Hydraulic Conductivity Characterisation and Effects of Scale in Fractured Rock
James R. Kunkel
Outline
Hydraulic Conductivity Measurement
Scale of Hydraulic Conductivity
Conclusions
Questions
2
Hydraulic Conductivity Measurement
Methods
3
Source: USEPA, 1998 and 2001; Burbey and
Murdoch, 2010 and Burbey et al., 2011
Hydraulic Conductivity Measurement
Scale of Measurement
4
Hydraulic Conductivity Measurement
Fractured Rock Characterization Issues
5
After Marchal, Dewandel and Subrahmanyam, 2004
LEGEND
CFZ = Conductive Fractures
Zone
PFN = Primary Fracture
Network
SFN = Secondary Fracture
Network
HSFN = Horizontal Fractures of
SFN
VSFN = Subvertical Fractures
of SFN
Kx = Hydraulic Conductivity
in x-type of
fracture/material
Sx = Storativity
in x-type of
fracture/material
Hydraulic Conductivity Measurement
6
0
100
200
300
400
500
600
700
800
900
1.00E-071.00E-061.00E-051.00E-041.00E-03
Dep
th (
m-b
gs)
Hydraulic Conductivity (cm/s)
Dacite Porphyry (P1*) Dacite Porphyry (P2) Andesite Porphyry (P4*)
Diorite Porphyry Schist Unidentified
Dacite Porphyry (P1) Basalt Linear (Trend)
Lugeon Tests (Various
Fractured Rock Types) Marmato Mine, Colombia
Hydraulic Conductivity Measurement
7
Time (sec)
Norm
alize
d H
ea
d
No
rma
lize
d H
ea
d
No
rma
lize
d H
ea
d
Falling Head Tests
(Fractured Gneiss) Edgar Experimental Mine,
Colorado USA (GEGN 581)
Hydraulic Conductivity Measurement
8
0
5
10
15
20
25
30
0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 5.00E-05
Dep
th (
mb
gs)
Hydraulic Conductivity (m/s)
0
5
10
15
20
25
30
0 1000 2000 3000 4000 5000 6000
Dep
th (
mb
gs)
Seismic Velocity (m/s)
1.00E-06
1.00E-05
1.00E-04
0 1000 2000 3000 4000 5000 6000
Hyd
rau
lic
Con
du
ctiv
ity (
m/s
)
Seismic Velocity (m/s)
Downhole Seismic Surveys Source: Urban and Pasquarell, 1992
Hydraulic Conductivity Measurement
9
0.1
1
10
100
0.1 1 10 100 1000 10000
Dra
wd
ow
n (
ft)
Time Since Pumping Started (min)
Pumping Well Y-2 Observation Well Y-1 Observation Well T-1 Observation Well T-2 Observation Well T-3
Pumping Tests (Fractured Basalt) Source: Paschis, Kunkel and Koenig, 1988
Hydraulic Conductivity Measurement
10
Tracer Test (Fractured
Basalt) Source: Kunkel and Way, 1992
Hydraulic Conductivity Measurement
Scale of Hydraulic Conductivity by Measurement Method
METHOD
LABORATORY TESTING
SLUG/LUGEON TESTS
BOREHOLE GEOPHYSICS
DOWNHOLE SEISMIC SURVEYS
STRAIN-DEFORMATION SURVEYS
PUMPING TESTS
TRACER TESTS
COMPUTER MODELS
11
INC
RE
AS
ING
SC
AL
E
Scale of Hydraulic Conductivity
What is SCALE?
12
Source: Kunkel, Way and McKee, 1988
REV = Representative
Elementary Volume (of
fractured rock)
Scale of Hydraulic Conductivity
What is SCALE?
A common scale measure is distance (m)
Valid for dispersivity and perhaps storativity
A better scale measure for K is volume (m3)
Volume measures eliminate the issues of length between field and laboratory testing for slug tests vs. laboratory core test
13
Source: Schulze-Makuch and Cherkauer, 1995
Scale of Hydraulic Conductivity
14
Source: Marchal, Dewandel and Subrahmanyam, 2004
PFN = Primary Fracture Network
SFN = Secondary Fracture Network
Scale of Hydraulic Conductivity
15
Source: Schulze-Makuch and Cherkauer, 1995
Scale of Hydraulic Conductivity
K = aLn where:
K = hydraulic conductivity in appropriate units
L = a characteristic length (volume) in appropriate units
a = a fit parameter whose physical meaning is a measure of the medium-characteristic (log hydraulic conductivity of fractured rock, for example)
n = the scale coefficient
16
Source: Kunkel, Way and McKee, 1988
C
o
n
c
e
p
t
u
a
l
l
y
Scale of Hydraulic Conductivity
17
Formation Type
Scale Coefficient
n (1)
Medium Characteristic
a (2)
L Lower
Bound (3)
L Upper
Bound (3)
Porous Flow 0.51 -5.7 >1 100,000
Fracture Flow 0.96 -8.0 50 106
(1) Average scale coefficient of all data.
(2) Average medium-characteristic parameter given as log value (m/s)
(3) Upper and lower bound of the average relationships in m3 of tested formation
Scale as a Volume
Source: Schulze-Makuch and others, 1999
Scale of Hydraulic Conductivity
18
Marmato Mine, Colombia
Hydraulic Conductivity in Fractured Rock Characterisation and Scale
Hydraulic conductivity measurement in fractured rock can include direct and indirect methods, as well as methods which measure at various scales
The most common methods are direct measurement using pumping tests for far-field results and slug/Lugeon tests for near-field results
Hydraulic conductivity in fractured rock may involve identification of various flow boundaries, heterogeneities, and directional issues
19
Hydraulic Conductivity in Fractured Rock
Characterisation and Scale
Use the characterization method appropriate for the scale of the problem
Typically, an order of magnitude change in the characteristic length scale results in about an order of magnitude change in hydraulic conductivity
A REV may not exist if large-scale features such as fracture zones or barrier boundaries exist. Additionally, several REVs may be necessary to adequately characterize a mine site.
20
Hydraulic Conductivity in Fractured Rock
21
FIN
??
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