On the value of induced polarisation in hydrogeophysics

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On the value of induced polarisation in hydrogeophysics Andrew Binley Lancaster University, Lancaster, UK Email: [email protected]

Acknowledgements Lancaster University researchers Ahmed Elshenawy, Melanie Fukes, John Keery, Nick Kettridge Others Giorgio Cassiani, Andreas Kemna, Sabine Kruschwitz, David Lesmes, Lee Slater

Outline Hydrogeophysical drivers Data dump (something old, something new, something borrowed, etc) -

Physical controls on SIP/IP Other controls Modelling constraints The way forward

Hydrogeophysical drivers

Static imaging

Dynamic imaging

Rock physics model(s)

Rock physics model(s)

structure

process

(e.g. permeability maps)

(e.g. transport of solute)

z (m)

20

10

0 20

30

40

Kowalsky et al. (2006)

Improved hydrogeological model

50 x (m)

60

70

80

Kemna (2003)

Hydrogeophysical drivers We can image geophysical parameters (resistivity, chargeability, dielectric constant, seismic velocity) in the subsurface …

British Geological Survey (2004)

… BUT we need geophysical parameters that are related to specific hydrological properties.

Some parameters may give us information about water content (from radar) or pore water salinity (from resistivity) but what about other structural properties (hydraulic conductivity, pore size characteristics, etc.) ? Induced polarization (IP) and spectral induced polarization (SIP) may give such information because of the implicit link with the pore/grain interface.

Hydrogeophysical drivers What got hydrogeophysics interested in IP? IP - permeability models Links to grain size

e.g. Vanhala (1997)

Good for mapping lithological boundaries?

Links to permeability

Dachnov (1975) Börner et al. (1996)

Hydrogeophysical drivers Polarisation linked to Grain size

σ”” (S/m)

σ” (µS/m) S/m)

Specific surface area to pore volume

Spor (µm-1) Slater, Ntarlagiannis & Wishart (2006)

d10 (mm) Slater & Lesmes (2002)

Hydrogeophysical drivers Allowing us to consider a link between polarisation and permeability (or hydraulic conductivity) Tube/crack models – Kozeny-Carman

k =

r

2 eff

aF

Grain models

k ∝

r

2 g

Hydrogeophysical drivers Grain size model: (e.g. modified Hazen model)

K calc = bd10n

1.E-02

1.0E-02

1.E-03

1.0E-03

Kcalc (m/s)

Kcalc (m/s)

Tube model: Börner (modified Kozeny Carmen) model a K calc = c FS por

1.E-04 1.E-05

1.0E-04 1.0E-05

1.E-06

1.0E-06

1.E-07 1.E-07

1.0E-07 1.0E-07

1.E-05 1.E-03 Kmeas (m/s)

sands & sand/clay mixes

1.0E-05

1.0E-03

Kmeas (m/s) tills

tills

sands/silts[1]

sands/silts[2]

Slater and Lesmes (2001)

Hydrogeophysical drivers A means of imaging permeability?

F & Spor (accounting for variation in fluid saturation, salinity, etc.)

σ’ (mS/m)

σ” (µS/m)

Kemna, Binley & Slater (2004)

Hydrogeophysical drivers

a k= FS cpor

k (darcies)

Kemna, Binley & Slater (2004)

Hydrogeophysical drivers Most models assume constant phase

Figure from Börner et al. (2006)

Hydrogeophysical drivers However, there is growing evidence that the frequency dependence of electrical conductivity is affected by properties that are, or influence, key hydrogeological parameters 50

ρ (Ωm)

-30

40

ρ

φ (mrad)

-20

30 20 10

-10

φ

0 0.01

0.1

1

10

100

Frequency (Hz)

1000

10000

Physical controls For a set of similar sandstones, what is the link between SIP and physical properties?

50

-30

40

ρ

ρ 30 (Ωm) 20 10

0.01

0.1

1

10

100

Frequency (Hz)

τ0 =

R

2

2 µ s kT

log (τ, in s)

2

Klein & Sill (1982)

1

0.001M NaCl 0

-4

-10

φ

0

According to Schwarz (1962) model for a single spherical unit of radius R:

φ (mrad)

-20

-3

log (grain size, in m)

1000

10000

Physical controls According to Schwarz (1962) model for a single spherical unit of radius R:

τ0 =

R

2

2 µ s kT

Which is clearly too simplified for a real porous media, but …

Physical controls For a real porous media, relaxation will be related to some length scale of the porous media

Figure from Titov et al.(2004)

Relaxation model Common to use phenomenological models For example, the Pelton Cole-Cole model Resistivity model

Conductivity model

   1  ρ (ϖ ) = ρ 0 1 − m1 − c    1 + (iϖτ ) 

m=

ρ0 − ρ∞ ρ0

ω = 2πf

ρ

ρ 30 (Ωm)

m=

-25

φ (mrad)

-20

20

-10

-5 0.1

1

10

100

Frequency (Hz)

ω = 2πf

σ’

σ’ 30 (Sm-1)

-25

σ” (Sm-1)

-20

20

φ 0.01

σ∞ −σ 0 σ∞

-15

-15

10

0 0.001

  1 1  1  = 1 − m1 − c  σ ′(ω ) + σ ′′(ω ) σ 0   1 + (iϖτ ) 

1000

10000

σ”

10

0 0.001

-10

-5 0.01

0.1

1

10

100

Frequency (Hz)

1000

10000

Physical controls The Cole-Cole relaxation model is (mathematically, at least) similar to the commonly used van Genuchten moisture-retention curve van Genuchten

Cole-Cole

θ (h) − θ r 1 = n 1−1 / n θs −θr 1 + (h / h0 )

[

]

Effective pore size We expect the time constant τ to be correlated to a characteristic pore size D0 [= f(1/h0) ] Pore size distribution We expect the Cole-Cole exponent c to be correlated to exponent n

ρ (ϖ ) − ρ ∞ 1 = ρ0 − ρ∞ 1 + (iϖτ )c ρ (ϖ ) = ρ ∞ +

mρ ∞

1 + (iϖτ )c

ρ0 − ρ∞ m= ρ∞

Sandstone samples Samples from a 20 m core were supplemented by local quarry blocks

1m

Physical controls

Physical properties Measurements made of hydraulic conductivity, particle size distribution, pore size distribution, porosity, CEC. SEM images also obtained. Geophysical properties Measurements of SIP spectra made on samples saturated with synthetic groundwater solution. Binley, Slater, Fukes & Cassiani (2005)

Physical controls Sandstone Sample P-

C+

C-

P+ End chamber (fluid or gel filled)

Binley, Slater, Fukes & Cassiani (2005)

Physical controls 10

ρ (Ωm)

8

ρ

water sample

-3 -2

6

φ

4

-1

2

1

0

2 1000

14

φ (mrad)

0

0.01

ρ (Ωm)

-4

0.1

1

10

100

-4

gel sample

ρ

12 10

-3 -2

φ

8 6

-1 0

4 2

1

0

2 1000

0.01

0.1

1

10

Frequency (Hz)

100

φ (mrad)

Physical controls Example mercury intrusion data Sample Depth in core (m) EC7-5 8.8 m EC15-5 15.96 m EC16-1 17.61 m Cumulative injection volume (ml/g)

D0 (µm)

n

16.99 µm 1.647 22.55 µm 2.247 52.95 µm 2.589

0.2

EC16-1

0.16

EC15-5 EC7-5

0.12 0.08 0.04 0 1000

100

10

1

Pore size (µm)

0.1

0.01

Physical controls Example van Genuchten model fit to mercury intrusion data 0.16

Cumulative injection volume (ml/g)

Sample EC7-5 depth: 8.81 m

0.12

0.08

vG fit with D0 = 16.99 µm n = 1.647

0.04

0 1000

100

10

1

Pore size (µm)

0.1

0.01

Physical controls Example SIP data fit ρ0 m τ c

(using Specfit from Andreas Kemna)

ρ (Ωm)

Cole-Cole fit = 33.76 Ωm = 0.120 = 0.180 s = 0.342 -25

ρ 30

-20 20

-15

VEC18-2 Depth: 19.06 m

φ

10

0 0.001

-10

-5 0.01

0.1

1

10

Frequency (Hz)

100

1000

10000

φ (mrad)

Physical controls EC16-1 EC15-5 EC7-5

0.2

Cumulative injection 0.16 volume 0.12 (ml/g) 0.08

Increasing pore size

0.04 0 1000

100

10

1

0.1

0.01

Pore size (µm) 50

VEC16-1 depth = 17.61 m VEC15-5 depth = 16.07 m VEC7-5 depth = 8.22 m

ρ (Ωm)

-30

φ (mrad)

ρ

40

-20

30 20

φ

10

-10

0 0.01

0.1

1

10

100

1000

10000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Physical controls Variation in relaxation time with dominant pore size 1 0.9 0.8 0.7

τ = 0.011 D0 1.04 r2 = 0.61

0.6

Time constant τ (s)

0.5 0.4 0.3

Graph 2 Eggborough core vertical Eggborough core horizontal Eggborough blocks vertical Eggborough blocks horizontal Hatfield blocks vertical Hatfield blocks horizontal

0.2

0.1 10

20

30

Pore diameter D0 (µm)

40

50

60

Physical controls Increase in relaxation time with pore size Similar trend observed by Scott and Barker (2003) Decreasing τ φ

Frequency

Increase in τ

Physical controls

τ (s)

Relaxation time observed to be a function of grain size for packed sands

Grain size (mm)

Kemna et al. (2005)

Physical controls Pore size distribution controls 2.6

2.4

Exponent n (−)

Graph 2 Eggborough core vertical Eggborough core horizontal Eggborough blocks vertical Eggborough blocks horizontal Hatfield blocks vertical Hatfield blocks horizontal

2.2

2.0

Relationship is not significant and reverse of expected

1.8

1.6 0.24

0.28

0.32

Exponent c (-)

0.36 0.40 Binley, Slater, Fukes & Cassiani (2005)

Physical controls Recall - specific surface area to pore volume – link to polarisation

Slater, Ntarlagiannis & Wishart (2006)

Physical controls Specific surface area to pore volume – no significant link to polarisation for sandstones studied

σ"[mS/m]

1

10

100

Spor [µm ] -1

Hydrogeophysical drivers However, recall the length scale link to hydraulic conductivity … Tube/crack models – Kozeny-Carman

k =

r

2 eff

aF

Grain models

k ∝

r

2 g

Physical controls We see link between relaxation time and hydraulic conductivity 1 0.9 0.8 0.7

τ = 0.37 K 0.26 r2 = 0.78

0.6

Time constant τ (s)

0.5 0.4 0.3 Graph 2 Eggborough core vertical Eggborough core horizontal Eggborough blocks vertical Eggborough blocks horizontal Hatfield blocks vertical Hatfield blocks horizontal

0.2

0.1 0.01

0.1

1

Hydraulic conductivity K (m/d)

10 Binley, Slater, Fukes & Cassiani (2005)

Physical controls Observed by others (but different relationship)

Kemna et al. (2005)

Physical controls Testing the universality of the relationships Compilation of 50 sandstones and 6 other materials No spectra Sturrock

Scott

Binley et al.

Breede

Kruschwitz

Börner &

Slater et

new

[1999]

[2003]

[2005]

[2006]

(2008)

Schön

al. [2006]

samples

sand-clay

sandstone

[1991] Material

sandstone

sandstone

sandstone

sandstone

sandstone,

sandstone

other

mixtures

building materials

Sample origin

USA

Germany,

UK

Germany,

UK

Number of samples

3 -3

UK

11 6

-3

Germany

24 3

-3

-3

USA

France

5 3

Germany,

8 3

-3

3

Germany, USA

29

12

5 12x103-10-3

Frequency range (Hz)

10 -10

10 -10

10 -10

10 -10

10 -10

-

-

Pore size distribution
















-

-

Spor (µm )

























σ’’(mS/m]

























φ (-]



















-




-1

Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls Testing the universality of the relationships Compilation of 50 sandstones and 6 other materials ion

Sturrock

Scott

Binley

Breede

Kruschwi

Börner

Slater

Penns’

Other

[1999]

[2003]

et al.

[2006]

tz

& Schön

et al.

Blue

new

[2008]

[1991]

[2006]

new

samples

[2005]

sample Cl-

10

3.4

0.9

8.6

-

~10

-

10

1.6

NO3-

-

-

11.4

-

-

-

10

-

0.1

SO4-

-

0.3

0.9

-

8.3

-

-

-

1.2

Na+

10

6.0

0.9

8.6

16.6

~10

10

10

1.7

Mg2+

-

0.7

0.9

-

-

-

-

-

03

Ca2+

-

0.6

5.7

-

-

-

-

-

2.5

K+

-

-

-

-

-

-

-

-

0.1

100

78

100

90

160

100

150

100

80

σw (mS/m)

Similar electrical conductivity of saturating fluid used – but chemistry different – [consequently some variation in ionic mobility] Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls Specific surface area to pore volume – link to polarisation

σ"[mS/m m]

1

Sturrock [1999] Scott [2003] Binley et al.[2005] Breede [2006] Kruschwitz [2008], sandstones Kruschwitz [2008], others New sandstones Börner and Schön [1991] Slater et al.[2006]

0.1

0.01

0.001 0.1

1

10

Spor [µm-1]

100

Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls Specific surface area to pore volume – link to polarisation

σ"[mS/m m]

1

Sturrock [1999] Scott [2003] Binley et al.[2005] Breede [2006] Kruschwitz [2008], sandstones Kruschwitz [2008], others New sandstones Börner and Schön [1991] Slater et al.[2006]

0.1

0.01

0.001 0.1

1

10

Spor [µm-1]

100

Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls Variation in relaxation time with dominant pore size 1000

100 Sturrock [1999] Scott [2003] Binley et al. [2005] Breede [2006] Kruschwitz [2007], sandstones Kruschwitz [2007], others New sandstones

τ [s]

10

1

?

0.1

0.01

0.001 0.1

1

10

Pore throat diameter D0 [µm]

100

Physical controls Variation in relaxation time with dominant pore size 1000 (omitting samples with small modal pore throat) 100

τ [s]

10

1

0.1

0.01

0.001 10

100

Pore throat diameter D0 [µm] Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls Outliers have high formation factor

Formation facctor F [-]

1000

100

10

1 0.1

1

10

100

Pore throat diameter D0 [µm]

Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls But are not necessarily those with high surface area 1000

Spor [µm m-1]

100

10

1 0.1

1

10

100

Pore throat diameter D0 [µm]

Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls σ' [S/m]

Elb

Spectra show distinctive peak?

1.0x10-2 9.0x10-3 8.0x10-3 0.001

0.01

0.1

1 10 Frequency [Hz]

100

1000 1000

σ" [S/m]

1.0x10-4 100

8.0x10-5 6.0x10-5

10

4.0x10 0.001

0.01

0.1

1 10 Frequency [Hz]

100

1000

τ [s]

-5

1

1.9x10

-2

0.01

1.8x10

-2

0.001

0.001

0.01

0.1

1 10 Frequency [Hz]

100

1000

0.01

0.1

1 10 Frequency [Hz]

100

1000

0.1

1

10

100

Pore throat diameter D0 [µm]

6.0x10-5

σ" [S/m]

Brick

σ' [S/m]

0.1

4.0x10-5 2.0x10-5 0.0x100 0.001

Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls ‘outlier’ spectra show flatter limb?

3x10-3 2x10-3

σ" [S/m]

1x10-3 0.001

0.01

0.1

1 10 Frequency [Hz]

100

1000 1000

4x10-5

100

2x10-5

10

0.001

0.01

0.1

1 10 Frequency [Hz]

100

1000

Gravenhorster 1x10 σ' [S/m]

1

0.1

1x10-2 -2

0.01

-3

9x10

8x10-3 0.001

σ" [S/m]

τ [s]

σ' [S/m]

Tennessee

0.001

0.01

0.1

1 10 Frequency [Hz]

0.01

0.1

100

1000

100

1000

0.1

1

10

100

Pore throat diameter D0 [µm]

2.0x10-4

1.0x10-4 0.001

1 10 Frequency [Hz]

Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls

Differential intrusion [ml/g]

Explained by long tails on ‘outlier’ pore size distributions? Brick 0.1 0.01

Diffferential intr trusion [m ml/g]

0.001

Differential intrusion [ml/g]

0.1

1

10

100

Pore throat diameter [µm]

Elb

0.1 0.01 0.01

0.1

Gravenhorster

1

10

100

Pore throat diameter [µm]

0.1 0.01 0.001

Differential intrusion [ml/g]

0.01

0.1

0.01

Tennessee

0.1

1

10

100

10

100

Pore throat diameter [µm]

0.01 0.001

0.01

0.1

1

Pore throat diameter [µm]

Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls Equivalent to an increase in surface roughness?

Leroy et al. (2008)

Physical controls Small pore throat, high surface area, high σ”, relaxation time, τ, not controlled by modal pore size but dominated by connected diffusion paths, flatter upper limb of the relaxation curve.

Spor [[µm-1]

100

10

σ" Frequency [Hz]

1 0.1

1

σ" Frequency [Hz]

Large pore throat, low surface area, small σ”, relaxation time, τ, increases with modal pore size. 10

100

Pore throat diameter D0 [µm] Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Physical controls - summary Experimental data to date suggests that there is a link between relaxation time and some measure of a hydraulic length scale for some media.

K = f (τ ) But how do the IP parameters vary due to other factors (states)?

Other controls - salinity Increase in polarisation due to increase in surface charge density. Observed peak at around EC = 1 S/m for Berea Decrease due to 0.1M NaCl

Berea sandstone

reduction in ionic mobility

Lesmes & Frye (2001)

Other controls - salinity Similar behaviour observed in other sandstones Helby sandstone

Phase

Decrease in σ”

Scott & Barker (2005) based on data in Flath (1989)

Other controls - salinity Less pronounced effect seen on relaxation times May be stable for normal range of groundwater salinity

Difference in pore fluid chemistry (different mobilities)

Slight decrease in τ with increase in salinity τpk (s)

log (τ, in s)

Changes attributed to reduction of electrical double layer thickness or ionic mobility?

Slight decrease in τ with increase in salinity log (grain size, in m) Klein & Sill (1982)

Scott & Barker (2005)

Other controls - salinity Relaxation time may be stable for normal range of groundwater salinity 1.5x10 Berea sandstone σ" [Sm-1]

-4

5.0x10-5

0.001 2.0x10-4

σ" [Sm-1]

0.01M NaCl 0.005M NaCl 0.002M NaCl

1.0x10-4

0.01

0.1

1 10 Frequency [Hz]

100

1000

Coconino sandstone

1.5x10-4

0.01M NaCl 0.005M NaCl 0.002M NaCl

1.0x10-4 5.0x10-5 0.001

0.01

0.1

1 10 100 1000 Frequency [Hz] Kruschwitz, Binley, Lesmes and Elshenawy (in review)

Other controls - salinity But variation in τ with salinity controlled by grain packing/pore structure

Kemna et al. (2005)

Other controls – fluid saturation We need to understand how the SIP parameters vary under unsaturated conditions in order to be able to characterise hydraulic properties from measurements in the vadose zone Effective pore size We may expect the time constant τ to decrease with decreasing saturation as the pores that contribute become smaller Pore size distribution We may expect the Cole-Cole exponent c to increase as the range of contributing pore sizes decreases

Cole-Cole Saturation = 1 Saturation < 1

φ

Frequency

Other controls – fluid saturation Legend Graph 1

Sample VEC16-1

100%

D0 = 52.95 µm

-15

φ (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC16-1

100% 88%

D0 = 52.95 µm

-15

φ (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC16-1

100% 88% 73%

D0 = 52.95 µm

-15

φ (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC16-1

100% 88% 73% 53%

D0 = 52.95 µm

-15

φ (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC16-1

100% 88% 73% 53% 48%

D0 = 52.95 µm

-15

φ (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC16-1

100% 88% 73% 53% 48% 36%

D0 = 52.95 µm

-15

φ (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC16-1

100% 88% 73% 53% 48% 36% 25%

D0 = 52.95 µm

-15

φ (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Sample VEC16-1 ρ0 (Ωm)

m/ρ0 (Ωm-1)

200

0.002

100 80

ρ0 = 51.6 S –1.27 r2 = 0.90

60

0.001 0.0008 0.0006

40 1 0.9 0.8 0.7

0.6

0.5

0.4

0.3

1 0.9 0.8 0.7

0.2

Saturation (-)

0.6

0.5

0.4

0.3

0.2

0.3

0.2

Saturation (-)

c (-) 0.28

τ (s) 1

τ = 1.71 S 3.30

0.26

r2 = 0.96

0.24

0.1

0.22 0.20 0.18

0.01 1 0.9 0.8 0.7

0.6

0.5

0.4

Saturation (-)

0.3

0.2

1 0.9 0.8 0.7

0.6

0.5

0.4

Saturation (-)

Other controls – fluid saturation Legend Graph 1

Sample VEC7-5

100%

D0 = 19.16 µm

-20

φ -15 (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC7-5

100% 83%

D0 = 19.16 µm

-20

φ -15 (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC7-5

100% 83% 75%

D0 = 19.16 µm

-20

φ -15 (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC7-5

100% 83% 75% 58%

D0 = 19.16 µm

-20

φ -15 (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC7-5

100% 83% 75% 58% 50%

D0 = 19.16 µm

-20

φ -15 (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC7-5

100% 83% 75% 58% 50% 42%

D0 = 19.16 µm

-20

φ -15 (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Legend Graph 1

Sample VEC7-5

100% 83% 75% 58% 50% 42% 30%

D0 = 19.16 µm

-20

φ -15 (mrad)

-10

-5 0.01

0.1

1

10

100

1000

Frequency (Hz) Binley, Slater, Fukes & Cassiani (2005)

Other controls – fluid saturation Sample VEC7-5 ρ0 (Ωm)

m/ρ0 (Ωm-1)

200

0.002

100 80

ρ0 = 50.6 S –1.35

60

r2 = 0.81

0.001 0.0008

40

0.0006

1 0.9 0.8 0.7

0.6

0.5

0.4

0.3

1 0.9 0.8 0.7

0.2

Saturation (-)

0.6

0.5

0.4

0.3

0.2

0.3

0.2

Saturation (-)

c (-) 0.36

τ (s) 0.1

τ = 0.32 S 2.51

0.34

r2 = 0.97

0.32 0.30 0.28 0.26

0.01 1 0.9 0.8 0.7

0.6

0.5

0.4

Saturation (-)

0.3

0.2

1 0.9 0.8 0.7

0.6

0.5

0.4

Saturation (-)

Other controls – fluid saturation SIP variation with saturation Time constant τ appears strongly correlated saturation – consistent with assumed relationship with effective pore size Cole-Cole exponent c show no clear relationship with saturation [limited coverage of parameter space ?]

These results imply that the length scales of the polarisation process reduce with fluid saturation.

Other controls – fluid saturation Contrary relationships have been observed

Increase in τ with reducing saturation

Ghorbani et al. (2009)

Other controls – temperature To date, the effects of temperature have been neglected in experimental studies. According to the Schwarz (1962) model for a single spherical unit of radius R:

R2 τ0 = 2 µ s kT Surface ionic mobility

Temperature

(1) How does temperature affect the electrical relaxation? (2) Do we need to account for temperature in any field data interpretation?

Other controls – temperature Sandstone samples Four different, well characterised, sandstones were selected: Berea (US), Cottaer (Germany), Bentheimer (Germany), Sherwood (UK). Several drill plugs (20 to 25 mm diameter) were obtained for each sandstone. Physical properties Various properties were available: pore size distribution, porosity, formation factor. Geophysical properties Each sample was saturated with same pore fluid and measurements made of spectral induced polarisation (SIP) spectra at temperatures: 5 to 30 °C in steps of 5 °C. The electrical conductivity of the pore fluid was measured at each step.

Other controls – temperature Properties of sandstone samples Dominant pore throat size D0 (µm)

Specific surface

Porosity

Formation factor

Spor (µm-1)

Φ (−)

F (-)

Berea

22.50

8.30

0.18

15.9

Cottaer

18.25

50.85

0.22

14.43

Bentheimer

20.79

10.73

0.19

22.1

Sherwood (VEC 7-5) Sherwood (VEC 16-3)

19.16 35.56

31.37 13.16

0.32 0.32

4.87 3.58

Sample

Properties of saturating fluid Ion

Cl-

NO3-

SO4-

Na+

Mg2+

Ca2+

K+

Conc (mmol L-1)

1.6

1.0

1.2

1.7

0.3

2.5

1.0

Electrical conductivity at 20 °C: ~800 µS cm-1

Other controls – temperature Berea: sample 11

1.5 Hz conductivity normalised to 25 °C 1.20

Variation in water conductivity is recognised to be around 2% per °C.

σ’ σ’(25°C)

Fluid: real Slope = 1.88

1.00 0.80 0.60 5

1.20

The bulk real and imaginary conductivity variation are consistently greater than that of the fluid.

σ’ σ’(25°C)

10

15

20

25

30

20

25

30

25

30

Temperature (°C)

Sample: real Slope = 2.12

1.00 0.80 0.60 5

1.20

σ” σ”(25°C)

10

15

Temperature (°C)

Sample: imaginary Slope = 2.37

1.00 0.80 0.60 5

10

15

20

Temperature (°C)

Results – change in conductivity spectra with temperature Berea: sample 11 Results expressed as real and imaginary conductivity spectra σ’ (Sm-1)

8.0x10-3 6.0x10

-3

4.0x10

-3

0.001

σ” (Sm-1)

10

-4

8.0x10

-5

6.0x10

-5

4.0x10

-5

2.0x10

-5

0.001

0.01

0.1

1

10

100

1000

100

1000

Frequency (Hz)

0.01

0.1

1

10

Frequency (Hz)

30 °C 25 °C 20 °C 15 °C 10 °C 5 °C

Results – change in relaxation time with temperature Recall Schwarz (1962) model of relaxation around suspended colloid: R2 τ0 = 2 µ s kT

Decreasing τ with increase in temperature 10-4

σ” (Sm-1)

8.0x10-5 6.0x10-5 4.0x10

2.0x10-5

T = temperature in °K 5.00

τ (s) 4.00

-5

0.001

0.01

0.1

1

Frequency (Hz)

Berea: samples 5, 11 & 12

3.00 2.00 1.00

5 °C

30 °C 0.0033

10

0.0034

0.0035

1/ T (°K-1)

0.0036

100

1000

Results – change in Cole-Cole parameters with temperature Other Cole-Cole parameters show variation with temperature

Berea: samples 5, 11 & 12

c (-) 0.60 0.56

5 °C

0.52 0.48

30 °C

0.44 0.0033

Pelton Cole-Cole 1 σ ′(ω ) + σ ′′(ω ) =

σ∞ −σ 0 σ∞

1.2x10

m=

0.0036

Berea: samples 5, 11 & 12

2.4x10-4 2.0x10-4

0.0035

1/ T (°K-1)

mσ0 (Sm-1)

  1  1   1 − m 1 −  c   σ 0   1 + (iϖτ ) 

0.0034

1.6x10-4 -4

0.0033

0.0034

0.0035

1/ T (°K-1)

0.0036

Results – change in conductivity spectra with temperature Cottaer: sample 2 Results expressed as real and imaginary conductivity spectra σ’ (Sm-1)

2.5x10

-2

1.5x10

-2

5.0x10

-3

0.001

σ” (Sm-1)

3.0x10

-4

2.0x10

-4

10

-4

0.001

Again – we see a 0.01 decreasing 0.1 1 τ with 10 100 increaseFrequency in temperature (Hz)

1000

0.01

1000

0.1

1

10

Frequency (Hz)

100

30 °C 25 °C 20 °C 15 °C 10 °C 5 °C

Results – change in relaxation times for all sandstones All samples Different sandstones show different response to temperature i.e. not the simple relationship expected

τ (s)

5.00 4.00 Berea Cottaer Bentheimer Sherwood

3.00 2.00 1.00 0.00 0.0033

30 °C

0.0034

0.0035

1/ T (°K-1)

0.0036

5 °C

Results – change in relaxation times for all sandstones All samples Relative trends appear related to formation factor

τ

2.00

τ @25°C 1.60

Formation factor F = 22.1

Berea Cottaer Bentheimer Sherwood

F = 15.9 F = 14.3

1.20

F = 4.2

0.80

0.0033

30 °C

0.0034

0.0035

1/ T (°K-1)

0.0036

5 °C

Results – removing effects of conductivity of solution Berea samples Comparison of relaxation time with fluid conductivity and temperature

τ (s)

Increase in σw due to conc.

6.00

5 °C 30 °C

5.00 4.00

Increase in σw due to T

3.00 2.00 1.00 0.02

0.04

0.06

0.08

0.1

σw (Sm-1) Temperature effects more pronounced than salinity effects

Other controls – temperature (implications) Relaxation models Experimental results suggest that the relaxation time is inversely related to temperature but affected by structural property of matrix. Impact on lab and field data Affect on temperature on relaxation could be greater than equivalent salinity effect. We observed affects of up to 5% change in τ per °C – Laboratory observations must report temperature Field observations must be corrected for temperature

Other controls – summary Relaxation models The relaxation process appears to be strongly affected by fluid saturation, temperature and (to a lesser degree) salinity of the pore fluid.

Modelling constraints Are there other constraints (related to modelling)? How realistic is our ultimate goal?

Static imaging Rock physics model(s)

structure (e.g. permeability maps)

Improved hydrogeological model

Modelling constraints Uncertainty in estimates of relaxation model parameters

Deterministic

Median of stochastic Chen et al. (2008)

Modelling constraints Are we using the right relaxation models?

Leroy et al. (2008)

Perhaps we should be considering a distribution of relaxation times, e.g. Morgan & Lesmes (1994); Nordsiek & Weller (2008)

Modelling constraints Our empirical relationships are not good for K estimation Unless we can estimate τ accurately 1 0.9 0.8 0.7 0.6

Time constant τ (s)

0.5 0.4 0.3

0.2

0.1 0.01

0.1

1

Hydraulic conductivity K (m/d)

10

Modelling constraints Imaging IP from field data is not trivial – e.g. impact of data errors Imaginary Real BH6125

[b] conductivity

[a] conductivity 0

0

5

5

10

10

BH6124

Depth (m)

Sand/Gravel 15

15 Sand/Silt

20

20 Silt/Clay

25

25

Gamma (c.p.s.)

30

30

35

35

40

40 0

5 10 Distance (m)

1

10 σ ' (mS/m)

0

100

1

5 10 Distance (m)

10 100 σ ′′ (µS/m)

200 400 600

200 400 600

Sandstone

Gamma (c.p.s.)

Kemna, Binley & Slater (2004)

Modelling constraints The sensitivity of the image varies within the image and is dependent on the technique and may be a function of the geophysical parameter Cross hole ERT example Hydrology

True geophysics

Resolution

Model geophysics

Day-Lewis, Singha and Binley (2005)

The way forward?

The way forward - modelling We cannot use geophysical imaging alone – we need to use geophysics to support other data (not replace it)

Static imaging Measurements of hydrological states

Rock physics model(s)

structure (e.g. permeability maps)

Well log data

The way forward – IP parameters Total polarisation models appear more robust than relaxation models for most hydrogeophysical needs K calc

a = c FS por

Kcalc (m/s)

1.E-02 1.E-03 1.E-04 1.E-05 1.E-06

Tube model: Börner (modified Kozeny Carmen) model

1.E-07 1.E-07

1.E-05 1.E-03 Kmeas (m/s)

sands & sand/clay mixes

tills

The way forward – IP parameters But note the scatter in our empirical relationships 1

σ"[mS/m]

Also note that other factors (e.g. salinity, temperature) have a significant effect on the total polarisation

0.1

0.01

0.001 0.1

1

10

Spor [µm-1]

100

The way forward - modelling We MUST appreciate data errors and have an assessment of uncertainty in geophysical and hydrogeophysical results Resistivity image

Corresponding probability

Ramirez et al (2005)

The way forward – understanding key relationships We need a better understanding of the fundamental processes 50

100 µm

-30

40

ρ

ρ (Ωm)

30

φ (mrad) -20

20

-10

10 0 0.01

0.1

1

10

φ

100

1000

Frequency (Hz)

SEM image of Sherwood Sandstone

Revil and Leroy (2004)

10000

The way forward - dynamics

Dynamic imaging

IP may have great value in the study of dynamic processes, e.g. reactive transport or biogeophysical mechanisms

Rock physics model(s)

process (e.g. transport of solute)

z (m)

20

10

0 20

30

40

Improved hydrogeological model

50 x (m)

60

70

80

Kemna (2003)

Don’t get put off if you look at SEM images!