Anouck FERROUD, Romain CHESNAUX, Silvain RAFINI · 2018. 3. 6. · Abstract n°2120 Anouck FERROUD,...
Transcript of Anouck FERROUD, Romain CHESNAUX, Silvain RAFINI · 2018. 3. 6. · Abstract n°2120 Anouck FERROUD,...
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Abstract n°2120
Anouck FERROUD, Romain CHESNAUX, Silvain [email protected]
Numerical investigations of the spherical flow
regimes induced by constant-rate pumping tests
25-29thSeptember, 2016
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1.1 Terms and concepts
1. Introduction
Pressure front pulse (or pressure wave)
Cross flow area A(r) (equipotential surface)
Radial distance r
r
Pumping well
Aquifer
Constant rate pumping test
Flow lines
Fig. 1: Conceptuel model of the pressure during a pumping test
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1. Introduction
1.2 Constant rate pumping tests : diagnostic tools
Fig. 3: Log-log plot of ds/dlogt
(Bourdet et al., 1989).Fig. 2: Semi-log plot of the s.
Drawdowns
Drawdown-log derivativeds/dlogt
Much more sensitive signalHelp to select the most adapted analytical model
Allows to investigate the flow regimes
+
" The new way " *
s (
m)
ds/d
log
tt (s)
t (s)
* Mattar (1997)
" The old way " *
…But the physical interpretation = still enigmatic
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1.3 Hydraulic interpretation of ds/dlogt
1. Introduction
n = 1 ; A ~ r0
n = 2 ; A~ r
n = 3 ; A ~ r²
Generalized Radial flow (GRF) Model
(Barker, 1988)
A(r): cross-flow area
r: radial distance from the well (m)
n: flow dimension parameter (= flow regime)
n reflects the geometry of the
pressure wave when it diffused
through the aquifer
"Flow geometry combined to the
hydraulic properties of the aquifer"
(Beauheim et Roberts, 1998).
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1.3 Hydraulic interpretation of ds/dlogt
1. Introduction
n = 3 ; A ~ r² spherical
flow regime
How to estimate n from transient well test data? n = 2.(1-v)
n: flow dimension
v: slope of ds/dlogt
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2. Objectives and issue of the study
Objective
To develop advanced tools of intepretation of pumping tests
based on ds/dlogt signal and Barker’s theory
Issue
What are the conceptual models producing a spherical flow
regime?
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1.4 Field data: observation of n in nature
Previous study:
Statistical occurrence of flow dimension in various geological
environments n distribution in nature.
2. Objectives and issue of the study
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 >3.6
Flow dimension
Interpretable n
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1.4 Field data: spherical flow regime
2. Objectives and issue of the study
27 m3/s32 m3/s
27 m3/s
23 m3/s32 m3/s
p = - 0.57 ; n = 3.1
Prof : 76 m
Diamètre : 304 mm
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3.1 The model: HydroGeoSphere (HGS)
3. Methodology
HydroGeoSphere (Therrien et al., 2010, Aquanty, 2015)
HGS = Spatially distributed and physically-based 3D modelling software.
Discretization :
• Finite element method,
• Control-volume finite element method.
Diffusivity equation
For sub-surface and saturated flow:
Numerical implementation:
K: Hydraulic conductivity (m/s)
Ss: Specific storage
h: hydraulic head (m)
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3. Methodology
3.2 The conceptual models
0 1500 3000
xy
z
Well
Pumped
aquifer
Initial head H = 200 m
100
0y = 3000 m
50Const
ant hea
d b
oundary
H =
200
m
Constant h
ead b
oundary H
= 200 m
0 500 1000
xy
z
Well
Inclined substratum
Pumped
aquifer
Inactive zone
Initial head = 600 m
500
0ywell
= 1000 mα
Partially penetrated aquiferInclined substratum
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4.1 Propagation of frontal the equipotential surface
4. Results
Pumpedaquifer
Inactive zone
Inclined substratumWell
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4.1 Propagation of frontal the equipotential surface
4. Results
Inactive zone
Well
A ~ r²Spherical flow regime
A ~ rEarly cylindrical-radial flow
regime
n = 2
0 500 1000
xy
z
Well
Inclined substratum
Pumped
aquifer
Inactive zone
Initial head = 600 m
500
0ywell
= 1000 mα
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4.2 The ds/dlogt signal: inclined substratum
4. Results
Inclined substratum
Interpretation of the hydraulic
signal and detection of the
boundary conditions = more
reliable
0 500 1000
xy
z
Well
Inclined substratum
Pumped
aquifer
Inactive zone
Initial head = 600 m
500
0ywell
= 1000 mα
Constant-head hydraulic boundary
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4.2 The ds/dlogt signal: inclined substratum
4. Results
0,01
0,1
1
10
1,E-02 1,E-01 1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08 1,E+09
ds/d
log
t
α5
10
20
65
75
Spherical flow regime
α: slope of the inclined substratum
0 500 1000
xy
z
Well
Inclined substratum
Pumped
aquifer
Inactive zone
Initial head = 600 m
500
0ywell
= 1000 mα
α↘
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4.2 The ds/dlogt signal: inclined susbtratum
4. Results
y = 4E-05x-0,487
y = 0,0013x-0,49
y = 0,0398x-0,49
y = 37,4x-0,489
0,000001
0,00001
0,0001
0,001
0,01
0,1
1
10
1,E-02 1,E-01 1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08 1,E+09
ds/d
logt
t (s)
K (m/s)10-5
10-3
10-2
10-1
0 500 1000
xy
z
Well
Inclined substratum
Pumped
aquifer
Inactive zone
Initial head = 600 m
500
0ywell
= 1000 mα
m: y intercept
T↗
y = 1E-06x-1,491
1,E-05
1,E-04
1,E-03
1,E-02
1,E-01
1,E+00
1,E+01
1,E+02
1,00E-05 1,00E-04 1,00E-03 1,00E-02 1,00E-01 1,00E+00
m
K (m/s)
log 𝑚 ≈ −1,5. log(𝐾)
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4. Results
0,001
0,01
0,1
1
10
1,E+00 1,E+02 1,E+04 1,E+06 1,E+08 1,E+10
ds/d
log
(t)
t (s)
bwell
1%
2%
3%
4%
5%
10%
25%
50%
75%
90%
100%
0 1500 3000
xy
z
Well
Pumped
aquifer
Initial head H = 200 m
100
0y = 3000 m
50
Const
ant hea
d b
oundary
H =
200
m
Constant h
ead b
oundary H
= 200 m
bwell↘
bwell
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5. Discussion and conclusion
The derivative approach doesn’t need more data, but it gives much more
information!
- qualititative: analysis of flow geometry
- quantitative: estimation of hydraulic properties with more reliability
Non-uniqueness of the flow regimes!!!
Partially penetrated aquifer n = 3
An inclined substratum n = 3
Geological settings = essential to inteprret a pumping test!
Sequences of n = help to reduce the non uniqueness!
Sensistivity analysis empirical equation estimation of K from a ds/dlogt
curve fitting
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02/11/2013Application et développement d’outils diagnostiques hydro-géo-physiques et géochimiques
pour la détermination des propriétés hydrauliques et physiques des aquifères 23
Marie-Claire Houmeau painting
Anouck FERROUD, Romain CHESNAUX, Silvain [email protected]
Quebec (CANADA)
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Well
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Algorithm of Bourdet et al. (1989)
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Estimation de n
General solution
Generalized difffusivity equation
Laplace transformation
Hyp:
Constant head head at the boundaries
Initial head = 0 m at the begining
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Estimation de n
For a little u,
𝑑ℎ
𝑑𝑙𝑜𝑔𝑡= 𝑡
𝑑ℎ
𝑑𝑡= 2,3. 𝐶. 𝑣 𝑡𝑣
Slope of ds/dlogt
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Rafini, S., & Larocque, M. (2012). Numerical modeling of the hydraulic
signatures of horizontal and inclined faults. Hydrogeology Journal, 20(2),
337-350
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1.4 Field data: spherical flow regime
1. Introduction
27 m3/s32 m3/s
27 m3/s
23 m3/s32 m3/s
p = - 0.57 ; n = 3.1
Prof : 76 m
Diamètre : 304 mm
Fig.: Hydraulic signal of s and ds/dlogt of the Mout_3 well,
Vendée, Pays-de-la-Loire, France.
Hyp 1 : Partial penetration
Geology: Granitic sand
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Case study 2
Altered granitic aquifer
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Water supply from the weathered horizon to the fissured
rock (Dewandel et al. 2006).
Fig. 13: Conceptual model of a partly eroded palaeo-weathering profile on hard rock
(Dewandel et al. 2006). Partial penetration or
Partial completion
Hydrogeological interpretationSpherical flow
and/orLeaky effects Wellbore effects
(Dewandel et al. 2006)
Fig. 14: Illustrations of a partial penetration /completion.http://www.fekete.com/
http://nptel.ac.in/courses/105103026/20
http://petrowiki.org/
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0,001
0,01
0,1
1
10
1,E+00 1,E+02 1,E+04 1,E+06 1,E+08 1,E+10
s(m
)
t (s)
Boundaries and
hydraulic properties
Tested parameter
3D grid
0,001
0,01
0,1
1
10
1,E+00 1,E+02 1,E+04 1,E+06 1,E+08 1,E+10
s(m
)
t (s)
0,001
0,01
0,1
1
10
1,E+00 1,E+02 1,E+04 1,E+06 1,E+08 1,E+10
ds/d
log
(t)
t (s)
0,001
0,01
0,1
1
10
1,E+00 1,E+02 1,E+04 1,E+06 1,E+08 1,E+10
ds/d
log
(t)
t (s)
bs
100%
bs2%
100%
bs
100%
bs2%
100%
Confined aquifer
Well
5. Discussion
3.2 The conceptual model 1: inclined substratum
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Screen thickness bs (m)
0,001
0,01
0,1
1
10
1,E+00 1,E+02 1,E+04 1,E+06 1,E+08 1,E+10
ds/d
log
(t)
t (s)
bs
1%
2%
3%
4%
5%
10%
25%
50%
75%
90%
100%
Boundaries and
hydraulic properties
Tested parameter
3D grid
Confined aquifer
5. Discussion
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1.4 Field data: spherical flow regime
2. Objectives and issue of the study
Geology: clay; sand; rock