Being aware of uncertainties in forecasts of production characteristics is important for reservoir management. Decisions concerning further appraisal drilling, flexibility in development plans, and selection among reservoir prospects all require that uncertainties are taken into account. This study addresses the problem of quantifying uncertainties due to incomplete knowledge of the initial reservoir characteristics, with emphasis on the difference between heterogeneity modeling and assessment of uncertainty. In this study we outline a formalism for uncertainty modeling in a Bayesian framework and present an extensive case study of a North Sea Brent Group reservoir. The results are obtained by computer software implemented such that no human interference is required once the stochastic reservoir model is established. Once the stochastic reservoir model is established, multiple realizations can be generated, rescaled, and fed into a fluid flow simulator to forecast production characteristics and quantify uncertainty associated with response parameters such as cumulative oil production, recovery factors, and water cuts. The results demonstrate that uncertainty in model parameters contributes significantly to the overall uncertainty. The most influential parameters in our case study include the sealing capacity of major faults, seismic velocities used in depth conversion, and average porosities and shale continuity within the main reservoir sandstone.