Recently different models have been proposed to describe two- and three-phase flow at the edge of a steam chamber developed during a SAGD process. However, two-dimensional scaled SAGD experiments and recent micro model visualizations demonstrate that steam-condensate is primarily in the form of micro bubbles dispersed in the oil phase (water-in-oil emulsion). Therefore, the challenging question is: Can 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 micro bubbles on oil flow can be different. Water micro bubbles increase the apparent oil viscosity, while 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 overall oil production rate during a SAGD process requires development of relevant mathematical models that is the focus of this paper.
In this paper, we develop an analytical model for lateral expansion of steam chamber that accounts formation and transport of water-in-oil emulsion. It is assumed that emulsion is generated due to condensation of steam, which is penetrated 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 due to heat conduction and micro bubble concentration gradient due to emulsification. We conduct a sensitivity analysis by using the measured data from scaled SAGD experiments. The sensitivity analysis shows that by increasing the value of m (viscosity temperature parameter), the effect of emulsification of oil flow rate decreases. Comparing the proposed model with previous analytical models reveals that emulsification effect should be included in the SAGD analysis. We also use the proposed model to estimate the oil flow rate measured in several fields, published in the literature and find a reasonable match.
The proposed mathematical model and its application to field and experimental data help the industry to understand the effect of emulsification on oil mobility during SAGD processes. Based on this understanding, steam chamber growth rate and oil production can be estimated more accurately.