We have studied the droplet growth dynamics in a water-oil-surfactant system, using the cell dynamics system simulations based on the time-dependent Ginzburg-Landau model with two order parameters. Our simulations are carried out in a two-dimensional system of uneven composition of water and oil. For various average surfactant concentrations, the spatial patterns and their time evolution are obtained. The Ostwald ripening behaviors in the sparse regime of the droplet distributions are obtained. Numerical simulations are also extended to the dense regime so that the interactions between the droplet domains cannot be neglected. In such a system, the dynamics of pattern formation become significantly slow as the average surfactant concentration increases and we cannot apply the familiar scaling law in this case.