Societal concern is growing regarding the effect fossil energy use has on our planet and societies. Many promising sustainable energy solutions, like hydrogen, carbon capture and storage, and district heating, require long-distance distribution and transmission through networked infrastructure. Often, existing infrastructure can be repurposed to reduce overall network costs. Examples are the repurposing of natural gas infrastructure for hydrogen transport or the repurposing of oil pipelines for transport of CO2. This repurposing of existing infrastructure is expected to have a major influence on future network layouts, which uncovers an interesting research question. What is a suitable network optimisation approach that aids in the design of costeffective future network layouts, taking into account repurposing of existing infrastructure?. Reviewing the available literature on network optimisation modelling in relation to repurposing of existing infrastructure, we find that Geometric Graph Theoretical methods are the most promising approach to the problem at hand. Mixed Integer (Non-)linear programming approaches are computationally heavy, and do not provide the flexibility necessary to gain quick insights into design implications. Agent Based models provide more than enough flexibility, but no suitable methodology for integrating repurposing was found. A network optimisation model by Heijnen et al. (2020) is selected for adaption because of its already integrated existing pipeline functionality. Limitations of the existing model are that it does not take into account costs related to the repurposing of existing infrastructure, and that it can not work with cycles in the network. These cycles, defined by a multitude of paths between two points, are necessary because existing infrastructure often contains cycles, and the optimal addition of new infrastructure can include cycles that contain existing infrastructure. To address these limitations, first, repurposing costs were integrated into the objective function of the model. A novel variable called the repurposing cost coefficient is used to allow model users to input the cost of repurposing relative to the building of new pipelines. Three novel heuristics are also introduced. The network simplex repurposing heuristic creates optimal network layouts for a single moment in time and allows for cycles in the network to be created if this is the most optimal layout. When investigating supply and demand patterns that differentiate over time, the heuristic is supplemented by the timesteps merged heuristic that combines the networks created for each separate moment in time into one network. Finally, the joined edges heuristic removes redundancies from the network to create a cost optimised network layout. The model was unit tested by applying it to small experiments, and the basic functionalities of the model were verified...