Model Output

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Model Output

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After the model has been executed, the output for the model will be displayed.

 

 

Probability vs Concentration

 

The Probability vs Concentration chart can be displayed by selecting the Probability vs Concentration item for the Chart Type. Using the chart of the probability of peak chloride concentration predictions can be made about the concentration in the aquifer. For example, in this case, the expected maximum concentration is 23.493 mg/L.

 

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Probability vs Time

 

The Probability vs Time chart can be displayed by selecting the Probability vs Time item for the Chart Type. Using this chart the expected time of the maximum concentration can be predicted. In this example, the expected time is 68.439 years.

 

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Probability vs Variable Value

 

The Probability vs Variable Value chart can be displayed by selecting the Probability vs Variable Value item for the Chart Type. Using this chart the distribution of the variable can be checked against the distribution that was specified. In this example, the specified distribution was a triangular distribution with a minimum of 15, mode of 25 and maximum of 50.

 

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Output Listing

 

To display the output as a text listing that will show the calculated concentrations as numbers, click on the List tab.

 

 

 

POLLUTEv8
 

Version 8.00 Beta
Copyright (c) 2021
GAEA Technologies Ltd., R.K. Rowe and J.R. Booker
 
 

Case 16: Monte Carlo Simulation

 
 
THE VARIABLE VELOCITY AND/OR CONCENTRATION OPTION HAS BEEN USED. NOTE THAT THE ACCURACY OF THE CALCULATIONS WITH THIS OPTION WILL DEPEND ON THE NUMBER OF SUBLAYERS USED.

 
 
THE PASSIVE SINK OPTION HAS BEEN USED. NOTE THE USER IS RESPONSIBLE FOR ENSURING THAT VELOCITY CHANGES ARE CONSISTENT WITH THE PASSIVE SINK.

 
 
Layer Properties

 

Version 8.00 Beta
Copyright (c) 2021
GAEA Technologies Ltd., R.K. Rowe and J.R. Booker
 
 

Case 16: Monte Carlo Simulation

 
 
THE VARIABLE VELOCITY AND/OR CONCENTRATION OPTION HAS BEEN USED. NOTE THAT THE ACCURACY OF THE CALCULATIONS WITH THIS OPTION WILL DEPEND ON THE NUMBER OF SUBLAYERS USED.

 
 
THE PASSIVE SINK OPTION HAS BEEN USED. NOTE THE USER IS RESPONSIBLE FOR ENSURING THAT VELOCITY CHANGES ARE CONSISTENT WITH THE PASSIVE SINK.

 
 
Layer Properties

 

Layer

Thickness

Number of Sublayers

Coefficient of Hydrodynamic Dispersion

Matrix Porosity

Distributon Coefficient

Dry Density

Clay

1 m

4

0.02 m²/a

0.4

0 cm³/g

1.5 g/cm³

Collection System

0.3 m

4

10 m²/a

0.3

0 cm³/g

1.5 g/cm³

Aquitard

2 m

4

0.02 m²/a

0.4

0 cm³/g

1.5 g/cm³

 
 
Boundary Conditions

 
   Finite Mass Top Boundary
 

   Fixed Outflow Bottom Boundary
 

         Landfill Length = 200 m
         Landfill Width = 1 m
         Base Thickness = 1 m
         Base Porosity = 0.3

 
 
Variation in Properties with Time
 

 Time Periods with the same Source and Velocity

Period

Start Time

No. of
Steps

Time Step

Source Conc

Rate of Change

Height of Leachate

Volume Collected

1

0  yr

1

20  yr

1000  mg/L

0

7.5  m

0.29  m/a

2

20  yr

5

2  yr

-1  mg/L

0

7.5  m

0.2  m/a

3

30  yr

2

10  yr

-1  mg/L

0

7.5  m

0.2  m/a

4

50  yr

5

10  yr

-1  mg/L

0

7.5  m

0.2  m/a

5

100  yr

5

20  yr

-1  mg/L

0

7.5  m

0.2  m/a

 

Period

Start Time

End Time

Proportion Mass

Dispersivity

Base Velocity

1

0  yr

20  yr

1  m/a

0.4  m

4  m/a

2

20  yr

30  yr

1  m/a

0.4  m

4  m/a

3

30  yr

50  yr

1  m/a

0.4  m

4  m/a

4

50  yr

100  yr

1  m/a

0.4  m

4  m/a

5

100  yr

200  yr

1  m/a

0.4  m

4  m/a

 
 
Velocity and Sink Profile
 

Time Period

Minimum Depth

Maximum Depth

Vertical Velocity

Horizontal Outflow

1 / 1

0  m

1  m

0.01  m/a

0  m/a

 

1  m

1.3  m

0.01  m/a

6.67  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 1

0  m

1  m

0.028  m/a

0  m/a

 

1  m

1.3  m

0.028  m/a

18.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 2

0  m

1  m

0.046  m/a

0  m/a

 

1  m

1.3  m

0.046  m/a

30.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 3

0  m

1  m

0.064  m/a

0  m/a

 

1  m

1.3  m

0.064  m/a

42.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 4

0  m

1  m

0.082  m/a

0  m/a

 

1  m

1.3  m

0.082  m/a

54.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 5

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

3 / 1

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

3 / 2

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 1

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 2

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 3

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 4

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 5

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 1

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 2

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 3

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 4

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 5

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

 
 
Laplace Transform Parameters
 

    TAU = 7     N = 20     SIG = 0     RNU = 2

 
 
Monte Carlo Simulation Results
 

    Number of Simulations = 2000

    Number of Variables = 1

    Number of Data Ranges = 20

 
    Variable # 1

      Variable Properties End Time
         Time Period = 1

         Triangular Distribution     ( Minimum = 15    Maximum = 50    Mode = 25 )

 
 
NOTICE
 

Although this program has been tested and experience would indicate that it is accurate within the limits given by the assumptions of the theory used, we make no warranty as to workability of this software or any other licensed material. No warranties either expressed or implied (including warranties of fitness) shall apply. No responsibility is assumed for any errors, mistakes or misrepresentations that may occur from the use of this computer program. The user accepts full responsibility for assessing the validity and applicability of the results obtained with this program for any specific case.

Layer

Thickness

Number of Sublayers

Coefficient of Hydrodynamic Dispersion

Matrix Porosity

Distributon Coefficient

Dry Density

Clay

1 m

4

0.02 m²/a

0.4

0 cm³/g

1.5 g/cm³

Collection System

0.3 m

4

10 m²/a

0.3

0 cm³/g

1.5 g/cm³

Aquitard

2 m

4

0.02 m²/a

0.4

0 cm³/g

1.5 g/cm³

 
 
Boundary Conditions

 
   Finite Mass Top Boundary
 

   Fixed Outflow Bottom Boundary
 

         Landfill Length = 200 m
         Landfill Width = 1 m
         Base Thickness = 1 m
         Base Porosity = 0.3

 
 
Variation in Properties with Time
 

 Time Periods with the same Source and Velocity

Period

Start Time

No. of
Steps

Time Step

Source Conc

Rate of Change

Height of Leachate

Volume Collected

1

0  yr

1

20  yr

1000  mg/L

0

7.5  m

0.29  m/a

2

20  yr

5

2  yr

-1  mg/L

0

7.5  m

0.2  m/a

3

30  yr

2

10  yr

-1  mg/L

0

7.5  m

0.2  m/a

4

50  yr

5

10  yr

-1  mg/L

0

7.5  m

0.2  m/a

5

100  yr

5

20  yr

-1  mg/L

0

7.5  m

0.2  m/a

 

Period

Start Time

End Time

Proportion Mass

Dispersivity

Base Velocity

1

0  yr

20  yr

1  m/a

0.4  m

4  m/a

2

20  yr

30  yr

1  m/a

0.4  m

4  m/a

3

30  yr

50  yr

1  m/a

0.4  m

4  m/a

4

50  yr

100  yr

1  m/a

0.4  m

4  m/a

5

100  yr

200  yr

1  m/a

0.4  m

4  m/a

 
 
Velocity and Sink Profile
 

Time Period

Minimum Depth

Maximum Depth

Vertical Velocity

Horizontal Outflow

1 / 1

0  m

1  m

0.01  m/a

0  m/a

 

1  m

1.3  m

0.01  m/a

6.67  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 1

0  m

1  m

0.028  m/a

0  m/a

 

1  m

1.3  m

0.028  m/a

18.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 2

0  m

1  m

0.046  m/a

0  m/a

 

1  m

1.3  m

0.046  m/a

30.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 3

0  m

1  m

0.064  m/a

0  m/a

 

1  m

1.3  m

0.064  m/a

42.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 4

0  m

1  m

0.082  m/a

0  m/a

 

1  m

1.3  m

0.082  m/a

54.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

2 / 5

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

3 / 1

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

3 / 2

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 1

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 2

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 3

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 4

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

4 / 5

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 1

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 2

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 3

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 4

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

5 / 5

0  m

1  m

0.1  m/a

0  m/a

 

1  m

1.3  m

0.1  m/a

66.7  m/a

 

1.3  m

3.3  m

0  m/a

0  m/a

 
 
Laplace Transform Parameters
 

    TAU = 7     N = 20     SIG = 0     RNU = 2

 
 
Monte Carlo Simulation Results
 

    Number of Simulations = 2000

    Number of Variables = 1

    Number of Data Ranges = 20

 
    Variable # 1

      Variable Properties End Time
         Time Period = 1

         Triangular Distribution     ( Minimum = 15    Maximum = 50    Mode = 25 )

 
    Depth = 3.3

 
  DISTRIBUTION OF PEAK CONCENTRATION
 

Minimum
Value

Maximum
Value

Number
Occur.

Probability

Cumulative
Probability

Expected
Value

2.286E+01

2.295E+01

37

0.02

0.02

4.237E-01

2.295E+01

2.303E+01

91

0.05

0.06

1.046E+00

2.303E+01

2.312E+01

91

0.05

0.11

1.050E+00

2.312E+01

2.321E+01

126

0.06

0.17

1.459E+00

2.321E+01

2.330E+01

150

0.07

0.25

1.744E+00

2.330E+01

2.339E+01

160

0.08

0.33

1.867E+00

2.339E+01

2.347E+01

178

0.09

0.42

2.085E+00

2.347E+01

2.356E+01

320

0.16

0.58

3.763E+00

2.356E+01

2.365E+01

608

0.30

0.88

7.176E+00

2.365E+01

2.374E+01

20

0.01

0.89

2.369E-01

2.374E+01

2.383E+01

16

0.01

0.90

1.903E-01

2.383E+01

2.391E+01

33

0.02

0.92

3.939E-01

2.391E+01

2.400E+01

31

0.02

0.93

3.714E-01

2.400E+01

2.409E+01

32

0.02

0.95

3.847E-01

2.409E+01

2.418E+01

23

0.01

0.96

2.776E-01

2.418E+01

2.427E+01

22

0.01

0.97

2.665E-01

2.427E+01

2.436E+01

20

0.01

0.98

2.431E-01

2.436E+01

2.444E+01

28

0.01

0.99

3.416E-01

2.444E+01

2.453E+01

11

0.01

1.00

1.347E-01

2.453E+01

2.462E+01

3

0.00

1.00

3.686E-02

 
Expected Maximum Concentration = 2.349E+01
 

 
  DISTRIBUTION OF TIME OF PEAK CONCENTRATION
 

Minimum
Value

Maximum
Value

Number
Occur.

Probability

Cumulative
Probability

Expected
Value

5.532E+01

5.650E+01

10

0.01

0.01

2.795E-01

5.650E+01

5.767E+01

30

0.01

0.02

8.562E-01

5.767E+01

5.884E+01

54

0.03

0.05

1.573E+00

5.884E+01

6.001E+01

73

0.04

0.08

2.169E+00

6.001E+01

6.118E+01

79

0.04

0.12

2.393E+00

6.118E+01

6.235E+01

99

0.05

0.17

3.057E+00

6.235E+01

6.352E+01

111

0.06

0.23

3.493E+00

6.352E+01

6.469E+01

107

0.05

0.28

3.430E+00

6.469E+01

6.586E+01

122

0.06

0.34

3.982E+00

6.586E+01

6.703E+01

117

0.06

0.40

3.887E+00

6.703E+01

6.820E+01

114

0.06

0.46

3.854E+00

6.820E+01

6.938E+01

154

0.08

0.53

5.297E+00

6.938E+01

7.055E+01

132

0.07

0.60

4.617E+00

7.055E+01

7.172E+01

150

0.07

0.68

5.335E+00

7.172E+01

7.289E+01

157

0.08

0.75

5.676E+00

7.289E+01

7.406E+01

124

0.06

0.82

4.555E+00

7.406E+01

7.523E+01

117

0.06

0.88

4.367E+00

7.523E+01

7.640E+01

89

0.04

0.92

3.374E+00

7.640E+01

7.757E+01

82

0.04

0.96

3.156E+00

7.757E+01

7.874E+01

79

0.04

1.00

3.087E+00

 
Expected Time of Maximum Concentration = 68.4391550021306
 

 
  VARIABLE NUMBER:     1
 

Minimum
Value

Maximum
Value

Number
Occur.

Probability

Cumulative
Probability

Expected
Value

1.532E+01

1.702E+01

21

0.01

0.01

1.698E-01

1.702E+01

1.873E+01

68

0.03

0.04

6.078E-01

1.873E+01

2.043E+01

101

0.05

0.10

9.886E-01

2.043E+01

2.213E+01

133

0.07

0.16

1.415E+00

2.213E+01

2.383E+01

166

0.08

0.24

1.907E+00

2.383E+01

2.553E+01

164

0.08

0.33

2.024E+00

2.553E+01

2.723E+01

162

0.08

0.41

2.137E+00

2.723E+01

2.893E+01

167

0.08

0.49

2.345E+00

2.893E+01

3.063E+01

159

0.08

0.57

2.368E+00

3.063E+01

3.233E+01

138

0.07

0.64

2.172E+00

3.233E+01

3.403E+01

141

0.07

0.71

2.339E+00

3.403E+01

3.573E+01

124

0.06

0.77

2.163E+00

3.573E+01

3.743E+01

108

0.05

0.83

1.975E+00

3.743E+01

3.913E+01

92

0.05

0.87

1.761E+00

3.913E+01

4.083E+01

65

0.03

0.90

1.299E+00

4.083E+01

4.254E+01

77

0.04

0.94

1.605E+00

4.254E+01

4.424E+01

50

0.03

0.97

1.085E+00

4.424E+01

4.594E+01

31

0.02

0.98

6.988E-01

4.594E+01

4.764E+01

20

0.01

0.99

4.679E-01

4.764E+01

4.934E+01

13

0.01

1.00

3.152E-01

0.000E+00

0.000E+00

0

0.00

0.00

0.000E+00

 
Expected Value = 2.984E+01
 

 
 
NOTICE
 

Although this program has been tested and experience would indicate that it is accurate within the limits given by the assumptions of the theory used, we make no warranty as to workability of this software or any other licensed material. No warranties either expressed or implied (including warranties of fitness) shall apply. No responsibility is assumed for any errors, mistakes or misrepresentations that may occur from the use of this computer program. The user accepts full responsibility for assessing the validity and applicability of the results obtained with this program for any specific case.