A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
A mixed multiscale finite element method for elliptic problems with oscillating coefficients
Mathematics of Computation
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
Journal of Computational Physics
Iterative multiscale finite-volume method
Journal of Computational Physics
Modeling complex wells with the multi-scale finite-volume method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Linearized reduced-order models for subsurface flow simulation
Journal of Computational Physics
Adaptive iterative multiscale finite volume method
Journal of Computational Physics
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
A hierarchical fracture model for the iterative multiscale finite volume method
Journal of Computational Physics
An adaptive multiscale method for density-driven instabilities
Journal of Computational Physics
Domain decomposition strategies for nonlinear flow problems in porous media
Journal of Computational Physics
Algebraic multiscale solver for flow in heterogeneous porous media
Journal of Computational Physics
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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, Adaptive multi-scale finite volume method for multi-phase flow and transport, Multiscale, Model. Simul. 3 (2005) 50-64]. 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.