Adaptive fully implicit multi-scale finite-volume method for multi-phase flow and transport in heterogeneous porous media.

*(English)*Zbl 1160.76373Summary: We describe a sequential fully implicit (SFI) multi-scale finite volume (MSFV) algorithm for nonlinear multi-phase flow and transport in heterogeneous porous media. The method extends the recently developed multiscale approach, which is based on an IMPES (IMplicit Pressure, Explicit Saturation) scheme [P. Jenny, S.H. Lee, H.A. Tchelepi, Multiscale Model. Simul. 3, No. 1, 50–64 (2004; Zbl 1160.76372)]. That previous method was tested extensively and with a series of difficult test cases, where it was clearly demonstrated that the multiscale results are in excellent agreement with reference fine-scale solutions and that the computational efficiency of the MSFV algorithm is much higher than that of standard reservoir simulators. However, the level of detail and range of property variability included in reservoir characterization models continues to grow. For such models, the explicit treatment of the transport problem (i.e. saturation equations) in the IMPES-based multiscale method imposes severe restrictions on the time step size, and that can become the major computational bottleneck. Here we show how this problem is resolved with our sequential fully implicit (SFI) MSFV algorithm. Simulations of large (million cells) and highly heterogeneous problems show that the results obtained with the implicit multi-scale method are in excellent agreement with reference fine-scale solutions. Moreover, we demonstrate the robustness of the coupling scheme for nonlinear flow and transport, and we show that the MSFV algorithm offers great gains in computational efficiency compared to standard reservoir simulation methods.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

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

76T10 | Liquid-gas two-phase flows, bubbly flows |

##### Keywords:

numerical simulation; multiscale methods; finite-volume; coupled flow and transport; heterogeneous porous media; immiscible multi-phase flow
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\textit{P. Jenny} et al., J. Comput. Phys. 217, No. 2, 627--641 (2006; Zbl 1160.76373)

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##### References:

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