Today, natural gas is transported by pipelines or in a liquefied state, which is extremely cost-intensive. Using gas hydrates for gas transportation can substantially reduce these costs. However, far too little attention has been paid to developing fast and economical ways to synthesize gas hydrates. To address this research gap, we conducted several series of experiments on the synthesis of methane and carbon dioxide hydrates in a reactor with a magnetic stirrer and a working volume of 500 mL. The thermobaric conditions, stirring speed, and initial volume of water were varied to determine the optimal parameters for hydrate production. The experiments have shown that the effective hydrate production requires nonmonotonic mechanical agitation of liquid and crystals in the reactor. The stirring speed should be varied during the transitions between hydrate formation phases. As a result, the reactor input power can be reduced by 10−15%, while maintaining high production efficiency. The research findings served as a basis for a newly developed conceptual framework for the use of gas hydrates in the power industry.