Numerical modeling of multiphase first-contact miscible flows. Part 1. Analytical Riemann solver |
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Authors: | Ruben Juanes Knut-Andreas Lie |
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Institution: | (1) Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Building 48, 77 Mass. Ave., Cambridge, MA 02139, USA;(2) Department of Applied Mathematics, SINTEF ICT, P.O. Box 124, Blindern, Oslo, NO-0314, Norway |
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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. |
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Keywords: | Porous media First-contact miscible displacement Water-alternating-gas Shocks Riemann problem Analytical solution Front-tracking |
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