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Transport in Porous Media

, Volume 67, Issue 3, pp 375–393 | Cite as

Numerical modeling of multiphase first-contact miscible flows. Part 1. Analytical Riemann solver

  • Ruben JuanesEmail author
  • Knut-Andreas Lie
Original Paper

Abstract

In this series of two papers, we present a front-tracking method for the numerical simulation of first-contact miscible gas injection processes. The method is developed for constructing very accurate (or even exact) solutions to one-dimensional initial-boundary-value problems in the form of a set of evolving discontinuities. The evolution of the discontinuities is given by analytical solutions to Riemann problems. In this paper, we present the mathematical model of the problem and the complete Riemann solver, that is, the analytical solution to the one-dimensional problem with piecewise constant initial data separated by a single discontinuity, for any left and right states. The Riemann solver presented here is the building block for the front-tracking/streamline method described and applied in the second paper.

Keywords

Porous media First-contact miscible displacement Water-alternating-gas Shocks Riemann problem Analytical solution Front-tracking 

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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Applied MathematicsSINTEF ICTBlindernNorway

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