Semi-Analytical Modeling of Steam-Solvent Gravity Drainage of Heavy Oil and Bitumen, Part 2: Unsteady-State Model with Curved Interface

Abstract Co-injection of solvent with steam in SAGD has shown promise for enhancing oil rates as well as in reduction of energy and water consumption. Modeling and optimization of hybrid steam-solvent recovery processes with commercial numerical simulators can be very time consuming. In addition, the complex interaction of heat and solvent effects in mobilizing heavy oil at the vapour chamber boundary are often difficult to ascertain from the numerical models. Semi-analytical mathematical models can provide insight into the physics of the processes and may be used to estimate production rates and thermal efficiency in much less time. In this study, an unsteady-state semi-analytical model was developed to predict the oil flow rate in the steam-solvent assisted recovery process. The model assumes a curved interface with transient temperature and solvent distribution in the mobile zone. It also accounts for transverse dispersion and concentration-dependent molecular diffusion for solvent distribution. The oil flow rate and interface profile are predicted at each time in an iterative fashion. The results show that the coefficient of diffusion-concentration function significantly affects the solvent penetration depth and its distribution. The semi-analytical model was able to predict oil production rates using different solvents co-injected with steam, in agreement with reported experimental data. The proposed model reveals the complex interaction of heat and solvent solubility and diffusion as they affect mobilization and production of viscous oil. This model may be used to find the optimal operation parameters for the process over a range of different reservoir qualities and pressures, in a very time-efficient manner. The final outcome may lead to an efficient design of a steam-solvent recovery process that utilizes less water and reduces the amount of energy and gas emissions per barrel of oil produced.