GUEDES, M. J. F.; http://lattes.cnpq.br/5145964107339166; GUEDES, Maria Joseane Felipe.
Resumo:
In this work we consider the Riemann probíem for a system of conservation laws
modeling the oil recovery for a three-phase flow in a porous médium by the injection of
a mixture of water and gas in a reservoir whieh is initially filled with a mixture of water
and oil. Using the theory of conservation laws, the solution of the Rieman problem
is determined considering ali possibilities for the production data. For each of these
production data. ali possible cases for the injected gas/ water mixture are considered
as well. For each production case it is shown the existence of some special injection
data separating distinct constmctions of Solutions in the state space. Moreover, among
these special injection data one of them is criticai in the sense that the wave sequence
that describes the solution can be represented by two or three distinct paths in the
state space, but consisting of the same solution in the physical space - xi. In general
the solution of the Riemann problem consists of a sequence of two waves separated by
one intermediate constant state when the production data are closed to the extreme
situations where the initial water or oil saturations are maximal. For production data
with a more homogeneous initial water and oil proportion, the solution may consists
up to three waves separated by two constant intermediate states for some injected
mixtures containing a hígher proportion of gas than water. In such cases a nonelassical
wave, i. e. a transitional wave, must be used.