Presentation of the scientific research 2002 2007

Scientific ResearchAmro M. M. Elfeki, Ph.D.

(2002-2007)

Main Research Interest Characterization of Subsurface Heterogeneity. Groundwater Flow and Contaminant Transport in

Aquifers. Soil-Contaminant Interaction in Porous Media. Reduction of Uncertainty in Geological

Formations, Groundwater Flow and Transport Models.

Design of Groundwater Monitoring System at Landfill Sites.

May 3, 2023 2Scientific Research Papers of Amro Elfeki, PhD






Characterization of Subsurface Heterogeneity

1. Elfeki, A. M. and Dekking F. M. (2005). Modeling Subsurface Heterogeneity by Coupled Markov Chains: Directional Dependency, Walther’s Law and Entropy. Journal of Geotechnical and Geological Engineering, Vol. 23: pp.721-756.

2. Park, E., Elfeki, A. M. M., Dekking, F.M. (2003). Characterization of subsurface heterogeneity: Integration of soft and hard information using multi-dimensional Coupled Markov chain approach. Underground Injection Science and Technology Symposium, Lawrence Berkeley National Lab., October 22-25, 2003. p.49. Eds. Tsang, Chin.-Fu and Apps, John A.http://www.lbl.gov/Conferences/UIST/index.html#topics


http://www.lbl.gov/Conferences/UIST/index.html

Characterization of Subsurface Heterogeneity (cont.)


Modelling Subsurface Heterogeneity by Coupled Markov Chains: Directional Dependency, Walther’s Law and Entropy Background: Extension of the two-dimensional coupled Markov chain

model developed by Elfeki and Dekking [2001] supplemented with extensive simulations to study:

1. Directional dependency of the model performance. 2. Walter’s Law utilization. 3. Entropy maps as a measure of uncertainty.


Modelling Subsurface Heterogeneity by Coupled Markov Chains: Directional Dependency, Walther’s Law and EntropyObjectives: 1. development of various coupled Markov chains models: the so-

called fully forward Markov chain, fully backward Markov chain and forward-backward Markov chain models.

2. address issues such as: sensitivity analysis of optimal sampling intervals in horizontal and lateral directions, directional dependency, use of Walther’s law to describe lateral variability, effect of conditioning on number of boreholes on the model performance, stability of the Monte Carlo realizations, various implementation strategies, use of cross validation techniques to evaluate model performance and image division for statistically non-homogeneous deposits.


Modelling Subsurface Heterogeneity by Coupled Markov Chains: Directional Dependency, Walther’s Law and EntropyApplications: Two sites are located in the Netherlands (Two Cross-sections), and One site in the USA (Two cross-sections).

Purpose of applications:- to show under which conditions these Markov models can be used.

- to provide guidelines for the practice.


Modelling Subsurface Heterogeneity by Coupled Markov Chains: Directional Dependency, Walther’s Law and Entropy

( )

Markov property (One-Step transition probability)Pr( )Pr( ) : ,

Marginal Distribution

limN

i i-1 i-2 i-3 0k l n pr

i i-1k l lk

Nklk

| , , S ,..., S S S SZ Z Z Z Z | pS SZ Z

p w

S So d

Markov Chain Theory:



-1Pr( | ) : ,i ik l lk pS SZ Z

SS S

i0 1 i+ 1i-1 N2

l k qdSSaN -1

S rSb

1-D Forward Markov Chain Theory:

1Pr( | ).i il kkl

S SZ Zp

1-D Backward Markov Chain Theory:

lk klp p



( 1)

1 0 ( ): Pr ( ) ,N

ab bqNb a qab q N

aq

p pp | , S S SZ Z Z

p

Conditioning FMC (Elfeki and Dekking2001)

1 0

( 1)1 1 0

( )0

Pr ( )

Pr ( ).Pr ( ),

Pr ( )

N Nr q aqr a

NN N Nq r r rq ara

NN q a aq

| , SS SZ Z Zp

p p | | SS S SZ Z Z Z | S pSZ Z

Conditioning BMC



, , 1, , 1

,

, 1, , 1 ,,

Unconditioinal Coupled Markov Chains: Pr( | , )

. 1,...

Conditioinal Coupled Markov Chains: Pr( | , , )

x

lm k i j k i j l i j m

h vlk mk

lm k h vlf mf

f

i j k i j l i j m N j qlm k q

l

p Z S Z S Z S

. p pp k n

. p p

p Z S Z S Z S Z S

p

( )

, ( ) , 1,... .x

x

h h N i vlk kq mk

m k q h h N i vlf fq mf

f

. . p p pk n

. . p p p

(Elfeki and Dekking, 2001)

Coupled Markov Chain “CMC” in 2D



, 1,,

, 1 0,

( )

, ( )

Conditioinal Backward CMC

: Pr( |

, , )

= ,

1,..., .

i j k i jdm k a

d i j m j a

h h i vkd ak mk

dm k a h h i vfd of mf

f

p Z S Z

S Z S Z S

. . p p p p

. . p p p

k n

, 1,,

, 1 ,

( )

, ( )

Conditioinal Forward CMC: Pr( |

, , )

,

x

x

x

i j k i jlm k q

l i j m N j q

h h N i vlk kq mk

lm k q h h N i vlf fq mf

f

p Z S Z

S Z S Z S

. . p p pp

. . p p p



? >? >

?< ?<

? > ?<

Forward M arkov C hain M odel (tw o forw ard steps)

Backw ard M arkov Chain M odel (two backw ard steps)

Forward-Backw ard M arkov Chain M odel (one forw ard step and one backward step)

W ell (1) W ell (2) W ell (1) W ell (2)

Methods of Implementation: FCMC, BCMC and FBCMC



1( )

0 .

ij k

k ij

if Z S I Z

otherwise

,

,

( )( )

1

#{ } 1i j

i j

R MCkk R

ij kR

Z SI Z

MC MC

1 2max{ , ..., }l nij ij ij ij

Let the realizations be numbered 1,…, MC, and let Zij (R) be the

lithology of cell (i,j) in the Rth realization. The empirical relative frequency of lithology Sk at cell (i,j) is:

In the final image Z* the lithology at cell (i, j) will be the lithology which occurs most frequently in the MC realizations. So, if Sl is such that

* ij lZ S

Procedure for Extracting a Final Geological Image



1

ln( ),

1,..., , 1,...,

nk k

ij ij ijk

x y

H

i N j N

Empirical Entropy

to provide some measure of the uncertainty in the final image. We have chosen for empirical entropy to convey this issue. The empirical entropy (see e.g., Arndt, 2001 page 54) at location (i, j) is given by



Case study no. 1 (Afsluitdijk-Lemmer), NL

Case study no. 2 (Casparde Roblesdijk part of Waddenzeedijken,), NL

Case study no. 3 (The Delaware river and its underlying aquifer system in the vicinity of the Camden metroplitan area, New Jersey)

Case Studies


Modelling Subsurface Heterogeneity by Coupled Markov Chains: Directional Dependency, Walther’s Law and EntropySensitivity Analysis

Various sampling intervals. Various horizontal transition probability matrices. Various degrees of diagonal dominancy of the horizontal transition

matrix. Use of Walther’s law to account for horizontal variability. Effect of conditioning on the model performance. Sensitivity of the Monte Carlo realizations. Various implementation strategies: forward, backward and forward-

backward methods. Use of cross validation to evaluate the model performance.



0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0- 2 0

- 1 0

0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0

- 1 0

0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0

- 1 0

0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0

- 1 0

0

1 2 3 4 5 6

A

B

C

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0

- 1 5- 1 0

- 50

1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0

0 .2

0 .4

0 .6

0 .8

1

0

0.2

0.4

0.6

0.8

1

0

0 .2

0 .4

0 .6

0 .8

1

0

0.2

0.4

0.6

0.8

1

- 1 0

0

1

- 1 0

0

2

- 1 0

0

3

- 1 0

0

4

- 1 0

0

5

- 1 0

0

6

(Afsluitdijk-Lemmer), NLCourtesy “GeoDelft”


Lithology Code

Clay, sandy to sand, clayey (deposition of Duinkerke,Westland - formation) 1Peat (Hollandpeat, Westland – formation) 2Sand, locally humous and / with loam layers (formation of Twente) 3Sand , locally loamy (formation of Drente) 4Mainly clay (artificial ground) 5Loam, frequently with sand and stones (formation of Drente) 6



State State 1 2 3 4 5 6 7 8

1 0.500 0.500 0.000 0.000 0.000 0.000 0.000 0.0002 0.000 0.500 0.500 0.000 0.000 0.000 0.000 0.0003 0.000 0.000 0.844 0.156 0.000 0.000 0.000 0.0004 0.000 0.000 0.000 0.830 0.000 0.034 0.000 0.1365 0.000 0.308 0.000 0.077 0.615 0.000 0.000 0.0006 0.000 0.000 0.000 0.333 0.000 0.667 0.000 0.0007 0.045 0.000 0.000 0.000 0.076 0.000 0.879 0.0008 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000

Table 2. Vertical transition probability matrix estimated from 8 boreholes sampled over 0.5 m (all boreholes depths are 20 m).

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0- 2 0

- 1 0

0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0- 2 0

- 1 0

0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0- 2 0

- 1 0

0

1 2 3 4 5 6

Results o f 30 R ealiza tions

Results o f 100 Realizations0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0

- 2 0

- 1 0

0

Results of 5 R ealiza tions

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0- 2 0

- 1 0

0

Results of 10 Rea liza tions

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0- 2 0

- 1 0

0

Results o f 1000 Realizations

1

1

nv v v

lk lqlkq

p = T T

where Tlkv is the number of observed

transitions from Sl to Sk in the vertical direction.

Stability of Monte Carlo Realizations


0 200 400 600 800 1000 1200 1400 1600-15

-10

-5

0

0 200 400 600 800 1000 1200 1400 1600-15

-10

-5

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

dx=10m

dx=40m

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

dx=20m

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

dx=5m

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

0 200 400 600 800 1000 1200 1400 1600

-10

-5

0

0

0.25

0.5

0.75

1

dx=2.5m

Influence of Sampling Interval in Horizontal



0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0- 1 5- 1 0

- 50

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0- 1 5- 1 0

- 50

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0- 1 5- 1 0

- 50

0 0.25 0.5 0.75 1 1.25 1.5 1 2 3 4 5 6 7 8 9 10 11 12 13

Litho logy C odingEntropy M easure

(Caspar de Roblesdijk part of Waddenzeedijken), NLCourtesy “GeoDelft”



8 boreholes

13 boreholes

19 boreholes

Effect of conditioning on boreholes



The Delaware river and its underlying aquifer system in the vicinity of the Camden metropolitan area, New Jersey

Section F-F

Section A-A



0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

a

b

c

d

e

f

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

p = 0 .603

p = 0 .699

p = 0 .801

p = 0.908

0

0.25

0.5

0.75

1

1.25

1.5

1.75

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0

- 3 0 0- 2 0 0- 1 0 0

0

p = 0.986

1

2

3

4

5

6

7

i i

i i

i i

i i

i i


1- 0.001( - 2)

hh iiij

ppn

where the value 0.001 is the transition probability from any state to the artificial state 8 for i=1,...,7 and therefore,

88 0.993hp

Diagonal Dominancy of The Horizontal Transition Probability Matrix



Comparison of Various Coupled Markov Chain Models:

FCMCBCMC FBCMC



Comparison of Various Coupled Markov Chain Models:

FCMCBCMC FBCMC



Application of Walther’s LawLithologies that are observed in the vertical depositional sequences must also be deposited in adjacent transects at another scale [Middleton, 1973 referenced by Parks, et al. 2000].

This law can be interpreted as: the observed variability in the boreholes at a certain scale (e.g., in the order of cm to m) in the boreholes must be present in the horizontal direction at a larger scale (e.g., in the order of 10 m to km).



The scale ratio, which we call Walther’s constant, is a key issue in subsurface characterization. In the case studies given in this paper we investigated this issue at three different sites.

0 4000 8000 12000 16000O verall H orizontal F ie ld Scale (m eters)

0

0.01

0.02

0.03

0.04

dy/d

x

A fslu itd ijk- Lem m er (Netherlands)A fs lu itd ijk Caspar de R oblesd ijk (N e therlands)D e law are R iver A qu ifer (Longitudinal-S ection), U S AD elaw are R iver A qu ifer (C ross-Section),U SAM A D E site a t Co lum bus, M ississ ippi [E lfek i and R ajabian i, 2002]

Modelling Subsurface Heterogeneity by Coupled Markov Chains: Directional Dependency, Walther’s Law and Entropy Conclusions:1. Entropy maps are good tools to indicate places where high

uncertainty is present, so can be used for designing sampling networks to reduce uncertainty at these locations.

2. Symmetric and diagonally dominant horizontal transition probabilities with proper sampling interval show plausible results (fits with geologists prediction) in terms of delineation of subsurface heterogeneous structures.

3. Walther’s law can be utilised with a proper sampling interval to account for the lateral variability.

4. Finding Walther’s constant will generalize the results of this paper for the practical applications.






Characterization of Subsurface Heterogeneity: Integration of Soft and Hard Information Using Multi-Dimensional Coupled Markov Chain Approach

Background: This was a project proposal which has been granted for two and a half

years from the Dutch Science Foundation for a postdoc position at TU-Delft.

Eungyu Park was the post doc researcher working under the supervision

of Prof. Dekking and myself at TU-Delft, the Netherlands.

Objective: The project was an extension of the Methodology of Elfeki and Dekking

(2001) to 3D and solving the scientific and technical questions that would appear due to this extension.




If the future in both directions x and y are given (Elfeki and Dekking, 2001)

, 1, , 1 , ,

( ) ( )

( ) ( )

Pr( | , , , )

, 1,... .

y x

x x x y y y

x x x y y y

i j k i j l i j m i N p N j q

h h N i h h N jlk kq mk kp

h h N i h h N jlf fq mf fp

f

Z S Z S Z S Z S Z S

p p p pk n

p p p p

2D CMC Theory Conditioned on Future States

y-chain

x-chain



y-chain

x-chainz-

chai

ny

x

z

3D CMC Theory



Likewise

, , 1, , , 1, , , 1 , , , ,

, , 1, , , , , , , 1, , ,

, , , , 1

( )

( 1)

Pr , , , ,

Pr , Pr ,

Pr

x y

x y

x

x

i j k o i j k l i j k m i j k n N j k p i N k q

i j k o i j k l N j k p i j k o i j k m i N k q

i j k o i j k n

hx N ihx hylo op mo

hx N ilp

Z S Z S Z S Z S Z S Z S

C Z S Z S Z S Z S Z S Z S

Z S Z S

p p pC

p

( )

( 1)

y

y

hy N joq v

nohy N jmq

pp

p

where 1( )( )

( 1)( 1)

yx

yx

hy N jhx N ihx hy vlr mr nr rp rq

hy N jhx N ir lp mq

p p p p pC

p p



Active ConditioningUse the tolerance angle along

scanning and perpendicular to scanning direction

x

y


May 3, 2023 Scientific Research Papers of Amro Elfeki, PhD 38

Algorithm 1. Discretizing domain2. Saving conditioning data3. Deriving transition probabilities4. Applying 1-, 2-, and 3D

equations to the domain5. Generate equally probable

single realizations6. Repeat step 1 through 5, if

multiple realization are desired7. Do Monte Carlo analysis if

desired using equally probable multiple realizations generated from step 6



The theory of 3D Coupled Markov Chain Model (3D CMC) is developed and programmed under MATLAB environment





3D Ensemble Indicator Function of Lithology 3



10 %

90 %

50 %

Statistical Mapping of 3D Ensemble Indicator Function of Lithology 2


Conclusions: 3D Coupled Markov Chain (3D CMC) is

developed through this study. Efficient way of utilization of the horizontal

data is added to 2D CMC.







Groundwater Flow and Contaminant Transport in Aquifers Elfeki, A. M. (2003). Transient Groundwater Flow in Heterogeneous

Geological Formations. Mansoura University Engineering Journal (MEJ), Vol. 28, no. 1, pp. c58-c67.

Elfeki, A.M.M., Uffink, G.J.M., Lebreton, S. (2007). Simulation of Solute Transport under Oscillating Groundwater Flow in Homogeneous Aquifers, Journal of Hydraulic Research, Vol. 45 (2), pp. 254-260.

Elfeki, A.M. (2006). Steady Groundwater Flow Simulation Towards Ains in a Heterogeneous Subsurface. Accepted for publication at the Forth International Conference on Ains, Water Recources Center at King Abdulaziz University, Jeddah, Saudi Arabia in Coorperation with UNESCO, April 2006.


Groundwater Flow and Contaminant Transport in Aquifers


Transient Groundwater Flow in Heterogeneous Geological Formations.


Background:This paper is carried out under TU-Delft project called “ Transientprocesses in geohydrology and hydraulic engineering”. responsible for theme 3:Analysis of Transient Flow Through Porous Sediments at Different Levels of Aggregation.

The objective :To study the effect of transient boundary conditions on the flow behavior in heterogeneous Aquifers via developing a numerical model.


( , ) ( , )

( , , )( , , ) ( , )

( , , )( , , ) ( , )

x

y

S T x y T x yt x x y y

x y tq x y t T x yx

x y tq x y t T x yy


water-ΔVS=ΔA.Δh


Finite difference formulation of the flow equation :

Implicit scheme :

1 1 1 1 1, ,1, , 1 1, , 1ij ij ij ij ij ijk k k k k ki j i ji j i j i j i j

F h A h B h C h D h E h

Solution by an iterative scheme : the conjugate gradient method h(x,y,t)


Transient Groundwater Flow in Heterogeneous Geological Formations.• Groundwater head :

• Darcy’s velocities :

0 50 100 150 200 250 300

-40

-20

0

Velocity field at a time t




Homogeneous Aquifer:With a compound signal in water level at RH side:- Water Table fluctuationsare in phase.

- Velocity fluctuations are out of phase.

- Delay response at high value of S.

-Smearing out of the small scale variability at high values of S.



Heterogeneous Aquifer: Sudden drop of water level at RH side


0 5 10 15 20 25

Tim e (days)

-0.02

0.00

0.02

0.04

0.06

0.08

Long

itudi

nal C

ompo

nent

of D

arcy

's V

eloc

ity

Res

pons

e (m

/day

)

S to ra g e C o e ffic ie n tS = 0.1S = 0.01S = 0.001S = 0.0001

0 5 10 15 20 25

Tim e (days)

-0.60

-0.40

-0.20

0.00

0.20

Late

ral C

ompo

nent

of D

arcy

's V

eloc

ity

Res

pons

e (m

/day

)

S to ra g e Co e ffic ie n tS = 0.1S = 0.01S = 0.001S = 0.0001

0 5 10 15 20 25

Tim e (days)

8

12

16

20

24

28

Hyd

raul

ic H

ead

Res

pons

e (m

)

S to ra g e Co e ffic ie n tS = 0.1S = 0.01

S=0.001S = 0.0001

0 5 10 15 20 25

Tim e (days)

-10

0

10

20

30

Inpu

t Hea

d S

igna

l at R

ight

Bou

ndar

y(m

)


Heterogeneous Aquifer: With a compound signal in water level at RH side

- Water Table fluctuations are in phase.- Long. Velocity fluctuations are out of phase, while trans. Velocity are in phase.- Delay response at high value of S.-Smearing out of the small scale variability at high values of S.



Conclusions:

Groundwater Flow and Contaminant Transport ...(cont.)


Simulation of Solute Transport under Oscillating Groundwater Flow in Homogeneous Aquifers

• confined aquifer• upstream water level constant• downstream water level

variable• constant thickness• constant hydraulic conductivity

K over the depth• constant specific storage SS

over the depth• aquifer modelled in a 2D

horizontal plane

The goal of the study :investigate the impact of oscillating flow conditions on solute transport in homogeneous aquifers


Simulation of Solute Transport under Oscillating Groundwater Flow in Homogeneous Aquifers Scope of the study :

injection of inert solutes, 2D homogeneous aquifer, periodical fluctuations at the downstream boundary with a

specified, amplitude and period, instantaneous injection.




Governing equation of the flow:

, , , , , ,, ,xx yy

h x y t h x y t h x y tS x y x yT Tt x x y y

Principle of the finite difference method :• discretization in space• discretization in time

where h hydraulic conductivity S the storativity or storage coefficient T=Kb the transmissivity

0

( , , ) 0 , (no-flow condition)

(0, , )( , , ) ( )

h x y t for x ynh y t hh d y t h t

Flow Model:



Transport Model:



Random Walk Equations:



Transport Simulation by Random Walk Particles Method



Fluctuating water level at the downstream boundary :

02

]

,cosh / -cos /

cos sinh / cos / sinh / cos /

-sin cosh / sin / sinh / cos /

sin sinh / cos / cosh / sin /

cos cosh / sin / cosh / sin /

hh x td l d l

t x l x l d l d l

t x l x l d l d l

t x l x l d l d l

t x l x l d l d l

with

l is the penetration length

• Upstream water level: 0 m Downstream level : 5 cos(2πt/10) • Aquifer characteristics: length d=200m Storativity S=0.01



Aquifer response to periodic forcing :

At the downstream boundary :h(t)=5 cos( 2πt/10)



Head profiles along the aquifer length. The downstream water level is a cosine function with an amplitude of 5m and with different periods: 1, 5, 10 days. The length of the aquifer is 300m, the storativity S=0.01.



Influence of Storativity:For high storativity : - small amplitude - delay of the response

- high variations of the velocity near the downstream boundary



This study has confirmed the decrease in the longitudinal dispersivity that is observed in the field by Kinzelbach and Ackerer (1986) due to temporal variation



Visual Interpretation of the decrease of the longitudinal dispersivity

Simulation of Solute Transport under Oscillating Groundwater Flow in Homogeneous Aquifers Conclusions: The model provides a good representation of the hydraulic head

variations. The response of the aquifer to periodic fluctuations is controlled by the

ratio,

When the penetration length l is large with respect to the length of the aquifer d, the propagation of oscillations within the aquifer is significant.

Transient flow conditions have an impact only if the amplitude of oscillations is large. Otherwise, results are very close to steady state.

Longitudinal dispersivity may decease due to temporal variation that confirms the earlier finding by Kinzelbach and Ackerer (1986).


2/ /d l Sd TP

Groundwater Flow and Contaminant Transport ...(cont.) Elfeki, A.M. (2006). Steady Groundwater Flow Simulation Towards Ains in

a Heterogeneous Subsurface. Published at the Forth International Conference on Ains, Water Recourses Center at King Abdulaziz University, Jeddah, Saudi Arabia in Cooperation with UNESCO, April 2006.


Steady Groundwater Flow Simulation Towards Ains in a Heterogeneous Subsurface.


Anis (Qanats) are underground tunnels, with a canal in the floor of the tunnel, which carries water. The difference between the qanat and a surface canal is that the qanat can get water from an underground aquifer.

Source: CharYu, Oz, Jun 21, 2005

http://www.urbandictionary.com/author.php?author=CharYu



Ain Zubidah:



Objective: How much water will flow to Ain in the case of heterogeneous subsurface?Modelling Heterogeneity (LU Decomposition Method)

)( Z, Z = Cov c jiij

...),(............),(

),(..),(

21

2

212

1212

2

1

p

i

Zp

Z

Z

pZ

ZZCov

ZZCovZZCovZZCov

C

ij

X

Y

0

ZZ

ij

1

p

2 3



0 2 4 6 8 10Hydrau lic Conductiv ity (m /day)

0

0.2

0.4

0.6

0.8

pdf

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0- 2 0

- 1 5

- 1 0

- 5

0

-1.4

-1.1

5-0

.9-0

.65

-0.4

-0.1

50.

10.

35 0.6

0.85 1.

11.

35

U L= C where, L is a unique lower triangular matrix, U is a unique upper triangular matrix, and U is LT , i.e., U is the transpose of L.

T21 },...,,{ p

ε U= X X + μ= Z

LU-Decomposition Procedure:

Realization of RFof mean = 0, Variance Ln(K)=0.5 and Lambda = 2 m

Steady Groundwater Flow Simulation Towards Ains in a Heterogeneous Subsurface.Steady Groundwater Flow Model “FLOW2AIN” :


where is the hydraulic conductivity, and is the hydraulic head at location

( )K x( ) x x

. ( ) ( ) 0K x x L x

L yB

H d

1

1( ) ( ),MC

kk

= MC

x x

22

1

1( ) ( ) ( )MC

kk

= MC

x x x

( )k x

2 ( ) x

Expected Values and Uncertainty is the hydraulic head at location x in the kth realization, and

represents the uncertainty in the predictions.



Variance Ln(K)=2.

Variance Ln(K)=1.5

Variance Ln(K)=.5

-1 .4 -1 -0.6 -0.2 0 .2 0.6 1 1.4

0 5 10 15 20 25 30 3 5 40 45 50-20

-15

-10

-5

0

0 5 1 0 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

-4 -3 -2 -1 0 1 2 3 4

0 5 10 15 20 25 30 3 5 40 45 50-20

-15

-10

-5

0

0 5 1 0 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

0 5 10 15 20 25 30 3 5 40 45 50-20

-15

-10

-5

0

0 5 1 0 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

Ln (K ) variab ility

2 ( ) x1

1( ) ( ),MC

kk

= MC

x x

Hydraulic Head Statistics (Expected value and Uncertainty):



L x

L yB

H d

Hydraulic Head Uncertainty Profile:



0 0.4 0.8 1.2 1.6 2V ariance of Ln(K)

-5

0

5

10

15

20

25

Exp

ecte

d Fl

ux to

Ain

(m^3

/day

/m'),

Var

ianc

e in

Flu

x

Expected F lux to A inVariance o f F lux to A inC V of Expected F lux

0 1 2 3 4 5H ydraulic Conductiv ity (m /day)

0

0.4

0.8

1.2

1.6

pdf

0 4 8 12 16 20H ydraulic C onductiv ity (m /day)

0

0.2

0.4

0.6

0.8

pdf

0 0.4 0.8 1.2 1.6 2Variance of Ln(K )

0

4

8

12

Flux

to A

in (m

^3/d

ay/m

')

Expected F lux to A in U pper L im it: E (Q )+Q

Low er L im it: E (Q )-Q

Flux to Ain Statistics (Expected Value and Uncertainty):


Conclusions:

FLOW2AIN has been developed to study the influence of subsurface heterogeneity on hydraulic head and water flux to Ains.

Increasing heterogeneity of the hydraulic conductivity leads to an increase in the hydraulic head uncertainty.

Increasing heterogeneity leads to an increase in the expected water discharge to Ain. This reflects the Log-normal distribution of K.

For Ln(K) Less than 1.5 the uncertainty is relatively low, however, it increases drastically over this value.







Soil-Contaminant Interaction in Porous Media. Elfeki, A.M.M. (2007). Modelling Kinetic Adsorption in Porous

Media by Two-State Random Walk Particle Method. Journal of King Abdulaziz University, Meteorology, Environment

and Arid Land Agriculture Sciences, vol. 18 (1) pp.61-74.


Modeling Kinetic Adsorption in Porous Media by Two-State Random Walk Particle Method.


Modeling Kinetic Adsorption In Porous Media by a Two-State Random Walk Particle Method

Amro Mohamed Mahmoud Elfeki

Department of Hydrology and Water Resources Management, Faculty of Meteorology, Environment and Arid Land Agriculture,

King Abdulaziz University, Jeddah, Saudi Arabia. E-mail: [email protected],


Background:DIOC project TU-Delft: “Transient processes under chemically interactive porous sediments”

Plume shape and its concentration distribution is due to:- Heterogeneity of the medium.

- Soil-Contaminant Interaction “Reactivity” [Linear or Non-linear].

- Transient Conditions.


Comparison between Reactive and Non-Reactive Plumes from the Cape Cod Site, Massachusetts [LeBlanc et al., 1991] .



Table 1. Comparison between Reactive and Non-Reactive Plumes from the Cape Cod Site.

FeatureNon-reactive Reactive

Degree of dilution Less diluted More diluted

Location peak concentration

In the middle of the plume

In the advancing edge

Plume width Wide Thin

Retardation Not retarded Retarded

Symmetry in the flow direction

Relatively symmetrical Non-symmetrical (negatively skewed)

vertically averaged concentration of the tracers (Bromid, Lithium and Molybdate).

Goal: devolvement of a simple stochastic model for kinetic adsorption that is based on a two-state random walk particle method where sorption de-sorption mechanisms are characterized by a two state Markov chain to model the exchange between the particle states.



where C is the aqueous concentration (mobile) at time t, S is the adsorbed mass of chemical constituent on a unit mass of solid part of the porous medium (immobile) at time t, is the bulk mass density of the porous medium, ε is the effective porosity, and Vx is the Eulerian velocity field in x direction defined as follows [Bear, 1972]:

2 2

, ,2 2b

d xx d yyxC S C C C V D Dt t x x y

xK = - V

where, K is the homogenous isotropic hydraulic conductivity, is the hydraulic gradient

Dd,xx, and Dd,yy are components of pore scale (micro-level) dispersion coefficients [Bear, 1972]:

, ,| | , | |d xx d yyl t V V D D

Model Equation in a Continuous Form (Kinetic Adsorption):

ka, and kd are adsorption desorption coefficients.

b ba d

S k C k St



for mobile paricles: ( ) ( ) ( ( ), ( )). . 2 ( ( ), ( )).

( ) ( ) 2 ( ( ), ( )).

p p p p p px l x

p p p pt x

t t t t t t Z V t t t VX X X Y X Y

t t t Z V t t tY Y X Y

( ) ( )for immobile particles: X

( ) ( )

pp

p p

t t t X t t t Y Y

where, (Xp(t), Yp(t)) are the x and y coordinates of a particle at time t, (Xp(t+Δt), Yp(t+Δt)) are the x and y coordinates of a particle at time t+Δt, Δt is the time step of calculations, Z, Z´ are two independent random numbers drawn from normal distribution with zero mean and unit variance.

1

, , and ,1lk

i mi a a

p l i m k i mm b b

Simulation of Kinetic Adsorption by Markov Chain RWPM:

lkp

is the transition probability to change between state l (mobile m or immobile i ) and state k (mobile m or immobile i ).

lkp


010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

ABC

DEF

.

00.1

110

1

1lk

i mi a a

pm b b


Case (A) No-adsorption a= 1.0 , b= 0.0

Case (B) Highly adsorbed medium

a= 0.1, b=0.9

Case (C) Moderate kinetic reaction

a= 0.5, b=0.5

Case (D) Very slow kinetic reaction

a= 0.1, b=0.1

Case (E) Fast kinetic reaction

a= 0.9, b= 0.9

Case (F) Poorly adsorbed medium

a= 0.9, b=0.1


010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

010

2030

4050

6070

8090

100-30

-20

-10 0

ABC

DEF

.

00.1

110

Case a bA 1.0 0.0

B 0.1 0.9

C 0.5 0.5

D 0.1 0.1

E 0.9 0.9

F 0.9 0.1


.Xc (t)

tx x

y y t

(Xo,Yo)



0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

A

B

C

.

0 0.1 1 10

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

D

E

F

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

0 10 20 30 40 50 60 70 80 90 100-30

-20

-10

0

.( , ,0) ( ) ( )m ow MC x y x yH

maw

a b

Comparison with Fundamental Analytical Solution

( , , ) 0C t

2

2--/( ).

( , , ) exp -4 44 4

xo

om o

x xx xl tl t

Vx tX y Hw M R YC x y t V VV V t tt t R RR R

1 bRa

2

2

( )

( ) 2

( ) 2

xc o

l xxx

t xyy

Vt tX XR

V t t RVt t R



1. The stochastic model, developed in this study to address sorption desorption mechanisims, is capable of handling linear kinetics in a fundamental way rather than of considering a retardation factor in the modeling process.

2. A computer code (called ADS_2D) has been developed to perform numerical adsorption experiments. The experiments show that adsorption which is characterized by slow kinetics can not adequately be modeled using retardation factor.

3. The analytical solution deviates from the numerical solution particularly the spreading. This is due to the fact that the analytical solution does not take into account the extra dispersion due to the kinetic reaction.

4. Some features of the slow kinetics which appeared in our simulations (thin elongated plumes) mimics the Lithium plume in Figure 1 (middle), however, the peak concentration is located in the Lithium plume front. This can be due non-linearity. This point will be considered in future studies using Markov chains with capacity.

Conclusions






Reduction of Uncertainty in Geological Formations, Groundwater Flow and Transport Models Elfeki, A. M. (2006). Reducing Concentration

Uncertainty Using the Coupled Markov Chain Approach. Journal of Hydrology vol. 317, pp 1-16.

Elfeki, A. M. (2006). Prediction of Contaminant Plumes (Shapes, Spatial Moments and Macro-dispersion) in Aquifers with insufficient Geological Information. Journal of Hydraulic Research, vol. 44 (6), pp 841-856.


Reduction of Uncertainty in Geological Formations, Groundwater Flow and Transport Models (cont.)


Reducing Concentration Uncertainty Using the Coupled Markov Chain Approach. Motivation of this research:

Test the applicability of CMC model on field data at many sites.

Incorporating CMC model in flow and transport models to study uncertainty in concentration fields.

Deviate from the literature: - Non-Gaussian stochastic fields: (Markovian

fields), - Statistically heterogeneous fields, and - Non-uniformity of the flow field (in the mean) due

to boundary conditions.


Reducing Concentration Uncertainty Using the Coupled Markov Chain Approach.

Classification of Uncertainty: -Conceptual Model Uncertainty: Darcy’s and Fick’s Laws.

Geological Uncertainty: Connectivity and dis-connectivity of the layers, geological sequence, boundaries between geological units.

Parameter Uncertainty: K, porosity.

Hydro-geological Uncertainty: Constant head boundaries, impermeable boundaries, Plume boundaries, source area

boundaries.


0 50 100 150 200 250

Horizontal D istance between W ells (m )

-50

0

Dept

h (m

)

W ell 1 Well 2

? K(x,y,z)?

(x,y,z)?

C(x,y,z)?H=?

H=?

?

???

? ?

?

?

?



- The uncertainty due to the lack of information about the subsurface structure which is known only at sparse sampled locations.

- The erratic nature of the subsurface parameters observed at field scale.

Why Addressing Uncertainty by Stochastic Approach?



1 2 3 4

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0-5 0

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0-5 0

0

tim e = 1 6 0 0 d ay s

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0-5 0

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0-5 0

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0-5 0

0

0 50 100 150 200 250 300

-40

-20

0

0 50 100 150 200 250 300

-40

-20

0

G eology is C erta in and Param eters are Uncerta in

G eology is Uncerta in and Param eters are Certa in

0 0.01 0.1 1

C

C

actualC

C

C

Elfeki, Uffink and Barends, 1998

Geological Uncertainty: Geological configuration.Parameter Uncertainty: Conductivity value of each unit.



Study Area The Schelluinen study area is located in the central Rhine-Meuse delta in the Netherlands. Figure 1 shows the geological cross-section, interpreted by geologists based on drillings made at 20 m apart (for details see Bierkens, 1994 and Bierkens, 1996, and Weerts, 1996). Augured drillings are used to describe the vertical sequence of the confining layers at boreholes. In addition to these drillings, a few measurements of hydraulic conductivity and porosity are performed on sediment cores. Merging soft geological information with a few hard hydraulic data yields estimation for the hydraulic properties of the entire confining layer at the scale of interest. A total number of 750 borings are available at a depth of 2 – 2.5 m below the surface


Soil Coding

Soil description

1 Channel deposits (sand)

2 Natural levee deposits (fine sand, sandy clay, silty clay)

3 Crevasse splay deposits (fine sand, sandy clay, silty clay)

4 Flood basin deposits (clay, humic clay)

5 Organic deposits (peaty clay, peat)

6 Subsoil (sand)

0 80 160 240-10

-5

0

0 200 400 600 800 1000 1200 1400 1600-10

-5

0

1 2 3 4 5 6

Data from Bierkens, 1994



Soil Properties at the core scale from Bierkens, 1996 .Soil Coding

Soil type Wi

6 Fine & loamy sand

0.12 0.60 1.76 4.40 0.09

5 Peat 0.39 -2.00 1.7 0.30 2.993 Sand & silty clay 0.19 -4.97 3.49 0.1 5.864 Clay & humic

clay0.30 -7.00 2.49 0.01 10.1

2( )iLog K( )iLog K ( / )iK m day 2

iK




Application of SIS at the Site

Geological Section

Deterministic and Stochastic Zones InSIS Model

Bierkens, 1996



0 200 400 600 800 1000 1200 1400 1600-10

-5

0

Conditioning on half of the drillings

SIS Model Simulation

CMC Model Simulation

Geological Section


( , ) ( , ) 0

( , )

( , )

x

y

K x y K x yx x y y

K x yV x

K x yV y

Contam inant Source

P lum e at T im e, t

Im perm eable boundary


is the hydraulic head, Vx and Vy are pore velocities, is the hydraulic conductivity, and is the effective porosity.

Hydrodynamic Condition: Non-uniform Flow in the Mean due to Boundary Conditions.

( , )K x y



Governing equation of solute transport :

C is concentration Vx and Vy are pore velocities, and Dxx , Dyy , Dxy , Dyx are pore-scale dispersion coefficients

x y xx xy yx yyC C C C C C CV V D D D Dt x y x x y y x y

* - i jmij ijL L TVV

D V DV

*mD

ij LT

is effective molecular diffusion,

is delta function, is longitudinal dispersivity, andis lateral dispersivity.




0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0

0.1

1

10

3 4

Litho logy C oding

6 5

T= 82 years

# drillings

2

3

5

9

25

31



0 4 8 12 16 20 24 28 32No. of Conditioning Boreholes

0

40

80

120

160

200

240

Pea

k C

once

ntra

tion

(mg/

lit)

Single Realization C m ax (t = 34.2 Years)S ingle Realization C m ax (t = 68.4 Years)S ingle Realization C m ax (t = 95.8 Years)S ingle Realization C m ax (t = 136.9 Years)O rig inal S ection (t = 34.2 Years)O rig inal S ection (t = 68.4 Years)O rig inal S ection (t = 95.8 Years)O rig inal S ection (t = 136.9 Years)

Practical convergence is reached after about 21 boreholes

0 50 100 150 200-10

-5

0

Effect of Conditioning Single Realiz. Cmax


0 10000 20000 30000 40000T im e (days)

0

20

40

60

80

100

120

X_C

oord

inat

e of

the

Cen

troid

(m)

O riginal SectionC ondition ing on 2 boreholesC ondition ing on 3 boreholesC ondition ing on 5 boreholesC ondition ing on 9 boreholesC ondition ing on 25 boreholes

0 10000 20000 30000 40000T im e (days)

-10

-8

-6

-4

-2

0

Y_C

oord

inat

e of

the

Cen

troid

(m)

Orig inal SectionCondition ing on 2 boreholesCondition ing on 3 boreholesCondition ing on 5 boreholesCondition ing on 9 boreholesCondition ing on 25 boreholes

Trend is reached at 3 boreholes

Convergence at 9 boreholes

Contam inant Source





0 10000 20000 30000 40000T im e (days)

0

0.5

1

1.5

2

2.5

Var

ianc

e in

Y_d

irect

ion

(m2 )

O rig ina l SectionCondition ing on 2 boreholesCondition ing on 3 boreholesCondition ing on 5 boreholesCondition ing on 9 boreholesCondition ing on 25 boreholes0 10000 20000 30000 40000

T im e (days)

0

1000

2000

3000

4000

Var

ianc

e in

X_d

irect

ion

(m2 )

O rigina l SectionC ondition ing on 2 boreholesC ondition ing on 3 boreholesC ondition ing on 5 boreholesC ondition ing on 9 boreholesC ondition ing on 25 boreho les

Trend is reached at 3 boreholes

Convergence at 5 and 25 boreholes


Contam inant S ource



Im perm eab le boundary


0 10000 20000 30000 40000 50000T im e (days)

0

0.2

0.4

0.6

0.8

1

Nor

mal

ized

Mas

s D

istri

butio

n

O riginal SectionC onditioning on 2 boreholesC onditioning on 3 boreholesC onditioning on 5 boreholesC onditioning on 9 boreholesC onditioning on 25 boreho les

0 50 100 150 200-10

-5

0



0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 0.1 1 10

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

CactualC C

T = 4.1 years

T = 82.2 years

T = 136.9 years

mg/lit

2 boreholes


0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 0.1 1 10

actualC C C

T = 4.1 years

T = 82.2 years

T = 136.9 years

5 boreholes

mg/lit


0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

0 50 100 150 200-10

-5

0

actualC C C

T = 4.1 years

T = 82.2 years

T = 136.9 years

31 boreholes



0

10

20

30

40

50

60

70

80

90

100

110

Ens

embl

e P

eak

Con

cent

ratio

n (m

g/lit

)

Ensem ble C m ax (t = 34.2 Y ears)Ensem ble C m ax (t = 68.4 Y ears)Ensem ble C m ax (t = 95.8 Y ears)Ensem ble C m ax (t = 136.9 Years)O rigina l Section (t = 34.2 Years)O rigina l Section (t = 68.4 Years)O rigina l Section (t = 95.8 Years)O rigina l Section (t = 136.9 Years)


0

1

2

3

4

5

6

CV

of C

max

t = 34.2 Yearst = 68.4 Yearst = 95.8 Yearst = 136.9 Years

max

1 for #boreholes 5 c

C

max

1 for #boreholes 5c

C

max

time c

C

Reducing Concentration Uncertainty Using the Coupled Markov Chain Approach. CMC model proved to be a valuable tool in predicting heterogeneous

geological structures which lead to reducing uncertainty in concentration distributions of contaminant plumes.

Convergence to actual concentration is of oscillatory type, due to the fact that some layers are connected in one scenario and disconnected in another scenario.

In non-Gaussian fields, single realization concentration fields and the ensemble concentration fields are non-Gaussian in space with peak skewed to the left.

Reproduction of peak concentration, plume spatial moments and breakthrough curves in a single realization requires many conditioning boreholes (20-31 boreholes). However, reproduction of plume shapes require less boreholes (5 boreholes).

Reduction of Uncertainty in Geological Formations, Groundwater Flow and Transport Models


Prediction of Contaminant Plumes (Shapes, Spatial Moments and Macro-dispersion) in Aquifers with insufficient Geological Information

Objectives: To what extent one can use less information to get plausible results,

for practical point of view. Proposing the use of the final image concept instead of Monte-

Carlo simulations for uncertainty estimation (efficient in terms of computer time and storage).

Test the capability of CMC on a field case study that is documented in the literature for testing theories.

Compare CMC with other techniques (polynomial regression trend, Kalman filter trend, hydro-facies trend and Kriging method) in the literature that is used by others (Eggleston and Rojstaczer, 1998).

Compare CMC with Adams and Gelhar theories for Macro-dispersion (1992).




MADE Site: Designed to test Stochastic Theories



0 50 100 150 200 250

-10

-5

0

0

1

2

3

4

5

MADE1 Exp.


Model Assumptions: 2D-Vertical Cross-Section. Steady State Flow System:

(Seasonal Variability is Negligible). Confined Aquifer Conditions. Non-reactive Transport (Bromid Tracer). Molecular Diffusion is Negligible.




0 50 100 150 200 250

-10

-5

0

0

1

2

3

4

5

S. 1 2 3 4 5 6 7

1 .879 .103 .009 .000 .009 .000 .000

2 .026 .911 .046 .009 .003 .000 .005

3 .003 .030 .897 .044 .010 .000 .016

4 .000 .006 .094 .869 .031 .000 .000

5 .000 .000 .003 .010 .961 .000 .026

6 .009 .014 .009 .005 .000 .963 .000

7 .000 .000 .000 .000 .000 .000 1.00

Vertical Sampling Interval=0.1 m

T

T = pvlq

n

q

vlkv

lk

1

Tlkv is the number of observed transitions

from Sl to Sk in the vertical direction.

Parameter Estimation



0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0 1

2

3

4

5

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

a

b

c

d

e

Effect of Horizontal Transition Probabilities

Incr

easi

ng th

e di

agon

al e

lem

ents

of t

he m

atrix

From

0.5

- sa

me

as v

ertic

al -

0.92

2



Facies Measured Conductivity (m/day) lower limit upper limit mid range

1. Open work gravel 86.4 864. 475.2

2. Fine gravel 8.64 86.4 47.52

3. Sand 0.864 8.64 4.752

4. Sandy gravel 0.0864 0.864 0.4752

5. Sandy clayey gravel 0.00864 0.0864 0.04752

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

b

1

2

3

4

5

Hydraulic Conductivies of the Facies



Parameter 16 Boreholes 9 Boreholes 6 Boreholes MADE dataRehfeldt, et al., [1992].

μLn(K)-5.28 (Upper)-5.87 (Mid Range)-7.68 (Lower)

-5.44 (Upper)-6.03 (Mid Range) -7.43 (Lower)

-5.15 (Upper)-5.75 (Mid Range)-7.47 (Lower)

-5.2(-10.1 - 0.4)

8.19 (Upper)8.19 (Mid Range)7.31 (Lower)

7.43 (Upper)7.43 (Mid Range)7.43(Lower)

5.25 (Upper)5.25 (Mid Range)5.03 (Lower)

4.5(3.4 - 5.6)2

ln( )K

Comparison of Statistics Computed from the Three Scenarios (with upper, lower and mid range conductivities) and the values estimated from the MADE site (Rehfeldt et al., 1992)



0 50 100 150 200 250

-10

-5

0

0

1

2

3

4

5

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

Eggleston and Rojstaczer, (1998)

CMC method (This study)

Comparison of various Models with CMC



0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

1

2

3

4

50 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

- 1 0

- 5

0

Effect of Number of Boreholes on Site Characterization

Piih = 0.922 produces the main heterogeneous features in the site when conditioned on 16 boreholes.



0 0.1 1 10 100

-10

-5

0

1 2 3 4 5

-10

-5

0

-10

-5

0

49 days

-10

-5

0

279 days

0 50 100 150 200 250

-10

-5

0

594 days

-10

-5

0

-10

-5

0

49 days

-10

-5

0

279 days

0 50 100 150 200 250

-10

-5

0

594 days

-10

-5

0

-10

-5

0

49 days

-10

-5

0

279 days

0 50 100 150 200 250

-10

-5

0

594 days

Lithology Cod ing

Concentration Scale (m g/L)

Simulation of the MADE 1 Exp



49 days

0 50 100 150 200 250

279 days

0 50 100 150 200 250594 days

0 50 100 150 200 250

49 days49 days

279 days279 days

594 days594 days

1 2

3

45

6

7 8 9 10

11

12

13

14

15

161

3

5 7 9

11 13 15

16161 5 7

11 13

-10

-5

0

-10

-5

0

0 0.1 1 10 100

-10

-5

0

-10

-5

0

49 days

0 50 100 150 200 250

-10

-5

0

-10

-5

0

279 days

0 50 100 150 200 250

-10

-5

0

594 days

-10

-5

0

-10

-5

0

-10

-5

0

0 50 100 150 200 250

-10

-5

0

-10

-5

0

49 days49 days

279 days279 days

594 days594 days

Effect of Number of Boreholes on the Simulated Plume (Upper conductivity)



Simulation







Conclusions:

2. The final image concept of chandelling uncertainty seems to perform well when compared with the data.








Design of Groundwater Monitoring System at Landfill Sites Yenigul, N.B., Elfeki, A. M. and den Akker, C. (2006). New

Approach for Groundwater Detection Monitoring at Landfills. Journal of Groundwater Monitoring and Remediation, 26, no. 2/Spring 2006/pp. 79-86.


Design of Groundwater Monitoring System at Landfill Sites (cont.)


New Approach for Groundwater Detection Monitoring at Lined Landfills

Background: This research was part of the PhD Dissertation of Buket Yenigul whom I was supervising at TU-Delft (finished 2006). It is also part of the DIOC project at TU-Delft.

Motivation and Objective:Formulation of a methodology for the design of an optimum monitoring well network at a landfill site.

Highest probability of contaminant

detection

Cost effectiveEarly detection










Objective of the paper: Proposing a new monitoring approach (PMA) at landfill sties and compare it with the conventional monitoring approach (CMA). Taking into account the uncertainty in leak location and subsurface Heterogeneity.

- Application on a hypothetical case study. - For detection monitoring design regulations at landfills (U.S. EPA 1986,

ECC 1999): at least one background well (hydraulically up gradient from a potential source) and three down gradient wells.

- Literature: Massmann and Freeze (1987) Yenigul et al. (2005).



Goals in the design: Maximizing the likelihood of detecting contaminants and minimizing the contaminated area are the conflicting design objectives.

The proposed monitoring approach (PMA):

The idea is to increase the interception of the contaminant plumes at early stages by broadening the capture zone of monitoring well (s) simply be continuous pumping from the monitoring well (s) with a small pumping rate.



0 50 100 150 200 250 300 350 400 450 500-400

-350

-300

-250

-200

-150

-100

-50

0

100

50

0

150

200

250

300

350

400

Flow

Land

fill

(m)

(m)

3-w

ell s

yste

m4-

wel

l sys

tem

5-w

ell s

yste

m6-

wel

l sys

tem

8-w

ell s

yste

m

12-w

ell s

yste

m

Problem set up:



Model Formulation



2 2

/( )( , , )4 4

( - - ( -) )exp -4 4

o

l x t x

o ox

l x t x

HMC x y t t tV V

x t yVX Y t tV V

0

/ ( )( )

1 ( ( () )exp( ) ( )

o

x l t

t 2 2o ox

l x t x

HMC x, y,t = 4 V

x - - t y -VX Y - + d t 4 t 4 tV V



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230Distance from the contaminant source (m)

(a)

Det

ectio

n pr

obab

ility

( Pd

)

3-well system6-well system12-well system

T = 0.01 m T = 0.03 m

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230Distance from the contaminant source (m)

(b)

Det

ectio

n pr

obab

ility

( Pd

)

3-well system6-well system12-well system

T = 0.01 m T = 0.03 m

System reliability as a function of distance from the source for selected monitoring systems for conventional monitoring approach: (a) homogenous medium, and (b) heterogeneous medium. 0 50 100 150 200 250 300 350 400 450 500

-400

-350

-300

-250

-200

-150

-100

-50

0

100

50

0

150

200

250

300

350

400

Flow

Land

fill

(m)

(m)

3-w

ell s

yste

m4-

wel

l sys

tem

5-w

ell s

yste

m6-

wel

l sys

tem

8-w

ell s

yste

m

12-w

ell s

yste

m



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230distance from the contaminant source (m)

(a)

Ave

rage

con

tam

inat

ed a

rea (

A av

) x 1

04 (m2 )

3-well system12-well system

T = 0.01 m T = 0.03 m

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230distance from the contaminant source (m)

(b)

Ave

rage

con

tam

inat

ed a

rea (

A av

) x 1

04 ( m2 )

3-well system12-well system

T = 0.01 m T = 0.03 m

Average contaminated area as a function of distance from the source for selected monitoring systems for conventional monitoring approach:(a) homogenous medium and (b) heterogeneous medium. 0 50 100 150 200 250 300 350 400 450 500

-400

-350

-300

-250

-200

-150

-100

-50

0

100

50

0

150

200

250

300

350

400

Flow

Land

fill

(m)

(m )

3-w

ell s

yste

m4-

wel

l sys

tem

5-w

ell s

yste

m6-

wel

l sys

tem

8-w

ell s

yste

m

12-w

ell s

yste

m



Influence of the pumping rate on (a) detection probability of a 3-well system

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Homogenous mediumaT=0.01 m

Homogenous mediumaT=0.03 m

Heterogeneous mediumaT=0.01 m

Heterogeneous mediumaT=0.03 m

(a)

Det

ectio

n pr

obab

ility

( P

d )

estimated minimum estimated maximumestimated optimal

100 l/day50 l/daypumping rate =



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13Number of wells in the monitoring system

(a)

Det

ectio

n pr

obab

ility

( Pd

)


proposed monitoring approach

conventional monitoring approach

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13Number of wells in the monitoring system

(b)

Det

ectio

n pr

obab

ility

( Pd

)



conventional monitoring approach

Comparison of the conventional and the proposed monitoring approaches (pumping rate = 100 l/day) in terms of reliability “in heterogeneous medium”: (a) transverse dispersivity, T = 0.01 m, and (b) transverse dispersivity, T = 0.03 m.



Expected cost as a function of number of wells in a monitoring system for transverse dispersivity, T = 0.03 m:

(a) homogenous medium and (b) heterogeneous medium.

0

2

4

6

8

10

12

14

16

18

3-wellmonitoring

system

4-wellmonitoring

system

5-wellmonitoring

system

6-wellmonitoring

system

8-wellmonitoring

system

12-wellmonitoring

system(a)

Expe

cted

tota

l cos

t (C

T) x

105 (d

olla

rs) conventional monitoring approach


0

2

4

6

8

10

12

14

16

18

3-wellmonitoring

system

4-wellmonitoring

system

5-wellmonitoring

system

6-wellmonitoring

system

8-wellmonitoring

system

12-wellmonitoring

system(b)

Expe

cted

tota

l cos

t (C

T) x

105 (d

olla

rs) conventional monitoring approach


New Approach for Groundwater Detection Monitoring at Lined Landfills Conclusions: The conventional methods (CMA) is not adequate to accomplish

the objectives of maximizing the detection probability while minimizing the contaminated area.

The (PMA) improved the efficiency of the optimum three-well monitoring system.