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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
3
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
4
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
5
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).
6
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
8
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?
9
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
10
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
12
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)
13
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
15
4.1 Propagation of frontal the equipotential surface
4. Results
Pumpedaquifer
Inactive zone
Inclined substratumWell
16
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
17
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
18
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↘
19
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)
20
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
22
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
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)
24
Well
25
Algorithm of Bourdet et al. (1989)
26Bonus
Estimation de n
General solution
Generalized difffusivity equation
Laplace transformation
Hyp:
Constant head head at the boundaries
Initial head = 0 m at the begining
27Bonus
Estimation de n
For a little u,
𝑑ℎ
𝑑𝑙𝑜𝑔𝑡= 𝑡
𝑑ℎ
𝑑𝑡= 2,3. 𝐶. 𝑣 𝑡𝑣
Slope of ds/dlogt
28
Rafini, S., & Larocque, M. (2012). Numerical modeling of the hydraulic
signatures of horizontal and inclined faults. Hydrogeology Journal, 20(2),
337-350
29
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
Case study 2
Altered granitic aquifer
30
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/
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
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
33
1.4 Field data: spherical flow regime
2. Objectives and issue of the study
Geology: clay; sand; rock