  We study the problem of the transformation of a given reactant species into
an immiscible product species, as they flow through a chemically active porous
medium. We derive the equation governing the evolution of the volume fraction
of the species -- in a one-dimensional macroscopic description --, identify the
relevant dimensionless numbers, and provide simple models for capillary
pressure and relative permeabilities, which are quantities of crucial
importance when tackling multiphase flows in porous media. We set the domain of
validity of our models and discuss the importance of viscous coupling terms in
the extended Darcy's law. We investigate numerically the steady regime and
demonstrate that the spatial transformation rate of the species along the
reactor is non-monotonous, as testified by the existence of an inflection point
in the volume fraction profiles. We obtain the scaling of the location of this
inflection point with the dimensionless lengths of the problem. Eventually, we
provide key elements for optimization of the reactor.
