460822 A Multicomponent Diffusional Model for Adsorption Dynamics of Asphaltenes at Water/Oil Interfaces
Keywords: Asphaltenes, Mixture Effects, Diffusion, Dilatational Rheology
Mixture effects were introduced in a previous communication1 to explain the deviation between single component models of diffusion-controlled adsorption and experimental data for adsorption of asphaltenes at water and organic phase interface. A two-component model coupling Langmuir isotherm, Langmuir equation of state and diffusion kinetics was demonstrated to capture with only four adjustable parameters (2 concentrations and 2 adsorption coefficient) both dynamic interfacial tension over 4 hours and dilatational rheology at various adsorption times (over two frequency decades). Only a few percent of the total asphaltenes solubility class was found to be significantly surface active, consistently with the observation that only a small fraction of them actually contribute to emulsion stability. However due to the diversity of asphaltenes molecular structures (and of their reported interfacial activity), the two-component model still suffers from some inaccuracies. This is particularly apparent at short times when adsorption is expected to be controlled by the bulk of asphaltenes. Increasing the number of pseudo-components would be expected to solve those issues. Unfortunately, due to an extreme mathematical complexity, no analytical model is available for diffusion controlled dilatational rheology with more than two components. This difficulty can be circumvented by numerically solving the set of first principle equations governing relaxation during dilatational rheology experiments (for each component one mass conservation/diffusion equation and one adsorption isotherm equation). A matrix type solving procedure is proposed that proves both extremely simple and robust. This procedure is applied to the well-known dataset from Freer and Radke who concluded to a non-diffusion controlled rheological behaviour. With a unique set of six adjustable parameters (3 concentrations, 3 adsorption coefficients) the mixture model captures with a great level of detail both dynamic interfacial tension over 24 hours and dilatational rheology over 7 frequency decades. Interestingly, the parameter optimization procedure naturally comes out with a total asphaltenes concentration (the sum of the 3 pseudo-components concentration) nearly equal to the nominal concentration of the asphaltenes solution. Some attempts to account for non-planarity of the droplet surface on diffusion kinetics and to model desorption during washout seem promising.
1 Mixture Effects on Adsorption Kinetics of Asphaltenes at the Water/Toluene Interface. Vincent Pauchard and Fang Liu. 2016 AICHE Spring Meeting. April 10-14, 2016. Houston.
2 Rane, J. P., Pauchard, V., Couzis, A., & Banerjee, S. (2013). Interfacial rheology of asphaltenes at oil–water interfaces and interpretation of the equation of state. Langmuir, 29(15), 4750-4759.
3 Freer, E. M., & Radke, C. J. (2004). Relaxation of asphaltenes at the toluene/water interface: Diffusion exchange and surface rearrangement. Journal of Adhesion, 80(6), 481-496.
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