The alternative gas injection could be time-varying due to the stochastic renewable generation. It could lead to fluctuations in the gas compositions across the gas network, adversely affecting the secure operation of integrated electricity and gas systems (IEGS), and the steady state model formulated in the last section could be incapable of characterising this dynamics in high time resolution. For managing the operating condition and guaranteeing the security of IEGS during operation, this chapter proposes a multi-period optimal energy flow model (MPOEF) for IEGS with alternative gas injections. First, a convex hull of the gas security range is derived from the Dutton method. Then, the MPOEF is proposed to mitigate the impacts of alternative gas injection on gas security over the entire operational period. Both the dynamics of gas composition and gas flow are modelled, which can accurately describe the travel of alternative gas concentrations at real-time level. The dynamics in the gas mixture properties (e.g., specific gravity) are modelled as variables to fully reveal the impacts of time-varying gas compositions. To tackle the high non-convexities in the MPOEF problem, second-order-cone relaxation is well-tailored and first used in the case of varying gas compositions, making the motion equations and advective transport equations more tractable. An advanced second-order-cone sequential programming is devised to drive the relaxation tighter more efficiently. Finally, an illustrative case is used to validate the proposed method [14].