Transitions from Monotonicity to Chaos in Gas Mixture Dynamics in Pipeline Networks

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.