2020/11/30 by Jiamin Jiang, Pavel Tomin, Yifan Zhou
Computer Science · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #CO2 Sequestration and Geologic Interactions #Computation #Convergence (economics) #Current (fluid) #Rate of convergence #Reduction (mathematics) #Reservoir Engineering and Simulation Methods #Residual #Solver #cs.CE #cs.NA #math.NA #physics.comp-ph
paper · pdf · doi:10.1007/s10596-021-10072-z
published as Computational Geosciences (2021) · arXiv admin note: text overlap with arXiv:1810.02326
openalex created_date 2020/11/23 · openalex publication_date 2021/07/06 · arxiv created 2021/08/04 · arxiv updated 2021/08/05 · openalex updated_date 2026/08/05
The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 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 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.