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 lifetime 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 which 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 that delimit periodic and monotone system responses and show that
any solution in the monotonic operating region eventually approaches a periodic
orbit. Our results are demonstrated for examples of a single pipeline and a
small test network