Simulation of Asphaltene Aggregation and Related Properties Using an Equilibrium-Based Mathematical Model

Abstract

Aggregation of asphaltenes was simulated using a mathematical model based on the following consecutive equilibrium: n A ⇄ K 1 A n and m A + A n ⇄ K 2 A n + m , where A, A n , A n+m , K 1, K 2 represent asphaltenes, n aggregates, n + m aggregates, and equilibrium constants, respectively. A mass balance lead to a n + m polynomial in C (C 0, n, m, K 1, K 2, M), where C is the concentration of free solute (monomer), M is the monomer molecular mass, and C 0 is the total monomer concentration added to solution. Using numerical methods, this polynomial was solved in terms of C 0, K 1, and K 2 for given values of n, m, and M. Selection of n = 3, m = 5, and M = 800 g L–1 was consistent with data in the literature, and determination of K 1 and K 2 was achieved by fitting to experimental data from ultrasound velocity, thermal diffusion [thermal lens and dual-beam photothermal reflection (DBPR)], and self-diffusion coefficient techniques. The good fittings found suggest that asphaltene aggregation is adequately described by the present model. A procedure based on the present model was employed to simulate the stepwise adsorption of asphaltenes at the toluene/glass interface. The above sequential equilibrium is discussed in terms of aggregation of the toluene-insoluble asphaltene fraction molecules (A1TM, first equilibrium), followed by incorporation into aggregates of toluene-soluble fraction molecules (A2TM, second equilibrium). This sequential scheme is proposed as a means to keep fraction A1 as nanoaggregates (first step), which, were it not by the presence of A2 (second step), would lead to phase separation. The formation of small aggregates at very low concentrations, predicted by the model, is consistent with the very low solubility of the A1 fraction. When the above mathematical model is combined with the Hansen solubility parameter (HSP) method, it is concluded that asphaltenes form stable colloid solutions in toluene and similar solvents where A1 is insoluble. In other words, for these colloidal solutions, interfacial tension would be zero.

Simple Statistical Model for Branched Aggregates: Application to Cooee Bitumen

“…This thermodynamics approach could be on 16 the line of that developed in Refs., 43,44 but based on the precise mechanism deduced from the MD simulations. Furthermore, the free energies of interaction necessary to the thermodynamics approach could be independently checked by MD simulations using for example umbrella sampling, as was carefully done for some asphaltene molecules and some geometries of interaction in Ref.…”

Determining the Kinetics of Asphaltene Adsorption from Toluene: A New Reaction–Diffusion Model

“…7(a). However, 32 when different experiments made using the same sensor were compared, the repeatability was good, see 33 for example data from Sensor X, 75 days and 127 days (open squares and crosses) in Fig. 7(a).…”

“…It is observed that at long times there is a deviation from 32 linearity as the system approaches equilibrium. At very short times the relationship is non-linear, 33 indicating that the initial rate of adsorption is not diffusion-controlled. (Note that the chosen flow rate in 34 this work, as shown in section S.9, is sufficiently high to ensure that our adsorption process is not 35 governed by mass transport.)…”

“…with respect to concentration of asphaltene, which corresponds to the instantaneous slope of the fit, 33 decreases with increasing concentration. At low concentration, the value is 1.30, however, at high 34 concentration the rate order is fractional, falling to 0.26 at the highest concentration of 10 gL⁻¹.…”

“…Asphaltene is defined by its solubility: soluble in aromatics like toluene, but insoluble in n-alkanes like 33 heptane. Since asphaltene is a solubility class of materials and not a single molecular species, its 34 chemistry is not unambiguously known.…”