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more representative of confined aquifer and more near from a storativity
value. The storavities calculated for the vertical and sub-vertical fracture sets
are a 'mix' between a storativity and a specific yield coefficient. That is why
the resulting storativity value (no unit) is calculated as following according
to the set of horizontal fracture parameters:
S
=
e
..
S
set1
.(
d
set1
.
R
2
set1
+
d
set2
.R
2
set2
+
d
set3
.
R
2
set3
) (6)
where
d
seti
= density, set i (centres/m
2
),
e
= fracture thickness (m),
R
seti
=
fracture radius, set i (m
2
) and
S
set1
= horizontal fracture storavity (1/m) and
falls within the range of 3.89 × 10
-6
, case 4 (Table 2) and 3.22 × 10
-7
,
case 5 (Table 2).
CONCLUSIONS
Numerical calibration was performed following a trial and error process.
Although the solution may not be unique, we end with a combination of
parameters that provides the set of responses shown in Fig. 1 when simulating
a slug-test in a random fracture network. Total fracture density is about
0.02 m
-3
, 30% of the fractures being sub-horizontal. Sizes are ranging in
between 1 and 10 m, fracture thickness is about 0.01 m and porosity of the
infilling material is set to 30%. Calibrated fracture permeability is close to
10
-2
m/s, while the fracture storativity lies in between 10
-3
and 10
-4
m
-1
.
Using these numbers to evaluate the permeability tensor by simulating
parallel flow in a 100 m × 100 m × 30 m cell, in two perpendicular directions
successively, leads to equivalent permeabilities ranging from 5.0 × 10
-6
to
7.3 × 10
-6
m/s, with a mean value of 6.2 × 10
-6
m/s. An anisotropy factor
of 1.25 is found in favour of the North/South direction, as a result of the
existence of a set of north-south sub-vertical fractures.
REFERENCES
Ahmed, S. and Ledoux, E., 1999. Optimal Development and Management of Ground-
water in Weathered Fractured Aquifers, CEFIPRA IFCGR Project no. 2013-1,
21 pp.
Bruel, D., 2002. Impact of Induced Thermal Stress During Circulation Tests.
Oil &
Gas Science and Technology Rev
.
IFP
,
57(5):
459-470.
Bruel, D., Cacas, M.C., Ledoux, E. and de Marsily, G., 1994. Modelling Storage
Behaviour in a Fractured Rock Mass.
J. of Hydrology
,
162:
267-278.
Cacas, M.C., Ledoux, E., Marsily, G.de, Barbreau, A., Tillie, B., Durand, E., Feuga,
P. and Peaudecerf, P., 1990. Modeling Fracture Flow with a Discrete Fracture
Network: Calibration and Validation, 1. The Flow Model,
Water Resources
Research
,
26(3):
479-489.
Rejeb, A. and Bruel, D., 2001. Hydromechanical Effects of Shaft Sinking at Sellafield
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Int. J. Rock of Mech and Min. Sci. & Geom. Abstr
,
38:
17-29.
