation factor F 19.80 (‐) St Bee's SST (Jaafar et al., 2009) ( ) ( f )

log log m F φ = −

Porosity φ 0.19 (‐) St Bee's SST (Jaafar et al., 2009) Rock/fluid interface parameters Surface site density Γs

  • 1×10+19

sites/m2 Adjusted to fit data Bi di f i Adj t d t fit d t Binding constant for cation (sodium) adsorption on quartz pKme 7.1 (‐) Adjusted to fit data Disassociation constant for dehydrogenisation of SiOH pK(‐) 7.5 (‐) Adjusted to fit data dehydrogenisation of SiOH Shear plane distance χζ 2.4×10‐10 m Revil and Glover (1997) Surface conduction (protonic) Σs

Prot

2.4×10‐9 S Revil and Glover (1997) Surface mobility βs 5×10‐9 m2/s/V Revil and Glover (1997)

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

12/18

  • 4. Plenary
  • 5. Individual

y βs / / ( )

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SLIDE 13

SPCC vs. Pore fluid salinity Silica, glass, sand and sand and sandstone 3 different pHs 4 different grain 4 different grain sizes General properties of properties of the SPCC database and absolute values are well described Grain size can b t l

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

13/18

be extremely important

  • 4. Plenary
  • 5. Individual
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SLIDE 14

Zeta potential

  • vs. Pore fluid

salinity Silica glass Silica, glass, sand and sandstone 3 different pHs 3 different pHs Database measurements are very are very scattered Highly sensitive to changes in pH

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

14/18

  • 4. Plenary
  • 5. Individual
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SLIDE 15
  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

15/18

  • 4. Plenary
  • 5. Individual
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SLIDE 16

Individual modelling suggests Individual modelling suggests that the operating pH is low (about pH 5.5).

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

16/18

  • 4. Plenary
  • 5. Individual
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SLIDE 17

Compiled: A database of SPCC vs. pore fluid salinity for silica‐based rocks Compiled: A database of zeta potential vs. pore fluid salinity for silica‐ based rocks Developped: A method for modelling the SPCC and zeta potential of Developped: A method for modelling the SPCC and zeta potential of porous media as a function of pore fluid salinity Theoretical model: Shows systematic variations with pH and grain size Using whole database: The theoretical approach is capable of describing the general properties of the database as well as the absolute values of SPCC and zeta potential absolute values of SPCC and zeta potential Using individual rocks: The theoretical approach is capable of describing some of the fine structure apparent in the individual SPCC

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

17/18

and zeta potential determinations as a function of salinity

  • 4. Plenary
  • 5. Individual
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SLIDE 18

This work has been made possible thanks to funding by the thanks to funding by the Natural Sciences and Engineering Research Council of Canada (NSERC) (NSERC) Discovery Grant Programme

  • 1. Introduction
  • 2. Database
  • 3. Theory
  • 6. Conclusions

18/18

  • 4. Plenary
  • 5. Individual