Summary of Reservoir Model Parameter Inversion Technology based on Artificial Intelligence
DOI:
https://doi.org/10.54691/7hqy9687Keywords:
Artificial Intelligence; Reservoir Model; Parameter Inversion; History Matching; Deep Learning; Proxy Model; Physics-Informed Neural Networks; Uncertainty Quantification.Abstract
Reservoir model parameter inversion (history matching) is a crucial step in oil and gas field development for reducing the uncertainty in reservoir description and improving the accuracy of production prediction. However, traditional methods face issues such as non-uniqueness of solutions and high computational cost. In recent years, advancements in artificial intelligence (AI) technology, particularly deep learning methods, have provided new solutions to these problems. This paper conducts a systematic review of AI-based techniques for reservoir model parameter inversion, including end-to-end inversion methods (Convolutional Neural Networks), Generative Adversarial Networks, Physics-Informed Neural Networks, proxy model-accelerated inversion techniques, and emerging methods like Reinforcement Learning and Meta-learning. It analyzes the principles, advantages, limitations, and applicable scenarios of various methods, investigates key challenges such as data scarcity, uncertainty quantification, physical consistency, and model interpretability, and proposes corresponding solutions. Predictions are made regarding future directions, including the deep integration of physics and AI, efficient uncertainty quantification, and industrial-scale application. This paper aims to serve as a reference for research and application in this field, promoting the use of AI-driven reservoir parameter inversion technology in the digital and intelligent transformation of the oil and gas industry.
Downloads
References
[1] Oliver, D. S., & Chen, Y. (2011). Recent progress on reservoir history matching: a review. Computational Geosciences, 15(1), 185-221. DOI: https://doi.org/10.1007/s10596-010-9194-2
[2] Tarantola, A. (2005). Inverse problem theory and methods for model parameter estimation. SIAM. DOI: https://doi.org/10.1137/1.9780898717921
[3] Oliver, D. S., Reynolds, A. C., & Liu, N. (2008). Inverse theory for petroleum reservoir characterization and history matching. Cambridge University Press. DOI: https://doi.org/10.1017/CBO9780511535642
[4] Aster, R. C., Borchers, B., & Thurber, C. H. (2018). Parameter estimation and inverse problems. Elsevier. DOI: https://doi.org/10.1016/B978-0-12-804651-7.00015-8
[5] Gao, G., & Reynolds, A. C. (2006). An improved implementation of the LBFGS algorithm for automatic history matching. SPE Journal, 11(01), 5-17. DOI: https://doi.org/10.2118/90058-PA
[6] Emerick, A. A., & Reynolds, A. C. (2013). Ensemble smoother with multiple data assimilation. Computers & Geosciences, 55, 3-15. DOI: https://doi.org/10.1016/j.cageo.2012.03.011
[7] Robert, C. P., & Casella, G. (2004). Monte Carlo statistical methods. Springer.
[8] Fonseca, R. M., Lee, R. D., & Rossa, E. D. (2018). Overview of the Olympus challenge: history matching and uncertainty quantification. ECMOR XVI, 1-13.
[9] LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436-444. DOI: https://doi.org/10.1038/nature14539
[10] Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT press.
[11] Badrinarayanan, V., Kendall, A., & Cipolla, R. (2017). SegNet: A deep convolutional encoder-decoder architecture for image segmentation. IEEE transactions on pattern analysis and machine intelligence, 39(12), 2481-2495. DOI: https://doi.org/10.1109/TPAMI.2016.2644615
[12] Ronneberger, O., Fischer, P., & Brox, T. (2015). U-net: Convolutional networks for biomedical image segmentation. International Conference on Medical image computing and computer-assisted intervention, 234-241.
[13] Sun, A., & Durlofsky, L. J. (2021). A deep learning approach for rapid estimation of permeability from pressure data. Journal of Computational Physics, 436, 110321. DOI: https://doi.org/10.1016/j.jcp.2021.110321
[14] Ronneberger, O., Fischer, P., & Brox, T. (2015). U-net: Convolutional networks for biomedical image segmentation. International Conference on Medical image computing and computer-assisted intervention, 234-241. DOI: https://doi.org/10.1007/978-3-319-24574-4_28
[15] Laloy, E., Hérault, R., Lee, J., Jacques, D., & Linde, N. (2018). Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network. Advances in Water Resources, 110, 387-405.
[16] Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., ... & Polosukhin, I. (2017). Attention is all you need. Advances in neural information processing systems, 30.
[17] Wang, Y., & Lin, Y. (2022). Attention-based deep learning for heterogeneous reservoir parameter estimation. Journal of Petroleum Science and Engineering, 208, 109234.
[18] Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., ... & Bengio, Y. (2014). Generative adversarial nets. Advances in neural information processing systems, 27.
[19] Creswell, A., White, T., Dumoulin, V., Arulkumaran, K., Sengupta, B., & Bharath, A. A. (2018). Generative adversarial networks: An overview. IEEE Signal Processing Magazine, 35(1), 53-65. DOI: https://doi.org/10.1109/MSP.2017.2765202
[20] Mosser, L., Dubrule, O., & Blunt, M. J. (2020). Stochastic seismic waveform inversion using generative adversarial networks as a geological prior. Mathematical Geosciences, 52(1), 53-79. DOI: https://doi.org/10.1007/s11004-019-09832-6
[21] Zhu, J. Y., Park, T., Isola, P., & Efros, A. A. (2017). Unpaired image-to-image translation using cycle-consistent adversarial networks. Proceedings of the IEEE international conference on computer vision, 2223-2232. DOI: https://doi.org/10.1109/ICCV.2017.244
[22] Dupont, E., Zhang, T., Tilke, P., Liang, L., & Bailey, W. (2021). Generating realistic geology conditioned on physical data with generative adversarial networks. arXiv preprint arXiv: 2102. 01179.
[23] Mirza, M., & Osindero, S. (2014). Conditional generative adversarial nets. arXiv preprint arXiv: 1411. 1784.
[24] Ho, J., Jain, A., & Abbeel, P. (2020). Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33, 6840-6851.
[25] Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021). Physics-informed machine learning. Nature Reviews Physics, 3(6), 422-440. DOI: https://doi.org/10.1038/s42254-021-00314-5
[26] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707. DOI: https://doi.org/10.1016/j.jcp.2018.10.045
[27] Almajid, M. M., & Abu-Al-Saud, M. O. (2022). Prediction of porous media fluid flow using physics-informed neural networks. Journal of Computational Physics, 448, 110775. DOI: https://doi.org/10.1016/j.petrol.2021.109205
[28] Kadeethum, T., O'Malley, D., Fuhg, J. N., Choi, Y., Lee, J., Viswanathan, H. S., & Bouklas, N. (2021). A framework for data-driven solution and parameter inversion of elastoplasticity problems. Computer Methods in Applied Mechanics and Engineering, 379, 113776.
[29] Baydin, A. G., Pearlmutter, B. A., Radul, A. A., & Siskind, J. M. (2018). Automatic differentiation in machine learning: a survey. Journal of Marchine Learning Research, 18, 1-43.
[30] Holl, P., Koltun, V., & Thuerey, N. (2020). Learning to control pdes with differentiable physics. International Conference on Learning Representations.
[31] Ren, P., Rao, C., Liu, Y., Ma, Z., Wang, J., & Sun, H. (2022). Differentiable reservoir simulation. SPE Journal, 27(03), 1753-1773.
[32] Stevens, B., & Colonius, T. (2020). Enforcing exact boundary and initial conditions in physics-informed neural networks. Journal of Computational Physics, 426, 109935.
[33] Forrester, A. I., & Keane, A. J. (2009). Recent advances in surrogate-based optimization. Progress in Aerospace Sciences, 45(1-3), 50-79. DOI: https://doi.org/10.1016/j.paerosci.2008.11.001
[34] Rasmussen, C. E., & Williams, C. K. (2006). Gaussian processes for machine learning. MIT press. DOI: https://doi.org/10.7551/mitpress/3206.001.0001
[35] Sarma, P., Durlofsky, L. J., & Aziz, K. (2008). Kernel principal component analysis for efficient, differentiable parameterization of multipoint geostatistics. Mathematical Geosciences, 40(1), 3-32. DOI: https://doi.org/10.1007/s11004-007-9131-7
[36] Wang, H., & Yeung, D. Y. (2016). Towards Bayesian deep learning: A framework and some existing methods. IEEE Transactions on Knowledge and Data Engineering, 28(12), 3395-3408. DOI: https://doi.org/10.1109/TKDE.2016.2606428
[37] Tang, M., Liu, Y., & Durlofsky, L. J. (2020). A deep-learning-based surrogate model for data assimilation in nonlinear subsurface flow problems. Mathematical Geosciences, 52(2), 205-234.
[38] Wang, K., Li, H., & Zhang, D. (2022). Multi-fidelity deep neural network for subsurface flow and transport modeling. Journal of Computational Physics, 448, 110720.
[39] Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural computation, 9(8), 1735-1780. DOI: https://doi.org/10.1162/neco.1997.9.8.1735
[40] Jiang, S., & Durlofsky, L. J. (2021). Data assimilation with a deep convolutional neural network surrogate model for subsurface flow and transport. Computational Geosciences, 25(3), 1085-1116.
[41] Zhou, J., Cui, G., Hu, S., Zhang, Z., Yang, C., Liu, Z., ... & Sun, M. (2020). Graph neural networks: A review of methods and applications. AI Open, 1, 57-81.
[42] Sanchez, S., Rongier, G., & Caumon, G. (2021). Graph neural networks for geological structure and property modeling. Mathematical Geosciences, 53(8), 1715-1742.
[43] Emerick, A. A. (2016). Analysis of the performance of ensemble-based assimilation of production and seismic data. Journal of Petroleum Science and Engineering, 139, 219-239. DOI: https://doi.org/10.1016/j.petrol.2016.01.029
[44] Canchumuni, S. W., Emerick, A. A., & Pacheco, M. A. (2021). Combining deep learning and ensemble data assimilation for reservoir characterization. Journal of Petroleum Science and Engineering, 196, 107869.
[45] Robert, C. P., & Casella, G. (2004). Monte Carlo statistical methods. Springer. DOI: https://doi.org/10.1007/978-1-4757-4145-2
[46] Laloy, E., Hérault, R., Lee, J., Jacques, D., & Linde, N. (2018). Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network. Advances in Water Resources, 110, 387-405. DOI: https://doi.org/10.1016/j.advwatres.2017.09.029
[47] Innes, M., Edelman, A., Fischer, K., Rackauckas, C., Saba, E., Shah, V. B., & Tebbutt, W. (2019). A differentiable programming system to bridge machine learning and scientific computing. arXiv preprint arXiv:1907.07587.
[48] Liu, Y., Sun, W., & Durlofsky, L. J. (2021). A deep-learning-based geological parameterization for history matching complex reservoirs. Mathematical Geosciences, 53(5), 949-975.
[49] Lakshminarayanan, B., Pritzel, A., & Blundell, C. (2017). Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30.
[50] Zhang, Y., & Yang, Q. (2021). A survey on multi-task learning. IEEE Transactions on Knowledge and Data Engineering, 34(12), 5586-5609.
[51] Sutton, R. S., & Barto, A. G. (2018). Reinforcement learning: An introduction. MIT press.
[52] Ma, X., Zhang, Y., & Wang, H. (2022). Deep reinforcement learning for reservoir management: A review. Journal of Petroleum Science and Engineering, 208, 109468. DOI: https://doi.org/10.1016/j.petrol.2021.109766
[53] Lillicrap, T. P., Hunt, J. J., Pritzel, A., Heess, N., Erez, T., Tassa, Y., ... & Wierstra, D. (2015). Continuous control with deep reinforcement learning. arXiv preprint arXiv:1509.02971.
[54] Miftakhov, R., Kuvaev, A., & Semenova, A. (2022). Reinforcement learning for closed-loop reservoir management. Fuel, 310, 122302.
[55] Vezhnevets, A. S., Osindero, S., Schaul, T., Heess, N., Jaderberg, M., Silver, D., & Kavukcuoglu, K. (2017). FeUdal networks for hierarchical reinforcement learning. International Conference on Machine Learning, 3540-3549.
[56] Finn, C., Abbeel, P., & Levine, S. (2017). Model-agnostic meta-learning for fast adaptation of deep networks. International Conference on Machine Learning, 1126-1135.
[57] Gonzalez, R., & Tran, M. (2021). Meta-learning for rapid adaptation of reservoir models to new geological scenarios. SPE Reservoir Simulation Conference. SPE-203937-MS.
[58] Snell, J., Swersky, K., & Zemel, R. (2017). Prototypical networks for few-shot learning. Advances in neural information processing systems, 30.
[59] Jing, L., & Tian, Y. (2021). Self-supervised visual feature learning with deep neural networks: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(11), 4037-4058. DOI: https://doi.org/10.1109/TPAMI.2020.2992393
[60] Liu, X., Zhang, F., Hou, Z., Mian, L., Wang, Z., Zhang, J., & Tang, J. (2021). Self-supervised learning: Generative or contrastive. IEEE Transactions on Knowledge and Data Engineering, 35(1), 857-876.
[61] Chen, T., Kornblith, S., Norouzi, M., & Hinton, G. (2020). A simple framework for contrastive learning of visual representations. International conference on machine learning, 1597-1607.
[62] Liu, M., & Grana, D. (2020). Multimodal deep learning for joint seismic inversion and petrophysical estimation. Geophysics, 85(4), WA255-WA267.
[63] Zhou, J., Cui, G., Hu, S., Zhang, Z., Yang, C., Liu, Z., ... & Sun, M. (2020). Graph neural networks: A review of methods and applications. AI Open, 1, 57-81. DOI: https://doi.org/10.1016/j.aiopen.2021.01.001
[64] Zhang, Y., & Yang, Q. (2021). A survey on multi-task learning. IEEE Transactions on Knowledge and Data Engineering, 34(12), 5586-5609. DOI: https://doi.org/10.1109/TKDE.2021.3070203
[65] Zhang, Z., & Li, L. (2022). Synthetic data generation for subsurface modeling using deep generative models. Journal of Petroleum Science and Engineering, 208, 109234. DOI: https://doi.org/10.1016/j.petrol.2021.109234
[66] Pan, S. J., & Yang, Q. (2010). A survey on transfer learning. IEEE Transactions on knowledge and data engineering, 22(10), 1345-1359. DOI: https://doi.org/10.1109/TKDE.2009.191
[67] Wang, H., & Marongiu-Porcu, M. (2022). Transfer learning for reservoir characterization: A case study. SPE Journal, 27(01), 617-632.
[68] Kendall, A., & Gal, Y. (2017). What uncertainties do we need in Bayesian deep learning for computer vision?. Advances in neural information processing systems, 30.
[69] Zhu, Y., & Zabaras, N. (2018). Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification. Journal of Computational Physics, 366, 415-447. DOI: https://doi.org/10.1016/j.jcp.2018.04.018
[70] Lakshminarayanan, B., Pritzel, A., & Blundell, C. (2017). Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30.
[71] Kingma, D. P., & Welling, M. (2013). Auto-encoding variational bayes. arXiv preprint arXiv: 1312. 6114.
[72] Sensoy, M., Kaplan, L., & Kandemir, M. (2018). Evidential deep learning to quantify classification uncertainty. Advances in neural information processing systems, 31.
[73] Stevens, B., & Colonius, T. (2020). Enforcing exact boundary and initial conditions in physics-informed neural networks. Journal of Computational Physics, 426, 109935.
[74] Peherstorfer, B., Willcox, K., & Gunzburger, M. (2018). Survey of multifidelity methods in uncertainty propagation, inference, and optimization. SIAM Review, 60(3), 550-591. DOI: https://doi.org/10.1137/16M1082469
[75] Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence, 1(5), 206-215. DOI: https://doi.org/10.1038/s42256-019-0048-x
[76] Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., ... & Polosukhin, I. (2017). Attention is all you need. Advances in neural information processing systems, 30.
[77] Lundberg, S. M., & Lee, S. I. (2017). A unified approach to interpreting model predictions. Advances in neural information processing systems, 30.
[78] Innes, M., Edelman, A., Fischer, K., Rackauckas, C., Saba, E., Shah, V. B., & Tebbutt, W. (2019). A differentiable programming system to bridge machine learning and scientific computing. arXiv preprint arXiv:1907.07587.
[79] Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). Fourier neural operator for parametric partial differential equations. International Conference on Learning Representations.
[80] Zhang, C., Bütepage, J., Kjellström, H., & Mandt, S. (2018). Advances in variational inference. IEEE transactions on pattern analysis and machine intelligence, 41(8), 2008-2026. DOI: https://doi.org/10.1109/TPAMI.2018.2889774
[81] Jordan, M. I., Lee, J. D., & Yang, Y. (2019). Communication-efficient distributed statistical inference. Journal of the American Statistical Association, 114(526), 668-681. DOI: https://doi.org/10.1080/01621459.2018.1429274
[82] Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., ... & Tarantola, S. (2008). Global sensitivity analysis: the primer. John Wiley & Sons. DOI: https://doi.org/10.1002/9780470725184
[83] He, J., & Durlofsky, L. J. (2022). Deep-learning-based framework for complex reservoir simulation. Journal of Computational Physics, 448, 110734.
[84] Chen, Z., Huan, G., & Ma, Y. (2006). Computational methods for multiphase flows in porous media. SIAM. DOI: https://doi.org/10.1137/1.9780898718942
[85] Li, L., & Jafarpour, B. (2021). Real-time reservoir management using deep reinforcement learning. Journal of Petroleum Science and Engineering, 196, 107748.
[86] Liu, X., Zhang, F., Hou, Z., Mian, L., Wang, Z., Zhang, J., & Tang, J. (2021). Self-supervised learning: Generative or contrastive. IEEE Transactions on Knowledge and Data Engineering, 35(1), 857-876. DOI: https://doi.org/10.1109/TKDE.2021.3090866
[87] Zhou, K., Liu, Z., Qiao, Y., Xiang, T., & Loy, C. C. (2021). Domain generalization: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(4), 4396-4415.
[88] Schölkopf, B., Locatello, F., Bauer, S., Ke, N. R., Kalchbrenner, N., Goyal, A., & Bengio, Y. (2021). Toward causal representation learning. Proceedings of the IEEE, 109(5), 612-634. DOI: https://doi.org/10.1109/JPROC.2021.3058954
[89] Samek, W., Montavon, G., Vedaldi, A., Hansen, L. K., & Müller, K. R. (2021). Explainable AI: interpreting, explaining and visualizing deep learning. Springer Nature.
[90] Robert, C. P. (2007). The Bayesian choice: from decision-theoretic foundations to computational implementation. Springer Science & Business Media.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Scientific Journal of Technology
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
