Three-way coupling of multiphase flow and poromechanics in porous media. (English) Zbl 1453.76080
Summary: We formulate a three-way coupling for both single phase flow and equation-of-state (EOS) compositional flow in a poroelastic medium. The algorithm is inspired by the previous work of R. Dean et al. [“A comparison of techniques for coupling porous flow and geomechanics”, SPE J. 11, No. 1, 132–140 (2006; doi:10.2118/79709-PA)]. An error indicator is calculated at each time step to determine if the mechanics equation must be solved and whether the fixed-stress iterative coupling is necessary; otherwise, only the flow equation is solved with an extrapolated mean stress. The convergence of three-way coupling is established by extending the a priori analyses of fixed-stress iterative coupling by V. Girault et al. [“A priori error estimates for a discretized poro-elastic-elastic system solved by a fixed-stress algorithm”, Oil Gas Sci. Technol.-Rev. IFP Energies nouvelles, 74, Article No. 24, 20 p. (2019; doi:10.2516/ogst/2018071)]. Numerical results for the Mandel’s problem confirm these theoretical results for single phase flow. Three-way coupling achieves speedup with a factor 2.7 and 6.6 for Mandel’s problem and field-scale coupled compositional flow and geomechanics simulations based on Cranfield field data respectively. Specifically, field-scale simulations of \(CO_2\) sequestration and surfactant-alternating-gas (SAG) process show that the three-way coupling substantially reduces mechanics solving time by 99.4% and 97.5% respectively compared to the fixed-stress split.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 76S05 | Flows in porous media; filtration; seepage |
| 86A05 | Hydrology, hydrography, oceanography |
| 76T30 | Three or more component flows |
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