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.

Multiobjective Pareto optimal solutions for a semibatch isothermal epoxy polymerization process are obtained by adapting the binary-coded nondominated sorting genetic algorithm II (NSGA II). The number-average molecular weight and polydispersity index are taken as two objectives, where the first one is maximized and the second one is minimized. The decision variables are addition profiles of various reagents, e.g., the amount of addition for monomer, sodium hydroxide, and epichlorohydrin at different times, whereas the solution of all species balance equations is treated as a constraint. Because the number-average molecular weight and polydispersity index are sometimes not sufficient to describe the desired species growth, additional objectives such as the maximization of preferential formation of lower oligomers with the minimization of NaOH addition are also studied. For all practical purposes, semibatch-mode operations are preferred even if for the fulfillment of certain objectives batch-mode operations are theoretically competitive.A well-validated model taking care of all physicochemical aspects of a reaction mechanism is a prerequisite for this kind of study. Process simulation and optimization with close proximity to the available experimental conditions is definitely a distinguishable feature of this work that can direct the results toward actual plant realizations.

On présente un modèle d'analyse de procédé pour la filtration sous pression. Le procédé a été divisé en deux étapes d'après les caractéristiques de filtration des suspensions colloïdales et des fines. Une fraction volumique de solides spatialement uniforme et ne variant pas dans le temps de l'approximation des solides est utilisée pour l'étape de croissance du gâteau de filtration (étape 1). L'hypothèse d'une fraction volumique de solides spatialement uniforme et dépendante du temps est utilisée pour l'étape de consolidation du gâteau (étape 2). Les deux modèles, qu'on appelle collectivement modèle M-P (Mean Phi), ont une base physique commune, à savoir une continuité sans interruption entre les étapes et une cohérence interne. Le modèle M-P n'a que trois paramètres : la fraction volumique terminale ou d'équilibre des solides dans le gâteau de filtration qui est reliée à la contrainte seuil de compression, la fraction volumique critique des solides, qui joint les étapes 1 et 2, ainsi qu'un facteur de perméabilité, qui est commun aux étapes 1 et 2. Le modèle est validé à l'aide d'un grand nombre de suspensions colloïdales filtrées dans des conditions de procédé physicochimique extrêmement diverses. On a déterminé un profil Pareto qui relie l'échelle de temps de la filtration et le degré de déshydratation obtenus, qui sont les deux plus importants indices du procédé.

A general kinetic framework to study epoxy polymerization is developed. Best-fit values of five rate constants are obtained using some experimental chromatographic data available in the open literature on a system involving a single liquid phase. Detailed sensitivity studies are then carried out to identify the most important rate constants. Average molecular weights and the polydispersity index are predicted using these parameters. The present model is more general than earlier kinetic models, and does not have the drawbacks of probabilistic models. The present model is used to predict the effect of intermediate addition of NaOH, to illustrate how general it really is. The model can easily be extended to apply to industrial reactors, which have additional physico-chemical phenomena associated with them, as for example, nonisothermal polymerization, presence of two liquid phases, etc.