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Inexact methods for sequential fully implicit (SFI) reservoir simulation

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Abstract

The sequential fully implicit (SFI) scheme was introduced (Jenny et al. J. Comput. Phys. 217(2), 627–641 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually solved with tight tolerances at every outer iteration. This can result in wasted computations that contribute little progress towards the coupled solution. The issue is known as ‘over-solving’. Our objective is to minimize the cost of inner solvers while maintaining the convergence rate of SFI. We first extended a nonlinear-acceleration (NA) framework (Jiang and Tchelepi, Comput. Methods Appl. Mech. Eng. 352, 246–275, 2019) to multi-component compositional models, for ensuring robust outer-loop convergence. We then developed inexact-type methods that alleviate ‘over-solving’. It is found that there is no need for one sub-problem to strive for perfection, while the coupled (outer) residual remains high due to the other sub-problem. The new SFI solver was tested using several complex cases. The problems involve multi-phase and EoS-based compositional fluid systems. We compared different strategies such as fixed relaxations on absolute and relative tolerances for the inner solvers, as well as an adaptive approach. The results show that the basic SFI method is quite inefficient. Away from a coupled solution, additional accuracy achieved in inner solvers is wasted, contributing to little or no reduction of the overall outer residual. By comparison, the adaptive inexact method provides relative tolerances adequate for the current convergence state of the sub-problems. We show across a wide range of flow conditions that the new solver can effectively resolve the over-solving issue, and thus greatly improve the overall efficiency.

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Acknowledgements

This work was supported by the Chevron/Schlumberger INTERSECT Research & Prototyping project. The authors thank Chevron for permission to publish the paper. Petroleum Research Institute for Reservoir Simulation (SUPRI-B) at Stanford University is gratefully acknowledged for providing the AD-GPRS platform.

We would like to thank Hamdi Tchelepi for inspiring discussions on the inexact methods. We also thank Jiawei Li, Huanquan Pan at Stanford University, and Olav Møyner at SINTEF Digital, for constructive discussions on AD-GPRS, compositional model, sequential formulation, etc.

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  1. Chevron Energy Technology Co., 1500 Louisiana St., Houston, TX, 77002, USA

    Jiamin Jiang, Pavel Tomin & Yifan Zhou

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  1. Jiamin Jiang
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Jiang, J., Tomin, P. & Zhou, Y. Inexact methods for sequential fully implicit (SFI) reservoir simulation. Comput Geosci 25, 1709–1730 (2021). https://doi.org/10.1007/s10596-021-10072-z

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