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This paper presents a model for the mixture of gases on
networks in the stationary case. The model is based on an equation
of state for the mixture, the stationary isothermal Euler equations and
coupling conditions for the flow and mixture. The equation of state or
pressure law is based on the change of the speed of sound in a mixture of
gases. We use this model to solve stationary gas flow problems to global
optimality on large networks and present computational results.
The construction of a cost minimal network for flows obeying
physical laws is an important problem for the design of electricity, water,
hydrogen, and natural gas infrastructures. We formulate this problem as
a mixed-integer non-linear program. Its non-convexity, due to the poten-
tial flow, together with the binary variables, indicating the decision to
build a connection, make these problems challenging to solve. We develop
a novel class of valid inequalities on the fractional relaxations of the bi-
nary variables. Further, we show that this class of inequalities can be sep-
arated in polynomial for solutions to a fractional relaxation. This makes
it possible to incorporate these inequalities into a branch-and-bound al-
gorithm. The advantage of these inequalities is lastly demonstrated in a
computational study on the design of real-world gas transport networks.
This chapter addresses mathematical models for isothermal mixtures of hydrogen and natural gas, motivated by the need for reliable simulation tools in future low-carbon energy systems. We analyze several classes of mixture models and investigate their convergence properties in the regime of strong interaction between constituents, covering stationary and instationary single-pipe settings as well as network flows. Since mixture models critically depend on the choice of pressure law, we compare the industry-standard GERG equation of state with simplified alternatives that preserve convex energies and reduce computational costs. For network applications, we discuss consistent coupling conditions across model classes, explore optimization of steady flows using the algebraic Weymouth formulation, and provide numerical evidence for its applicability in relevant operating regimes. The study reveals when simplified models are justified and outlines key open challenges for the modeling of gas mixtures.
This paper deals with the mixing of gases in stationary networks. We first derive a model and pressure law for mixing, for which there is empirical evidence for its accuracy. The model is based on the change of the speed of sound in gas mixtures.
We then consider stationary gas networks. The existence result for solutions of single gas flow on networks is extended to mixtures. Further, we establish an easy to check criterion for uniqueness of solutions on the network. This results in a uniqueness proof of solutions on all networks with a mixture of natural gas and low hydrogen percentages. We then develop a solution algorithm that alternates between the solution of a single gas problem and update of the mixture ratios. In a computational study, different model variants and their impact on performance are compared.
Moreover, the increased complexity of solving stationary gas transport problems with mixing is evaluated.
