  We investigate a two-dimensional network simulator that model the dynamics of
two-phase immiscible bulk flow where film flow can be neglected. We present a
method for simulating the detailed dynamical process where the two phases are
allowed to break up into bubbles, and bubbles are allowed to merge together.
The notions of drainage and imbibition are not adequate to describe this
process since there is no clear front between the fluids. In fact, the
simulator is constructed so that one can study the behaviour of the system far
from inlets and outlets, where the two fluids have been mixed together so much
that all initial fronts have broken up. The simulator gives the fractional flow
as a function of the saturation of each of the fluids. For the case of two
fluids with equal viscosity, we classify flow regimes that are parametrized by
the capillary number.
