Well Tests to Characterize Idealized Lateral Heterogeneities by Vasi Passinos and Larry Murdoch...
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Transcript of Well Tests to Characterize Idealized Lateral Heterogeneities by Vasi Passinos and Larry Murdoch...
Well Tests to Characterize Idealized Lateral Heterogeneities
by
Vasi Passinos and Larry Murdoch
Clemson University
K1,S1
K2,S2
Igneous Rocks
Facies Change
Reef
Marine Clay
BatholithBatholith Country Country rockrock
Dike
Channel sand
Floodplain deposits
Conceptual Models
Local Neighboring
T1 S1 T2 S2=S1
L L
2-Domain Model 3-Domain Model
Region 1 Region 3Strip
T1 S1T3 = T1
S3 = S1
L Lw
T2
S2=S1
Methods• 2-Domain Model
– Transient analytical solution using Method of Images (Fenske, 1984)
• 3-Domain Model– Transient numerical model using MODFLOW– Tr and w of the strip were varied. – Grid optimized for small mass balance errors
),,(
11
,,,,1
11Lyxf
dt
Er
Sr
Ttyxd
tE
ds
2-Domain T Contrast – 0.125L
0
2
4
6
8
10
12
14
16
0.1 10 1000 100000td
s d
homogeneous No Flow T1/T2=10
T1/T2=100 T1/T2=5 T1/T2=0.1
T1/T2=0.01 T1/T2=0.5 CH
0
1
2
0.1 10 1000 100000td
ds d
/dln
(t d)
3-Domain T Contrast - 0.125L
0
2
4
6
8
10
12
14
16
0.1 10 1000 100000td
sd
homogeneous No Flow T1/T2=10T1/T2=100 T1/T2=5 T1/T2=0.1T1/T2=0.01 T1/T2=0.5 CH
0
0.5
1
1.5
2
0.1 10 1000 100000td
m =
ds d
/dln
(td)
3-Domain T Contrast - 0.5L
0
2
4
6
8
10
12
14
0.1 10 1000td
sd
homogeneous No Flow T1/T2=10T1/T2=100 T1/T2=5 T1/T2=0.1T1/T2=0.01 T1/T2=0.5 CH
0
0.5
1
1.5
2
0.1 10 1000td
m =
ds
d/d
ln(t
d)
Strip Transmissivness & Conductance
• Hydraulic properties of the strip depend on strip conductivity and width
• Strip is a higher K than matrix
• Strip is a lower K than matrix
LK
wKT
a
ssd
a
sd K
L
w
KC
wKT ss
w
KC s
Strip Transmissivness & Conductance
010 52.1 98831min
min1
.CB.A
B
Cm
CmA
sdT
0.001
0.01
0.1
1
10
1 1.5 2
mmaxC
d
18.1 094.0
1maxmax2
BA
B
mm
Ad
C
0.1
1
10
100
1000
10000
0 0.5 1mmin
Tsd
Graphical EvaluationBoundary Type and Location
WellHigh T to Low TLow T to High T
0
5
10
15
20
0.1 10 1000 100000
td
s d
00.5
11.5
22.5
33.5
44.5
0.1 10 1000 100000
td
s d
Graphical EvaluationEstimate Aquifer Properties
0
2
4
6
8
10
12
14
16
0.001 0.01 0.1 1 10 100 1000
tdL
s d
to=0.029 S=0.017s=2.3 T=1
to=0.42 S=0.35s=4.1 T = 0.55
Graphical EvaluationEstimate Aquifer Properties
0
2
4
6
8
10
12
0.01 0.1 1 10 100 1000
tdL
s d
to = 2.7 S=0.136s = 4.1 T=0.55
TE=1SE=0.0179
TTLL=0.55=0.55SL=0.25
TE=1SE=0.0179
TTLL=0.55=0.55SL=0.136
TTLL=0.55=0.55SL=0.06
TTLL=0.55=0.55SL=0.27
TTLL=0.55=0.55SL=0.021
TTLL=0.55=0.55SL=0.068
TTLL=0.55=0.55SL=0.029
TTLL=0.55=0.55SL=0.021
L
L L
Graphical EvaluationEstimate Aquifer Properties
to=0.09 S = 0.054s = 2.3 T = 1
to=0.028 S = 0.017s = 2.3 T = 1
Determine Properties of Strip
• SSL analysis on the first line will give T and S of the area near the well.
• Take the derivative of time and determine the maximum or minimum slope.
• Using equations from curve fitting determine Tsd or Cd of the layer.
• Solve for Ts or C
Drawdown from Piezometers
0
1
2
3
4
5
6
7
8
9
0.0001 0.01 1
t/r2
s
BW-109 BW-2
0
0.5
1
0.0001 0.001 0.01 0.1t (min)
m =
ds
/dln
(t)
Drawdown from Pumping Well
0
5
10
15
20
25
30
35
40
45
50
10 1000 100000
t/r2
s
0
0.5
1
1.5
2
10 100 1000 10000
time (min)
m =
ds/
dln
(t)
• Using Semi-Log Straight-Line Analysis :
• Minimum slope using the derivative curve is 0.5
• Tsd=33.99=Ksw/KaL
Determining Hydraulic Properties
0
2
4
6
8
10
1 10 100 1000 10000
t (min)
s
00.5
11.5
0.0001 0.001 0.01 0.1
t/r2
ds
/dln
(t)
L = 280 ft Distance to fault
b = 21.5 ft screened thickness
T = 0.053 ft2/minS = 2x10-4 ???
Ts = 23.79 ft2/minTs/Ta = 450
Conclusions 2-Domain Model
Semi-Log Straight-line Method• Piezometers r<0.3L gives T, S of local region.• Piezometers r>0.3L gives average T of both
regions.• Piezometers r>0.3L unable to predict S• Piezometers in neighboring region also give
average T of both regions.• Analyzing piezometers individually poor approach
to characterizing heterogeneities.
Conclusions 3-Domain Model• Drawdown for low conductivity vertical layer
controlled by conductance.
C=Ks/w • Drawdown for high conductivity vertical layer
controlled by strip transmissivness.
Ts=Ks*w• Feasible to determine properties of a vertical layer
from drawdown curves.• Drawdown curves non-unique. Require
geological assessment.