Petroleum reservoirs are heterogeneous and, therefore, uncertain. Heterogeneity and uncertainty are important for reservoir management. The transfer of geologic uncertainty through process performance is commonly achieved with flow simulation; however, full physics flow simulation requires significant professional and computer time. A proxy model tuned to the specific recovery process provides a means to quickly predict performance uncertainty caused by multiple geologic models and uncertain operating conditions. A limited number of flow simulation runs are used to calibrate the proxy, then calculations proceed quickly. The classical response surface approach is also illustrated. Details are given to the application of proxy models to the steam-assisted gravity drainage process. A proxy model based on the Butler steam-assisted gravity drainage theory is developed to predict the oil flow rate, cumulative oil production, and cumulative steam injection profiles during the rising and spreading steam chamber periods of a steam-assisted gravity drainage well pair. A synthetic example shows the efficiency of the methodology in terms of computation time and predictability.