Blöcher, G.

Engelmann, S.

Milsch, H.

Earth-prints Repository

Coupling of hydraulic and electrical transport 
properties in sandstones
Harald Milsch, Guido Blöcher and Silvio Engelmann
GeoForschungsZentrum Potsdam, Section Geothermics
1. Introduction
- In geothermal reservoirs a characterization of the rock permeability (k) is 
essential and a knowledge of the permeability dependence on effective 
pressure (peff) is important.
- The electrical rock conductivity (σ) is significantly easier to measure both in 
the lab and in situ.
- Finding a link between both rock transport properties is therefore desirable.
- Such a link should exist if the rock conductivity is governed by the 
conductivity of a fluid within the pore space as in that case both k and σ
were shown to be dependent on effective pressure. 
- Scope: search suitable coupling through microstructural parameters.
2. Experimental details
Sandstone samples:
Fontainebleau Flechtinger Eberswalder
Fontainebleau Flechtinger Eberswalder
Microstructure:
(optical, crossed nicols)
Sample Porosity         
[%]
Permeability 
[mD]
Formation 
factor [1]
Fontainebleau 7.5 20 125
Flechtinger 9.0 0.03 38
Eberswalder 4.0 0.01 66
Fluid: 0,1 molar NaCl-solution (σ at 40°C = 13 mS/cm)
Sample properties:
Experimental set-up:
Experimental procedure:
- the experiments were performed at T = 40 °C
- k and σ were simultaneously measured
- effective pressure ramping was performed by successively increasing and decreasing
both confining- (pc) and pore pressure (pp):   
pc = [10 - 50 MPa] 
pp = [5 - 45 MPa] 
Intervall = [2.5 - 15 MPa]
3. Experimental results
Effective pressure dependence of permeability and electrical conductivity:
Permeability – conductivity relationship:
4. Microstructural analysis
1) 2D Image Analysis:
Fontainebleau Flechtinger Eberswalder
1) 2D Image Analysis (cont.):
Sample Average 
Porosity [%]
Average 
Pore Radius 
[µm]
Fontainebleau 15.1 21.7
Flechtinger 8.9 14.4
Eberswalder 3,2 12,3
2 ) Hg-Porosimetry:
Sample Porosity [%] Average 
Pore Radius 
[µm]
Specific Inner 
Surface [m2/g]
Fontainebleau 7.1 7.1 0.23
Flechtinger 9.7 1.3 1.40
Eberswalder 5.0 0.4 1.14
5. Integrated comparison of different scaling models
V σ J     :Ohm                   pη
k q     :Darcy ∇⋅−=∇⋅−=
F
1  L  c  k 2 ⋅⋅=
Model ´c [1] L [m]
Hydraulic radius 
(Walsh and Brace (1984))
1/2 (tube)
1/3 (crack)
m = (Vp/Ap)
Hg-Porosimetry
(Katz and Thompson (1986) 
and (1987))
1/226 lc
Tube-Crack 
(Guéguen and Dienes (1989))
1/8 (tube)
8/15 (crack)
rA (tube) 
wA (crack)
Comparison of different scaling models (cont.):
F
1  L  c  k 2 ⋅⋅=
Comparison of different scaling models (cont.):
rF
1  L  c  k 2 ⋅⋅=
- experiments yield sample
dependent parameters 
r and (c · L2)
- (c · L2) is a constant defining
the “permeability” of an
equivalent tube-like channel
for which F = 1
- c and L2 cannot be derived
separately from the experiments
but have to be calculated from
the model of choice
- L is thus a parameter with no
true microstructural meaning F
1  L  c  k 2 ⋅⋅= but
Comparison of different scaling models (cont.):
rF
1  L  c  k 2 ⋅⋅=
Sample r [1] cL2 [mD] L [µm] with
c = 1/8
ftb 1.44 21.23 · 103 13.03
flg 1.03 1.124 0.095
ebe 2.88 1.43 · 103 3.38
6. Conclusions
- At present, the investigated models have to be adjusted for each rock by additional 
empirical parameters to reproduce the experimentally observed k-F relationship 
adequately.
- Potentially, an independent evaluation of k and F as a function of the (pressure
dependent) sample microstructure could yield improved k-F relationships.
- Microstructure-based models require improved analytical methods.
- All models have to be experimentally testable.


Coupling of hydraulic and electrical transport properties in sandstones

http://www.earth-prints.org/bitstream/2122/2702/1/Milsch.pdf

Coupling of hydraulic and electrical transport properties in sandstones

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