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Groundwater Modeling
Irwan Iskandar, PhD KK Eksplorasi Sumberdaya Bumi
Teknik Pertambangan
Fakultas Teknik Pertambangan dan Perminyakan ITB
What Hydrogeologist
do?
Apakah yang dikerjakan dalam pemodelan hidrogeologi?
• Kuantifikasi Distribusi (keterdapatan)
• Kuantifikasi aliran (recharge-discharge)
• Prediksi dan simulasi pengambilan airtanah
• Interaksi air permukaan dan airtanah
• Interaksi air dengan batuan (hidro-geo-kimia)
• Perencanaan dewatering
• Perencanaan eksplorasi - produksi (geothermal, CBM, Migas)
Hidrogeologi dalam bidang
pertambangan (tambang terbuka,
tambang bawah tanah, geothermal,
perminyakan ): Why do we need
Hydrogeologist in our business?
Mine environment:
Could we ask the hydrogeologist, “How”:
could we control our mine water? so people can say our business is
‘green’ and eco-friendly
Bagaimana pengelolaan air (drainase), desain pompa, dan kontrol
kualitas air di tambang?
Parameter apa saja yang perlu dipertimbangkan?
Tujuan (Pemodelan Hidrogeologi Tambang Terbuka)
• Pola aliran airtanah dan air permukaan pra, selama, dan pasca
tambang (kuantitatif)
• Kuantifikasi jumlah air yang harus diatur dalam penyaliran
tambang
• Environmental impact (prediksi, verifikasi lingkungan)
• Desain sump, ditch, pump, pond
• Depressurization
• “Water Management”
Pola Aliran Air Permukaan Pra Tambang
[email protected] Kursus Hidrogeologi IAGI Bandung, 25 – 26 April 2013
Perkiraan perimeter Pit
Head Equipotential Line
Groundwater Table Drawdown (max -50 in pit high wall
Pola Aliran Air Airtanah dan Penurunan Air Tanah Akibat Tambang
Drain Hole Desain
• Metode drain
• Spasi
• Kedalaman lubang
• Time frame
• Evaluasi drain
• Efek ke kesetimbangan lingkungan airtanah di sekitarnya
Pola Aliran Air Airtanah dan Penurunan Air Tanah Akibat Tambang
[email protected] Kursus Hidrogeologi IAGI Bandung, 25 – 26 April 2013
Time [day]
Rate Dewatering
in m3/day
Rate Dewatering
in liter/sec
Volume
Cumulative
[m3]
365 -196.73 -2.28 -71808
730 -392.42 -4.54 -286464
1095 -421.41 -4.88 -461440
1460 -403.90 -4.67 -589696
1825 -368.43 -4.26 -672384
2190 -340.22 -3.94 -745088
2555 -328.64 -3.80 -839680
2920 -312.28 -3.61 -911872
3285 -306.42 -3.55 -1006592
3650 -290.47 -3.36 -1060224
Kuantifikasi Airtanah yang keluar dari dinding tambang
PIT
Debit Air
Limpasan Debit Air Tanah
Total Debit
Maksimum Air
Masuk Pit
(m3/detik) (m3/detik) (m3/detik)
PIT (Kedalaman
pit 150 m)
1.81 0.004 1.814
PIT (Kedalaman
pit 70 m)
1.75 0.003 1.753
Kuantifikasi Airtanah dan Air Permukaan yang keluar dari dinding tambang
Desain Saluran Drainase
X=lebar muka saluran
Z = kemiringan
saluran
h = kedalaman saluran
basah
B = lebar dasar saluran
Freeboard = 10-30 cm
3/2
2/13/5
.Pn
SAQ
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 De
bit
MA
X (
lite
r/d
etik
)
Tinggi Muka Air (m)
Kapasitas Debit Maks Saluran Air
[email protected] Kursus Hidrogeologi IAGI Bandung, 25 – 26 April 2013
Desain Saluran Di Sekitar Dinding Tambang dan Inpit Sump
[email protected] Kursus Hidrogeologi IAGI Bandung, 25 – 26 April 2013
Pongsesa Infiltration Pond Harapan Infiltration Pond
Concentration Cr6+ ppm
Simulasi contaminant transport
3D-Permeability Modeling
• 3D-spatial distribution of permeability in a block modeling
• Combination K value (primary variable) and RQD value as (secondary)
• Replace previous layer (stratigraphical modeling) to grid based model
Field work
Conceptual model
Groundwater modeling
SIMULASI NUMERIK dalam HIDROGEOLOGI
Governing Equation
xK
h
x yK
h
y zK
h
zS
h
tx y z s( ) ( ) ( )
2
2
2
2
2
20
h
x
h
y
h
z
•Transient
•Steady state
INTI SIMULASI NUMERIK
• Teknik untuk mencari solusi persamaan differensial
• Merupakan pendekatan
• Persamaan differensial didekati dengan persamaan linier simultan (persamaan matrix)
DUA JENIS UTAMA SIMULASI NUMERIK
1. Finite Difference (beda hingga)
2. Finite element (elemen hingga)
Kelas kita: Finite Difference
FINITE DIFFERENCE
• Introduced firstly by Richardson (1910)
• The basic idea: to replace derivative at a point by ratio of change over a small but finite interval
LANGKAH-LANGKAH DALAM METODA
FINITE DIFFERENCE
1. Pendekatan Terhadap Differensial
A
P
B
x x-h x+h
h(x)
x
...6
1
2
1)(
3
33
2
22
dx
hdx
dx
hdx
dx
dhxxhxxh
...6
1
2
1)(
3
33
2
22
dx
hdx
dx
hdx
dx
dhxxhxxh
(1)
(2)
...)()(2)( 4
2
22 xO
dx
hdxxhxxhxxh
+
(3)
Deret Taylor:
Abaikan 0(h4): )()(2)(1
22
2
xxhxhxxhxdx
hd
xx
(4)
Error orde h2
(1)-(2):
)()(2
1xxhxxh
xdx
dh
xx
Error orde h2
Pendekatan slope pada P dengan menggunakan garis AB:
CENTRAL DIFFERENCE
(5)
Abaikan orde O(x4):
Dari Pers. (1):
Abaikan orde h2:
)()(1
xhxxhxdx
dh
xx
Forward Difference
(CD)
)()(1
xxhxhxdx
dh
xx
Backward Difference
(BD)
2. Pembagian dalam sistem grid
i,j+1
i,j-1
i+1,j i-1,j i,j
h
y
x
2 - D
i+1 i-1 i
h
1 - D
3. Penulisan pendekatan pers. differensial
pada setiap titik dalam sistem grid
i,j+1
i,j-1
i+1,j i-1,j i,j
h
y
x
2 - D
jijiji
xx
hhhxx
h,1,,122
2
21
x
y
jiji
xx
hhxx
hCD ,1,1
2
1:
jiji
xx
hhxx
hFD ,,1
1:
jiiji
xx
hhxx
hBD ,,
1:
Dalam arah y
1,,1,22
2
21
jijiji
xx
hhhyy
h
1,1,
2
1:
jiji
yy
hhyy
hCD
jiji
yy
hhyy
hFD ,1,
1:
ijiji
yy
hhyy
hBD
,,
1:
5. Penyelesaian Persamaan Linier Simultan (Persamaan Matrix)
• Eliminasi Gauss
• Algoritma Thomas
• Iterasi:
1. Jacobi
2. Gauss - Seidel
3. SOR
Exercise 1 15 menit x
y = x
02
2
2
2
x
h
x
h
h1,1 h2,1 h3,1 h4,1
h1,2 h2,2 h3,2 h4,2
h1,3 h2,3 h3,3 h4,3
h1,4 h2,4 h3,4 h4,4
6,82 7,56 7,99 8,29
7,19 ? ? 8,33
7,68 ? ? 8,41
8,04 8,18 8,36 8,53
Tugas: Cari h2,2,
h3,2, h2,3, dan h3,3
Steady state: hi,j sama pada tiap waktu n
1,,1,22
2
21
jijiji
xx
hhhyy
h
jijiji
xx
hhhxx
h,1,,122
2
21
t
hSW
z
hK
zy
hK
yx
hK
xszzyyxx
Transient Condition
Metode Beda Hingga Salah satu solusi pemecahan masalah persamaan dalam kondisi transient
hi,j = (1/4) (hi-1,j + hi+1,j + hi,j-1 + hi,j+1)
1 1 1 1 1 2 1
1, 1, , 1 , 1 , , ,4 1/ 1/n n n n n n n
i j i j i j i j i j i j i jh h h h h T Sa t h h
Steady state: hi,j sama pada tiap waktu n
Transient: pencarian hi,j pada tiap waktu n
Pemodelan Lapisan (Pemodelan Parameter Hidraulik)
1. Layer Based LPF (Later Package File)
2. Grid Cell Base
Physical Model (Layer Based)
• Pembagian Unit Hidrostratigrafi
• Setiap unit lapisan hidrostratigrafi diterjemahkan sebagai
“layer”
• Setiap layer relatif homogen (K, S, θ dan parameter lainnya)
• Lapisan bisa datar, miring ataupun membentuk antiklinorium
• Korelasi bisa manual oleh hydrogeologist atau dengan
software pembentukkan kontur struktur “layer”
Physical Model (Layer Based)
• Easy when hydrostratigraphical unit has been defined
• Limited number of aquifer parameter e.g. 1 value in each unit.
• Suitable in layered / sedimentary rock
• Number of cells relatively low
• Time of simulation relatively short
Topo: [ID, x, y, z]
Bottom Layer 1: [ID, x, y, z, K, S, θ]
Bottom Layer 2: [ID, x, y, z, K, S, θ] Bottom Layer 3: [ID, x, y, z, K, S, θ]
Bottom Layer 3: [ID, x, y, z, K, S, θ]
Bottom Layer 4: [ID, x, y, z, K, S, θ]
Bottom Layer 5: [ID, x, y, z, K, S, θ]
Bottom Layer 5: [ID, x, y, z, K, S, θ]
Unit : akuitard, impermeabel, K<10-9 m/detik
Unit : akuitard, impermeabel, K<10-7 m/detik
Unit : akuifer, permeabel, K> 10-5 m/detik
Unit : akuitard, impermeabel, K<10-9 m/detik
Unit : akuitard, impermeabel, K<10-7 m/detik
Physical Model (Database)
Hole ID ID X Y Z Bottom 1 Bottom 2 Bottom 3 Bottom 4 Bottom 5 Bottom n
Data (Physical Model)
• Topografi
X, Y, Z (ASCII file) atau (.DXF) 3D polyline
• Log Bor
ID, X, Y, Z (ASCII) atau (.DXF) 3D polyline
• Hydrologic Features (River, Lake, Sea, Pond, Stream) in dxf
• Hydrogeological Parameter (K, S, θ,) dalam 3 D data
(X, Y, Z, K, S, θ) atau (ID, Layer, K, S, θ)
Physical Model (Grid Cell Based)
• stratigraphy unit is not a must
• Each cell unit is translated to valued grid
• Each cell is has one value (K, S, θ and other parameter)
• Block model of the grid would hydrostratigraphical pattern
depend on the structure
• Adjustment and interpolation were made by Hydrogeologist
• A lot of Number of cells
• Time of simulation is relatively long
y = 8E-06x - 5E-06
0,00E+00
5,00E-07
1,00E-06
1,50E-06
2,00E-06
2,50E-06
3,00E-06
3,50E-06
4,00E-06
0,5 0,6 0,7 0,8 0,9 1
Hyd
rau
lic C
on
du
ctiv
ity
(m/s
)
RQD Factor = (1-RQD/100) Linear (RQD vs K) Poly. (RQD vs K)
Hydraulics Conductivity and RQD
Higher Hydraulic
Conductivity
Higher RQD
Lower Hydraulic
Conductivity
Lower RQD
Model Dimension Distance Grid
Size
Grid
Sum
Total
Block Grid
Easting
(column)
Min 403500 2000 10 200
3,200,000
Max 405500
Northing
(row)
Min 306000 2000 10 200
Max 308000
Elevation Min 400
800 10 80 Max 1200
10 x 10 x 10 meter
Contoh Grid Cell Based
Bor ID X (m) Y (m) Depth (m) k (m/s) log k
GW-01 24300 -1200 6.4 1.14× 10-5 -4.943
24300 -1200 12.5 5.08× 10-6 -5.294
24300 -1200 20.6 2.77× 10-4 -3.557
24300 -1200 28.0 1.81× 10-5 -4.742
24300 -1200 33.1 5.47× 10-4 -3.262
24300 -1200 35.6 1.82× 10-5 -4.739
GW-02 37.2 2.89× 10-4 -3.539
GW-03 23000 1000 3.3 1.50× 10-5 -4.822
23000 1000 6.5 1.85× 10-5 -4.732
23000 1000 7.7 8.22× 10-5 -4.085
GW-04 23800 0 12.4 2.89× 10-5 -4.538
23800 0 18.1 3.39× 10-4 -3.469
23800 0 24.4 7.29× 10-5 -4.137
23800 0 36.4 1.25× 10-4 -3.903
23800 0 39.4 4.78× 10-4 -3.320
GW-05 25000 -1100 6 2.08× 10-5 -4.681
25000 -1100 11.1 3.24× 10-5 -4.489
25000 -1100 21.2 7.41× 10-5 -4.130
25000 -1100 23.2 1.85× 10-5 -4.732
25000 -1100 29.1 1.50× 10-6 -5.822
25000 -1100 47.1 2.08× 10-5 -4.681
GW-06 22500 -2300 6.5 1.10× 10-4 -3.957
22500 -2300 16.7 2.55× 10-5 -4.593
22500 -2300 21.5 3.88× 10-5 -4.411
22500 -2300 26 6.74× 10-5 -4.171
22500 -2300 30.5 2.35× 10-5 -4.628
22500 -2300 35.9 1.04× 10-4 -3.981
22500 -2300 39.5 5.65× 10-6 -5.247
CGW-07 23200 -2000 3.5 3.44× 10-5 -4.464
23200 -2000 12.5 7.13× 10-4 -3.147
23200 -2000 32.9 1.27× 10-4 -3.895
23200 -2000 40.3 2.69× 10-4 -3.570
CGW-08 22700 -1300 6.2 3.89× 10-5 -4.409
22700 -1300 13.4 2.67× 10-6 -5.573
Data (Physical Model) Grid Cell Based
Contoh Grid Cell Based Data
Number of data 95 Minimum value -5.57
Mean -4.40 First quartile -4.74
Standard deviation 0.68 Median -4.46
Coefficient of variation -0.15 Third quartile -3.40
Skewness -0.20 Maximum value -3.15
Statistical summary of log transformed k value
Data (Physical Model) Grid Cell Based
Sill
Range
Lag or Separation Distance/data
g Nugget (may be zero)
= Data Points
= variogram model
• Estimasi parameter Hidraulik di daerah yang tidak ada data
• 3D/4D space-time distribution modeling
3D Spatial
Distribution
Geostatistic-ordinary kriging
The spatial correlation dianalisis menggunakan semivariogram γ(h)
m
i
iik xZxZ1
)()(ˆ
)(ˆ)(ˆ1
ikij
n
j
i hh
2
1
1ˆ( ) ( ) ( )
2
n
i
h Z X Z X hn
)(ˆ kxZ
North
Co Located Co Kriging (CK)
2
1
222
1
1
1111 )()()(ˆ
n
j
ji
n
i
ii zλzλz xxx0
,11
1
1
n
i
i,0
2
1
2
n
i
i
(h)
1
1112(h)
1
2
1(h)
N
i
iiii zzzzN
γ )))) xhxxhx 22 ()((()((
0 1000 2000 3000
0
50
100
150
200
250
300
350
400
450
|h|
(|h|)c)
4000
aCC
aaa
CCγ
h
hhh
for
0for 22
3)h(ˆ
10
3
3
10sph
Grid besar(merah)
adalah data
parameter hidraulik
Size = 125 x 125
Grid kecil adalah RQD di batuan point/grid (size = 10 x 10)
3D Spatial Distribution Konduktivitas hidraulik (K)
Contoh Grid Cell Based Data dengan data struktur (RQD)
Conductivity Distribution (section view)
A
B
C D
A B
C D
Conductivity Based on Lithology Distribution (section view)
A B
A
B
EXAMPLE
• Case Study Underground Mine
Hydraulics Conductivity and RQD
Conductivity Distribution (section view)
A
B
C D
A B
C D
Initial Head Condition (Based On 2011)
Mine Design
N N
N
Mining Drain Scenario (Assumption)
• Mining Development assumption finished in two period, always open during mining activity.
• Mine Production assumption finished in seven period. Closed every period with filling material, where filling material assumption is impermeable.
Drain Scenario (Assumption)
File Volume (m3) Surface Area (m2) Accumulatif Volume
Opening (m3)
Dev1 243,342.00 190,504.00 243,342.00
Dev2 215,307.00 177,459.00 458,649.00
Mine1 244,681.00 92,227.00 703,330.00
Mine2 243,566.00 88,920.00 702,215.00
Mine3 246,932.00 109,066.00 705,581.00
Mine4 251,695.00 91,688.00 710,344.00
Mine5 241,731.00 98,695.00 700,380.00
Mine6 231,848.00 91,410.00 690,497.00
Mine7 234,107.00 120,843.00 692,756.00
Mining Drain Scenario (Assumption)
Mine opening
Closed mining
Mine opening
Closed mining
Mining Development
Mine opening
Mine opening
Closed mining
Mine opening
Closed mining
Mine opening
Closed mining
Mine opening
Closed mining
Model Scenarios
Model based on Conductivity Distribution (K values is not depend the lithology condition)
1. K values average 10-7 m/sec, rock condition is in low RQD mostly (worst scenario)
2. K values average 10-8 m/sec, rock condition is in moderate RQD mostly (moderate scenario)
3. K values average 10-9 m/sec, rock condition is in fair RQD mostly
MODEL TYPE- 1 K VALUES AVERAGE 10-7 M/SEC, ROCK CONDITION IS IN LOW RQD MOSTLY (WORST SCENARIO)
Observation Head (2011) vs Calculation Head (Model) – Steady State Condition
Model Calibration (Head Calibration on Steady State)
Head contour Based On Observation Data (Env Field Measurements, 2011)
Head contour Based On Model Calculation (Steady State Condition)
Model Calibration (Contour Head Calibration on Steady State)
Change of Groundwater Head and Flow (Plan View) Year: 1, 2, 3, 5,7 and 9
Change of Groundwater Head and Flow (Plan View) Year: 10, 20, 30, and 40
Head and Groundwater Flow (Section View) Year: 1, 2, 3, 5,7 and 9
N N
N N
N N
1
3
2
4
Observation Well Location
Head vs Time (Observation Well)
760
780
800
820
840
860
880
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30
Gro
un
dw
ate
r H
ead
(m
)
Year
OBSERVATION 1/AInterpolated OBSERVATION02/AInterpolated
OBSERVATION3/AInterpolated OBSERVATION4/AInterpolated
Head Drawdown
• Head Drawdown Radius Maximum: ± 139 m
• Head Drawdown Depth Maximum: ± 127 m
• Water table drawdown may not affected to unsaturated zone above the aquifer
• All Drawdown will recover in ± 30 - 45 years after mine closure
