Deep Graph Learning-Based Surrogate Model for Inverse Modeling of Fractured Reservoirs
Abstract
:1. Introduction
- (1)
- A novel deep graph learning-based feature learning method for the complex multi-scale fracture network is proposed. In this approach, the fracture network is represented as graph data, and the feature learning is performed based on parameters of each discrete fracture, which can effectively retain the discrete characteristics and geometric information of the fracture network. To the best of our knowledge, no work has reported using the deep graph learning method for the feature learning of a fracture network.
- (2)
- Based on the deep graph learning and multi-layer recurrent neural networks, a surrogate model for the embedded fracture numerical simulation was developed for the inversion of fracture distribution. This surrogate model can predict the production dynamics of wells under different fracture distribution conditions. Compared with EDFM simulation, the proposed surrogate model significantly reduces the computation cost of production prediction.
- (3)
- An effective surrogate-based inverse modeling framework was designed, which integrates the population-based differential evolution (DE) algorithm with the proposed surrogate model. Because of the cheap computational cost of the surrogate model, the search performance of the DE algorithm can be fully released and improve the solving efficiency of the inversion.
2. Methods
2.1. Generation of 2D Multi-Scale Fracture Network
2.2. GAT-LSTM Surrogate Model
2.3. The GAT-LSTM Surrogate-Based Inverse Modeling Workflow
3. Case Studies
3.1. Two-Dimensional Fractured Reservoir Model
3.2. Analysis of the Surrogate Model Performance
3.3. Test the Performance of the Model under Varying Operational Conditions
3.4. Results of Surrogate-Based Inverse Modeling
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Component | Layers | Hyper Parameters |
---|---|---|
Multi-layer GAT Block | Graph Embedding | d = 128, σ = ReLU |
GAT Layer 1/2/3/4 | d = 128, w = 3, σ = ReLU | |
Node-level Global Pool | Max pool | |
Multi-layer ANN Block | Dense Layer 1 | d = 256, σ = ReLU |
Dense Layer 2 | d = 128, σ = ReLU | |
Dense Layer 3 | d = 100, σ = ReLU | |
Multi-layer LSTM Block | Repeat Vector | t = 30 |
LSTM Layer 1 | d = 100 | |
LSTM Layer 2 | d = 100 | |
Dense Layer 4 | d = 8, σ = tanh |
x-Coordinate (m) | y-Coordinate (m) | Length (m) | Orientation (Degrees) | |||||
---|---|---|---|---|---|---|---|---|
Fracture | True | Initial Range | True | Initial Range | True | Initial Range | True | Initial Range |
1 | 109 | 90–130 | 121 | 100–140 | 140 | 130–150 | 120 | 80–130 |
2 | 113 | 90–130 | 76 | 70–100 | 125 | 100–130 | 20 | 10–40 |
3 | 99 | 80–120 | 156 | 120–160 | 103 | 90–120 | 15 | 10–50 |
4 | 70 | 60–100 | 100 | 80–130 | 70 | 60- 80 | 50 | 30–80 |
5 | 155 | 130–160 | 90 | 70–120 | 65 | 50–70 | 120 | 100–150 |
Parameters | True Value | Initial Range |
---|---|---|
Fractal Dimension | 1.6 | 1.4–1.7 |
Intensity D1 (Set 1) | 0.45 | 0.3–0.6 |
Intensity D2 (Set 2) | 1−D1 | - |
Mean of Orientation (Set 1) | 35 | 45–75 |
Sd of Orientation (Set 1) | 10 | 8–15 |
Mean of Orientation (Set 2) | 150 | 138–178 |
Sd of Orientation (Set 2) | 10 | 8–15 |
Proportion Score of Region 1 | 0.1 | 0.1–1 |
Proportion Score of Region 2 | 0.3 | 0.1–1 |
Proportion Score of Region 3 | 0.1 | 0.1–1 |
Proportion Score of Region 4 | 0.3 | 0.1–1 |
Surrogate Model | R2 > 0.8 | R2 > 0.85 | R2 > 0.9 |
---|---|---|---|
ANN-LSTM | 33% | 15.5% | 6% |
GAT-LSTM | 91% | 81% | 66.5% |
Inversion Method | Building the Data Set | Training the Model | DE Optimization | Evaluation of the Solutions | Total Time |
---|---|---|---|---|---|
Surrogate-based | 150 | 2 | 10 | 10 | 172 |
Simulation Based | - | - | 2000 | - | 2000 |
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Ma, X.; Zhao, J.; Zhou, D.; Zhang, K.; Tian, Y. Deep Graph Learning-Based Surrogate Model for Inverse Modeling of Fractured Reservoirs. Mathematics 2024, 12, 754. https://doi.org/10.3390/math12050754
Ma X, Zhao J, Zhou D, Zhang K, Tian Y. Deep Graph Learning-Based Surrogate Model for Inverse Modeling of Fractured Reservoirs. Mathematics. 2024; 12(5):754. https://doi.org/10.3390/math12050754
Chicago/Turabian StyleMa, Xiaopeng, Jinsheng Zhao, Desheng Zhou, Kai Zhang, and Yapeng Tian. 2024. "Deep Graph Learning-Based Surrogate Model for Inverse Modeling of Fractured Reservoirs" Mathematics 12, no. 5: 754. https://doi.org/10.3390/math12050754
APA StyleMa, X., Zhao, J., Zhou, D., Zhang, K., & Tian, Y. (2024). Deep Graph Learning-Based Surrogate Model for Inverse Modeling of Fractured Reservoirs. Mathematics, 12(5), 754. https://doi.org/10.3390/math12050754