Fickian and Non-Fickian Diffusion in Heavy Oil + Light Hydrocarbon Mixtures

Abstract

Diffusive mass transfer is expected to play a key role in existing and proposed solvent-added processes for heavy oil production. Composition–distance profiles arising during free diffusion scale as a function of the joint variable (distance/time^<i>n</i>_<i>w</i>). Simple fluids are governed by Fickian diffusion, where <i>n</i>_<i>w</i> = 0.5. For nanostructured fluids, the value of <i>n</i>_<i>w</i> can be as low as <i>n</i>_<i>w</i> = 0.25, known as the single-file limit, but more typically, the value for the exponent falls between these two limits and is composition-dependent. In this work, five published data sets, comprising free diffusion composition profiles for Athabasca bitumen fractions and for Cold Lake bitumen + light hydrocarbons obtained using diverse apparatus, are probed from this perspective. Additional experimental results are provided for Athabasca bitumen + toluene mixtures over the temperature range of 273–313 K, and results from positive and negative control experiments for two well-defined mixtures(0.25 mass fraction carbon nanotubes + polybutene) + toluene, and polybutene + tolueneare also provided. The value of <i>n</i>_<i>w</i> for the negative control experiment remains at 0.50 ± 0.05 over the entire composition range, and for the positive control experiment, the value drops to <i>n</i>_<i>w</i> = 0.30 ± 0.02 at low toluene mass fraction. Although the quality of the diffusion profile data in the data sets analyzed is variable, the values of the exponent <i>n</i>_<i>w</i> are shown to be light-hydrocarbon-dependent and increase from <i>n</i>_<i>w</i> ∼ 0.25 at low light-hydrocarbon mass fraction up to <i>n</i>_<i>w</i> ∼ 0.50 at high light-hydrocarbon mass fraction. Secondary convective effects are also noted in free diffusion experiment outcomes at long times. The industrial applications of these findings are currently being evaluated, but it is clear that the time for light hydrocarbons to penetrate a fixed distance into nano- and micro-structured hydrocarbon resources is greater than the value anticipated for unstructured fluids