Thursday, March 25

Mathematics of Multiphase Flow in Porous Media

10:30 AM-1:00 PM
Room: Executive Salon 3

Nonlinear waves occurring in multi-phase flow in porous media have a rich structure. In contrast to two-phase flow, the structure is often very sensitive to diffusive terms, i.e., capillary pressure. The substantial body of available theory for hyperbolic systems of conservation laws is of limited utility in multi-phase flow, which is of mixed elliptic-hyperbolic type and displays more pronounced nonlinear effects. The speakers in this minisymposium will address questions of existence, uniqueness, stability, structure of solutions, and consequences for petroleum engineering.

Organizer: Dan Marchesin
IMPA, Brazil

10:30-10:55 Riemann Problem for Two-Phase Flow in Porous Media: System of Nonconservation Laws
Pavel Bedrikovetsky, Petrobras, Brazil
11:00-11:25 Nonexistence and Oscillatory Solutions in a Quadratic Model Deriving from Petroleum Engineering
Suncica Canic, Iowa State University
11:30-11:55 Combustion Fronts in Porous Media
Jesus Carlos Da-Mota, U. F. Goias, Brazil; Wilson B. Dantas, U. F. Minas Gerais, Brazil; and Dan Marchesin, Organizer
12:00-12:25 Instability in Models of Three-Phase Flow
Bradley Plohr, State University of New York, Stony Brook; Arthur Azevedo, University of Brasilia, Brazil; Dan Marchesin, Organizer; and K. Zumbrun, Indiana University, Bloomington
12:30-12:55 Fundamental Solutions for Hysteretic Three-Phase Flow in Porous Media
Aparecido J. de Souza, U. F. Paraiba, Brazil

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MMD, 11/19/98