The dynamics of a process in which a solvent in the form of a vapor or gas is introduced in a heavy-oil reservoir is considered. The process is called the solvent vapor-extraction process (VAPEX). When the vapor dissolves in the oil, it reduces its viscosity, allowing oil to flow under gravity and be collected at the bottom producer well. The conservation-of-species equation is analyzed to obtain a more-appropriate equation that differentiates between the velocity within the oil and the velocity at the interface, which can be solved to obtain a concentration profile of the solvent in oil. We diverge from an earlier model in which the concentration profile is assumed. However, the final result provides the rate at which oil is collected, which agrees with the previous model in that it is proportional to √h, where h is the pay-zone height; in contrast, some of the later data show a dependence on h. Improved velocity profiles can capture this dependence. A dramatic increase in output is seen if the oil viscosity decreases in the presence of the solvent, although the penetration of the solvent into the oil is reduced because under such conditions the diffusivity decreases with decreased solvent. One other important feature we observe is that when the viscosity-reducing effect is very large, the recovered fluid is mainly solvent. Apparently, some optimum might exist in the solubility φo, where the ratio of oil recovered to solvent lost is the largest. Finally, the present approach also allows us to show how the oil/vapor interface evolves with time.