A locally conservative Eulerian-Lagrangian numerical method and its application to nonlinear transport in porous media

Jim Douglas, Felipe Pereira, Li-Ming Yeh

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

Abstract

Eulerian-Lagrangian and Modified Method of Characteristics (MMOC) procedures provide computationally efficient techniques for approximating the solutions of transport-dominated diffusive systems. The original MMOC fails to preserve certain integral identities satisfied by the solution of the differential system; the recently introduced variant, called the MMOCAA, preserves the global form of the identity associated with conservation of mass in petroleum reservoir simulations, but it does not preserve a localized form of this identity. Here, we introduce an Eulerian-Lagrangian method related to these MMOC procedures that guarantees conservation of mass locally for the problem of two-phase, immiscible, incompressible flow in porous media. The computational efficiencies of the older procedures are maintained. Both the original MMOC and the MMOCAA procedures for this problem are derived from a nondivergence form of the saturation equation; the new method is based on the divergence form of the equation. A reasonably extensive set of computational experiments are presented to validate the new method and to show that it produces a more detailed picture of the local behavior in waterflooding a fractally heterogeneous medium. A brief discussion of the application of the new method to miscible flow in porous media is included.

Original languageEnglish
Pages (from-to)1-40
Number of pages40
JournalComputational Geosciences
Volume4
Issue number1
DOIs
StatePublished - May 2000

Keywords

  • Miscible flow
  • Modified method of characteristics
  • Transport-dominated diffusion processes
  • Two-phase flow
  • Waterflooding

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