Characterization of one-dimensional VAPEX
Figure 1 shows a model of Vapex Process modeled in a vertical thin sandpack (cylindrical), which is saturated with heavy oil. Solvent Injector and oil producer are placed at the bottom of the sandpack. When solvent is injected, it moves upwards due to buoyancy and comes in contact with the heavy oil and heavy oil is extracted and diluted and drained downward by gravity force.
We make these following assumptions for our 1D VAPEX Process:
1. We have 2 areas: 2 phase area and 1 phase area, and they are divided by the interface between solvent chamber and transition zone;
2. The solvent chamber is filled with diluted oil (saturated oil) which is in liquid phase and the gaseous solvent vapor;
3.…show more content… The correlation between diffusion coefficient and the concentration of solvent (light hydrocarbon) in crude oil is usually expressed via the viscosity of the heavy oil−solvent mixture. The dependence of the viscosity on the solvent concentration was proposed by Lederer  (3) where Shu  formulated the following correlation to determine the weighting factor, λ, for a mixture of heavy oil and light hydrocarbons where γo and γs are the specific gravities of the crude oil and liquid solvent, respectively.
The diffusion coefficient is usually correlated with viscosity as
Duaub (4) where a and b are both constants depending on the properties of oil and gas sample as well as the operation condition (pressure and temperature). Hayduk and and Das−Butler proposed different correlations for normal paraffin solute/solvent system and propane/heavy oil system, respectively.
Symbol v in Eq. (2) denotes convection velocity between solvent vapour and diluted oil in the transition zone. Darcy’s law  is commonly used to depict the fluid flow rate in porous medium, (5) where m s Heavy oil−solvent mixture is commonly treated as ideal solution and its density, ρm, is calculated by
m css coo (6)
Moving boundary of transition zone
The transition zone is assumed bounded by two interfaces : one is next to the solvent chamber and the other is neighboring the untouched heavy oil zone. The former interface is defined as the plane where