Improved modeling of the steam-assisted gravity drainage (SAGD) process
The Steam-Assisted Gravity Drainage (SAGD) Process involves the injection of steam through a horizontal well and the production of heavy oil through a lower horizontal well. Several authors have tried to model this process using analytical, semi-analytical and fully numerical means. In this dissertation, we improve the predictive ability of previous models by accounting for the effect of anisotropy, the effect of heat transfer on capillarity and the effect of water-in-oil (W/O) emulsion formation and transport which serves to enhance heat transfer during SAGD. We account for the effect of anisotropy during SAGD by performing elliptical transformation of the resultant gravity head and resultant oil drainage vectors on to a space described by the vertical and horizontal permeabilities. Our results, show that unlike for the isotropic case, the effect of anisotropy is time dependent and there exists a given time beyond which it ceases to have any effect on SAGD rates. This result will impact well spacing design and optimization during SAGD. Butler et al. (1981) derived their classical SAGD model by solving a 1-D heat conservation equation for single phase flow. This model has excellent predictive capability at experimental scales but performs poorly at field scales. By assuming a linear saturation -- temperature relationship, Sharma and Gates (2010b) developed a model that accounts for multiphase flow ahead of the steam chamber interface. In this work, by decomposing capillary pressure into its saturation and temperature components, we coupled the mass and energy conservation equations and showed that the multi-scale, multiphase flow phenomenon occurring during SAGD is the classical Marangoni (or 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 and Gates solution. The Marangoni flow concept was extended to the Expanding Solvent SAGD (ES-SAGD) process and our results show that there exists a given Marangoni number threshold below which the ES-SAGD process will not fare better than the SAGD process. Experimental results presented in Sasaki et al. (2002) demonstrate the existence of water-in-oil emulsions adjacent to the steam chamber wall during SAGD. In this work we show that these emulsions enhanced heat transfer at the chamber wall and hence oil recovery. We postulate that these W/O emulsions are principally hot water droplets that carry convective heat energy. We perform calculations to show that their presence can practically double the effective heat transfer coefficient across the steam chamber interface which overcomes the effect of reduced oil rates due to the increased emulsified phase viscosity. Our results also compared well with published experimental data. The SAGD (and ES-SAGD) process is a short length-scaled process and hence, short length-scaled phenomena (typically ignored in other EOR or conventional processes) such as thermo-capillarity and in-situ emulsification should not be ignored in predicting SAGD recoveries. This work will find unique application in predictive models used as fast proxies for predicting SAGD recovery and for history matching purposes.