Determination of Leaky-Confined, Unconfined and Fractured Double-Porosity Aquifers Parameters by Artificial Neural Networks (ANNs)

Chapter 1

Research Objectives and Literatures Review

 

• Research Objectives……………………………………………………………………………….2

• Literatures Review…………………………………………………………………………………2

1. GroundwaterRemediation………………………………………………………………….3

2. Subsurface Characterization……………………………………………………………….3

3. Prediction of Groundwater Levels……………………………………………………….4

4. Groundwater Pollution………………………………………………………………………5

5. Rainfall-Runoff Modeling………………………………………………………………….6

6. Aquifer Parameters Estimation……………………………………………………………8

Chapter 2

Artificial Neural Networks: Theory and Methodology

2.1 An Introduction to Artificial Neural Networks………………………………………….12

2.2 Artificial Neurons and How They Work……………………………………………………13

2.3 Training an Artificial Neural Network……………………………………………………..14

2.3.1 Supervised Training…………………………………………………….15

2.3.2 Unsupervised, or Adaptive Training………………………………………………..15

2.4 Feed-forward Neural Networks………………………………………………………………16

2.4.1 Single Layer Perceptron…………………………………………………………………16

2.4.2 Multilayer Perceptron Networks (MLPNs) ………………………………………17

 

2.5 Generalization of the Network………………………………………………………………..20

2.6 Pre-processing of Data…………………………………………………………………………..21

2.6.1 Principal Components Analysis (PCA) ……………………………………………21

2.7 Criteria of Performance………………………………………………………………………….23

2.8 Modeling Strategy of Artificial Neural Networks Development…………………..24

Chapter 3

Two Artificial Neural Network Models for the Determination of leaky-Confined Aquifer Parameters

3.1 Leaky Confined Aquifers………………………………………………………………………26

3.2. Modeling Strategy……………………………………………………………………………….29

Step I. Generation and Selection of Input Data Patterns………………………………29

Step II. Selection of the Network Architecture………………………………………….32

Step III. Network Training (Calibration) ………………………………………………….33

Step IV. Determination of Network Optimum Structure……………………………..34

Step V. Testing the Developed Network…………………………………………………..36

Step VI. Validation of the Developed Network………………………………………….40

1. a) First Pumping Test……………………………………………………………………….40

2. b) Second Pumping Test……………………………………………………………………40

3. c) Third Pumping Test………………………………………………………………………41

3.3. Determination of Aquifer Parameter Values…………………………………………….43

3.4. Summary and Conclusions……………………………………………………………………45

Chapter 4

An Artificial Neural Network Model for the Determination of Unconfined Aquifer Parameters

4.1. Unconfined Aquifers……………………………………………………………………………48

4.2. Modeling Strategy……………………………………………………………………………….51

Step I. Generation and Selection of Input Data Patterns………………………………51

Step II. Selection of the Network Architecture………………………………………….53

Step III. Network Training (Calibration) ………………………………………………….54

Step IV. Determination of Network Optimum Structure……………………………..55

Step V. Testing the Developed Network…………………………………………………..57

Step VI. Validation of the Developed Network………………………………………….60

1. a) First Pumping Test……………………………………………………………………….60

2. b) Second Pumping Test……………………………………………………………………60

4.3. Determination of Aquifer Parameter Values…………………………………………….63

4.4. Summary and Conclusions……………………………………………………………………65

Chapter 5

An Artificial Neural Network Model for the Determination of Fractured Double Porosity Aquifer Parameters

5.1. Fractured Double Porosity Aquifers……………………………………………………….68

5.2. Modeling Strategy……………………………………………………………………………….71

Step I. Generation and Selection of Input Data Patterns………………………………71

Step II. Selection of the Network Architecture………………………………………….73

Step III. Network Training (Calibration) ………………………………………………….74

Step IV. Determination of Network Optimum Structure……………………………..75

Step V. Testing the Developed Network…………………………………………………..77

Step VI. Validation of the Developed Network………………………………………….80

1. a) First Pumping Test……………………………………………………………………….80

2. b) Second Pumping Test……………………………………………………………………80

5.3. Determination of Aquifer Parameter Values…………………………………………….83

5.4. Summary and Conclusions……………………………………………………………………85

Chapter 6

Summary and Conclusions……………………………………………………………………….88

 

 

References……………………………………………………………………………………………….91

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

List of Figures

 

Fig. 1. A simple neuron……………………………………………………………………………….13

Fig. 2. A basic artificial neuron…………………………………………………………………….14

Fig. 3. Schematic presentation of a MLP network……………………………………………17

Fig. 4. Hyperbolic tangent and linear transfer functions…………………………………..18

Fig. 5. Generalization of the network…………………………………………………………….20

Fig. 6. Leaky confined aquifer with fully penetrating wells, S’= 0 for the aquitard without water in storage………………………………………………………………………………27

Fig. 7. Family of Walton’s type curves (1960), W(u, r/B) versus 1/u for different values of r/B………………………………………………………………………28

Fig. 8. Family of Hantush’s type curves (1961), W(u, ψ) versus 1/u for different values of ψ…………………………………………………………………………29

Fig. 9. Graphical presentation of input vectors and target outputs generation for the training of the aquifer type (a) ANN……………………………………………………………..30

Fig. 10. Graphical presentation of input vectors and target outputs generation for the training of the aquifer type (b) ANN………………………………………………………..31

Fig. 11. The scree plot of the training patterns………………………………………………..32

Fig. 12. Structure of the single-hidden-layer network before and after conducting PCA on the input training data sets (ξ: r/B or ψ) ……………………………………………..33

Fig. 13. Structure of the developed ANN in the training stage (ξ: r/B or ψ)…..……34

Fig. 14. Sensitivity plots for the model structure…………………………….…….35

Fig. 15. Convergence plot of networks with different topology…………………..36

Fig. 16. Structure of the developed ANN in the testing stage…………………..…37

Fig. 17. a) Idealized versus calculated type (a) aquifer parameter values, b) QQ plot of residuals………………………………………..………………………………38

Fig. 18. a) Idealized versus calculated type (b) aquifer parameter values, b) QQ plot of residuals……………………………..…………………………………………39

Fig. 19. Time-drawdown graphs for three sets of real pumping test……………….42

Fig. 20. RRMSE plot locating the optimum drawdown-time record for three sets of real pumping test data………………………………..……………………..…….44

Fig. 21. Unconfined aquifer with fully penetrating wells………………………….48

Fig. 22. Family of Neuman’s type curves (1975), W(u_A, u_B, β) versus values of 1/u_A and 1/u_B for different values of β……………………………………………………….50

Fig. 23. The input vectors and target outputs of the training pattern for the unconfined aquifer..………………………………………………………………52

Fig. 24. The scree plot of the unconfined aquifer……………………..……………..…53

Fig. 25. Structure of the single-hidden-layer network before and after conducting PCA on the input training data sets…………………………..………..…………..54

Fig. 26. The optimum structure of the trained ANN………………….……………55

Fig. 27. Sensitivity plots for the model structure…………………………….…….56

Fig. 28. Convergence plot of networks with different topology…………………..57

Fig. 29. Structure of the developed ANN in the testing stage…………………….58

Fig. 30. a) Idealized versus calculated aquifer parameter values, b) QQ plot of residuals……………………………………………………………………………59

Fig. 31. Time-drawdown graphs for two sets of real pumping test…………….….62

Fig. 32. RRMSE plot locating the optimum drawdown-time record for the two sets of real pumping test dat………………………………………………………………65

Fig. 33. Schematic representation of a fractured double porosity aquifer with fully penetrating pumping well………………………………………………………….68

Fig. 34. Family of Bourdet-Gringarten’s type curves (1980),  versus values of  for different values of …………………………………..……71

Fig. 35. Graphical presentation of input vectors and target outputs generation for the training of the ANN……………………….……………………….………….72

Fig. 36. The scree plot of the training patterns…………………………………….73

Fig. 37. Structure of the single-hidden-layer network before and after conducting PCA on the input training data sets……………………………..……..…….……74

Fig. 38. The optimum structure of the trained ANN…………………………….…75

Fig. 39. Sensitivity plots for the model structure………………………………..….76

Fig. 40. Convergence plot of networks with different topology…………………..77

Fig. 41. Structure of the developed ANN in the testing stage………………….….78

Fig. 42. a) Idealized versus calculated aquifer parameter values, b) QQ plot of residuals……………………………………………………………………………79

Fig. 43. Time-drawdown graphs for two sets of real pumping test………………..82

Fig. 44. RRMSE plot locating the optimum drawdown-time record for the two sets of real pumping test data………………………………………………..…………85

List of Tables

 

Table 1. The principal component parameters of the training set for the type (a) aquifer…………………………………………………..…………………..…….32

Table 2. The principal component parameters of the training set for the type (b) aquifer…………………………………………………………………………………………………..32

Table 3. The ANN parameters applied during training for both types of leaky confined aquifers………………….……………………………………………….34

Table 4. R2 and RRMSE (%) values of the estimated parameter values by the developed networks during the testing process……..………………..…………….37

Table 5. Time-drawdown data in the first and second pumping tests………………….40

Table 6. Time-drawdown data in the third pumping test (Neuman and Witherspoon, 1972) ………………………………………………………………………………41

Table 7. Aquifer parameter values estimated by the developed ANN and the type-curve matching method for the type (a) aquifer (First and second pumping test) and their RRMSE……………………………………………………………………..44

Table 8. Aquifer parameter values estimated by the developed ANN and the type-curve matching method for the type (b) aquifer (Third pumping test) and their RRMSE……………………………………………………………………………………………………44

Table 9. The principal component parameters of the training set for the unconfined aquifer….…………………………..…………………………………………….53

Table 10. The ANN parameters applied during training………..…………………54

Table 11. Values of the RRMSE (%) and R² of T, S, S_y and β for the developed ANN during the testing process……………….……………….…………………58

Table 12. Time-drawdown data in the first pumping test……………………..…..60

Table 13. Time-drawdown data in the second pumping test (De Ridder, 1966)…. 61

Table 14. Values of the match points coordinates determined by the developed ANN and the type-curve matching method for the unconfined aquifer…………….63

Table 15. Aquifer parameter values estimated by the developed ANN and the type-curve matching method (First pumping test) and their RRMSE………………..…64

Table 16. Aquifer parameter values estimated by the developed ANN and the type-curve matching method (Second pumping test) and their RRMSE…………….….65

Table 17. The principal component parameters of the training set for the double porosity aquifer……………………………………………………………………73

Table 18. The ANN parameters applied during training……..……………………74

Table 19. Values of the RRMSE (%) and R2 of Tf, Sf, Sm, λ and ω for the developed ANN during the testing process……..…………………………………………….78

Table 20. Time-drawdown data in the first pumping test (Moench, 1984)…..….. 80

Table 21. Time-drawdown data in the second pumping test (McConnell, 1993)… 81

Table 22. Values of the match points coordinates determined by the developed ANN and the type-curve matching method for the double porosity aquifer………83

Table 23. Aquifer parameter values estimated by the developed ANN and the type-curve matching method (First pumping test) and their RRMSE…………………..84

Table 24. Aquifer parameter values estimated by the developed ANN and the type-curve matching method (Second pumping test) and their RRMSE…….…………84