Groundwater Modeling - · PDF fileRQD value as (secondary) •Replace previous layer...

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)

irwan@mining.itb.ac.id

Hidrogeologi dalam bidang

pertambangan (tambang terbuka,

tambang bawah tanah, geothermal,

perminyakan ): Why do we need

Hydrogeologist in our business?

irwan@mining.itb.ac.id

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?

irwan@mining.itb.ac.id

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”

irwan@mining.itb.ac.id

Air ke dalam Pit Tambang

irwan@mining.itb.ac.id

Pola Aliran Air Permukaan Pra Tambang

irwan@mining.itb.ac.id Kursus Hidrogeologi IAGI Bandung, 25 – 26 April 2013

Pola Aliran Air Permukaan Pasca Tambang

irwan@mining.itb.ac.id

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

irwan@mining.itb.ac.id

Slope Remediation

Infiltration Control Crest Drain

Well Control Toe Drain

irwan@mining.itb.ac.id

Pola Aliran Air Airtanah dan Penurunan Air Tanah Akibat Tambang

irwan@mining.itb.ac.id

Pola Aliran Air Airtanah dan Penurunan Air Tanah Akibat Tambang

irwan@mining.itb.ac.id 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

irwan@mining.itb.ac.id

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

irwan@mining.itb.ac.id

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

irwan@mining.itb.ac.id Kursus Hidrogeologi IAGI Bandung, 25 – 26 April 2013

Desain Saluran Di Sekitar Dinding Tambang dan Inpit Sump

irwan@mining.itb.ac.id Kursus Hidrogeologi IAGI Bandung, 25 – 26 April 2013

Arah Aliran Air Tanah dan Kontur Head Tabel Balance Hasil Simulasi

irwan@mining.itb.ac.id

Simulasi Dewatering

irwan@mining.itb.ac.id Kursus Hidrogeologi IAGI Bandung, 25 – 26 April 2013

Pongsesa Infiltration Pond Harapan Infiltration Pond

Concentration Cr6+ ppm

Simulasi contaminant transport

irwan@mining.itb.ac.id

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