In this work, we have extended the existence and uniqueness of solution result in literature for the porous medium flow problem based on the nonlinear Brinkman-Forchheimer-extended Darcy law
. The existing result is valid only for constant porosity and without the considered convection effects, and our result holds for variable porosity and it includes convective effects.
is considered in two-phase system without the gravitational forces; the differential form of the Darcy law
can be extended to three-phase system with and without gravitational forces.
From here on, all our numerical experiments are carried out within the range of the modified Darcy law
validity (namely around former experimental values) in spite of the variety of conditions tested; namely different values of k and n (therefore [[mu].sub.app]) which correspond to different sago concentrations C and temperatures T in the experimental rheology for the solutions.
Furthermore, when free C[O.sub.2] phase evolves, the flow dynamics become more complicated because of complicated phase interference (e.g., gas-lifting phenomena) which may not be accounted by a Darcy law