Characterizing the effect of heat transfer on multiphase flow during the steam-assisted gravity drainage (SAGD) process

By solving a 1-D heat equation for single phase flow, Butler et al. (1981, 1985) derived their classical SAGD equation, which has excellent predictive capability at experimental scales but performs poorly at field scales. Several authors have tried to remedy this by accounting for multiphase flow at the steam-bitumen boundary and their efforts have resulted in modified expressions for the oil rate incorporating rate multipliers. The practice of applying rate multipliers, however results in models that seem to vary for each reservoir or experiment. Recently, by making the prior assumption that fluid saturations ahead of the steam chamber vary linearly with temperature, Sharma and Gates (2010) derived a SAGD equation that accounts for multiphase flow ahead of the steam chamber, which performs excellently at field scales but poorly at experimental scales. In this work, we couple the multiphase mass conservation equations with the energy equation and show that the multi-scale, multiphase flow phenomenon associated with SAGD is the classical Marangoni (thermo-capillary) effect which can be characterized by the Marangoni number. At low Marangoni numbers (typical of experimental scales) we get the Butler solution while at high Marangoni numbers (typical of field scales), we approximate the Sharma & Gates solution. We present results from our model in dimensionless space so they can be used as a fast SAGD predictive model within a proxy-based history matching process.