In this paper, we introduce two computer simulation models to study molecular exchange between aggregates in a colloidal dispersion. The Brownian motion of the colloidal aggregates is simulated as a random walk with a Gaussian distributed step length. In model I, the exchanging molecules are simulated as discrete particles with the exchange process characterized by desorption, molecular diffusion, and adsorption. A molecule desorbed from an aggregate is registered in the simulation and allowed to undergo individual Brownian motion until it adsorbs onto another colloidal aggregate or returns to the same aggregate from which it originated. In this detailed simulation, random size fluctuations are obtained in addition to a net variation in a relaxing, nonequilibrium size distribution. For many processes, net variations are very slow compared to the random fluctuations, making this detailed method very time consuming for studying a relaxing size distribution. For this reason, we also consider, in model II, a more approximate method where only the net flow of molecules between aggregates is considered. Here, the flow of molecules is for each time step calculated assuming steady state conditions and pair wise additivity. The flow between an isolated pair of aggregates can be solved exactly. Although the pair flow is a good approximation at short separations, it becomes significantly reduced at larger separations because of the presence of other aggregates. This screening of the flow at larger separations is accounted for by introducing an exponential damping function. With these models, we have simulated the solubilization of larger oil drops by smaller micelles which has previously been experimentally studied in a nonionic surfactant-water-oil system. Besides comparing with experiments, the simulations provides a test of a previous mean-field cell model analysis of the solubilization process.