  The blending of hydrogen generated using clean energy into natural gas
pipeline networks is proposed in order to utilize existing energy systems for
their planned lifetimes while reducing their reliance on fossil fuels. We
formulate a system of partial differential equations (PDEs) that govern the
flow dynamics of mixtures of gases in pipeline networks under the influence of
time-varying compressor and regulator control actions. The formulation is
derived for general gas networks that can inject or withdraw arbitrary
time-varying mixtures of gases into or from the network at arbitrarily
specified nodes. The PDE formulation is discretized in space to form a
nonlinear control system that is used to prove that homogeneous mixtures are
well-behaved and heterogeneous mixtures may be ill-behaved in the sense of
monotone-ordering of solutions. We use numerical simulations to compute
interfaces in the parameter region of sinusoidal boundary conditions that
delimit monotonic, periodic, and chaotic system responses. The interfaces
suggest that any solution in the monotonic response region is not chaotic and
will eventually approach a periodic orbit. The results are demonstrated using
examples for a single pipeline and a small test network.
