1

A stepwise approximation for estimations of multilevel hydraulic

tests in heterogeneous aquifersPRESENTER: YI-RU HUANG

ADVISOR: CHUEN-FA NIDATE: 2011-3-10

2011/3/10

2

Outline

Objective Methodology

Conclusions

Results & Discussion

Future work

IntroductionMotivation

2011/3/10

3

Introduction

Ground water investigations have relied on the determination of aquifer parameters.Knowledge of detailed spatial distributions of hydraulic properties is important to improve our ability to predict water and solute movement in the subsurface.

Detailed spatial distributions of hydraulic properties.

Hydraulic tomography is a viable technology to estimate the parameters in heterogeneous aquifer.[Gottlieb & Dietrich, 1995, Butler et al, 1999, Vasco et al., 2000, Yeh & Liu, 2000, Liu et al., 2002, Bohling et al., 2002, McDermott et al., 2003, Brauchler et al., 2003, Zhu & Yeh, 2005, Liu et al., 2007, Straface et al., 2007, Illman et al., 2007]

2011/3/10

42011/3/10

DATA

52011/3/10

Pumping observation

observation

packerpacker

packer packer

packer packer

Pumpingobservation

observation

Pumping observation

observation

Pumpingobservation

observation

well well

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

(a) (b)

(c) (d)

6

• Data collection: Cross-hole pumping test

To obtain many independent pumping test data.

• Data integration: Numerical inversion

To integrate information of aquifer and estimate parameters.

Introduction Hydraulic tomography

The K tomogram2011/3/10

7

Motivation

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

PACKER

PUMP

OBS.

0 40 80 120 160 200

T im e (s)

84

88

92

96

100

104

Pre

ssu

re (

mH

2O

)

obs no.1

obs no.2

obs no.3

0 40 80 120 160 200

84

88

92

96

100

104

obs no.4

0 40 80 120 160 200

84

88

92

96

100

104

obs no.5

0 40 80 120 160 200

Tim e (s)

88

92

96

100

104

Pre

ssu

re H

2O (

m)

obs no.1

obs no.2

obs no.3

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

PACKER

PUMP

OBS.

2011/3/10

8

Motivation

2011/3/10

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer

packer packer

packer

packer

packer

packer

packer

packer

packer

10

0 1000 2000 3000

Tim e (s)

4

6

8

10

Pre

ssur

e (m

H2O

)

D ruck 14m

Druck 13m

D ruck 12m

D ruck 11m

Changing the packer position.

0 40 80 120 160 200

T im e (s)

88

92

96

100

104

Pre

ssur

e H

2O (

m)

obs no.1

obs no.2

obs no.3

The field pumping test data.

The limit of equipment in field test.

2011/3/10

11

Objective

To conduct numerical investigations to assess how and to what degree the accuracy of the field tests for estimation.

2011/3/10

12

Generation of random field

Many packers, obtain data simultaneously

Limited packers, obtain data sequentially

A series of pumping events

Numerical model

Comparison of the results

Methodology

2011/3/10

13

Generation of random field

X (m)

0 5 10 15 20

Depth

(m)

0

5

10 1.60E-041.50E-041.40E-041.30E-041.20E-041.10E-041.00E-049.00E-058.00E-057.00E-056.00E-055.00E-05

K (m/s)

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

OBS.

PUMP

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

2011/3/10

Mean: 0.0001m/sVariance: 0.1Correlation length: 20x5m

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

OBS.

PUMP

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

14

A series of pumping events

0 40 80 120 160 200

Tim e (s)

88

92

96

100

104

Pre

ssur

e H

2O (

m)

obs no.1

obs no.2

obs no.3

0 200 400 600

Tim e (s)

88

92

96

100

104

Pre

ssur

e H

2O (

m)

obs no.1

obs no.2

obs no.3

obtain data simultaneously obtain data sequentially

Numerical model2011/3/10

15

Results & Discussion

X (m)

0 5 10 15 20

Depth

(m)

0

5

10 1.60E-041.50E-041.40E-041.30E-041.20E-041.10E-041.00E-049.00E-058.00E-057.00E-056.00E-055.00E-05

K (m/s)

X (m)

0 5 10 15 20

Depth

(m)

0

5

10

1.40E-041.35E-041.30E-041.25E-041.20E-041.15E-041.10E-041.05E-041.00E-049.50E-059.00E-058.50E-058.00E-057.50E-057.00E-056.50E-056.00E-05

K (m/s)X (m)

0 5 10 15 20

Depth

(m)

0

5

10 1.60E-041.50E-041.40E-041.30E-041.20E-041.10E-041.00E-049.00E-058.00E-057.00E-056.00E-055.00E-05

K (m/s)

X (m)

0 5 10 15 20

Depth

(m)

0

5

10 1.20E-041.15E-041.10E-041.05E-041.00E-049.50E-059.00E-058.50E-058.00E-057.50E-057.00E-056.50E-05

K (m/s)

X (m)

0 5 10 15 20

Depth

(m)

0

5

10 1.60E-041.50E-041.40E-041.30E-041.20E-041.10E-041.00E-049.00E-058.00E-057.00E-056.00E-055.00E-05

K (m/s)

obtain data simultaneously

obtain data sequentially

0 4E-005 8E-005 0.00012 0.00016 0.0002

O bjective K va lue

0

4E-005

8E-005

0.00012

0.00016

0.0002

Est

imat

ed K

val

ue

C orre lation coeffic ient 0 .743

0 4E-005 8E-005 0.00012 0.00016 0.0002

O bjective K va lue

0

4E-005

8E-005

0.00012

0.00016

0.0002

Est

imat

ed K

val

ue

C orre lation coeffic ient 0 .867

2011/3/10

16

• To obtain the data in each depth by changing packer position is practicable in field test.

• The field data we obtained are usability to estimate the spatial distribution of hydraulic properties.

Conclusions

2011/3/10

17

• To conduct more numerical examples and insight the application for practical problem.

Future work

2011/3/10

the observation intervals

the extension of numerical boundaries

the degree of heterogeneity

the duration of sampling time

18

Thanks for your attention~

2011/3/10