Analytical Modeling of Emulsion Flow at the Edge of a Steam Chamber During a Steam-Assisted-Gravity-Drainage Process

Recently, different models were proposed to describe two- and three-phase flow at the edge of a steam chamber developed during a steam-assisted-gravity-drainage (SAGD) process. However, 2D-scaled SAGD experiments and recent micromodel visualizations demonstrate that steam condensate is primarily in the form of microbubbles dispersed in the oil phase (water-in-oil emulsion). Therefore, the challenging question is: Can the multiphase Darcy equation be used to describe the transport of water as a discontinuous phase? Furthermore, the physical impact of water as a continuous phase or as microbubbles on oil flow can be different. Water microbubbles increase the apparent oil viscosity, whereas a continuous water phase decreases the oil relative permeability. Investigating the impact of these two phenomena on oil mobility at the steam-chamber edge and on overall oil-production rate during an SAGD process requires development of relevant mathematical models, which is the focus of this paper. In this paper, we develop an analytical model for lateral expansion of the steam chamber that accounts for formation and transport of water-in-oil emulsion. It is assumed that emulsion is generated as a result of condensation of steam, which penetrates into the heated bitumen. The emulsion concentration decreases from a maximum value at the chamber interface to zero far from the interface. The oil viscosity is affected by both temperature gradient caused by heat conduction and microbubble concentration gradient resulting from emulsification. We conduct a sensitivity analysis with the measured data from scaled SAGD experiments. The sensitivity analysis shows that, by increasing the value of m (temperature viscosity parameter), the effect of emulsification on oil- flow rate decreases. It also shows that the effect of temperature on oil mobility is much stronger than that of emulsion. We also compare the model predictions with field production data from several SAGD operations. Butler's model overestimates oil- production rate caused by the single-phase assumption, whereas the proposed model presents more-accurate oil- flow rate, supporting the fact that one should include emulsification effect in the SAGD analysis.