Construction of adaptive reduced-order reservoir models based on POD‑DEIM approach
https://doi.org/10.18599/grs.2023.4.4
Abstract
This paper introduces a method for constructing adaptive reduced-order reservoir simulation models based on the POD-DEIM approach for field development optimization and assisted history matching problems. The approach is based on adapting the orthogonal decompositions bases to the varying model configuration. The method utilizes information contained in the bases of the original model and supplements them with new components instead of constructing a new model from scratch. Adapting the bases significantly reduces the computational costs of building reduced-order models and allows the application of such models to tasks requiring multiple simulations with different configurations. The paper presents an implementation of the POD-DEIM model for a two-phase flow problem and discusses examples of adapting this model to changes in well configuration and geological properties of the reservoir. We propose a generalized approach using POD-DEIM models in combination with the bases adaptation technique to solve optimization problems, such as field development optimization, selection of the optimal well locations, geometries, and well regimes, as well as history matching.
Keywords
reservoir simulation,
reduced order modelling,
field development optimization,
assisted history matching
Supporting agencies: This work was supported by the Ministry of Science and Higher Education of the Russian Federation under agreement No. 075-10-2022-011 within the framework of the development program for a world-class Research Center.
About the Authors
D. S. Voloskov
Skolkovo Institute of Science and Technology
Russian Federation
Russian Federation
Dmitry S. Voloskov – Research Engineer
30, build. 1, Moscow, 121025
D. A. Koroteev
Skolkovo Institute of Science and Technology
Russian Federation
Russian Federation
Dmitry A. Koroteev – PhD, Professor
30, build. 1, Moscow, 121025
References
1. Cardoso M. A. (2010). Use of Reduced-Order Modeling Procedures for Production Optimization. SPE Journal, 15(2010), pp. 426–435. https://doi.org/10.2118/119057-PA
2. Chaturantabut S., Sorensen D.C. (2010). Nonlinear Model Reduction via Discrete Empirical Interpolation. SIAM Journal on Scientific Computing, 32(5), pp. 2737–2764. https://doi.org/10.1137/090766498
3. Efendiev Y., Gildin E., Yang Y. (2016). Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media. Computation, 4(2), 22. https://doi.org/10.3390/computation4020022
4. Fanchi J. R. (2018). Principles of applied reservoir simulation (Fourth edition). Gulf Professional Publishing, Elsevier. https://doi.org/10.1016/ C2017-0-00352-X
5. Fraces C.G., Papaioannou A., Tchelepi H. (2020). Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem. ArXiv:2001.05172. http://arxiv.org/abs/2001.05172
6. Gasmi C. F., Tchelepi H. (2021). Physics Informed Deep Learning for Flow and Transport in Porous Media. ArXiv:2104.02629. http://arxiv.org/abs/2104.02629
7. He J., Sætrom J., Durlofsky L.J. (2011). Enhanced linearized reducedorder models for subsurface flow simulation. Journal of Computational Physics, 230(23), pp. 8313–8341. https://doi.org/10.1016/j.jcp.2011.06.007
8. Illarionov E., Temirchev P., Voloskov D., Kostoev R., Simonov M., Pissarenko D., Orlov D., Koroteev D. (2022). End-to-end neural network approach to 3D reservoir simulation and adaptation. Journal of Petroleum Science and Engineering, 208, 109332. https://doi.org/10.1016/j.petrol.2021.109332
9. Jansen J.D., Durlofsky L.J. (2017). Use of reduced-order models in well control optimization. Optimization and Engineering, 18(1), pp. 105–132. https://doi.org/10.1007/s11081-016-9313-6
10. Jin Z.L., Liu Y., Durlofsky L.J. (2020). Deep-learning-based surrogate model for reservoir simulation with time-varying well controls. Journal of Petroleum Science and Engineering, 107273. https://doi.org/10.1016/j.petrol.2020.107273
11. Kani J.N., Elsheikh A.H. (2017). DR-RNN: A deep residual recurrent neural network for model reduction. ArXiv:1709.00939. http://arxiv.org/abs/1709.00939
12. Kani J.N., Elsheikh A.H. (2018). Reduced-Order Modeling of Subsurface Multi-phase Flow Models Using Deep Residual Recurrent Neural Networks. Transport in Porous Media, (126), pp. 713–741 https://doi.org/10.1007/s11242-018-1170-7
13. Kunisch K., Volkwein S. (2003). Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics. SIAM Journal on Numerical Analysis, 40(2), pp. 492–515.
14. Monteagudo J.E.P., Firoozabadi A. (2004). Control-volume method for numerical simulation of two-phase immiscible flow in two- and threedimensional discrete-fractured media. Water Resources Research, 40(7). https://doi.org/10.1029/2003WR002996
15. Pacheco T.B., Silva A.F.C.D., Maliska C. (2017). Comparison of impes, sequential, and fully implicit formulations for two-phase flow in porous media with the element-based finite volume method. Rewienski M., White J. (2003). A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 22(2), pp. 155–170. https://doi.org/10.1109/TCAD.2002.806601
16. Tan X., Gildin E., Florez H., Trehan S., Yang Y., Hoda N. (2019). Trajectory-based DEIM (TDEIM) model reduction applied to reservoir simulation. Computational Geosciences, 23(1), pp. 35–53. https://doi.org/10.1007/s10596-018-9782-0
17. Temirchev P., Simonov M., Kostoev R., Burnaev E., Oseledets I., Akhmetov A., Margarit A., Sitnikov A., Koroteev D. (2020). Deep neural networks predicting oil movement in a development unit. Journal of Petroleum Science and Engineering, 184, 106513. https://doi.org/10.1016/j.petrol.2019.106513
18. Trehan S., Durlofsky L.J. (2016). Trajectory piecewise quadratic reduced-order model for subsurface flow, with application to PDE-constrained optimization. Journal of Computational Physics, 326, pp. 446–473. https://doi.org/10.1016/j.jcp.2016.08.032
19. Voloskov D., Pissarenko D. (2021). Adaptive POD-Galerkin Technique for Reservoir Simulation and Optimization. Mathematical Geosciences, 53, pp. 1951–1975. https://doi.org/10.1007/s11004-021-09958-6
20. Yang Y., Ghasemi M., Gildin E., Efendiev Y., Calo V. (2016). Fast Multiscale Reservoir Simulations With POD-DEIM Model Reduction. SPE Journal, 21(06), pp. 2141–2154. https://doi.org/10.2118/173271-PA
21. Young L. C. (1981). A Finite-Element Method for Reservoir Simulation. Society of Petroleum Engineers Journal, 21(01), pp. 115–128. https://doi.org/10.2118/7413-PA
Review
For citations:
Voloskov D.S., Koroteev D.A. Construction of adaptive reduced-order reservoir models based on POD‑DEIM approach. Georesursy = Georesources. 2023;25(4):69-81. (In Russ.) https://doi.org/10.18599/grs.2023.4.4
Views:
128
.png){kind=logo}
Email this article 