The current level of air pollution in the world, as well as the dependence on fossil fuels, has led to global commitments and public policies aimed at mitigating the damage caused, seeking mainly to reduce emissions of polluting gases, for which the objective is to change the energy matrix centered on fossil fuels in favor of renewable energies. Among them, hydrogen stands out, and while its benefits are numerous, it is not currently possible for it to dominate the fuel market, mostly due to uncertainty surrounding government policies and regulations, consumer acceptance, and lack of infrastructure. In this context, the problem of design and sizing of natural gas pipelines with hydrogen injection is introduced, where the objective is to establish both the network topology and the diameter dimensions of each pipeline section for hydrogen distribution. To address the proposed problem, two approaches for pipeline diameters, continuous and discrete diameters, have been studied and compared. For the first one, the model proposed by Jean André et al.\cite{ANDRE2013239} and their heuristic solution method, Delta Change, based on fixing the network topology, were studied. For the second group, considering discrete diameters, a non-convex mixed integer nonlinear programming (MINLP) model of degree six has been proposed. Several reformulations have been studied to convert it into a convex quadratic MINLP problem (MIQP). Finally, a Delta Change routine is proposed to allow the application of this heuristic to the discrete diameter problem. Five solution methods have been implemented in a real case study in France, including the solution of the sizing problem on a fixed Minimum Weight Spanning Tree topology, considering continuous and discrete diameters, the Delta Change heuristic, also for both approaches, and the solution of the MIQP problem, showing the strengths and weaknesses of each of these proposals.

[1] J. André, S. Auray, D. De Wolf, M.M. Memmah, and A. Simonnet. Time development of new hydrogen transmission pipeline networks for France. International Journal of Hydrogen Energy, 39(20):10323--10337, 2014.