Mathematical modeling of steam-assisted gravity drainage

A mathematical model for gravity drainage in heavy-oil reservoirs and tar sands during steam injection in linear geometry is proposed. The mathematical model is based on experimental observations that the steam zone shape is an inverted triangle with the vertex fixed at the bottom production well. Both temperature and asphaltene content dependence of viscosity of the drained heavy oil and their impact on heavy oil production are considered. The developed model has been validated using experimental data presented in the literature. It is seen that the oil production rate is affected as the asphaltene content of the crude oil changes as a function of temperature. The oil production rate conforms well to previously published data covering a wide range of heavy oils and sands for gravity drainage.