Mathematical modeling of the solvent chamber evolution in a vapor extraction heavy oil recovery process

In a vapor extraction (VAPEX) process, a vaporized solvent (such as light alkanes) is injected underground to dilute and recover heavy oil. A solvent chamber forms due to the depletion of oil, and goes through three phases: rising, spreading, and falling phases during a VAPEX process. Existing analytical models of VAPEX can only roughly estimate an oil production rate but are unable to accurately describe the solvent chamber evolution. Simulation models are somewhat unreliable due to extremely small physical diffusivity and relatively large numerical dispersion. This study develops a comprehensive mathematical model for the VAPEX process to characterize a transition zone and describe the solvent chamber evolution. Major recovery mechanisms occurring in the transition zone such as dynamic mass transfer, gravity drainage, multiphase flow, and surface renewal are accounted for in the model. Modeling results show that the solvent concentration in the transition zone grows slower at the top than at the bottom while rather stable at the middle along the drainage surface. In addition, it is found that a stabilized oil production rate depends on the square root of a heavy oil-solvent effective diffusion coefficient. Moreover, this new VAPEX model can accurately describe the relationship between oil production rates and diffusion coefficients in different scales thanks to the absence of numerical dispersion.