Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations

  • Authors:

  • S. H. Lee;H. Zhou;H. A. Tchelepi

  • Affiliations:

  • Chevron Energy Technology Co., 6001 Bollinger Canyon Road, San Ramon, CA 94583-2324, USA;Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA;Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

In the previous multiscale finite-volume (MSFV) method, an efficient and accurate multiscale approach was proposed to solve the elliptic flow equation. The reconstructed fine-scale velocity field was then used to solve the nonlinear hyperbolic transport equation for the fine-scale saturations using an overlapping Schwarz scheme. A coarse-scale system for the transport equations was not derived because of the hyperbolic character of the governing equations and intricate nonlinear interactions between the saturation field and the underlying heterogeneous permeability distribution. In this paper, we describe a sequential implicit multiscale finite-volume framework for coupled flow and transport with general prolongation and restriction operations for both pressure and saturation, in which three adaptive prolongation operators for the saturation are used. In regions with rapid pressure and saturation changes, the original approach, with full reconstruction of the velocity field and overlapping Schwarz, is used to compute the saturations. In regions where the temporal changes in velocity or saturation can be represented by asymptotic linear approximations, two additional approximate prolongation operators are proposed. The efficiency and accuracy are evaluated for two-phase incompressible flow in two- and three-dimensional domains. The new adaptive algorithm is tested using various models with homogeneous and heterogeneous permeabilities. It is demonstrated that the multiscale results with the adaptive transport calculation are in excellent agreement with the fine-scale solutions. Furthermore, the adaptive multiscale scheme of flow and transport is much more computationally efficient compared with the previous MSFV method and conventional fine-scale reservoir simulation methods.