Presentation of the scientific research 2002 2007

Scientific Research
Amro 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.
5 August 2016 2Scientific Research Papers of Amro Elfeki, PhD

Aquifers.
Models.
Landfill Sites.

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

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.

Objectives:
 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.

Applications:
 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.

( )
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
N
klk
| , , S ,...,S S S SZ Z Z Z Z
| pS SZ Z
p w
     
  

S S
o d
Markov Chain Theory:

-1Pr( | ) : ,i ik l lkpS SZ Z  
SS S
i0 1 i+1i-1 N2
l k qdSSa
N-1
SrSb
1-D Forward Markov Chain Theory:
1Pr( | ).i il k
kl
S SZ Zp

  
1-D Backward Markov Chain Theory:
lk klp p



( 1)
1 0 ( )
: Pr ( ) ,
N
ab bq
Nb a qab q N
aq
p p
p | ,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 a
qr a
N
N N Nq r r rq ara
N
N 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 v
lk mk
lm k h v
lf 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 p
p k n
.p p
p Z S Z S Z S Z S
p
 
 
   
 
    

( )
, ( )
, 1,... .
x
x
h h N i v
lk kq mk
m k q h h N i v
lf fq mf
f
. .p p p
k 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 v
kd ak mk
dm k a h h i v
fd 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 v
lk kq mk
lm k q h h N i v
lf fq mf
f
p Z S Z
S Z S Z S
. .p p p
p
. .p p p




 
  



? >? >
?< ?<
? > ?<
Forward Markov Chain Model (two forward steps)
Backward Markov Chain Model (two backward steps)
Forward-Backward Markov Chain Model (one forward step and one backward step)
Well (1) Well (2) Well (1) Well (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
MC
kk R
ij k
R
Z S
I Z
MC MC



  
1 2
max{ , ..., }l n
ij 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,...,
n
k k
ij ij ij
k
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

Sensitivity 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.

0 200 400 600 800 1000 1200 1400 1600
-20
-10
0
0 200 400 600 800 1000 1200 1400 1600
-10
0
0 200 400 600 800 1000 1200 1400 1600
-10
0
0 200 400 600 800 1000 1200 1400 1600
-10
0
1 2 3 4 5 6
A
B
C
0 200 400 600 800 1000 1200 1400 1600
-15
-10
-5
0
1 2 3 4 5 6
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
0
0.2
0.4
0.6
0.8
1
-10
0
1
-10
0
2
-10
0
3
-10
0
4
-10
0
5
-10
0
6
(Afsluitdijk-Lemmer), NL
Courtesy “GeoDelft”
Lithology Code
Clay, sandy to sand, clayey (deposition of Duinkerke,Westland - formation) 1
Peat (Hollandpeat, Westland – formation) 2
Sand, locally humous and / with loam layers (formation of Twente) 3
Sand , locally loamy (formation of Drente) 4
Mainly clay (artificial ground) 5
Loam, 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 0.000
2 0.000 0.500 0.500 0.000 0.000 0.000 0.000 0.000
3 0.000 0.000 0.844 0.156 0.000 0.000 0.000 0.000
4 0.000 0.000 0.000 0.830 0.000 0.034 0.000 0.136
5 0.000 0.308 0.000 0.077 0.615 0.000 0.000 0.000
6 0.000 0.000 0.000 0.333 0.000 0.667 0.000 0.000
7 0.045 0.000 0.000 0.000 0.076 0.000 0.879 0.000
8 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).
0 200 400 600 800 1000 1200 1400 1600
-20
-10
0
0 200 400 600 800 1000 1200 1400 1600
-20
-10
0
0 200 400 600 800 1000 1200 1400 1600
-20
-10
0
1 2 3 4 5 6
Results of 30 Realizations
0 200 400 600 800 1000 1200 1400 1600
-20
-10
0
0 200 400 600 800 1000 1200 1400 1600
-20
-10
0
0 200 400 600 800 1000 1200 1400 1600
-20
-10
0
1
1
n
v v v
lk lqlk
q
p =T T


 
 
 

where Tlk
v 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

0 500 1000 1500 2000 2500
-15
-10
-5
0
0 500 1000 1500 2000 2500
-15
-10
-5
0
0 500 1000 1500 2000 2500
-15
-10
-5
0
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
Lithology CodingEntropy Measure
(Caspar de Roblesdijk part
of Waddenzeedijken), NL
Courtesy “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 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
a
b
c
d
e
f
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
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 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
-300
-200
-100
0
p = 0.986
1
2
3
4
5
6
7
ii
ii
ii
ii
ii
1- 0.001
( -2)
h
h ii
ij
p
p
n
 
  
 
where the value 0.001 is the
transition probability from
any state to the artificial state
8 for i=1,...,7 and therefore,
88 0.993h
p 
Diagonal Dominancy of The
Horizontal Transition
Probability Matrix

Comparison of
Various Coupled
Markov Chain Models:
FCMC
BCMC
FBCMC

Application of Walther’s Law
Lithologies 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 16000
Overall Horizontal Field Scale (meters)
0
0.01
0.02
0.03
0.04
dy/dx
Afsluitdijk- Lemmer (Netherlands)
Afsluitdijk Caspar de Roblesdijk (Netherlands)
Delaware River Aquifer (Longitudinal-Section), USA
Delaware River Aquifer (Cross-Section),USA
MADE site at Columbus, Mississippi [Elfeki and Rajabiani, 2002]

 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 j
lk kq mk kp
h h N i h h N j
lf fq mf fp
f
Z S Z S Z S Z S Z S
p p p p
k n
p p p p
 
 
 
     


2D CMC Theory Conditioned
on Future States x-chain

x-chain
z-chain
y
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 hy
lo op mo
hx N i
lp
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 p
C
p
  
 


 
      
       
   

( )
( 1)
y
y
hy N j
oq v
nohy N j
mq
p
p
p

 
where 1( )( )
( 1)( 1)
yx
yx
hy N jhx N ihx hy v
lr mr nr rp rq
hy N jhx N i
r lp mq
p p p p p
C
p p

  
 
   
 
 


Active Conditioning
Use the tolerance angle along
scanning and perpendicular to
scanning direction
x
y

5 August 2016 Scientific Research Papers of Amro Elfeki, PhD 38
Algorithm
1. Discretizing domain
2. Saving conditioning data
3. Deriving transition probabilities
4. Applying 1-, 2-, and 3D
equations to the domain
5. Generate equally probable
single realizations
6. Repeat step 1 through 5, if
multiple realization are desired
7. 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.

Aquifers.
Models.
Landfill Sites.

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.


Transport in Aquifers

Transient Groundwater Flow in
Heterogeneous Geological Formations.
 Background:
This paper is carried out under
TU-Delft project called “ Transient
processes 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 y
t x x y y
x y t
q x y t T x y
x
x y t
q x y t T x y
y
      
    
       

 


 

water
-ΔV
S=
ΔA.Δh

Finite difference formulation of the flow equation :
Implicit scheme :
1 1 1 1 1
, ,1, , 1 1, , 1ij ij ij ij ij ij
k k k k k k
i 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)

• 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 fluctuations
are 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
Time (days)
-0.02
0.00
0.02
0.04
0.06
0.08
LongitudinalComponentofDarcy'sVelocity
Response(m/day)
Storage Coefficient
S = 0.1
S = 0.01
S = 0.001
S = 0.0001
0 5 10 15 20 25
Time (days)
-0.60
-0.40
-0.20
0.00
0.20
LateralComponentofDarcy'sVelocity
Response(m/day)
Storage Coefficient
S = 0.1
S = 0.01
S = 0.001
S = 0.0001
0 5 10 15 20 25
Time (days)
8
12
16
20
24
28
HydraulicHeadResponse(m)
Storage Coefficient
S = 0.1
S = 0.01
S=0.001
S = 0.0001
0 5 10 15 20 25
Time (days)
-10
0
10
20
30
InputHeadSignalatRightBoundary(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:

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

 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 t
S 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 y
n
h y t h
h 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 :
 
   
         
         
         
         
0
2
]
,
cosh / -cos /
cos sinh / cos / sinh / cos /
-sin cosh / sin / sinh / cos /
sin sinh / cos / cosh / sin /
cos cosh / sin / cosh / sin /
h
h x t
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
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

 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

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

Ain Zubidah:

Objective: How much water will flow to Ain in the case of heterogeneous
subsurface?
Modelling Heterogeneity
(LU Decomposition Method)
)( Z,Z= Covc jiij
...),(
.....
....
...),(
),(..),(
2
1
2
2
12
121
2
2
1

















p
i
Zp
Z
Z
pZ
ZZCov
ZZCov
ZZCovZZCov




C


i
j
X
Y
0
Z
Z
sij
1
p



2 3


0 2 4 6 8 10
Hydraulic Conductivity (m/day)
0
0.2
0.4
0.6
0.8
pdf
0 5 10 15 20 25 30 35 40 45 50
-20
-15
-10
-5
0
-1.4
-1.15
-0.9
-0.65
-0.4
-0.15
0.1
0.35
0.6
0.85
1.1
1.35
UL=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.
T
21 },...,,{ p
εU=X X+μ=Z
LU-Decomposition Procedure:
Realization
of RF
of mean = 0,
Variance
Ln(K)=0.5
and Lambda
= 2 m

Steady Groundwater Flow Model “FLOW2AIN” :
where
is the hydraulic conductivity, and
is the hydraulic head at location
( )K x
( ) x x
 . ( ) ( ) 0K  x x
Lx
Ly
B
H d
1
1
( ) ( ),
MC
k
k
=
MC 
  x x
 
22
1
1
( ) ( ) ( )
MC
k
k
=
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 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
-4 -3 -2 -1 0 1 2 3 4
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
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) variability
2
( ) x 1
1
( ) ( ),
MC
k
k
=
MC 
  x x
Hydraulic Head Statistics (Expected value and Uncertainty):

Lx
Ly
B
H d
Hydraulic Head Uncertainty Profile:

0 0.4 0.8 1.2 1.6 2
Variance of Ln(K)
-5
0
5
10
15
20
25
ExpectedFluxtoAin(m^3/day/m'),VarianceinFlux
Expected Flux to Ain
Variance of Flux to Ain
CV of Expected Flux
0 1 2 3 4 5
0
0.4
0.8
1.2
1.6
pdf
0 4 8 12 16 20
0
0.2
0.4
0.6
0.8
pdf
0 0.4 0.8 1.2 1.6 2
Variance of Ln(K)
0
4
8
12
FluxtoAin(m^3/day/m')
Expected Flux to Ain
Upper Limit: E(Q)+Q
Lower Limit: 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.

Aquifers.
Models.
Landfill Sites.

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: elfeki_amr@yahoo.co.uk,

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.
Feature
Non-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 2
b
d xx d yyx
C S C C C
V D D
t t x x y
     
     
      
x
K
= -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 tV VD D  


Model Equation in a Continuous Form (Kinetic Adsorption):
ka, and kd are
adsorption
desorption
coefficients.
b b
a d
S
k C k S
t
    
    
     

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 tVX 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 tX
t t tY 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 ,
1
lk
i m
i a a
p l i m k i m
m 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

0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
A
B
C
D
E
F
.
00.1110
1
1
lk
i m
i a a
p
m 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

0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
0102030405060708090100
-30
-20
-10
0
A
B
C
D
E
F
.
00.1110
Case a b
A 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)
txx
yy 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 M
C x y x y
H
  

m
a
w
a b


Comparison with Fundamental Analytical
Solution
( , , ) 0C t  
 
2
2-
-/( ).
( , , ) exp -
4 44 4
x
o
om o
x xx x
l tl t
Vx tX
yHw M R Y
C x y t
V VV V t tt t
R RR R
   
        
                             
1
b
R
a
 
2
2
( )
( ) 2
( ) 2
x
c o
l x
xx
t x
yy
V
t tX X
R
V
t t
R
V
t 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

Aquifers.
Models.
Landfill Sites.

Reduction of Uncertainty in Geological
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.

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.

 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 Distance between Wells (m)
-50
0
Depth(m)
Well 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 50 100 150 200 250 300
-50
0
0 50 100 150 200 250 300
-50
0
time = 1600 days
0 50 100 150 200 250 300
-50
0
0 50 100 150 200 250 300
-50
0
0 50 100 150 200 250 300
-50
0
0 50 100 150 200 250 300
-40
-20
0
0 50 100 150 200 250 300
-40
-20
0
Geology is Certain and Parameters are Uncertain
Geology is Uncertain and Parameters are Certain
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 2.99
3 Sand & silty clay 0.19 -4.97 3.49 0.1 5.86
4 Clay & humic
clay
0.30 -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
In
SIS 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 y
x x y y
K x yV
x
K x yV
y
  
  
  
   
    
   



















Contaminant Source
Plume at Time, t
Impermeable 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 yy
C C C C C C CV V D D D D
t x y x x y y x y
   
   
   
   
   
             
        
* - i j
mij ijL L T
VV
D V D
V
   
       
     
*mD
ij L

T

is effective molecular diffusion,
is delta function,
is longitudinal dispersivity, and
is 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
Lithology Coding
6 5
T= 82 years
# drillings
2
3
5
9
25
31

0 4 8 12 16 20 24 28 32
No. of Conditioning Boreholes
0
40
80
120
160
200
240
PeakConcentration(mg/lit)
Single Realization Cmax (t = 34.2 Years)
Original Section (t = 34.2 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 40000
Time (days)
0
20
40
60
80
100
120
X_CoordinateoftheCentroid(m)
Original Section
Conditioning on 2 boreholes
0 10000 20000 30000 40000
Time (days)
-10
-8
-6
-4
-2
0
Y_CoordinateoftheCentroid(m)
Original Section
Trend is reached at
3 boreholes
Convergence at
9 boreholes













Contaminant Source
Plume at Time, t

0 10000 20000 30000 40000
Time (days)
0
0.5
1
1.5
2
2.5
VarianceinY_direction(m2)
Original Section
0 10000 20000 30000 40000
Time (days)
0
1000
2000
3000
4000
VarianceinX_direction(m2)
Original Section
Trend is reached at
3 boreholes
Convergence at 5 and 25 boreholes
Convergence at
9 boreholes













Contaminant Source
Plume at Time, t

0 10000 20000 30000 40000 50000
Time (days)
0
0.2
0.4
0.6
0.8
1
NormalizedMassDistribution
Original Section
0 50 100 150 200
-10
-5
0
Convergence at
25 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 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 4 8 12 16 20 24 28 32
0
10
20
30
40
50
60
70
80
90
100
110
EnsemblePeakConcentration(mg/lit)
Ensemble Cmax (t = 34.2 Years)
0 4 8 12 16 20 24 28 32
0
1
2
3
4
5
6
CVofCmax
t = 34.2 Years
t = 68.4 Years
t = 95.8 Years
t = 136.9 Years
max
1 for #boreholes 5

 c
C
max
1 for #boreholes 5

c
C
p
max
time

 c
C

 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).

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=p
v
lq
n
q
v
lkv
lk
1
Tlk
v is the number of observed transitions from
Sl to Sk in the vertical direction.
Parameter Estimation

0 50 100 150 200 250
-10
-5
0
0 50 100 150 200 250
-10
-5
0
0 50 100 150 200 250
-10
-5
0 1
2
3
4
5
0 50 100 150 200 250
-10
-5
0
0 50 100 150 200 250
-10
-5
0
a
b
c
d
e
Effect of Horizontal Transition Probabilities
Increasingthediagonalelementsofthematrix
From0.5-sameasvertical-0.922

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 data
Rehfeldt,
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 50 100 150 200 250
-10
-5
0
0 50 100 150 200 250
-10
-5
0
1
2
3
4
5
0 50 100 150 200 250
-10
-5
0
0 50 100 150 200 250
-10
-5
0
0 50 100 150 200 250
-10
-5
0
0 50 100 150 200 250
-10
-5
0
0 50 100 150 200 250
-10
-5
0
Effect of Number of Boreholes on Site Characterization
Pii
h = 0.922 produces
the main
heterogeneous
features in the
site when
conditioned on
16 boreholes.

Simulation
of the
MADE 1
Exp

49 days
0 50 100 150 200 250
279 days
0 50 100 150 200 250
594 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.

Aquifers.
Models.
Landfill Sites.

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
Landfill
(m)
(m)
3-wellsystem
4-wellsystem
5-wellsystem
6-wellsystem
8-wellsystem
12-wellsystem
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 2
o 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 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230
Distance from the contaminant source (m)
(a)
Detectionprobability(Pd)
3-well system
6-well system
12-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 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230
Distance from the contaminant source (m)
(b)
3-well system
6-well system
12-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
Landfill
(m)
(m)
3-wellsystem
4-wellsystem
5-wellsystem
6-wellsystem
8-wellsystem
12-wellsystem

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 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230
distance from the contaminant source (m)
(a)
Averagecontaminatedarea(Aav)x10
4
(m
2
)
3-well system
12-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 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230
distance from the contaminant source (m)
(b)
Averagecontaminatedarea(Aav)x10
4
(m
2
)
3-well system
12-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
Landfill
(m)
(m)
3-wellsystem
4-wellsystem
5-wellsystem
6-wellsystem
8-wellsystem
12-wellsystem

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 medium
aT=0.01 m
Homogenous medium
aT=0.03 m
Heterogeneous medium
aT=0.01 m
Heterogeneous medium
aT=0.03 m
(a)
estimated minimum
estimated maximum
estimated 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 13
Number of wells in the monitoring system
(a)
estimated minimum
estimated maximum
estimated optimal
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 13
Number of wells in the monitoring system
(b)
estimated minimum
estimated maximum
estimated optimal
proposed
monitoring
approach
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-well
monitoring
system
4-well
monitoring
system
5-well
monitoring
system
6-well
monitoring
system
8-well
monitoring
system
12-well
monitoring
system
(a)
Expectedtotalcost(CT)x10
5
(dollars)
conventional monitoring approach
proposed monitoring approach
0
2
4
6
8
10
12
14
16
18
3-well
monitoring
system
4-well
monitoring
system
5-well
monitoring
system
6-well
monitoring
system
8-well
monitoring
system
12-well
monitoring
system
(b)
Expectedtotalcost(CT)x10
5
(dollars)
conventional monitoring approach
proposed monitoring approach

 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.

Presentation of the scientific research 2002 2007

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Presentation of the scientific research 2002 2007