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**Convergence of iterative coupling for coupled flow and geomechanics.**
*(English)*
Zbl 1392.35235

Summary: In this paper, we study solving iteratively the coupling of flow and mechanics. We demonstrate the stability and convergence of two widely used schemes: the undrained split method and the fixed stress split method. To our knowledge, this is the first time that such results have been rigorously obtained and published in the scientific literature. In addition, we propose a new stress split method, with faster convergence rate than known schemes. These results are specially important today due to the interest in hydraulic fracturing [R. H. Dean and J. H. Schmidt, “Hydraulic-fracture predictions with a fully coupled geomechanical reservoir simulator”, SPE J. 14, No. 4, 707–714 (2009; doi:10.2118/116470-PA); L. Ji, A. Settari and R. B. Sullivan, “A novel hydraulic fracturing model fully coupled with geomechanics and reservoir simulation”, ibid. 14, No. 3, 423–430 (2009; doi:10.2118/110845-PA); P. Samier and S. De Gennaro, “Practical iterative coupling of geomechanics with reservoir simulation”, in: Proceedings of the SPE reservoir simulation symposium, 26–28 February, Houston, Texas, USA (2007; doi:10.2118/106188-MS); A. Settari and F. M. Mourits, “A coupled reservoir and geomechanical simulation system“, SPE J. 3, No. 3, 219–226 (1998; doi:10.2118/50939-PA)], in oil and gas shale reservoirs.

### MSC:

35Q35 | PDEs in connection with fluid mechanics |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76S05 | Flows in porous media; filtration; seepage |

86A60 | Geological problems |

86-08 | Computational methods for problems pertaining to geophysics |

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\textit{A. Mikelić} and \textit{M. F. Wheeler}, Comput. Geosci. 17, No. 3, 455--461 (2013; Zbl 1392.35235)

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### References:

[1] | Dean, RH; Schmidt, JH, Hydraulic-fracture predictions with a fully coupled geomechanical reservoir simulator, SPE J., 14, 707-714, (2009) |

[2] | Kim, J., Tchelepi, H.A., Juanes, R.: Stability, accuracy and efficiency of sequential methods for coupled flow and geomechanics, SPE International, SPE 119084, p. 1-19 |

[3] | Ji, L; Settari, A; Sullivan, RB, A novel hydraulic fracturing model fully coupled with geomechanics and reservoir simulation, SPE J., 14, 423-430, (2009) |

[4] | Samier, P., De Gennaro, S.: Iterative coupling of geomechanics with reservoir simulation, SPE Reservoir Simulation Symposium, Houston, TX, USA. (2007) |

[5] | Settari, A; Maurits, F, Coupled reservoir and geomechanical simulation system, SPE J., 3, 219-226, (1998) |

[6] | Tolstoy, I. (ed.): Acoustics, elasticity, and thermodynamics of porous media. Twenty-one papers by M. A. Biot, Acoustical Society of America, New York (1992) |

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