In this work, molecular dynamics simulation is employed to understand the intrinsic growth of pure carbon dioxide and pure methane hydrate starting from a seed crystal.  Seed crystal was allowed to grow from a super-saturated mixture of carbon dioxide or methane molecules in water. This system was chosen because it has relevance in recovery of methane gas from natural gas hydrate reservoirs by simultaneously sequestering a greenhouse gas like CO₂. The concentration of carbon dioxide or methane molecules in water for production run was chosen from the gas dissolution study of CO₂ gas in water. Two different concentration of 1:6 and 1:8.5 CO₂ molecules per water molecule were arrived upon based on the equilibration study which showed a phase separated system and well dispersed system respectively. The growth was then investigated under suitable temperature and pressure range which was well above the hydrate stability zone for significantly faster growth kinetics. The force-field used was TIP4P/ICE for water, EPM2 for carbon dioxide, OPLS-UA for methane. Concentration of guest molecules in water played a significant role in growth kinetics, suggesting that an optimum CO₂ concentration needs to be maintained in the aqueous phase for growth of CO₂ hydrate and replacements of maximum methane from the hydrate cages. It was observed that higher concentration of carbon dioxide molecule in the aqueous phase is favorable for formation of CO₂ clusters and reduces the hydrate growth significantly. On the contrary, methane hydrate did not exhibit such behavior and the growth rate is largely independent of gas concentration in the aqueous phase.