This paper describes an experimental study of clathrate hydrate formation from a model natural gas, i.e., a mixture of methane, ethane, and propane in a 90:7:3 molar ratio, in an unstirred gas/liquid system containing a surfactant additive. The specific process of interest in this study is the hydrate formation in a semi-batch-type reactor charged with a quiescent aqueous phase containing sodium dodecyl sulfate and a well-mixed gas phase, to which the above methane + ethane + propane mixture is continuously supplied to compensate for the loss in the gas as a result of hydrate formation and thereby to maintain a constant pressure inside the reactor. We performed continual gas chromatographic measurements of the gas phase inside the reactor during each hydrate-forming operation to determine how the gas-phase composition chronologically changes as a result of the fractionation accompanying the hydrate formation. These measurements showed an anomalous pattern of change in the gas-phase composition, such that the methane fraction first increased and then, subsequently, decreased, while the fractions of ethane and propane inversely changed. We have provided a hypothetical interpretation of these results, assuming a change from structure II to structure I in the dominant structure of the instantaneously formed hydrates during each hydrate-forming operation as a result of local methane gas enrichment promoted by the vertical growth of porous hydrate layers on the reactor wall, a phenomenon specific to unstirred surfactant-containing systems.