In a previous paper,(1) we proposed a complete model for methane hydrate crystallization from pure water and methane gas in a semibatch reactor. This model takes into account the crucial importance of the rate-determining mass transfer at the gas/liquid interface, coupled with primary nucleation and growth. The validity of this model has been proved on a large number of experimental results. However, due to the complexity of the equations, only a numerical solution is possible, so that comparison between theory and experiment is not straightforward. In this paper, we consider a simple model of primary nucleation/growth and we propose an analytical solution for the time evolution of the total number of particles, mean diameter, and methane gas consumption rate during the first time of the crystallization. This model is used to analyze experimental results obtained in the presence of a kinetic additive: polyvinylpyrrolidone (PVP), in order to understand the origin of its effect.