Presentation made at the International Conference on Emerging Trends in Engineering, (ICETE 2012),
NMAM Institute of Technology, Nitte, Karnataka State, India, 15th and 16th May,
2012.
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The system dynamics modeling method in application of geo-membranes as landfill liners
1. THE SYSTEM DYNAMICS MODELING
METHOD IN APPLICATION OF
GEO-MEMBRANES AS LANDFILL
LINERS
By
Samson O. OJOAWO, Ph.D
Department of Civil Engineering,
Ladoke Akintola University of Technology Ogbomoso,
Nigeria
6. * Geo-membranes = highest durability of
between 50 to 65 years (Rowe and Rinal, 2008)
* System dynamics model = one of the latest
and comprehensive and is therefore
extensively applied in WM (Ojoawo, 2009)
*System dynamics modeling technique thus
employed in this paper
7. CENTRAL AIM
To model the applications of Geo-
membranes as landfill liners using case
study of Ogbomoso North Local
Government Area (LGA) of Oyo State
Nigeria, in Africa
8. The Case Study
• Ogbomoso North LGA, Oyo State
Nigeria, in Africa & has an average
population of 198,720 (National Population
Commission, 2011)
• It lies on Long 40 15’East, Lat 80 07’ North
• It’s situated in the transitional zone
between rain forest and savannah region
(Edward and Joel, 1998)
20. (c) Governing Equations:
(i) For leachate generation (Safari and Baronian, 2002)
N cells
LQnT (nΔt) = W4(t) – Wg(t) + Σ LQn( i, (n – i + 1) Δt
i = 1 -------(1)
21. where
LQnT = Accumulative amount of leachate
generated from the system
nΔt = No of waste cells at the given time
W4 = Overall mass of water entering or
leaving the dumpsite
Wg = Total water loss due to degradation
LQn = Overall leachate quantity generated
from a single cell
n & i = Counters
t = Breakthrough time of the liner
d = Thickness of the liner
α’ = Effective porosity
K = Coefficient of permeability and
h = Hydraulic head
22. (ii) Breakthrough time, t (Kadlec and
Knight, 1996)
t = d2α’ / K( d + h) ------(2)
where
d = thickness of the liner (m)
α’ = effective porosity
K = coefficient of permeability (m/s)
23. (iii ) Leackage rate through the liners
qi, also by Kadlec & knight, 1996:
qi = K [ 1 + y cos ϕ ]
d
----- (3)
where
K = coefficient of permeability (m/s)
d = liner thickness (m)
ϕ = the liner slope (measured in angles)
y = the leachate depth over liner (m)
24. (d) Computer programming and Simulation:
*V B language was employed in coding the equations
*Key elements of the Model were defined and quantified as
variables
*Relationships were formulated mathematically
*System dynamics structures applied in developing
the source codes
*Stock flow diagram of the system designed using
STELLA 9.1.4 software and simulation package
25. Population
Births
?
BirthRate
Death Rate
Deaths
?
Initial Field Capactiy
Runoff Coefficient
Total Precipitation
Chemical Reaction
Total Waste Generated
?
Initial Dry Weight of SW
Primary Leachate
Gas Generation Rate Increasing
?
Decay Process
Water Consumption DueTo Waste Decomposition
?
Mass of Water Consumed per CubicMeter of Ga Produced Decreasing
?
Effective Precipitation
Overall mass of WaterEntering or Leaving Dumpsite
?
Actual Evapotranspiration
?
Correction Factor
Overall leachate
Quantity for Single Cell
?
Field Capacity
?
Accumulative Amount of Lechate
?
Moisture Content of Waste
?
Estimated Population
Effective Porosity
Coefficient of Permeability
Hydraulic Head
Breakthrough Time
Saturated Vertical
Hydraulic Conductivity
Liner Slope in angle
Rate of Leakage
Thickness of Liner
?
Figure 11. The Stella flow diagram of the system
26. (e) Validation of the model:
Through assessment of practical
problems of leachate pollution
containment with Geo-membranes
of Ogbomoso North LGA
27. Material Hydraulic
Conductivit
y
(x 10-9) m/s
Porosity Thickness
(m)
Maximu
m slope
Smooth
HDPE
0.58 0.62 0.004 16
Textured
HDPE
0.93 1.75 0.005 16
Smooth
LDPE
0.81 2.27 0.002 16
Textured
LDPE
1.16 1.85 0.003 16
TABLE I: VALIDATION DATA FOR THE GEO-MEMBRANE SAMPLES
28. RESULTS AND DISCUSSION
On Simulation for 100 years the yearly
behavioural patterns are as shown below:
29. 10:33 PM Sun, Apr 15, 2012
Fig 12. Breakthrough time graph of Smooth HDPE
Page 1
0.00 25.00 50.00 75.00 100.00
Time (yrs)
1:
1:
1:
23526458
23526458
23526458
1: Selected Breakthrough Time
1
1
1
1
30. 10:44 PM Sun, Apr 15, 20
Fig 13. Breakthrough time graph for Textured HDPE
Page 1
0.00 25.00 50.00 75.00 100.00
Time (yrs)
1:
1:
1:
10190915
10190915
10190915
1: Selected Breakthrough Time
1
1
1
1
31. 10:47 PM Sun, Apr 15, 2012
Fig 14. Breakthrough time graph of Smooth LDPE
Page 1
0.00 25.00 50.00 75.00 100.00
Time (yrs)
1:
1:
1:
10194942
10194942
10194942
1: Selected Breakthrough Time
1
1
1
1
32. 10:50 PM Sun, Apr 15, 2012
Fig 15 . Breakthrough time graph for Textured LDPE
Page 1
0.00 25.00 50.00 75.00 100.00
Time (yrs)
1:
1:
1:
10185531
10185531
10185531
1: Selected Breakthrough Time
1
1
1
1
33. Material Breakthrough
time (s)
Breakthrough
time (day)
Smooth HDPE 23,524,658 273
Textured HDPE 10,190,915 118
Smooth LDPE 10,194,942 119
Textured LDPE 10,185,531 117
TABLE II
BREAKTHROUGH TIMES OF THE STUDIED GEO-MEMBRANES
34. FINDINGS
*Smooth HDPE has the highest
simulated retention capability
for the leachate volume
----- this is explainable by the fact that of the 4 samples,
Smooth HDPE possesses the lowest water absorption rate
[Dauda & Salami, 2012]
35. **The texture LDPE on the other
hand recorded the lowest
breakthrough period
42. REFERENCES
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36, 1996.
[10] R.K Rowe and G.J Rinal “Durabiltiy of Landfill liners”. Prentice Hall, pp 4-6, 2008.
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2006.
[12] B. Edward and L.M Joel “World Atlas”. 16th ed., USA, pp 21-35, 1978
[13] E. Safari and C. Baronian “ Modelling temporal variations in leachate quantity generated at
Kahrizah landfill”. Proceedings of International Environmental Modeling Software, 482 – 484, 2002.
[14] T. Kadlec and M. Knight “Leachate management in landfills”. Environmental Hydrology, Chapter 12,
94 – 105, 1996.
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[16] J. Dauda and B. Salami “ An investigation into the physical properties of landfill liners”.
Unpublished B. Tech Project Report, Department of Civil Engineering, Ladoke Akintola University of
Technology, Ogbomoso, Nigeria, pp 56-59, 2012