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.
