Home About us Contact
|
Home About us Contact | ||
|
|
||
Population Balance Model (population + balance_model)
Selected AbstractsA Simpler Approach to Population Balance Modeling in Predicting the Performance of Ziegler-Natta Catalyzed Gas-Phase Olefin Polymerization Reactor SystemsMACROMOLECULAR REACTION ENGINEERING, Issue 2-3 2009Randhir Rawatlal Abstract In this work, an alternative formulation of the Population Balance Model (PBM) is proposed to simplify the mathematical structure of the reactor model. The method is based on the segregation approach applied to the recently developed unsteady state residence time distribution (RTD). It is shown that the model can predict the performance of a reactor system under unsteady flow and composition conditions. Case studies involving time-varying catalyst flowrates, reactor temperature and reactor pressure were simulated and found to predict reactor performance with reasonable accuracy. The model was used to propose a grade transition strategy that could reduce transition time by as much as two hours. [source] The Use of a Population Balance Model in the Study of Inoculation of Soybean Seeds in a Spouted BedTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 1 2004Claudio R. Duarte Abstract The coating of soybean seeds with bacteria and micronutrients favours the vigorous growth of the plant, dispensing with the use of ammoniacal fertilizers. The optimum thickness of the coating should allow the fundamental gaseous interchanges for the germination and the ideal conditions for the activity of the bacteria. The objective of this work was to simulate dynamic mass distribution of soybean seeds covered with bacteria and macronutrients in spouted bed through a specific program developed in Maple V®. The validation of the model is done through 16 experiments carried out in a spouted bed with spray at the top. L'enduction de graines de soja par des bactéries et des micronutriments favorise une croissance vigoureuse des plantes, ce qui dispense de recourir à des fertilisants ammoniaqués. Une épaisseur optimale de l'enduit devrait permettre les échanges gazeux de base nécessaires à la germination et correspondre aux conditions idéales pour l'activité des bactéries. L'objectif de ce travail est de simuler la distribution en masse dynamique des graines de soja recouvertes de bactéries et micronutriments dans un lit jaillissant par un logiciel spécifique mis au point dans Maple V®. La validation du modèle est réalisée par seize expériences menées en lit fluidisé avec atomisation par le sommet. [source] Population balance model for nucleation, growth, aggregation, and breakage of hydrate particles in turbulent flowAICHE JOURNAL, Issue 8 2010Boris V. Balakin Abstract This article describes a computational model for the size evolution of hydrate particles in a pipeline-pump system with turbulent flow. The model is based on the population balance principle, and the simulation results were validated with data from an experimental study of a flow loop containing hydrate particles reported in the literature. It is found that the particle size is significantly influenced by aggregation and breakage, related to shear in the flow, and that these effects are comparable to those of growth and nucleation, related to diffusional processes. Two different approaches for hydrate growth and nucleation, one of continuous nucleation during the process and one of only an initial nucleation-pulse, were used. This was done to compare the aggregation and breakage parameters which come out when fitting the models output to experiment. These two approaches are found to give rise to similar aggregation/breakage parameters, lending credence to the pbm-based modeling. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Bubble size distribution modeling in stirred gas,liquid reactors with QMOM augmented by a new correction algorithmAICHE JOURNAL, Issue 1 2010Miriam Petitti Abstract Local gas hold-up and bubbles size distributions have been modeled and validated against experimental data in a stirred gas,liquid reactor, considering two different spargers. An Eulerian multifluid approach coupled with a population balance model (PBM) has been employed to describe the evolution of the bubble size distribution due to break-up and coalescence. The PBM has been solved by resorting to the quadrature method of moments, implemented through user defined functions in the commercial computational fluid dynamics code Fluent v. 6.2. To overcome divergence issues caused by moments corruption, due to numerical problems, a correction scheme for the moments has been implemented; simulation results prove that it plays a crucial role for the stability and the accuracy of the overall approach. Very good agreements between experimental data and simulations predictions are obtained, for a unique set of break-up and coalescence kinetic constants, in a wide range of operating conditions. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Population balance modeling of particle size distribution in monomer-starved semibatch emulsion polymerizationAICHE JOURNAL, Issue 12 2009Shahriar Sajjadi Abstract The evolution of particle size distribution (PSD) in the monomer-starved semibatch emulsion polymerization of styrene with a neat monomer feed is investigated using a population balance model. The system under study ranges from conventional batch emulsion to semicontinuous (micro)emulsion polymerization depending on the rate of monomer addition. It is shown that, contrary to what is often believed, the broadness of PSD is not necessarily associated with the length of nucleation period. The PSDs at the end of nucleation are found to be independent of surfactant concentration. Simulation results indicate that at the completion of nucleation the particle size is reduced and the PSD narrows with decreasing rate of monomer addition despite nucleation time increasing. The broad distribution of particles frequently encountered in semibatch emulsion polymerizations is therefore attributed to stochastic broadening during the growth stage. The zero-one-two-three model developed in this article allows perceiving that the dominant kinetic mechanism may be different for particles with different sizes. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Morphological population balance model in principal component spaceAICHE JOURNAL, Issue 9 2009Xue Z. Wang Abstract Multidimensional and morphological population balance (PB) models for crystallization processes have been proposed in literature, which can be used to simulate the dynamic evolution of particle shape as well as particle size distribution. These models, however, can become computationally expensive when the crystal has a large number of independent faces, and are not applicable to noncrystalline, irregularly shaped particles such as those encountered in granulation and milling. This article addresses these challenges by introducing principal component analysis (PCA) into morphological PB modeling. PCA transforms the shape description of a particle from a high-dimensional domain to a lower dimensional, principal component (PC) space. Morphological PB models can then be built in this latent variable space, greatly reducing the computational complexity. It also makes it possible to model noncrystalline irregularly shaped particles. The original particle shape at any time can be reconstructed from the PCs. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Particle shape manipulation and optimization in cooling crystallization involving multiple crystal morphological formsAICHE JOURNAL, Issue 8 2009Jian Wan Abstract A population balance model for predicting the dynamic evolution of crystal shape distribution is further developed to simulate crystallization processes in which multiple crystal morphological forms co-exist and transitions between them can take place. The new model is applied to derive the optimal temperature and supersaturation profiles leading to the desired crystal shape distribution in cooling crystallization. Since tracking an optimum temperature or supersaturation trajectory can be easily implemented by manipulating the coolant flowrate in the reactor jacket, the proposed methodology provides a feasible closed-loop mechanism for crystal shape tailoring and control. The methodology is demonstrated by applying it to a case study of seeded cooling crystallization of potash alum. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Crystal growth rate dispersion modeling using morphological population balanceAICHE JOURNAL, Issue 9 2008Cai Y. Ma Abstract Crystal growth in solution is a surface-controlled process. The variation of growth rates of different crystal faces is considered to be due to the molecular arrangement in the crystal unit cell as well as the crystal surface structures of different faces. As a result, for some crystals, the growth rate for a specific facet is not only a function of supersaturation, but also dependent on some other factors such as its size and the lattice spread angle. This phenomenon of growth rate dispersion (GRD) or fluctuation has been described in literature to have attributed to the formation of some interesting and sophisticated crystal structures observed in experimental studies. In this article, GRD is introduced to a recently proposed morphological population balance model to simulate the dynamic evolution of crystal size distribution in each face direction for the crystallization of potash alum, a chemical that has been reported to show GRD phenomenon and sophisticated crystal structures. The GRD is modeled as a function of the effective relative supersaturation, which is directly related to crystal size, lattice spread angle, relative supersaturation, and solution temperature. The predicted results clearly demonstrated the significant effect of GRD on the shape evolution of the crystals. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] A CFD,PBM coupled model for gas,liquid flowsAICHE JOURNAL, Issue 1 2006Tiefeng Wang Abstract A computational fluid dynamics,population balance model (CFD-PBM) coupled model was developed that combines the advantages of CFD to calculate the entire flow field and of the PBM to calculate the local bubble size distribution. Bubble coalescence and breakup were taken into account to determine the evolution of the bubble size. Different bubble breakup and coalescence models were compared. An algorithm was proposed for computing the parameters based on the bubble size distribution, including the drag force, transverse lift force, wall lubrication force, turbulent dispersion force, and bubble-induced turbulence. With the bubble breakup and coalescence models and the interphase force formulations in this work, the CFD-PBM coupled model can give a unified description for both the homogeneous and the heterogeneous regimes. Good agreement was obtained with the experimental results for the gas holdup, liquid velocity, and bubble size distribution. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source] Reaction-limited aggregation in presence of short-range structural forcesAICHE JOURNAL, Issue 4 2005Venkataramana Runkana Abstract A geometrically discretized sectional population balance model for reaction-limited aggregation of colloidal suspensions is presented. The two important model parameters are collision frequency factor and collision efficiency factor. The collision frequency factor is derived from physically realistic arguments proposed for collision of fractal aggregates. The collision efficiency factor is computed as a function of total interaction energy between particles, including short-range structural repulsion forces. The irregular and open structure of aggregates is taken into account by incorporating their mass fractal dimension. The characteristic time constant of reaction-limited aggregation, derived from dynamic scaling of mean aggregate size-aggregation time data, is found to correlate with electrolyte concentration. The population balance model is tested with published experimental data for aggregation of ,-alumina suspensions in the presence of different electrolytes. It is shown that the slow kinetics of aggregation under certain conditions of pH and electrolyte concentration require inclusion of short-range structural repulsion forces along with van der Waals attraction and electrical double layer repulsion forces in an extended DLVO theory. The model predictions are in good agreement with experimental data for time evolution of mean aggregate diameter in the reaction-limited aggregation regime. © 2005 American Institute of Chemical Engineers AIChE J, 2005 [source] Flocculation of biological cells: Experiment vs. theoryAICHE JOURNAL, Issue 7 2003Binbing Han Flocculation of biological cells is important in the biotechnology industry, as it could lead to improved efficiencies for bioreactor harvesting operations such as microfiltration. Experimental studies for flocculation of yeast and CHO cells using cationic polyelectrolytes suggest the existence of a steady-state, self-similar floc size distribution. The experimentally determined floc size distributions were modeled using a population balance approach. For flocculated yeast suspensions, the variation of the floc volume fraction with dimensionless particle diameter is predicted by the population balance model assuming a binary breakage distribution function. However, the variation of floc number fraction with dimensionless particle diameter is better predicted assuming a log normal fragment distribution function probably due to the presence of submicron-sized yeast cell debris. For CHO cell flocs, the floc volume and number fractions are predicted using a log normal fragment distribution function. CHO cells are far more fragile than yeast cells. Thus, individual CHO cells in a CHO cell floc can lyse leading to the formation of a number of small particles. [source] Population balance modeling of aggregation kinetics of recombinant human interleukin-1 receptor antagonistJOURNAL OF PHARMACEUTICAL SCIENCES, Issue 12 2005Eva Y. Chi Abstract The kinetics of benzyl alcohol-induced nonnative aggregation of recombinant human interleukin-1 receptor antagonist (rhIL-1ra) were investigated using a population balance model. Steady-state size distributions of rhIL-1ra aggregates formed in a continuous mixed suspension, mixed product removal (MSMPR) reactor were measured and used to extrapolate aggregate nucleation and growth rates parameters. Aggregate growth rate was size-dependent and a linear growth rate model was used to derive a population density function. Addition of 0.9 wt/v% benzyl alcohol increased the nucleation rate by approximately four orders of magnitude. The growth rate for aggregates, however, changed little as a function of benzyl alcohol concentration in the range of 0,0.9%. The addition of sucrose to buffer containing 0.9% benzyl alcohol decreased rhIL1-ra nucleation rate by orders of magnitude and had little impact on growth rate kinetics. The simplicity of the population balance model and the physical relevance of the information obtained from this model render it a useful tool to study protein aggregation kinetics and the effects of excipients on this process. © 2005 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 94:2735,2748, 2005 [source] Simultaneous Controllability of PSD and MWD in Emulsion PolymerisationMACROMOLECULAR REACTION ENGINEERING, Issue 5 2008Stephen J. Sweetman Abstract A sensitivity study of particle size distribution (PSD) and molecular weight distribution (MWD) responses to perturbations in initiator, surfactant, monomer and chain transfer agent in a semi-batch emulsion polymerisation is presented. The objective is to provide a systematic study on the ability to simultaneously control both PSD and MWD, towards inferential control of end-use product properties. This would lead towards identification of the practical feasible regions of operability. All inputs appeared to have an intrinsic and simultaneous influence on end-time PSD and MWD. Trends shown in experimental results have been explained in a mechanistic sense and also compared to simulation results from a combined PSD/MWD population balance model. The preliminary comparison between experiment and simulation highlights areas to be focussed on with respect to model improvement. [source] Numerical Simulation of Absorbing CO2 with Ionic LiquidsCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 10 2010X. Wang Abstract Although separating CO2 from flue gas with ionic liquids has been regarded as a new and effective method, the mass transfer properties of CO2 absorption in these solvents have not been researched. In this paper, a coupled computational fluid dynamic (CFD) model and population balance model (PBM) was applied to study the mass transfer properties for capturing CO2 with ionic liquids solvents. The numerical simulation was performed using the Fluent code. Considering the unique properties of ionic liquids, the Eulerian-Eulerian two-flow model with a new drag coefficient correlation was employed for the gas-liquid fluid dynamic simulation. The gas holdup, interfacial area, and bubble size distribution in the bubble column reactor were predicted. The mass transfer coefficients were estimated with Higbie's penetration model. Furthermore, the velocity field and pressure field in the reactor were also predicted in this paper. [source] Bubble Size Distribution in Oil-Based Bubble ColumnsCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 11 2008S.-S. Homayouni Abstract A practical population balance model was used to evaluate the bubble size distribution in a bubble column. In addition, the bubble size distribution in the bubble column was measured at different gas velocities by photography and analysis of the pictures. Four types of liquid, i.e., water and three petroleum-based liquids, were used in the experiments. The gas phase was air. It was found that the existing models in the literature are not able to satisfactorily predict the experimentally measured bubble size distribution. The model can be corrected by applying a correction factor to the energy dissipation rate. The corrected model fits the experimental bubble size distribution considerably better than the existing models. The variation of this correction factor is reported for different systems at different gas velocities. [source] A Genetic Algorithm Based Approach to Coalescence Parameters: Estimation in Liquid-Liquid Extraction ColumnsCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 12 2006A. Hasseine Abstract The population balance model is a useful tool for the design and prediction of a range of processes that involve dispersed phases and particulates. The inverse problem method for the droplet population balance model is applied to estimate coalescences parameters for two-phase liquid-liquid systems. This is undertaken for two systems, namely toluene/water and n-butyl acetate/water in a rotating disc contactor (RDC), using a droplet population balance model. In the literature, the estimation procedure applied to this problem is often based on the deterministic optimization approach. These methods generate instabilities near a local minimum, inevitably requiring information about the derivatives at each iteration. To overcome these limitations, a method providing an estimate for the coalescences parameters is proposed. It is based on a simple and adapted structure of the genetic algorithm, for this particular problem. The agreement between the experimental observations and the simulations is encouraging and, in particular, the models used have proven to be suitable for the prediction of hold-up and Sauter diameter profiles for these systems. Finally, these results demonstrate that the optimization procedure proposed is very convenient for estimating the coalescences parameters for extraction column systems. [source] | ||||||||||