Diffusion-convection mass-transfer process in porous medium is one of the major enhanced oil recovery (EOR) mechanisms of Vapor extraction (VAPEX). Previous work tried Fick’s Law to model the diffusion process, and mostly assumes the diffusion coefficient as a constant in the equation. However, the diffusion coefficient factually is a function of concentration, and thus the effect of its gradient should be included in the governing equation. In addition, bulk flow exist during the VAPEX especially during the solvent chamber rising phase, hence the process may be a diffusion-convection process rather than a pure diffusion process as presumed in previous works.
This paper proposes a new one-dimensional (1D) VAPEX mathematical model on the basis of diffusion–convection equation, gravity-based fluid flow equation (Darcy’s law), and mass-conservation equation. The model is directed at a vertical thin cylindrical VAPEX process with injector and producer both setted at the bottom. The solvent chamber is considered as a two-phase area and the oil in it is completely saturated, while the matiral beyond the chamber is thought as in liquid phase. First, the diffusion-convection model is developed to obtain the concentration distribution in the transition zone; the boundary between solvent chamber and transiton zone is seen as moving with time. Second, the drainage velocity of the saturated oil in solvent chamber is calculated and combined with the mass conservation equation, to model the saturation of the oil phase changing with time. On the basis of the saturation model the oil production rate can be obtained.
The recovery factor profile is divided into two distinct stages: solvent diluting-dominated stage and saturated oil flowing-dominated stage. During the first stage, it is found the solvent chamber growing rate tends to be constant; the oil production rate is proportional to the square root of permeability, which constists with the existing VAPEX theoretical model. During the second stage, the production rate is linearly related to the 1.1–1.3 power of the model length rather than the square root of it. This agrees perfectly with the lab observations in previous work.