A fuel gas network (FGN) in a petrochemical complex can save energy costs substantially and reduce flaring by utilizing purge/waste fuel streams (Hasan et al. Ind. Eng. Chem. Res. 2011, 50, 7414-7427). A properly designed FGN can involve complex and nonintuitive mixing scenarios and equipment arrangements. Furthermore, the purge/waste gases and their characteristics can vary significantly with changing operation modes in a plant, which makes routing them into an FGN a challenge. This article reports a multiperiod two-stage stochastic programming model to design and operate an FGN that caters to all operating modes, and shows the usefulness of optimized FGN on a refinery case study. Results show that the proposed model produces a resilient FGN and reduces capital costs versus the single-mode model of (Hasan et al. Ind. Eng. Chem. Res. 2011, 50, 7414-7427). In addition, several strategies to minimize flaring and environmental penalties in a refinery operation are examined.