We present the use of a streamtube approach to study the uncertainty in reservoir performance resulting from a stochastic description of the flow domain. The streamtube technique is an efficient numerical method which is particularly effective for modeling convective displacements that are dominated by large-scale heterogeneities. Stable, numerical-diffusion-free solutions can be obtained in a fraction of the time taken by conventional finite difference simulators, thereby allowing a statistical approach to reservoir simulation and forecasting.