Hydrogen valleys, which integrate renewable energy sources, hydrogen infrastructure, and end-use applications, play a crucial role in decarbonizing industrial energy hubs. However, the large-scale deployment of hydrogen is constrained by limited renewable electricity availability and high technology costs. To address these challenges, we develop a framework for optimally allocating renewable hydrogen across end-use sectors to maximize social welfare. A key insight from our analysis is that the merit order of hydrogen end-uses is dynamic, evolving with an increasing Social Cost of Carbon (SCC). When the SCC surpasses a threshold defined by the Social Opportunity Cost of Abatement (SOCA), allocating hydrogen to the most emissions-intensive sector becomes socially optimal, even if that sector has a higher sectoral abatement cost. Additionally, we demonstrate that minimizing welfare losses requires prioritizing sectors with limited viable low-carbon alternatives, ensuring that hydrogen is deployed where it delivers the greatest marginal benefit. A two-period dynamic model further illustrates how investment decisions should prioritize applications with higher learning potential in the initial period to accelerate cost reductions and long-term efficiency gains. We also evaluate second-best policy instruments in scenarios where carbon taxation alone fails to fully internalize externalities. Our findings indicate that demand-side subsidies, which directly support hydrogen adoption in end-use sectors, are more effective than production subsidies in ensuring a better alignment of hydrogen allocation with the social welfare optimum. We calibrate the model to the Industrial-Port-Zone of Marseille-Fos, revealing that sectors with limited low-carbon alternatives, such as chemicals and sectors with high learning potential such as steel industry, rank highest in the merit order for hydrogen deployment.
