Green hydrogen from renewable sources can be blended with natural gas and serves as a potentially feasible measure for contributing to the net zero energy sector. The time-varying nature of hydrogen injection, influenced by stochastic renewable generations, can result in fluctuations in gas concentrations in the entire network. It poses a potential threat to the secure regulation of integrated electricity and gas systems (IEGS). For managing the operating condition and guaranteeing the security of IEGS during operation, a multi-period operation framework with alternative gas (e.g., hydrogen) blending is developed. First, a convex gas security range is derived using the Dutton method. Then, the multi-period operation framework is devised to mitigate the impacts of alternative gas injection on gas security over the entire operational period. Both the dynamics from gas composition and gas flow are modelled, accurately describing the real-time travel of alternative gas concentrations. The dynamics in the gas mixture properties (e.g., relative density) are fully revealed with time-varying gas concentrations. To tackle the high non-convexities in the optimization problem, second-order-cone relaxation is well-tailored and firstly 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 tight more efficiently. Finally, our operation strategy is illustrated in IEEE and Belgium Electricity and Gas Systems. Results indicate that hydrogen concentrations take about 12.5 h to travel from the injection point to the end of the pipeline route in the Belgium gas system. By incorporating this unique characteristic into the model, operational scheduling and dispatch in IEGS can be more practical when integrating hydrogen in the future.