표제지
초록
목차
1. 서론 17
2. 이론적 배경 24
2.1. 앙상블 기반 방법 24
2.2. Beta-variational autoencoder 30
2.3. 합성곱 신경망 36
2.4. 저류층 모델 생성 방법 41
2.5. 제안하는 채널저류층 히스토리매칭 기법 45
1) 트레이닝 이미지 생성 45
2) 채널저류층 모델 데이터셋 생성 45
3) Beta-CVAE 네트워크 학습 45
4) 초기 앙상블 및 참조 모델 시뮬레이션 46
5) 초기 앙상블의 잠재벡터 계산 46
6) ES-MDA를 사용하여 잠재벡터 업데이트 46
7) 최종 히스토리매칭 결과 획득 46
3. 제안하는 기법을 사용한 채널저류층 특성화 48
3.1. 2D 채널저류층 모델 48
3.1.1. 모델 생성에 사용한 인자 정리 48
3.1.2. Case 1 - 좋은 초기 앙상블 55
3.1.3. Case 2 - 좋지 않은 초기 앙상블 71
3.2. 3D 채널저류층 모델 86
3.2.1. 모델 생성에 사용한 인자 정리 87
3.2.2. Case 3 - 층에 따라 채널의 위치가 다른 모델 95
3.2.3. Case 4 - 층에 따라 채널의 모양이 다른 모델 126
4. 결론 159
참고 문헌 162
부록 A. 채널저류층 학습을 위한 VAE 손실함수 167
Abstract 172
Table 3.1. TiGenerator parameters on 2D training image generation. 49
Table 3.2. Number of 2D realizations generated by SNESim. 50
Table 3.3. SNESim parameters on 2D training image generation. 51
Table 3.4. Parameters on 2D beta-CVAE network training. 51
Table 3.5. 2D reservoir simulation conditions. 53
Table 3.6. MAE of oil rate and watercut prediction, case 1. 70
Table 3.7. MAE of oil rate and watercut prediction, case 2. 86
Table 3.8. Fluvsim parameters on 3D training image generation. 88
Table 3.9. Number of 3D realizations generated by SNESim. 89
Table 3.10. SNESim parameters on 3D training image generation. 89
Table 3.11. Parameters on 3D beta-CVAE network training. 90
Table 3.12. 3D reservoir simulation conditions. 93
Table 3.13. MAE of oil rate and watercut prediction, case 3. 126
Table 3.14. MAE of oil rate and watercut prediction, case 4. 158
Fig. 1.1. Example of reservoir characterization: (a) petrophysical data, (b) static data, (c) initial reservoir model, (d) history matching. 19
Fig. 2.1. Procedures of typical ensemble-based methods: (a) EnKF, (b) ES, (c) ES-MDA. 26
Fig. 2.2. Typical VAE network structure. 31
Fig. 2.3. Posteriori probability distributions by difference of KL divergence: (a) high KL divergence, (b) low KL divergence. 34
Fig. 2.4. Data reconstruction with VAE network(left) and beta-VAE network(right): first row is original data, second row is the... 36
Fig. 2.5. Example of convolutional neural network calculation where padding=1, stride=1. 38
Fig. 2.6. Applying padding and stride for convolutional neural network calculation: (a) adding 1 padding around the input data, (b)... 39
Fig. 2.7. Comparison of the number of learning parameters between artificial neural network and convolutional neural network. 40
Fig. 2.8. Procedure of constructing a search tree: (a) training image, (b) template, (c) example of search tree calculation. 42
Fig. 2.9. Estimation process of rock facies distribution for every grid of a reservoir model using SNESim and partial hard data. 43
Fig. 2.10. Flow chart of the proposed method. 47
Fig. 3.1. Structure of 2D beta-CVAE network for case 1 and case 2. 52
Fig. 3.2. (a) Training images, (b) hard data, and (c) the reference model of case 1. 56
Fig. 3.3. Initial permeability distribution of case 1: (a)-(c) selected models, (d) mean permeability. 57
Fig. 3.4. Training loss and validation loss vs epoch in case 1. 58
Fig. 3.5. Model reconstruction using beta-CVAE in case 1: (a)-(c) original models, (d)-(f) corresponding reconstructions. 59
Fig. 3.6. Permeability distribution and well placement of the reference model of case 1. 61
Fig. 3.7. Mean permeability distribution of case 1, updated by the proposed method. 61
Fig. 3.8. Permeability distribution of the model in Fig. 3.3a, updated by the proposed method. 62
Fig. 3.9. Permeability distribution of the model in Fig. 3.3b, updated by the proposed method. 62
Fig. 3.10. Permeability distribution of the model in Fig. 3.3c, updated by the proposed method. 63
Fig. 3.11. Mean permeability distribution of case 1, updated only by ES-MDA. 63
Fig. 3.12. Permeability distribution of the model in Fig. 3.3a, updated only by ES-MDA. 64
Fig. 3.13. Permeability distribution of the model in Fig. 3.3b, updated only by ES-MDA. 64
Fig. 3.14. Permeability distribution of the model in Fig. 3.3c, updated only by ES-MDA. 65
Fig. 3.15. Performance prediction of the initial ensemble models in case 1: (a) oil production, (b) watercut. 67
Fig. 3.16. Performance prediction of the updated models using the proposed method in case 1: (a) oil production, (b) watercut. 68
Fig. 3.17. Performance prediction of the updated models using only ES-MDA in case 1: (a) oil production, (b) watercut. 69
Fig. 3.18. (a) Training images, (b) hard data, and (c) the reference model of case 2. 72
Fig. 3.19. Initial permeability distribution of case 2: (a)-(c) selected models, (d) mean permeability. 73
Fig. 3.20. Training loss and validation loss vs epoch in case 2. 74
Fig. 3.21. Model reconstruction using beta-CVAE in case 2: (a)-(c) original models, (d)-(f) corresponding reconstructions. 75
Fig. 3.22. Permeability distribution and well placement of the reference model of case 2. 77
Fig. 3.23. Mean permeability distribution of case 2, updated by the proposed method. 77
Fig. 3.24. Permeability distribution of the model in Fig. 3.19a, updated by the proposed method. 78
Fig. 3.25. Permeability distribution of the model in Fig. 3.19b, updated by the proposed method. 78
Fig. 3.26. Permeability distribution of the model in Fig. 3.19c, updated by the proposed method. 79
Fig. 3.27. Mean permeability distribution of case 2, updated only by ES-MDA. 79
Fig. 3.28. Permeability distribution of the model in Fig. 3.19a, updated only by ES-MDA. 80
Fig. 3.29. Permeability distribution of the model in Fig. 3.19b, updated only by ES-MDA. 80
Fig. 3.30. Permeability distribution of the model in Fig. 3.19c, updated only by ES-MDA. 81
Fig. 3.31. Performance prediction of the initial ensemble models in case 2: (a) oil production, (b) watercut. 83
Fig. 3.32. Performance prediction of the updated models using the proposed method in case 2: (a) oil production, (b) watercut. 84
Fig. 3.33. Performance prediction of the updated models using only ES-MDA in case 2: (a) oil production, (b) watercut. 85
Fig. 3.34. Structure of 3D beta-CVAE network for case 3. 91
Fig. 3.35. Structure of 3D beta-CVAE network for case 4. 92
Fig. 3.36. (a) Training image and (b) hard data of case 3. 97
Fig. 3.37. The reference model of case 3. 98
Fig. 3.38. Initial mean permeability distribution of case 3. 99
Fig. 3.39. Initial permeability distribution of model #1 in case 3. 100
Fig. 3.40. Initial permeability distribution of model #2 in case 3. 101
Fig. 3.41. Initial permeability distribution of model #3 in case 3. 102
Fig. 3.42. Training loss and validation loss vs epoch in case 3. 103
Fig. 3.43. Reconstruction of model #1 using beta-CVAE in case 3: (a) original model, (b) corresponding reconstruction. 104
Fig. 3.44. Reconstruction of model #2 using beta-CVAE in case 3: (a) original model, (b) corresponding reconstruction. 105
Fig. 3.45. Reconstruction of model #3 using beta-CVAE in case 3: (a) original model, (b) corresponding reconstruction. 106
Fig. 3.46. Permeability distribution and well placement of the reference model of case 3. 108
Fig. 3.47. Mean permeability distribution of case 3, updated by the proposed method. 109
Fig. 3.48. Permeability distribution of the model in Fig. 3.39, updated by the proposed method. 110
Fig. 3.49. Permeability distribution of the model in Fig. 3.40, updated by the proposed method. 111
Fig. 3.50. Permeability distribution of the model in Fig. 3.41, updated by the proposed method. 112
Fig. 3.51. Mean permeability distribution of case 3, updated using CAE instead of beta-CVAE. 113
Fig. 3.52. Permeability distribution of the model in Fig. 3.39, updated using CAE instead of beta-CVAE. 114
Fig. 3.53. Permeability distribution of the model in Fig. 3.40, updated using CAE instead of beta-CVAE. 115
Fig. 3.54. Permeability distribution of the model in Fig. 3.41, updated using CAE instead of beta-CVAE. 116
Fig. 3.55. Mean permeability distribution of case 3, updated using CVAE instead of beta-CVAE. 117
Fig. 3.56. Permeability distribution of the model in Fig. 3.39, updated using CVAE instead of beta-CVAE. 118
Fig. 3.57. Permeability distribution of the model in Fig. 3.40, updated using CVAE instead of beta-CVAE. 119
Fig. 3.58. Permeability distribution of the model in Fig. 3.41, updated using CVAE instead of beta-CVAE. 120
Fig. 3.59. Performance prediction of the initial ensemble models in case 3: (a) oil production, (b) watercut. 122
Fig. 3.60. Performance prediction of the updated models using the proposed method in case 3: (a) oil production, (b) watercut. 123
Fig. 3.61. Performance prediction of the updated models using CAE in case 3: (a) oil production, (b) watercut. 124
Fig. 3.62. Performance prediction of the updated models using CVAE in case 3: (a) oil production, (b) watercut. 125
Fig. 3.63. (a) Training image and (b) hard data of case 4. 128
Fig. 3.64. The reference model of case 4. 129
Fig. 3.65. Initial mean permeability distribution of case 4. 130
Fig. 3.66. Initial permeability distribution of model #1 in case 4. 131
Fig. 3.67. Initial permeability distribution of model #2 in case 4. 132
Fig. 3.68. Initial permeability distribution of model #3 in case 4. 133
Fig. 3.69. Training loss and validation loss vs epoch in case 4. 134
Fig. 3.70. Reconstruction of model #1 using beta-CVAE in case 4: (a) original model, (b) corresponding reconstruction. 135
Fig. 3.71. Reconstruction of model #2 using beta-CVAE in case 4: (a) original model, (b) corresponding reconstruction. 136
Fig. 3.72. Reconstruction of model #3 using beta-CVAE in case 4: (a) original model, (b) corresponding reconstruction. 137
Fig. 3.73. Permeability distribution and well placement of the reference model of case 4. 140
Fig. 3.74. Mean permeability distribution of case 4, updated by the proposed method. 141
Fig. 3.75. Permeability distribution of the model in Fig. 3.66, updated by the proposed method. 142
Fig. 3.76. Permeability distribution of the model in Fig. 3.67, updated by the proposed method. 143
Fig. 3.77. Permeability distribution of the model in Fig. 3.68, updated by the proposed method. 144
Fig. 3.78. Mean permeability distribution of case 4, updated using CAE instead of beta-CVAE. 145
Fig. 3.79. Permeability distribution of the model in Fig. 3.66, updated using CAE instead of beta-CVAE. 146
Fig. 3.80. Permeability distribution of the model in Fig. 3.67, updated using CAE instead of beta-CVAE. 147
Fig. 3.81. Permeability distribution of the model in Fig. 3.68, updated using CAE instead of beta-CVAE. 148
Fig. 3.82. Mean permeability distribution of case 4, updated using CVAE instead of beta-CVAE. 149
Fig. 3.83. Permeability distribution of the model in Fig. 3.66, updated using CVAE instead of beta-CVAE. 150
Fig. 3.84. Permeability distribution of the model in Fig. 3.67, updated using CVAE instead of beta-CVAE. 151
Fig. 3.85. Permeability distribution of the model in Fig. 3.68, updated using CVAE instead of beta-CVAE. 152
Fig. 3.86. Performance prediction of the initial ensemble models in case 4: (a) oil production, (b) watercut. 154
Fig. 3.87. Performance prediction of the updated models using the proposed method in case 4: (a) oil production, (b) watercut. 155
Fig. 3.88. Performance prediction of the updated models using CAE in case 4: (a) oil production, (b) watercut. 156
Fig. 3.89. Performance prediction of the updated models using CVAE in case 4: (a) oil production, (b) watercut. 157