A model for Ostwald ripening of oil-in-water emulsion in the presence of small amount of surfactants is presented. It accounts for the transfer of oil from small to larger drops when the interfacial resistance is rate controlling. In this case, the continuous breakdown and reformation of the micellar structure during mass transfer through the interface, is assumed to be the rate-controlling step. A discretized population balance equation for the change in the number concentration of drops due to Ostwald ripening is solved using the method of characteristics. The third moment of the distribution (average volume) is found to increase linearly with time, consistent with available experimental observations, before reaching an abrupt equilibrium. The rate of change of drop volume is found to be strongly dependent on the solubility and is fairly insensitive to the volume fraction. The transients of the drop size distributions indicate an initial rapid decrease in the small droplets with a corresponding increase in the larger drops followed by a very slow change in the number distributions at longer times. The rate constants involved can be roughly correlated with the components of several experimental measurements, and allow comparison with the data of Kabalnov (Langmuir 10 (1994) 680), but only at small surfactant concentrations. The numerical agreement is not good but it is able to predict the anomalous direction of change with increased surfactant concentrations. The basis of the lack of numerical agreement is discussed.