In this work we present a method for optimizing cryogenic liquefaction networks to minimize operating cost using the Infinite DimEnsionAl State-space (IDEAS) approach. IDEAS can be used to synthesize globally optimal cryogenic liquefaction networks which include splitters, mixers, compressors, turbines, valves, flash units, and heat exchangers. No a priori network structure is presumed; the organization and interconnection of the unit operations involved is determined and optimized by the formulation itself. A similar approach was employed by Martin et al. [Globally optimal power cycle synthesis via the Infinite DimEnsionAl State-space (IDEAS) approach featuring minimum area with fixed utility; Chemical Engineering Science (58) p. 4291 – 4305, 2003] in the optimization of power cycle networks wherein heat exchange area was minimized for a fixed utility cost; here, the overall goal is to find the network which minimizes operating (energy, hot utility, cold utility, etc.) cost while obeying a given upper bound on total capital cost (heat exchange area, etc.).

The global optimality of the cryogenic liquefaction network is guaranteed, since IDEAS gives rise to infinite-dimensional convex (linear) programs whose finite-dimensional approximations are guaranteed to converge to the optimum value of the infinite problem. We will apply this approach to a hydrogen liquefaction system and compare the results with the thermodynamically ideal case and with the current state of the art in hydrogen liquefaction systems.