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CAN EQUIVALENT CONTINUUM MODELS SIMULATE FLOW AND POLLUTANT TRANSPORT IN
FRACTURED LIMESTONE AQUIFER?
EGU 2011 HS8.2 - 1407
C. Masciopinto (1) ([email protected]) and D. Palmiotta (1,2) ([email protected])
(1) Water Research Institute of National Research Council, IRSA-CNR , Bari, Italy – (2) Polytechnic University of Bari, Italy
Pumping tracer test
NAVIER–STOKES SOLUTIONS
Model predictions of flow and
pollutant transport in fractured rocks
are subject to uncertainties due to
imprecise knowledge of the position,
orientation, length, aperture and
density of the fractures. These
properties are difficult to quantify
precisely because fractures are
located in depth in subsoil and,
generally, tectonic and stratigraphic
studies may provide only fracture
frequency and their orientation. The
use of the “equivalent” continuum
models might help hydro-geologists
to solve flow and pollutant transport
problems in fractured aquifers, when
fracture properties are unknown.
Test results have shown a delay of
velocity estimated using continuum
models, with respect to the discrete
model, that decreases by increasing
the hydraulic conductivity of the
limestone
aquifer
under
consideration.
Maximum
discrepancies have been noted for
-4
conductivity (< 10 m/s) typically
associated with non - karst limestone
aquifers.
The tortuosity has been then included
into the codes in order to address
flow velocity calculations in numerical
codes, such as MT3DMS (Zheng, C.
2010).
The known analytical solutions of the NS
equations can be defined in very
simplified conceptual models (Figure 2),
under laminar flow. The presented (Figure
2) conceptual models assume that matrix
blocks are impermeable and, similarly to
MT3DMS, contain a dual domain
mathematical
representation
to
approximate the effects of a fast system
(fractures) and an immobile system (rock
matrix).
APULIA
Calcarenite di Gravina
-4m
well #C
72.5 L/s
p.c.
2.2 m above sea
An improvement of the fissure model has
been achieved. By including a tortuosity
factor  [-] to define b and δch [L], i.e. the
apparent enlarged fissure aperture or tube
size, as
MT3DMS
(Cretaceous)
0.2
-34 m
Injection well #E
0.0
0.3 m
20 m
160
Contour heads (m) during winter 2002
in an equivalent porous media
pz6
140
Water velocity
scale:
120
pz4
100
Water velocity
scale:
120
pz3
80
pz8
100
92 m/d
pz10
pz3
pz11
3.5 m/d
pz7
60
pz2
pz12 pz1
20
pz5
0
20
40
60
80
100
120
140
60
160
pz9
s19
40
pz12
20
Monitored
Wells
0
0.3 m/d
pz7
pz8
pz9
40
35 m/d
pz10
80
Pollution
sources
Observation
Wells
pz4
PT1
PT1
pz11
k: permeability
Calcare di Bari (Cretaceous)
0
20
pz1
roads
Figure 1. Study area
railroad
5
6
7
8
1
9
2
3
4
5
6
7
8
10
Time (min)
Figure 5. Tracer breakthrough curve and expected
concentrations given by IHS (Masciopinto et al., 2008),
MT3DMS and MT3DMS modified codes
40
pz5
60
80
100
IHS
Tortuosity: 0.24
MT3DMS modified
MT3DMS
PT1
Total phenols (26.7 mg/L) during
2004 in the sampled groundwater
from well PT1
s19
Dispersivity: 10m
120
140
Time (d)
Figure. 8 Expected (model) outputs and observed concentrations during
winter 2004 in well PT1 at the contaminated site with conductivity 0.01
cm/s, porosity 0.003 and tortuosity 0.24.
TORTUOSITY/CONDUCTIVITY RELATIONSHIP
k
n
n: porosity
4
pz1
pz2
Figure 7. Velocity vectors
derived from MODFLOW
Figure 6. Apparent contaminant
pathways (outputs) using IHS and
the particle tracking code.
CONCLUSIONS
0.35
Bari (ITALY)
gasification site
0.30
Bari - IRSA
West – Central
Barton Springs, Florida (USA)
Texas (USA)
As the best conceptual model must reproduce the fissure geometry (i.e. apertures,
number, orientation, etc.) of the real medium as closely as possible, tortuosity must be
included in conductive tube models in order to explain groundwater velocities. By using
tortuosity in conductive tubes, underestimations of groundwater velocities in an
equivalent continuum model (i.e. porous medium) can be eliminated. Successful
simulations of flow and pollutant transport have been carried out at the Bari fractured
aquifers by using tortuosity.
0.25
0.20
The tortuosity is a fundamental parameter
in describing the complexity of the path0.15
Walkerton, Ontario (CANADA)
line of water flow propagating within a
0.10
single fracture or a porous medium. That
tortuous paths play an important role in
0.05
0.1
1
10
affecting flow in a rough fractures was
Conductivities of fractured limestone aquifers (m/s)
experienced by Tsang (1984).
An improved solution of MT3DMS was Figure 8. Best-fit of  values obtained by comparing the
obtained by introducing the tortuosity.
5
Alluvial deposits (sand)
Lame
 ch
1
 2

3
Case test of the Bari contaminated site (Southern Italy)
6
7
8
9
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
9
results of tracer tests in some fractured limestone aquifers
REFERENCES
k
n
Tracer: chlorophyll
V: 200 L of solution
C: 0.5 g/L
pz6
140
2
Figure 4. Study area of the field test in Bari (IRSA-CNR)
Apparent pollutant pathways
Contour heads (m)
during winter 2002
Tortuosity (-)
1
b 2

Modified
MT3DMS
Calcare di Bari
0.40
Calcarenite di Gravina (Lower Pliocene)
C/Cmax
0.4
160
and by USING TORTUOSITY…
Chlorophyll
0.6
Figure 3. Stratigraphic
section of the study area
These equations provide different water
velocities when a set of parallel fractures
is modified in an "equivalent" tube model,
by reducing size of the tube diameter and
increasing the tube number. When the
conceptual model of groundwater is not
properly selected velocity underestimation
will occur.
IHS output
0.8
p.c. 16.2 m above sea
-54 m
STUDY AREA
Bari
Schematic cross-section in the
fractured limestone of the tested area
Jurassic fractured
dolomite
Figure 2. Conceptual model
2
2
b
 
 c  
U
U
12  x
32  x
1.0
Total phenols (mg/L)
INTRODUCTION
Masciopinto, C., La Mantia, R. and C.V. Chrysikopoulos 2008. Fate and transport of pathogens in a fractured aquifer in the Salento area, Italy. Water
Resources Research, 44, W01404,doi:10.1029/2006WR005643.
Tsang, Y. W. 1984. The effect of tortuosity on fluid flow through a single fracture. Water resources research, 20 (9), 1209-1215.
Zheng, C. 2010. MT3DMS v 5.3: Modular three-dimensional multispecies transport model for simulation of advection, dispersion and chemical reactions of
contaminants in groundwater systems Supplemental User’s Guide. Department of Geological Sciences, The University of Alabama Tuscaloosa, Alabama 35487,
Technical Report, February 2010.