This study discusses the development of a generalized geometric population balance model for simulating the growth of asphaltene aggregates from the nanometer scale to micrometer-sized particles. The Smoluchowski kernel has been incorporated to describe the aggregation of asphaltene nanoaggregates, which is induced by the addition of a precipitant, e.g., heptane. Rather than using the discretization of particle sizes based on the particle volumes, a discretization scheme based on the number of asphaltene molecules is incorporated, which ensures that the mass is conserved in this model. The model is in good agreement with the experimental data for the evolution of asphaltene aggregates at different times collected by centrifugation. The particle size distribution (PSD) of the asphaltene aggregates as a function of time is also determined. It was observed that the shift of the PSD to larger diameters is faster in the case of higher heptane concentrations because of the greater mass of asphaltenes precipitated and the higher driving force for their aggregation at these conditions. Additionally, predictions for the onset time for asphaltene precipitation at lower heptane concentrations are also presented.

This study is the first to show that silica precipitation under very acidic conditions ([HCl] = 2-8 M) proceeds through two distinct steps. First, the monomeric form of silica is quickly depleted from solution as it polymerizes to form primary particles approximately 5 nm in diameter. Second, the primary particles formed then flocculate. A modified Smoluchowski equation that incorporates a geometric population balance accurately describes the exponential growth of silica flocs. Variation of the HCl concentration between 2 and 8 M further showed that polymerization to form primary particles and subsequent particle flocculation become exponentially faster with increasing acid concentration. The effect of salt was also studied by adding 1 M chloride salts to the solutions; it was found that salts accelerated both particle formation and growth rates in the order: AlCl(3) > CaCl(2) > MgCl(2) > NaCl > CsCl > no salt. It was also found that ionic strength, over cation identity, determines silica polymerization and particle flocculation rates. This research reveals that precipitation of silica products from acid dissolution of minerals can be studied apart from the mineral dissolution process. Thus, silica product precipitation from mineral acidization follows a two-step process--formation of 5 nm primary particles followed by particle flocculation--which becomes exponentially faster with increasing HCl concentration and with salts accelerating the process in the above order. This result has implications for any study of acid dissolution of aluminosilicate or silicate material. In particular, the findings are applicable to the process of acidizing oil-containing rock formations, a common practice of the petroleum industry where silica dissolution products encounter a low-pH, salty environment within the oil well.

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Summary: An epoxy polymerization process is studied in semi‐batch mode. Caustic has a very critical influence on epoxy polymerization process, which is modeled as a set of highly nonlinear coupled ODE's (ordinary differential equations). Owing to the highly complicated, nonlinear domain of analysis, “Differential Evolution (DE)” and “Genetic Algorithm (GA)” are used as optimization tools to identify the $\overline M _{\rm n}$‐PDI Pareto set and study the best operating strategy with respect to NaOH addition. The moment of various oligomeric components during the semi‐batch polymerization is also presented for a better understanding of the process. This study demonstrates the potential of evolutionary optimization algorithm to identify various operating philosophies of a semi‐batch epoxy reactor for a targeted product quality.