  In this paper, we consider an online enrichment procedure using the
Generalized Multiscale Finite Element Method (GMsFEM) in the context of a
two-phase flow model in heterogeneous porous media. The coefficient of the
elliptic equation is referred to as the permeability and is the main source of
heterogeneity within the model. The elliptic pressure equation is solved using
online GMsFEM, and is coupled with a hyperbolic transport equation where local
conservation of mass is necessary. To satisfy the conservation property, we aim
at constructing conservative fluxes within the space of multiscale basis
functions through the use of a postprocessing technique. In order to improve
the accuracy of the pressure and velocity solutions in the online GMsFEM we
apply a systematic online enrichment procedure. The increase in pressure
accuracy due to the online construction is inherited by the conservative flux
fields and the desired saturation solutions from the coupled transport
equation. Despite the fact that the coefficient of the pressure equation is
dependent on the saturation which may vary in time, we may construct an
approximation space using the initial coefficient where no further basis
updates follow. Numerical results corresponding to four different types of
heterogeneous permeability coefficients are exhibited to test the proposed
methodology.
